Organic spin clusters. A dendritic-macrocyclic poly(arylmethyl) polyradical with very high spin of S = 10 and its derivatives: Synthesis, magnetic studies, and small-angle neutron scattering

Article abstract of DOI:10.1021/ja031548j

Synthesis and characterization of organic spin clusters, high-spin poly(arylmethyl) polyradicals with 24 and 8 triarylmethyls, are described. Polyether precursors to the polyradicals are prepared via modular, multistep syntheses, culminating in Negishi cross-couplings between four monofunctional branch (dendritic) modules and the tetrafunctional calix[4]arene-based macrocyclic core. The corresponding carbopolyanions are prepared and oxidized to polyradicals in tetrahydrofuran-d₈. The measured values of S, from numerical fits of magnetization vs magnetic field data to Brillouin functions at low temperatures (T = 1.8-5 K), are S = 10 and S = 3.6-3.8 for polyradicals with 24 and 8 triarylmethyls, respectively. Magnetizations at saturation (M _sat) indicate that 60-80% of unpaired electrons are present at T = 1.8-5 K. Low-resolution shape reconstructions from the small-angle neutron scattering (SANS) data indicate that both the polyradical with 24 triarylmethyls and its derivatives have dumbbell-like shapes with overall dimensions 2 × 3 × 4 nm, in agreement with the molecular shapes of the lowest energy conformations obtained from Monte Carlo conformational searches. On the basis of these shapes, the size of the magnetic anisotropy barrier in the polyradical, originating in magnetic shape anisotropy, is estimated to be in the milliKelvin range, consistent with the observed paramagnetic behavior at T ≥ 1.8 K. For macromolecular polyradicals, with the elongated shape and the spin density similar to the polyradical with 24 triarylmethyls, it is predicted that the values of S on the order of 1000 or higher may be required for single-molecule-magnet behavior, i.e., superparamagnetic blocking (via coherent rotation of magnetization) at the readily accessible temperatures T > 2 K.

Full text of DOI:10.1021/ja031548j

Published on Web 05/07/2004
Organic Spin Clusters. A Dendritic-Macrocyclic
Poly(arylmethyl) Polyradical with Very High Spin of S ) 10
and Its Derivatives: Synthesis, Magnetic Studies, and
Small-Angle Neutron Scattering
Suchada Rajca,*,† Andrzej Rajca,*,† Jirawat Wongsriratanakul,† Paul Butler,‡ and
Sung-min Choi§
Contribution from the Department of Chemistry, UniVersity of Nebraska,
Lincoln, Nebraska 68588-0304, and The National Center for Neutron Research, NIST,
Gaithersburg, Maryland 20899-8562
Received December 5, 2003; E-mail: srajca1@unl.edu; arajca1@unl.edu
Abstract: Synthesis and characterization of organic spin clusters, high-spin poly(arylmethyl) polyradicals
with 24 and 8 triarylmethyls, are described. Polyether precursors to the polyradicals are prepared via modular,
multistep syntheses, culminating in Negishi cross-couplings between four monofunctional branch (dendritic)
modules and the tetrafunctional calix[4]arene-based macrocyclic core. The corresponding carbopolyanions
are prepared and oxidized to polyradicals in tetrahydrofuran-d8. The measured values of S, from numerical
fits of magnetization vs magnetic field data to Brillouin functions at low temperatures (T ) 1.8-5 K), are
S ) 10 and S ) 3.6-3.8 for polyradicals with 24 and 8 triarylmethyls, respectively. Magnetizations at
saturation (Msat) indicate that 60-80% of unpaired electrons are present at T ) 1.8-5 K. Low-resolution
shape reconstructions from the small-angle neutron scattering (SANS) data indicate that both the polyradical
with 24 triarylmethyls and its derivatives have dumbbell-like shapes with overall dimensions 2 × 3 × 4 nm,
in agreement with the molecular shapes of the lowest energy conformations obtained from Monte Carlo
conformational searches. On the basis of these shapes, the size of the magnetic anisotropy barrier in the
polyradical, originating in magnetic shape anisotropy, is estimated to be in the milliKelvin range, consistent
with the observed paramagnetic behavior at T g 1.8 K. For macromolecular polyradicals, with the elongated
shape and the spin density similar to the polyradical with 24 triarylmethyls, it is predicted that the values
of S on the order of 1000 or higher may be required for “single-molecule-magnet” behavior, i.e.,
superparamagnetic blocking (via coherent rotation of magnetization) at the readily accessible temperatures
T > 2 K.
Introduction
defects. Therefore, connectivity between radicals should be such
that strong exchange interaction between the radicals is sustained
Molecules with large values of quantum spin number S in
the electronic ground states may be viewed as models for or-
ganic polymers with magnetic ordering.1-4 Design and synthesis
of such molecules (polyradicals) must ensure that strong
through-bond exchange interactions between multiple sites with
unpaired electrons (radicals) are maintained.4 Even if very effi-
cient synthetic methods for generation of radicals are employed,
the finite probability that generation of radicals will not be
complete must be taken into account, i.e., formation of chemical
in the presence of small density of chemical defects.5-7
Furthermore, out-of-plane twistings of the conjugated system
may lead to the ferromagnetic-to-antiferromagnetic coupling
reversals, diminishing the net value of S.8-12 The effectiveness
of various approaches to this problem may be measured by the
values of S in the electronic ground state.4,13-19
(5) Rajca, A.; Utamapanya, S. J. Am. Chem. Soc. 1993, 115, 10688-10694.
(6) Rajca, A.; Rajca, A.; Padmakumar, R. Angew. Chem., Int. Ed. Engl. 1994,
33, 2091-2093.
† University of Nebraska.
(7) Rajca, A.; Rajca, S.; Desai, S. R. J. Am. Chem. Soc. 1995, 117, 806-816.
(8) Dvolaitzky, M.; Chiarelli, R.; Rassat, A. Angew. Chem., Int. Ed. Engl. 1992,
31, 180-181.
‡ National Center for Neutron Research. Present address: Neutron
Scattering Section, ORNL, Bldg 7962, 1 Bethel Valley Rd., P.O. Box 2008,
Oak Ridge, TN 37831-6393.
(9) Fang, S.; Lee, M.-S.; Hrovat, D. A.; Borden, W. A. J. Am. Chem. Soc.
1995, 117, 6727-6731.
§ National Center for Neutron Research. Present address: Department
of Nuclear and Quantum Engineering, Korea Advanced Institute of Science
and Technology, 373-1 Gusong-dong, Yusong-gu, Daejon 305-701,
Republic of Korea.
(10) Silverman, S. K.; Dougherty, D. A. J. Phys. Chem. 1993, 97, 13273-
13283.
(11) Kanno, F.; Inoue, K.; Koga, N.; Iwamura, H. J. Am. Chem. Soc. 1993,
115, 847-850.
(1) Rajca, A.; Wongsriratanakul, J.; Rajca, S. Science 2001, 294, 1503-1505.
(2) Rajca, A.; Rajca, S.; Wongsriratanakul, J. J. Am. Chem. Soc. 1999, 121,
6308-6309.
(12) Rajca, A.; Rajca, S. J. Chem. Soc., Perkin Trans. 2 1998, 1077-1082.
(13) Nakamura, N.; Inoue, K.; Iwamura, H. Angew. Chem., Int. Ed. Engl. 1993,
32, 872.
(3) Rajca, A. Encyclopedia of Polymer Science and Technology, 3rd ed.;
Kroschwitz, J. I., Ed.; Wiley: New York, 2002.
(14) Iwamura, H.; Koga, N. Acc. Chem. Res. 1993, 26, 346-351.
(15) Matsuda, K.; Nakamura, N.; Inoue, K.; Koga, N.; Iwamura, H. Bull. Chem.
Soc. Jpn. 1996, 69, 1483-1494.
(4) Rajca, A. Chem.sEur. J. 2002, 8, 4834-4841.
9
6972
J. AM. CHEM. SOC. 2004, 126, 6972-6986
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Organic Spin Clusters
A R T I C L E S
Scheme 1. Synthesis of Diols 6 and Tetraethers 7
distorted ions.25 For organic polyradicals, in particular hydro-
carbons, the contribution to magnetic anisotropy from the class-
ical magnetic dipole-dipole interactions is expected to be
relatively important.26 Therefore, it might be expected that the
barriers for coherent rotation of magnetization in organic
polyradicals may be related to the molecular shape of polyradical
and its spin density.4,26,27 Such magnetic shape anisotropies may
be significant in polyradicals with elongated shapes.26,27
The title 24-radical 1 with S ) 10, which is the highest spin
organic molecule to date,4,22 provides an excellent model for
study of both exchange coupling and the possibility of magnetic
shape anisotropy in organic macromolecules. This article
describes details of synthesis and characterization of 24-radical
1 and its homologue octaradical 2 (Figure 1), including quan-
titative magnetic studies. For 1, shape determinations with small-
angle neutron scattering (SANS) are reported. These studies
should provide an insight into the magnetic behavior (e.g.,
related to the magnetic shape anisotropy) in the first conjugated
polymer with magnetic ordering.1,28
Figure 1. Target polyradicals 1 and 2 as spin pentamers and tetra-
radical 3.
Tetracosaradical (24-radical) 1 and octaradical 2 are designed
as “organic spin clusters”.20-22 One of the key elements of this
design is the S ) 2 macrocyclic core, as illustrated by
tetraradical 3.7 Because ferromagnetic coupling through the 1,3-
phenylene moiety is significantly stronger than that through the
3,4′-biphenylene, “unpaired” electrons in the four branches and
the macrocyclic core can effectively be lumped into component
spins (S′).21,22 Such ferromagnetically coupled S′ ) 5/2, 5/2,
5/2, 5/2, 4/2 spin pentamer should have S ) 12 ground state;
similarly, the S′ ) 1/2, 1/2, 1/2, 1/2, 4/2 spin pentamer should
have S ) 4 ground state (Figure 1).22
Another aspect of molecules with large values of S is the
magnitude of their magnetic anisotropy barrier. Numerous
transition metal ion based molecules (clusters) show substantial
barriers for inversion of magnetization, thus acting effectively
as “single-molecule-magnets” (SMM) at cryogenic tempera-
tures.23,24 The magnetic anisotropy of SMM’s is primarily based
on the single-ion anisotropies, especially of the Jahn-Teller
Results and Discussion
1. Synthesis of Polyethers. Modular and convergent synthesis
is employed to prepare tetracosaether (24-ether) 1-(OMe)24 and
octaether 2-(OMe)8, precursors to 24-radical 1 and octa-
radical 2. The synthesis is carried out in two stages: (1)
preparation of the tetrafunctionalized macrocyclic module 7E
with an effective C4V point group of symmetry (Scheme 1 and
Figure 2); (2) attachment of four monofunctionalized dendritic
821 or monoether 920 modules to the macrocyclic module 7E,
using Negishi coupling (Scheme 2).29
Compound 4 and diketone 5 are prepared according to the
published procedure.30 Bis(aryllithium), which is obtained via
Li/Br exchange on 4, is condensed with the diketone 5 to give
(25) Boskovic, C.; Pink, M.; Huffman, J. C.; Hendrickson, D. N.; Christou, G.
J. Am. Chem. Soc. 2001, 123, 9914-9915.
(26) Rajca, A. Chem. ReV. 1994, 94, 871-893.
(27) Aharoni, A. Introduction to the Theory of Ferromagnetism, 2nd ed.;
Oxford: Oxford, U.K., 2000.
(28) (a) The alternative design of organic spin clusters, addressing the develop-
ment of net ferri- or ferromagnetic correlations in the conjugated polymer
with magnetic ordering, is described in the following: Rajca, A.; Wong-
sriratanakul, J.; Rajca, S. Organic Spin Clusters: Macrocyclic-Macrocyclic
Poly(arylmethyl) Polyradicals with Very High Spin S ) 5-13. J. Am. Chem.
Soc. 2004, 126, in press. (b) The design annelated macrocyclic organic
spin clusters, addressing the dimensionality of the conjugated polymer with
magnetic ordering, is described in the following: Rajca, A.; Wongsrira-
tanakul, J.; Rajca, S.; Cerny, R. L. Organic Spin Clusters: Annelated
Macrocyclic Polyarylmethyl Polyradicals and Polymer with Very High Spin
S ) 6-18. Chem.sEur. J. 2004, 10, in press.
(16) Nishide, H.; Ozawa, T.; Miyasaka, M.; Tsuchida, E. J. Am. Chem. Soc.
2001, 123, 5942-5946.
(17) Michinobu, T.; Inui, J.; Nishide, H. Org. Lett. 2003, 5, 2165-2168.
(18) Bushby, R. J.; McGill, D. R.; Ng, K. M.; Taylor, N. J. Chem. Soc., Perkin
Trans. 2 1997, 7, 1405-1414.
(19) Anderson, K. K.; Dougherty, D. A. AdV. Mater. 1998, 10, 688-692.
(20) Rajca, A.; Rajca, S. J. Am. Chem. Soc. 1996, 118, 8121-8126.
(21) Rajca, A.; Wongsriratanakul, J.; Rajca, S. J. Am. Chem. Soc. 1997, 119,
11674-11686.
(22) Rajca, A.; Wongsriratanakul, J.; Rajca, S.; Cerny, R. Angew. Chem., Int.
Ed. 1998, 37, 1229-1232.
(29) (a) Negishi, E.; King, A. O.; Okukado, N. J. Org. Chem. 1977, 42, 1821-
1823. (b) Negishi, E.; Takahashi, T.; King, A. O. Org. Synth. 1987, 66,
67-74.
(23) Lis, T. Acta Crystallogr., Sect. B 1980, 36, 2042-2046.
(24) Sessoli, R.; Gatteschi, D.; Caneschi, A.; Novak, M. A. Nature 1993, 365,
141-143.
(30) Rajca, A.; Lu, K.; Rajca, S. J. Am. Chem. Soc. 1997, 119, 10335-10345.
9
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A R T I C L E S
Rajca et al.
Figure 2. Cis/trans isomers of calix[4]arene diols 6 and tetraethers 7. Open and closed circles correspond to the relative orientation of the OMe (blue) and
OH (red) groups.
(M - OH)+ cluster ions. Measured and calculated isotopic
Scheme 2. Synthesis of Polyethers 1-(OMe)24 and 2-(OMe)8
distributions for both cluster ions show satisfactory agreement.
IR spectra show the presence of the OH groups in diols, as two
broad peaks (6A-D) or one broad peak (6E) in the 3400-
1
3600 cm-1 range. The H and 13C NMR spectra allow for
unambiguous assignment of diols 6A,B,D, and the correspond-
ing tetraethers 7A,D (Tables 1s-3s, Supporting Information).
However, the most symmetric diols 6C,E (and the corresponding
tetraethers 7C,E) have similar NMR spectral patterns, precluding
their assignment by NMR spectroscopy (Tables 1s-3s, Sup-
porting Information). These two isomer sets are assigned with
the help of X-ray crystallography.
The molecular structure from X-ray crystallography of 7E
shows the all-cis isomer; i.e., all four methoxy groups are located
on the same face of the macrocycle (Figure 3). This implies
that isomer 7C must have all-trans methoxy groups. Interest-
ingly, the calix[4]arene macrocycle 7E adopts the 1,3-alternate
conformation.31,32 One of the tert-butyl groups is disordered over
two positions. The carbon atoms of the tert-butyl groups show
large displacement parameters, especially C16A-C18A, which
are in the vicinity of the solvent void. This suggests the
flexibility of the calix[4]arene macrocycle. The inefficient
packing of the calix[4]arene results in large voids that contain
macrocyclic diols as five cis/trans isomers 6A-E in overall yield
of 34-46% (Scheme 1).
an unknown amount of solvent (Experimental Section).
The C4V-symmetric isomer 7E, which shows 4-fold symmetry
on the NMR scale at ambient temperature and is readily
separable, is selected as the macrocyclic module. Conditions
for the Li/Br exchange for the branch module 8 are optimized
by isolation of monodeuterated module 8-D after the MeOD
quench of the corresponding aryllithium (Scheme 2). Negishi
couplings between the branch modules (8 and 9, 6 equiv as
organozinc derivatives) and the macrocyclic module (7E, 1
equiv) give 24- and 8-ethers 1-(OMe)24 and 2-(OMe)8 in
13-40 and 12-16% isolated yields, respectively (Scheme 2).
The following side products are isolated: homocoupling
products of the branch modules (10 and 11, ∼10%); debromi-
nated branch module (module 8-H, 23%); tricoupling product
(12-(OMe)19, 1%) (Chart 1).
(6A-E are labeled alphabetically in the order of increasing
polarity on silica.) Although all five possible isomers are
isolated, only 6A (14-17%), 6D (5-10%), and 6E (4%) are
readily separable on silica; the remaining two isomers are
isolated as a mixture of 6B and 6C (8-14%, 3.5:1-2.5:1),
though small amounts of both isomers are obtained for
spectroscopic characterization. Etherification of diols 6A,D,E
with MeI yields the corresponding ethers 7A (62%), 7D
(63-84%), and 7E (38-61%); analogously, a mixture of diols
6B,C (3.5:1) provides a mixture of ethers 7D,C (88%, 3.6:1),
i.e., diols 6B,D are related to an identical ether 7D.
All five possible cis/trans isomers of diols 6 and all four
possible cis/trans isomers of tetraethers 7 are shown in Figure
2. Their point groups of symmetry, as expected under conditions
of fast exchange between different calix[4]arene conformations,
are also indicated. For each isomer, FAB MS gives the expected
(M - OCH3)+ cluster ions; the diols 6 show additional, intense
(31) Gutsche, C. D. Calixarenes ReVisited; RSC, Cambridge, U.K., 1998; Chapter
4.
(32) Rajca, A.; Padmakumar, R.; Smithhisler, D. J.; Desai, S. R.; Ross, C. R.;
Stezowski, J. J. J. Org. Chem. 1994, 59, 7701-7703.
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Organic Spin Clusters
A R T I C L E S
Figure 3. Molecular conformation (two views) for macrocyclic tetraether 7E as determined by a single-crystal X-ray crystallography. The hydrogen atoms
and molecules of solvent of crystallization (benzene) are not shown. Carbon, bromine, and oxygen atoms are depicted with ellipsoids representing the 50%
probability level.
Chart 1. Structures of Side Products in Synthesis of 1-(OMe)24
and 2-(OMe)8
Figure 4. Gel permeation chromatography of 1-(OMe)24, 1-H24, 12-
(OMe)19, and 2-(OMe)8. Only plots from the refractive index detector are
shown.
the formula mass of 6314 g mol-1. For all three polyethers Mw’s
are overestimated by about 10% (Table 4s, Supporting Informa-
tion); assuming that only about 90% of the injected mass of
polyether is eluted into detectors, good agreement with the
formula masses is obtained. Such partial retention on the
tetrahydrofuran-eluted GPC column is reasonable in view of
The target polyethers (and the isolated side products) show
the relatively high reactivity of triarylmethyl ethers.
expected monocharged (M - OCH3)+ cluster ions as the most
1H and 13C NMR spectra corroborate the expected 4-fold
intense signals in the high-mass range of FAB MS (Figure 1s,
symmetry for 24-ether 1-(OMe)24 and 8-ether 2-(OMe)8.33 The
Supporting Information).22 The FAB MS for 24-ether 1-(OMe)24,
NMR spectra for dendritic fragments of polyethers 1-(OMe)24,
including the doubly charged (M - (OCH3)2)2+ cluster ion, was
8-H, and 10 are best interpreted in terms of two nonequivalent
discussed previously.22
Gel permeation chromatography (GPC) with multiangle light
scattering (MALS) provides another absolute measure of
molecular mass and column-dependent measure of monodis-
sets of 4-tert-butylphenyl groups, analogously to the previously
discussed NMR spectra of branch module 8.21,33a In the aromatic
1
region of the H NMR spectra for 24-ether 1-(OMe)24 at 348
K, the expected COSY off-diagonal peaks are observed, except
persity (or polydispersity). The elution time is decreasing in
for the two most downfield, broadened resonances at 7.97 (4H)
the order 1-(OMe)24, 1-H24, 12-(OMe)19, and 2-(OMe)8,
reflecting decreasing hydrodynamic radii for the decreasing
molar masses (Figure 4). (The structure of 1-H24 is shown in
and 7.90 (8H).22 In the aromatic region the of 1H-13C HMQC
spectrum at 348 K, 9 out of 10 expected (assuming insufficient
Scheme 3.) All four compounds are monodisperse, giving PD
) 1.00 for the first-order polynomial fit (Table 4s, Figure 2s,
Supporting Information). The measured Mw for hydrocarbon
1-H24 is 6.3-6.4 kDa, which is in an excellent agreement with
(33) (a) In the t-Bu region of 1-(OMe)24, the 1H NMR spectrum at 293 K shows
three singlets in the expected ratio (16:16:4); at 348 K, the 1H and 13C
resonances for the diastereotopic t-Bu groups are not resolved. (b) In the
MeO-group region of 1-(OMe)24, three (1:1:4) 1H resonances are resolved
at 293 K.
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A R T I C L E S
Rajca et al.
Scheme 3. a Generation of Polyradicals 1 and 2
resonances in 1-(OMe)24 are assigned to the four 1,3,5-
trisubstituted benzene rings of the calix[4]arene core.
2. Generation of Carbopolyanions and Polyradicals. The
generation of carbopolyanions and polyradicals is shown in
Scheme 3. When polyethers 1-(OMe)24 and 2-(OMe)8
(0.5-30 mg) are treated with Na/K alloy in THF-d8 (0.06-
0.12 mL), the reaction mixture briefly turns blue and, subse-
quently, deep purple red or purple blue. After about 5 days at
283 K, the solutions of deep purple red carbopolyanion 124-
and purple blue carbooctaanion 28- are filtered into a SQUID,
NMR, ESR, or SANS sample container (Figure 13). Addition
of iodine in small portions at 170-167 K leads to a blue, green
(or blue gray), and, finally, yellow-brown to red-brown reaction
mixture to give polyradicals 1 and 2 (Scheme 3).34
Unlike previously studied low molecular weight carbopolya-
nions, which typically possessed well-resolved NMR spectra,7,34a,35
1
24- has broadened 1H NMR spectra in the 293-193 K range,
preventing peak assignment. The broadening of the resonances
is reversible and increases significantly at low temperatures.
(The solutions of 124- appear as more viscous compared to the
solutions of the corresponding 24-ether 1-(OMe)24 and 24-
radical 1.) The 13C NMR spectrum at 293 K shows fewer than
expected, relatively broad resonances (Figure 6).
The 13C resonance at 85.8 ppm is in the chemical shift range
of the triarylmethyl carbons in analogous carbopolyanions.34a,35
Moreover, no resonances corresponding to methoxy carbons are
detected. Addition of MeOH to carbopolyanion 124- gives the
isomeric mixture of the corresponding hydrocarbon 1-H24.
Similarly, hydrocarbon 2-H8 is obtained, when octaradical 2 is
treated with Na/K alloy at 178-195 K, and then the resultant
carbopolyanion is quenched with MeOH.
a Conditions: (i) Na/K, 283 K for ∼5 d; (ii) I2, 167-170 K; (iii) MeOH;
(iv) Na/K, 178-195 K for several hours.
FAB MS for poly(arylmethyl) hydrocarbons are relatively
difficult to obtain, compared to the corresponding polyethers.21
The expected molecular ion for 2-H8 is detected with the signal-
to-noise of only 2-3, and for much larger 1-H24, no molecular
ion is found in FAB MS. However, GPC MALS of 1-H24 in
THF gives values of Mw that are in excellent agreement with
the formula molecular mass. Furthermore, molecular size as
measured by radius of gyration (see section on SANS studies)
for 1-H24 is similar to that for 24-ether 1-(OMe)24. The 1H NMR
integrations of the aromatic, Ar3CH, and tert-butyl regions are
in good agreement with the expected ratio of 196:24:324 for
hydrocarbon 1-H24; the 13C NMR spectrum shows the expected
resonances for Ar3CH in the 56-57 ppm region. Both NMR
and IR spectra indicate the absence of the arylmethyl ether
linkages.
3. Magnetic Studies of Polyradicals. 3.1. ESR Spectros-
copy. The CW X-band ESR spectrum of octaradical 2 in THF-
d8/2-methyltetrahydrofuran at 77 K shows only one unresolved
resonance in both ∆ms ) 1 and ∆ms ) 2 regions. It is expected
that the spectrum possesses too many closely spaced lines to
be resolved. The ∆ms ) 1 region for the previously studied
1,3-phenylene-based octaradical also showed a broad resonance,
and only 12 (out of expected 16) barely resolved shoulders have
been tentatively assigned to the S ) 4 ground state with axial
zero field splitting parameter |D/hc| ≈ 0.001 27 cm-1.7 The
Figure 5. 13C NMR (125 MHz, benzene-d6) spectrum for 24-ether
1-(OMe)24 at 348 K. Main plot: full spectrum. Inset plot: 1H-13C HMQC
correlation in the aromatic region.
resolution for diastereotopic 4-tert-butylphenyls) cross-peaks are
observed; in particular, the 1H resonance at 7.90 ppm correlates
to a broad 13C resonance at 127.0 ppm (Figure 5). The absence
of the cross-peak to the 1H resonance at 7.97 ppm corresponds
to the missing nonquaternary 13C resonance in the aromatic
region, which is perhaps too broad to be detected under the
present experimental conditions.
In the less sterically congested octaether 2-(OMe)8, the most
downfield 1H resonances appear at similar chemical shifts, 8.06
(4H) and 7.95 (8H), and do show off-diagonal peaks in the
COSY correlation at ambient temperature (Figure 3s, Supporting
1
Information). Similarly, both downfield H resonances show
(34) (a) Rajca, A. J. Am. Chem. Soc. 1990, 112, 5889-5890. (b) Rajca, A. J.
Am. Chem. Soc. 1990, 112, 5890-5892.
(35) NMR spectroscopy of triarylmethyl-based carbopolyanions: (a) Utama-
panya, S.; Rajca, A. J. Am. Chem. Soc. 1991, 113, 9242-9251. (b) Rajca,
A.; Utamapanya, S. J. Org. Chem. 1992, 57, 1760-1767.
cross-peaks in the 1H-13C HSQC correlation at ambient
temperature, i.e., (8.06, 130.4) and (7.95, 127.5) (Figure 4s,
Supporting Information). Therefore, the two most downfield 1H
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Organic Spin Clusters
A R T I C L E S
Figure 6. 13C NMR (125 MHz, THF-d8) spectrum for carbopolyanion 124-. Exponential line broadenings of 10 and 1 Hz are applied to the downfield
(relative scale of 12) and upfield (relative scale of 1) parts of the spectrum, respectively.
Table 1. Summary of Magnetic Data for 24-Radical 1
presence of the biphenylene moieties in 2 is expected to
One-Brillouin
−Θ (K)
Two-Brillouin
sample mass anneal
label (mg) (K)
increased delocalization of spin density in 2 compared to the
1,3-phenylene-based octaradical.6 This suggests relatively small
values of the predominant magnetic dipole-based contribution
to |D/hc|.20,21,36-38 Consequently, the ESR resonances in the S
) 4 state of 2 may be about 2-3 times more densely spaced
within the spectral width of 14|D/hc|, leading to an unresolved
spectrum. In addition, the thermal population of the low-spin
excited states (see bulk magnetization and magnetic susceptibil-
ity studies) may further complicate the ESR spectrum at 77 K.
Because the spectral width is approximately constant within the
homologous series of poly(arylmethyls), resonances in the CW
ESR spectra become rapidly more congested with increasing
values of S (number of resonances increases as 4S or 6S
depending on symmetry). Therefore, bulk magnetic susceptibil-
ity and magnetization studies are techniques of choice for
determination of large values of S.39,40
3.2. Bulk Magnetic Susceptibility and Magnetization
Studies. For magnetic studies, samples of polyradicals 1 and 2
are typically prepared from 0.5 to 1.8 mg of polyethers
1-(OMe)24 and 2-(OMe)8 in THF-d8 (0.06-0.08 mL). Special
care is taken to ensure accurate weight for the polyethers.41
Magnetization (M) is measured as a function of magnetic field
(H ) 0-50 kOe) and temperature (T ) 1.8-150 K) for 1 and
2 in THF-d8. For selected samples, the following sequences of
measurements is carried out: first, without annealing (with
sample chamber degassed at 90 K); second, with prior annealing
at 170 K (slightly above the melting point of the matrix); third,
after exposure of the sample to room temperature for about
0.5 h.
b
S
S
−Θ (K) M
a (µB) øTmax J/k (K)
s
sat
1087c 1.50
90 10.0 0.03
170 10.5 0.3
0.70
0.71
0.18
0.54
0.53
0.63
0.63
0.24
0.46
0.60
46.6 6.6d
6.5d
293
90
170
2.8 0.25
3.8
1109 1.26
1756 1.54
9.8
9.8
0
0
9.9
0
35.8 6.9d
35.4 7.1d
43.0 7.3e
44.6 7.7e
6.2
90 10.0 0.05 10.0 0.05
170 10.0 0.05 10.1 0.05
293
90
3.3 0.1
3.3 0.1
8.2
9.7 0.1
1911f 0.50
1923 1.13 170
0
26.6 7.5e
38.3 7.2e
9.6 0.1
a Msat/mol of triarylmethyl ether. b øTmax/mol of 24-ether 1-(OMe)24.
c Point-by-point correction for diamagnetism, except for samples 1911 and
1923. d At 5000 Oe. e At 500 Oe. f Polyradical preparation at T > 170 K.
2; the M/Msat vs H/T plots are nearly overlapping with the S )
10 and S ) 4 Brillouin functions, respectively (Figure 7). The
observed temperature dependence of S is consistent with an ideal
paramagnet behavior for dilute samples of 1 and 2 below 5 K.
For more concentrated samples of 1 and 2, the additional mean-
field parameters (Θ) are used to correct for small intermolecular
antiferromagnetic (Θ < 0) interactions. Numerical fits to
modified Brillouin functions, M vs H/(T - Θ), with Θ ) -0.03
or -0.05 K, give S ) 10.0 at 1.8, 3, and 5 K and S ) 9.8 at 10
K for 1. For 2, S ) 3.6 (|Θ| ) 0.1-0.2 K) at 1.8, 3, and 5 K
are obtained (Tables 1 and 2).43
Additional numerical fits of the M vs H data for 1 are car-
ried out with linear combination of two Brillouin functions,
B(S) and B(1/2), using three variable parameters: S, Msat, and
w (eq 1).
For the most dilute samples of 1 (∼0.002 M) and 2 (<0.005
M), the M vs H data at 1.8, 3, 5, and 10 K are numerically fit
to one Brillouin function (B(S)),42 with spin (S) and magnetiza-
tion at saturation (Msat) as variable parameters (Tables 1 and
2). The values of S ) 9.8 and S ) 3.8 are obtained for 1 and
(40) In the most favorable case of the |E/hc|, polyradical with S ) 12 would
possess 48 resonances in the ∆ms ) 1 region; with the expected spectral
width of the order of 0.006 cm-1, only a broad single line would be
observed. The spectral width, due to the magnetic dipole-dipole couplings,
may be significantly greater (elongated or flat shapes) or smaller (spherical-
like shapes) than 0.006 cm-1
.
(41) (a) The weighed amount of polyether must be viewed as an upper bound
for the actual amount used for generation of polyradical because of the
difficulty in quantitative transfer of electrostatic powder in to the reaction
vessel. (b) One sample of 2 is prepared on a 9.4-mg scale for SQUID-
measurement-followed-by-quenching experiment (Table 2, entry 1).
(42) Carlin, R. L. Magnetochemistry; Springer: Berlin, 1986.
(43) The mean-field correction with parameter Θ, as implemented here, provides
an approximate description of small exchange couplings, in particular
intermolecular antiferromagnetic couplings in more concentrated solutions.
Such a description is valid as long as |Θ| is relatively small compared to
the studied temperature range. The origin of the large value of |Θ| ) 0.25
K, shown by one sample of 1 after annealing at 170 K (Table 1, entry 1),
is not known. The increased values of |Θ| for the lower molecular weight
polyradicals (2 vs 1) follow the previously observed trends (e.g., ref 21).
(36) The zero field splitting parameter (|D|) vs the interdipole distance in
diradicals: Rohde, O.; Van, S. P.; Kester, W. R.; Griffith, O. H. J. Am.
Chem. Soc. 1974, 96, 5311-5318.
(37) The values of |D/hc| (cm-1) for 3,4′-biphenylene-based di-, tri-, and
pentaradicals are smaller by a factor of about 2-3, compared to their 1,3-
phenylene counterparts, e.g., for 3,4-′biphenylene- vs 1,3-phenylene-based
polyradicals:20,21 0.0025 vs 0.0066 (diradicals); 0.0016 vs 0.004-0.006
(triradicals); 0.0016 vs 0.0027 (pentaradicals).
(38) Minato, M.; Lahti, P. M.; van Willigen, H. J. Am. Chem. Soc. 1993, 115,
4532-4539.
(39) Rajca, A.; Utamapanya, S.; Thayumanavan, S. J. Am. Chem. Soc. 1992,
114, 1884-1885.
9
J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004 6977

A R T I C L E S
Rajca et al.
Table 2. Summary of Magnetic Data for Octaradical 2
Numerical Fits
Brillouin
Heisenberg Hamiltonian
sample labelc
mass (mg)
concn (M)
anneal (K)
S
M
sat
a (µB)
−Θ (K)
J/k (K)
−Θ (K)
øTmaxb (emu K mol-1
)
Suk98d
Sul13
na
1.50
<0.005
90
90
170
90
3.8
3.6
3.6
3.5
3.6
na
0.0
0.2
0.2
0.2
0.1
na
33
34
37
30
na
na
0.008
0.77
0.76
0.81
na
0.15
0.16
0.14
0.06
7.0
7.3
na
1138
1.64
<1.8
0.011
<0.01
Sul08e
90
a Msat/mol of triarylmethyl ether. b øTmax/mol of octaether 2-(OMe)8. c Point-by-point correction for diamagnetism, except for sample Sul08. d 0.009 M
octaradical 2 prepared from 9.4 mg of octaether in the old-style generation vessel and then further diluted. e Preparation in glovebox.
Figure 8. Plots of øT vs T for concentrated solutions of polyradicals 1
(0.003 M, sample label 1756) and 2 (0.008 M, sample label Sul13) in THF-
d8. The symbols and lines are the experimental points and numerical fits to
the spin-pentamer models, respectively. For 1 at H ) 500 Oe, the fitting
parameters and their parameter dependencies are J/k ) 7.7 K (0.46) and N
) 1.16 × 10-7 mol (0.46); for 2 at 5000 Oe, J/k ) 33.8 K (0.59), N )
4.17 × 10-7 mol (0.76), and Θ ) -0.16 K (0.62) are obtained. All
experimental data here are obtained after annealing at 170 K and point-
by-point correction for diamagnetism.
Figure 7. SQUID magnetometry (H ) 0-50 kOe) for dilute solutions of
polyradicals 1 (0.002 M, sample label 1109) and 2 (<0.005 M, sample
label Suk98) in THF-d8. Experimental points at T ) 1.8, 3, 5, and 10 K
and Brillouin functions with S ) 4, 10, and 12 are shown, as symbols and
lines, respectively. Numerical fitting to Brillouin function, using two variable
parameters (S and Msat), gives S ) 9.8 and 3.8 for 1 and 2, respectively, at
1.8, 3, and 5 K. At 10 K, S ) 9.6 is obtained for 1. The parameter
dependencies are 0.26-0.72 and 0.32-0.74 for 1 and 2, respectively. All
experimental data here are plotted after point-by-point correction for
diamagnetism.
The S ) 1/2 Brillouin function (B(1/2)) may account for some
of the polydispersity in the value of S. Parameter w is a measure
of relative contribution from different Brillouin functions to
overall M. Taking into account that contribution to overall M
from each Brillouin function has to be effectively multiplied
by its value of S,42 w is dependent on another variable parameter
S, as well. Consequently, values of spin-weighed average spin
(Ss) are calculated using the following expression: Ss ) (S +
0.5w)/(1 + w). Addition of the third variable parameter
somewhat improves the numerical fits, though the values of Ss
are very similar to the values of S obtained from one-Brillouin
fits (Table 1). This may suggest that the amount of the
impurities, with very low values of S, is relatively insignificant.44
weak ferromagnetic coupling. At low temperatures and modest
magnetic fields (H ) 5000 Oe), the downward turn in øT is
predominantly, if not exclusively, associated with the paramag-
netic saturation. Ideal paramagnetic behavior (flat øT vs T plot)
is established for 1 at T e 5 K, using low magnetic fields (H )
50 Oe) (Figure 8, inset).
The øT vs T dependence is fit to a model on the basis of a
pentamer of four spin carriers with S ) 5/2 (for 1) or S ) 1/2
(for 2) ferromagnetically coupled to one with a spin of S )
4/2.22 Energy eigenvalues for Heisenberg Hamiltonian are
obtained by vector decoupling technique.45-48 For 2, only
relatively concentrated solutions are used for the øT vs T fits;
this provides adequate signal-to-noise, especially in the higher
temperature range, where the overall magnetic moment of the
sample is diamagnetic. Equations for magnetization, including
saturation effects, are derived using standard formulas.47,48
M ) Msat[(B(S) + wB(1/2))]/(1 + w)
(1)
The M vs T data at H ) 5000, 500, and 50 Oe are plotted as
the product of magnetic susceptibility per mol of starting
polyether (ø ) M/H) and temperature vs temperature, i.e., øT
vs T (Figure 8). For both 1 and 2, the values of øT are increasing
with decreasing temperature, indicating the thermal depopulation
of the low spin excited states, i.e., suggesting the presence of a
(44) For 1 at 1.8 and 2.5 K, the maximum value of the parameter dependence
in the numerical fits to eq 1 does not exceed 0.91 (Table 1).
(45) Heisenberg, W. Z. Phys. 1928, 49, 619-636.
(46) Beloritzky, E.; Fries, P. H. J. Chim. Phys. (Paris) 1993, 90, 1077-1100.
(47) Rajca, A. In Hyper-structured Molecules III; Sasabe, H., Ed.; Gordon and
Breach: Reading. U.K., 2001; Chapter 3, pp 46-60.
(48) Rajca, A. Mol. Cryst. Liq. Cryst. 1997, 305, 567-577.
9
6978 J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004

Organic Spin Clusters
A R T I C L E S
Numerical fits use J/k (spin coupling constant in Kelvin) and
N (number of moles of polyradical), as variable parameters. J/k
) 7 ( 1 K and J/k ) 34 ( 4 K, corresponding to a pairwise
ferromagnetic couplings of spins 5/2 to 4/2 and 1/2 to 4/2,
respectively, through 3,4′-biphenylene moiety, are obtained
(Figure 8, Tables 1 and 2). For such values of J/k, it is calculated
that both 1 and 2 should behave as ideal paramagnets at T e 5
K; i.e., their S ) 12 and S ) 4 ground states are nearly
completely populated.49 This is consistent with a flat øT vs T
plot at low magnetic fields, such as 50 Oe for 1 in the inset of
Figure 8.50
Although øT vs T plots fit reasonably well to the pentamer
models for both 1 and 2, the values of S from the curvatures of
Brillouin functions (M vs H/T plots) are somewhat below the
theoretical values of S ) 12 for ferromagnetically coupled 24
unpaired electrons in 1 and S ) 4 for ferromagnetically coupled
8 unpaired electrons in 2, respectively. For the quantitative
values of Msat and øT, based upon the amount of polyethers
weighed for polyradical generation, the discrepancy between
the experiment and the theory is even greater. This may in part
arise from incomplete transfer of samples of polyethers, which
are highly electrostatic powders, to the reaction vessel, mass
losses at the stage of filtration of carbopolyanion, or chemical
defects in generation of polyradicals.
defects.22 The corresponding percolation model (Experimental
Section) gives density of chemical defects at the level of about
2%.22,51 Such defects may result from less than 100% yield for
generation of “unpaired” electrons or synthetic impurities in
polyether precursors. However, Msat ) 0.6-0.7 µB would
correspond to the density of chemical defects in the 30-40%
range; this would imply highly nonstatistical (rather than
random) distribution of chemical defects, with the predominant
density of defects at the 16 terminal triarylmethyl sites. Because
of low temperatures employed for measurement of Msat,
antiferromagnetic interactions may contribute to the low values
of Msat. For example, antiferromagnetic exchange coupling
arising from a near 90° twisting of one of the biphenyls (at the
phenyl-phenyl CC bond) would lead to cancellation of 10
electron spins; i.e., Msat ) 14 µB/24 ≈ 0.58 µB and S ) 7.
Analogously, two such twistings, would give polyradical with
Msat ) 4 µB/24 ≈ 0.17 µB and S ) 2. A mixture of conformers
with 0, 1, and more twistings could qualitatively account for
the experimentally found averages for Msat and S.52
Thermal Stability (Persistence) of Polyradical 1. Annealing
at 170 K (just above the melting point of the matrix) for a few
minutes does not affect the results for two samples of 1;
however, the third sample shows increased values of S and |Θ|
after after annealing (Table 1). For two samples, magnetic
moment is continuously measured at 170 K for 12+ h. The
sample, which is somewhat overtitrated with iodine, shows a
slow decrease of moment over time. However, the other sample
possesses unchanged magnetic moment after 12+ h at 170 K,
suggesting that polyradical 1 is persistent (stable) at 170 K. Two
samples of 1 are annealed at room temperature for 30 min, and
subsequently, repeat magnetic studies are carried out (Table 1).
For both samples, the values of S ≈ 3 are obtained, i.e., about
30% of the original value. Similar relative decreases are
observed for values of Msat (Table 1).
For quantitative conversion of polyethers to ferromagnetically
coupled polyradicals 1 and 2, øTmax should reach 78 and 10
emu K mol-1, respectively. However, the maximum values of
øT are only about 45 and 7 emu K mol-1 for 1 and 2,
respectively.
M
sat measures the number of unpaired electron spins (or spin
concentration) in the limit of low temperature and high magnetic
field. For the best samples of 1, Msat is about 0.6-0.7
µB/arylmethyl; i.e., 60-70% of the expected value for quantita-
tive conversion of 1-(OMe)24 to 1 with 24 unpaired electrons.
Analogous percentages for 2 are somewhat higher at about 80%.
The values of Msat for 1 imply that only 14-17 electron spins
are effectively present in an average molecule of 1 within the
limit of low T and high H. How could this relatively small
Conformational Searches. Monte Carlo conformational
searches for polyradical 1 provided low-energy conformations
with elongated shapes with overall dimensions of 4 × 3 × 2
nm (Figure 9). As shown by the color coding for polyradical 1
in Figure 9, the core calix[4]arene adopts a 1,3-alternate
conformation. Consequently, each pair of the diagonally posi-
tioned dendritic branches occupies the opposite faces of the core
calix[4]arene. The conformation of polyradical 1 has an ap-
proximate D2d symmetry; the two pairs diagonally positioned
dendritic branches are interchangeable by the S4 axis, collinear
with the C2 axis of the molecule (Figure 9).
1
number of radicals (S ) /2) lead to relatively high value of S
) 10 for 1? Analogous question arises for 2. Such discrepancies
may in principle be reconciled, considering that both Msat and
S are different averages for polydisperse spin systems. Msat
corresponds to a number average; S, as fit to the curvature of
the Brillouin function, is approximately a weighed average (Ss).51
For polydisperse systems, weighed average may be significantly
greater than the corresponding number average. Furthermore,
Msat may be underestimated by incomplete mass balance, as
mentioned in the preceding paragraphs.41a
In the preliminary report, only qualitative magnetic data for
1 were available.22 The discrepancy between the theoretical
value of S ) 12 and the experimental value of S ) 10, obtained
from the curvature of the Brillouin plot, was ascribed to the
presence of small and randomly distributed density of chemical
Monte Carlo conformational searches for tetraradical 3 give
the analogous 1,3-alternate conformations for the lowest energy
structures. In 3, the eight CCCC torsional angles along the inner
macrocyclic carbon backbone of the calix[4]arene core are
moderate, at about 47°, consistent with the S ) 2 ground state
found in THF (or 2-MeTHF/THF) matrixes.7 However, in 1,
the analogous torsional angles are in the 40-70° range, e.g.,
63, 47, 72, 42, 55, 49, 67, and 49°. Such conformations should
(49) Equations for M(T,H) derived from Heisenberg Hamiltonians for the spin
pentamers are used.
(52) A percolation model for 1, in which random distribution of chemical defects
and random distribution of ferromagnetic vs antiferromagnetic couplings
across the four biphenylene moieties are assumed, is developed (eq 5,
Experimental Section). Analogous percolation models are described in detail
in ref 28a. However, the numerical fits of the M vs H/T data to such models
are not satisfactory. Possibly, steric congestion of the dendritic branches
in 1, as found in conformational searches, affects the distribution of
conformations, leading to nonrandom distribution of exchange couplings
across biphenylene coupling units.
(50) The energy gaps between the ground state and the lowest excited state are
identical in units of J/k for both spin pentamers, i.e., 4J/k. The overall
span of energy levels is 20J/k (680 K) and 84J/k (588 K) for pentamers
corresponding to 1 and 2, respectively. For reliable calculation of thermal
behavior, all energy levels, including multiplicities and ms sublevels, should
be taken into account.
(51) Number average Sn in refs 2 and 22 should be replaced with weighed
average Ss.
9
J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004 6979

A R T I C L E S
Rajca et al.
Figure 9. Low-energy conformation for polyradical 1 that is obtained using
Monte Carlo conformational searches with the MM2* force field (Macro-
model 6.5).
Figure 10. Main plot: SANS intensity (I) vs momentum transfer (q )
0.049-0.419 Å-1) for 9 × 10-4 M polyradical 1 (sample label 1907) in
THF-d8 at 170 K. The symbols and solid line correspond to the experimental
data points and the numerical fit using GNOM/DAMMIN simulated
annealing (ø ) 4.712), respectively. Inset: Low-resolution particle shape
reconstruction for 1 obtained from the GNOM/DAMMIN fit. Two side views
(rotated by 90°), using both the DAMMIN spheres and the spherical
harmonics-based envelopes, are shown.
still be compatible with the ferromagnetic coupling for the four
unpaired electrons in the macrocyclic core of 1.10,53
The torsional angles, involving 1,3-phenylene moieties within
the dendritic branches, are in the 20-57° range; however, the
higher angles (e.g., above 47°) are found only at the periphery
of the dendritic branch. The torsional angles for the biphenyl
moieties in 1 are typically about 48° for the lowest energy
conformations. However, conformations, in which one of the
biphenyls has a torsional angle approaching 90°, are at ∼8 kcal/
mol relative to the lowest energy conformations. Severe twisting
of the biphenyl moiety does not appear to affect significantly
the overall molecular shape of 1.
Conclusions about the exchange coupling based upon calcu-
lated conformations must take into consideration that it is not
absolutely certain whether the conformation associated with the
global minimum was found and whether the calculated confor-
mations in the gas phase represent adequately those in THF-d8
frozen solutions.54 With these precautions in mind, the lowest
energy conformations of 1 are probably compatible with
ferromagnetic coupling; the somewhat higher in energy con-
formations may have antiferromagnetic coupling between the
dendritic branch and the macrocyclic core.
Figure 11. Main plot: SANS intensity (I) vs momentum transfer (q )
0.012-0.534 Å-1) for 1.6 × 10-3 M 24-ether 1-(OMe)24 in THF-d8 at
room temperature. The symbols and solid line correspond to the experi-
mental data points and the numerical fit using GNOM/DAMMIN simulated
annealing (ø ) 1.020), respectively. Inset: Low-resolution particle shape
reconstruction for 1-(OMe)24 obtained from the GNOM/DAMMIN fit. Two
side views (rotated by 90°), using both the DAMMIN spheres and the
spherical harmonics-based envelopes, are shown.
The calculated, dumbbell-like molecular shapes for 1 have
overall sizes exceeding 1 nm making possible their experimental
verification using small-angle scattering techniques.55
Small-Angle Neutron Scattering. Solutions of polyradical
1, 24-ether 1-(OMe)24, hydrocarbon 1-H24, and carbopolyanion
1
24- in THF-d8 are studied with small-angle neutron scattering
formation of frozen moisture or frozen organic solvent on the
outside wall of the sample cell; (2) incomplete melting of the
frozen sample solution or inadvertent particles (e.g., precipitate)
inside the sample cell. Either of these two problems will lead
to an excess of SANS intensity, especially in the low-q range.
Elaborate procedures for the sample preparation and handling
are developed as described in the Supporting Information.
The logarithmic plots of SANS intensity (I) vs momentum
transfer (q) for polyradical 1, 24-ether 1-(OMe)24, and hydro-
carbon 1-H24 are shown in Figures 10-12. The numerical fits
to the SANS data are obtained using the simulated annealing
approach of Svergun, as implemented in GNOM/DAMMIN
software packages.56,57 Representative reconstructions of low-
resolution particle shapes in the insets of Figures 10-12 are
(SANS).
Polyradical 1 is handled at temperatures e170 K at all times
to prevent any substantial decomposition. This poses technical
problems for obtaining the SANS data of high quality: (1)
(53) For each 1,3-phenylene moiety of the macrocyclic core of 1, at most one
torsional angle is relatively large near 70°, with the other torsional angle
approaching 50°. Severe twisting on one side of 1,3-phenylene moiety does
not appear to lead to antiferromagnetic coupling, e.g., ref 10.
(54) There is no detailed quantitative data on the dependence of the exchange
coupling vs torsional angles in either 1,3-phenylene or 3,4′-biphenylene
moieties. However, a “Karplus-Conroy-type” relationship for exchange
coupling in trimethylene-based bis(semiquinone) diradicals was proposed:
Shultz, D. A.; Fico, R. M., Jr.; Bodnar, S. H.; Kumar, K.; Vostrikova, K.
E.; Kampf, J. W.; Boyle, P. D. J. Am. Chem. Soc. 2003, 125, 11761-
11771.
(55) Roe, R. J. Methods of X-ray and Neutron Scattering in Polymer Science;
Oxford University: New York, 2000; Chapter 5.
9
6980 J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004

Organic Spin Clusters
A R T I C L E S
One of the samples of 1 is allowed to attain room temperature
for about 4 min. Following cleaning of outside windows of the
sample cell at room temperature, the sample is reinserted to
the cryostat and the SANS data are collected at 170 K again.
The excess of I is still visible at low-q values, and more
importantly, the molecular shapes are now qualitatively different,
suggesting decomposition of 1 (Figure 5s, Supporting Informa-
tion).62
SANS data for carbopolyanion 124- in THF-d8 are obtained
at room temperature and 170 K (Figure 6s, Supporting Informa-
tion). However, DAMMIN-based shape reconstructions for 124-
may not be reliable because of high dependence of the obtained
shapes on the applied constraints. Overall, the shapes for 124-
might be significantly different and of greater size compared
to 1 and/or 124- forms aggregates. The possibility of aggregation
is supported by the observation of highly viscous solutions of
1
24- in THF-d8 at low temperatures (e.g., 170 K) and apparent
Figure 12. Main plot: SANS intensity (I) vs momentum transfer (q )
0.012-0.549 Å-1) for 1.1 × 10-3 M hydrocarbon 1-H24 in THF-d8 at room
temperature. The symbols and solid line correspond to the experimental
data points and the numerical fit using GNOM/DAMMIN simulated
annealing (ø ) 1.109), respectively. Inset: Low-resolution particle shape
reconstruction for 1-H24 obtained from the GNOM/DAMMIN fit. Two side
views (rotated by 90°), using both the DAMMIN spheres and the spherical
harmonics-based envelopes, are shown.
increase in Rg with extending the Rgq range of the Guinier law
analysis.
Magnetic Shape Anisotropy. The possible shapes for
polyradical 1, which are obtained from conformational searches
and SANS-based shape reconstructions, may be viewed as
elongated. The simplest approximations for such a shape, for
which demagnetizing factors are readily calculated, are ellipsoids
of rotation, e.g., a prolate ellipsoid.63 In such a case, the barrier
for coherent rotation of magnetization (EA) arising from the
shape anisotropy is described by eq 2, where ∆N, Is, and V are
the difference of demagnetizing factors between the two longest
semiaxes of ellipsoid, magnetization at saturation (per unit
volume), and volume of the ellipsoid, respectively.4,5,27,64a
illustrated using both DAMMIN spheres and spherical harmon-
ics envelopes (up to 6th order); two orientations, related by
rotation of about 90° with the respect to the long axis of the
molecule, are shown. The spherical harmonics are employed
to smooth out the excessive detail of the DAMMIN shapes.58
The radii of gyration (Rg) for these shapes are 1.5 nm (for 1)
and 1.4 nm (for 1-(OMe)24 and 1-H24). Guinier law analysis,59
which does not consider any particular shape, gives identical
values of Rg for 1-(OMe)24 and 1-H24. For 1, Guinier law
analysis is not carried because of excess of I, especially in the
low-q range. The cause for this excess of I in all samples of 1
is not known. However, this excess of I leads to large values of
ø2 in the DAMMIN fits, though the information concerning
molecular shape is contained primarily at the relatively high-q
values.60
EA ) (∆NIs2V)/2
(2)
Using a prolate ellipsoid (anisometry, a/b ) 2) of volume
and spin density similar to that of 1, the shape anisotropy barrier
(62) After cleaning of the external windows of the sample cell for 1 at room
temperature, the excess of I was still present at 170 K. However, the color
of the sample is too dark to see whether the precipitate is present after 4
min at room temperature. After longer times, the color fades and precipitate
becomes clearly visible.
(63) (a) Demagnetizing factors for ellipsoids: Osborn, J. A. Phys. ReV. 1945,
67, 351-357. (b) Stoner, E. C. Philos. Mag. 1945, 36, 803-821. (c)
Inversion of magnetization in single-domain ellipsoids: Stoner, E. C.;
Wohlfarth, E. P. Philos. Trans. R. Soc. London 1948, A240, 599-642.
Reprinted in: IEEE Trans. Magn. 1991, 27, 3475-3518.
Overall shapes for 1, 1-(OMe)24, and 1-H24 have some
similarity to a dumbbell (large on the top and the bottom with
the narrow middle part). The experimental resolution of the
SANS experiment hardly allows for more detailed description
of the reconstructed shape.60,61 Such a general “dumbbell-like”
description also applies to the lowest energy conformations of
1 found by conformational searches (Figure 9).
(64) (a) In eq 2, magnetization at saturation is defined by Is rather than Msat
(defined in the preceding sections) according to typical notation. (b) For
an ellipsoid with nel ferromagnetically coupled electron spins (total S )
nel/2) with Is ) nelµB/V, EA in the units temperature (i.e., EA/k, where k is
a Boltzman constant) is as follows: EA/k ) [(µB2/k)∆N(nel/V)]S. Thus, for
homologous ellipsoids with identical shape (∆N ) constant) and with
identical spin density (nel/V ) constant), EA/k varies linearly with the value
of S. (c) For an idealized 4 × 2 × 2 nm prolate ellipsoid (a/b ) 2) with
24 electron spins, ∆N ≈ 3.0 and nel/V ) (9/π) × 1021 electron cm-3. Thus,
for this ellipsoid and homologous ellipsoids, EA/k ≈ 5S mK; for S ) 12,
EA/k is approximately 60 mK. (d) The 4 × 3 × 2 nm general ellipsoid
may possibly be a better approximation to the “dumbbell-like” shape of 1
with dimensions of 4 × 3 × 2 nm. For such ellipsoid, ∆N ≈ 1.2 is obtained
from demagnetizing factors, leading to EA/k that is significantly below 60
mK (by a factor of 2-3). (e) One of the reviewers commented on a possible
relationship between the anisotropy barriers derived from values of D and
those obtained from demagnetizing factors. The discussion will be limited
to prolatelike shapes, in which D < 0 arises solely from the magnetic
dipole-dipole interactions (couplings). For a homologous series of high-
spin polyradicals (with similar spin densities and similar shapes), values
of |D|, scale approximately as 1/S;26,40 such polyradicals have approximately
constant ESR spectral width, |D(4S - 2)|. Therefore, the anisotropy barrier
for such polyradicals (or ellipsoids), which is related to the value of |DS2|,
varies linearly with the value of S, similarly as determined from
demagnetizing factors in ellipsoids.64b Furthermore, if the ESR spectral
width of 0.006 cm-1 (i.e., 4|D/hc|S ≈ 0.006 cm-1) is assumed for 1 with
S ) 12, then the value of |DS2| is of the order of 30 mK, i.e., similar to
that obtained from demagnetizing factors.40
(56) (a) GNOM: Svergun, D. I. J. Appl. Crystallogr. 1992, 25, 495-503. (b)
DAMMIN: Svergun, D. I. Biophys. J. 1999, 76, 2879-2886. (c) Svergun,
D. I. J. Appl. Crystallogr. 2000, 33, 530-534. (d) Svergun, D. I.; Stuhrman,
H. B. Acta Crystallogr., Sect. A 1991, 47, 736-744.
(57) Several approaches to reconstruction of three-dimensional solution structures
of macromolecules (proteins) from one-dimensional small-angle scattering
data are available; however, the ab initio approach, based upon Svergun’s
simulated annealing GNOM/DAMMIN programs, appears to give the best
results, e.g.: Zipper, P.; Durchschlag, H. J. Appl. Crystallogr. 2003, 36,
509-514.
(58) CRYSOL: Svergun, D. I.; Barberato, C.; Koch, M. H. J. J. Appl.
Crystallogr. 1995, 28, 768-773.
(59) Guinier law: (a) Reference 55, pp 167-174. (b) Guinier, A.; Fournet, G.
Small Angle Scattering of X-rays; Wiley: New York, 1955.
(60) Resolution of SANS scales with 2π/q.
(61) Because the shapes in this size range close to 1 nm is determined at
relatively high q, there is a possibility for the interference from the internal
structure and the solvent structure. For 1, the excess of I, which is found
at low q, may tail into the high-q region, leading to further decrease in
reliability of the shape reconstruction.
9
J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004 6981

A R T I C L E S
Rajca et al.
Å3, T ) 173(2) K, space group P1h, Z ) 2, Mo KR (λ ) 0.710 73 Å).
The structure was solved by direct methods and refined by full-matrix
least-squares on F2. A total of 14 492 reflections were observed, and
8206 reflections with I > 2σ(I) were recorded. Refinement statistics
with 852 parameters was as follows: wR ) 0.0847 (I > 2σ(I)), R )
0.0415 (I > 2σ(I)), GOF ) 0.968.
for inversion of magnetization of about 60 mK is predicted.64
This estimate should be viewed as an upper bound.64 Such a
low barrier is consistent with the paramagnetic behavior of 1
at 1.8 K and above. However, for homologous prolate ellipsoids
with a/b ≈ 2 (and same spin density), the shape anisotropy
barrier scales as 5S mK;64 i.e., for macromolecules with values
of S of the order of several thousands (and spin density similar
to that of 1), the magnetization may become blocked at the
readily accessible temperatures of the order of 10 K.
Tetrabromocalix[4]arene Diols 6. t-BuLi (13.20 mL of 1.5 M
solution in pentane, 19.80 mmol, 4 equiv) was added to a solution of
tetrabromo ether 4 (3.195 g, 4.946 mmol) in THF (500 mL) at -78 °C
over the period of about 10 min. After 2-3 h, a solution of diketone
5 (4.000 g, 4.946 mmol) in THF (200 mL) was cannulated to the
reaction mixture at -78 °C. The reaction mixture was allowed to warm
to ambient temperature for 2 days. Two such reaction mixtures were
worked up with water (500 mL) and ether (300 + 200 mL). The
combined organic layer was dried over MgSO4 and then concentrated
in vacuo to give the light yellow glassy solid (or light yellow oil).
Column chromatography (TLC grade silica gel, 2-10% ether in hexane)
gave four fractions (in order of increasing polarity) corresponding to
the following isomers: 6A (2.19 g, 17%), mixture of 6B,C (1.06 g,
3.5:1, 8%), 6D (0.604 g, 5%), and 6E (0.489 g, 4%) as white solids.
Small amounts of isomers 6B,C were further separated (column
chromatography or preparative TLC) for spectroscopic characterization.
Another set of two reactions on identical scales gave the following
results: 6A (1.778 g, 14%), mixture of 6B,C (2.312 g, 2.5:1, 18%),
6D (1.276 g, 10%), and 6E (0.536 g, 4%). The calculated isotopic
intensities for the most intense ions in FABMS of 6A-E are as
follows: C69H69O3Br4 at (M - OCH3)+, 1261.2 (15), 1262.2 (11),
1263.2 (61), 1264.2 (45), 1265.2 (100), 1266.2 (69), 1267.2 (80), 1268.2
(48), 1269.2 (30), 1270.2 (15); C70H71O3Br4 at (M - OH)+, 1275.2
(15), 1276.2 (11), 1277.2 (61), 1278.2 (45), 1279.2 (100), 1280.2 (70),
1281.2 (80), 1282.2 (49), 1283.2 (31), 1284.2 (15), 1285.2 (5).
Conclusion
Quantitative magnetic measurements on dendritic-macrocyclic
polyradical 1 and its lower homologue 2 confirm the presence
of high-spin ground states. The detailed interpretation of the
these measurements is complicated by the possible presence of
conformations with different exchange couplings, different types
of averages for the measured quantities (S, Msat, and øT), and
the possibility of incomplete mass transfers. Molecular sizes
and shapes for 1 obtained from conformational searches show
fair agreement with the shape reconstructions derived from the
SANS experiments.
Polyradical 1 with average S ) 10 may be viewed as a
nanometer-sized organic spin cluster, for which estimated shape
anisotropy barrier for inversion of magnetization is rather small,
in the miliKelvin range. Because the shape anisotropy barriers
may scale with S, significant barriers for inversion of magne-
tization in macromolecules with average S ) 103-104 and
elongated shapes may be found. The shape anisotropy may in
part be responsible for blocking of magnetization in the recently
reported organic polymer with average S ≈ 5000.1
Diol 6A. The product was softened at 150 °C and melted and became
a yellow liquid at 158-160 °C. Anal. Calcd for C70H72O4Br4: C, 64.83;
H, 5.60. Found: 64.96; H, 4.86. FABMS (3-NBA) cluster m/z (% RA
for m/z ) 200-1400): at (M - OCH3)+, 1261.3 (28), 1262.3 (28),
1263.3 (73), 1264.3 (56), 1265.3 (100), 1266.3 (66), 1267.3 (74), 1268.3
(44), 1269.3 (31), 1270.3 (14); at (M - OH)+, 1275.4 (24), 1276.4
(20), 1277.4 (66), 1278.4 (55), 1279.3 (100), 1280.4 (68), 1281.4 (77),
Experimental Section
Addition of Small Volumes of Reagents. Reagent volumes of less
than 0.3 mL (e.g., of solutions of t-BuLi, ZnCl2, etc.), encountered in
micromolar-scale syntheses, were added by counting drops of the
reagent solution. Typically, the volumes were calibrated by counting
number of drops in 0.4 mL of the reagent solution that was dispensed
using 1-mL syringe with a 22-gauge stainless steel needle. Care was
taken to mimic the conditions of the actual reaction (rate of addition,
position of the needle, temperature, etc.) as closely as possible, using
the identical 22-gauge needle.
X-ray Crystallography for 7E. The data were collected on a Bruker
SMART system at the University of Minnesota. A colorless, clear
crystal (approximate dimensions 0.185 × 0.105 × 0.050 mm3), which
was obtained from benzene/methanol solution by slow evaporation, was
selected for analysis. Two solvent molecules (benzene) were found from
the E-map and refined using restraints for the thermal parameter in the
bond direction (DELU). Another 1.3 benzene molecules found were
heavily disordered in a void and could not be refined to a satisfactory
result. An investigation of the void space in the structure, excluding
the disordered 1.3 benzene molecules from the refinement, showed that
107 electrons are located in a major void of approximately 640 Å3.
(Each benzene molecule occupies 116 Å3 with 42 electrons.) The dataset
was corrected for disordered solvent using the program PLATON/
SQUEEZE.65 The refinement using the corrected data improved the
overall structure and the R-value by 0.015. However, as the exact
amount of solvent is not known, selected values below (and the CIF
file deposited on the Web) are incorrect, e.g., formula, formula weight,
F(000). Crystal data for 7E were as follows: C84H88Br4O4, M )
1481.18, triclinic, a ) 16.249(2) Å, b ) 16.659(2) Å, c ) 16.959(2)
Å, R ) 90.301(2)°, â ) 108.949(2)°, γ ) 107.420(2)°, V ) 4115.9(6)
1
1282.4 (46), 1283.3 (32), 1284.3 (18). H NMR (500 MHz, EM )
-0.61, GB ) 0.47, CDCl3, 1H-1H COSY cross-peaks in aromatic
region): 293 K, 7.557 (t, J ) 1.5, 2 H, 7.399, 6.511), 7.557 (t, J )
1.5, 2 H, 7.365, 6.560), 7.399 (s, 2 H, 7.557, 6.511), 7.365 (t, J ) 1,
2 H, 7.557, 6.560), 7.286 (d, J ) 8, 4 H, 6.969), 7.248 (d, J ) 8, 4 H,
6.969), 6.969 (d, J ) 9, 4 H, 7.286), 6.969 (d, J ) 9, 4 H, 7.248),
6.560 (s, 2 H, 7.557, 7.365), 6.511 (s, 2 H, 7.557, 7.399), 2.876 (s, 6
H), 2.589 (bs, 2 H, D2O exch.), 1.326 (s, 18 H), 1.273 (s, 18 H), 1.258
(s, impurity). 13C NMR (125 MHz, CDCl3; 293 K): aromatic region,
expected, 20 resonances, found, 20 resonances at 150.8, 150.5, 148.3,
147.7, 146.4, 145.6, 141.9, 137.7, 129.5, 129.4, 129.12, 129.09, 128.7,
127.26, 127.20, 126.8, 125.0, 124.8, 122.4, 122.2; aliphatic region, 86.0,
81.1, 52.0, 34.51, 34.47, 31.30, 31.27, 29.7 (impurity). IR (cm-1): 3565
(O-H), 3458 (O-H), 1567 (Ar), 1084 (C-O-C).
Diol 6B. The product was softened at 152 °C and melted and became
a brown liquid at 187-189 °C. FABMS (3-NBA) cluster m/z (% RA
for m/z ) 200-1520): at (M - OCH3)+, 1261.1 (26), 1262.2 (24),
1263.2 (73), 1264.2 (56), 1265.2 (100), 1266.2 (71), 1267.2 (73), 1268.2
(48), 1269.2 (27), 1270.2 (13); at (M - OH)+, 1275.2 (20), 1276.2
(18), 1277.2 (64), 1278.2 (48), 1279.2 (94), 1280.2 (64), 1281.2 (72),
1
1282.2 (42), 1283.2 (28), 1284.3 (14). H NMR (500 MHz, EM )
-0.59, GB ) 0.48, CDCl3, 1H-1H COSY cross-peaks in aromatic
region; 293 K): 7.560 (s, 2 H, 7.518, 6.389), 7.518 (s, 2 H, 7.560,
6.389), 7.434 (s, 2 H, 7.270, 6.914), 7.299 (d, J ) 9, 2 H, 7.036),
7.278 (d, J ) 9, 4 H, 6.977), 7.278 (d, J ) 9, 2 H, 6.938), 7.270 (s, 2
H, 7.434, 6.914), 7.036 (d, J ) 8, 2 H, 7.299), 6.977 (d, J ) 8, 4 H,
7.278), 6.938 (d, J ) 8, 2 H, 7.278), 6.914 (s, 2 H, 7.434, 7.270),
6.389 (s, 2 H, 7.560, 7.518), 2.885 (s, 6 H), 2.829 (s, 1 H, exch D2O),
(65) PLATON: Spek, A. L. Acta Crystallogr., Sect. A 1990, 46, C34.
(66) Suffert, J. J. Org. Chem. 1989, 54, 509-510.
9
6982 J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004

Organic Spin Clusters
A R T I C L E S
2.616 (s, 1 H, exch D2O), 1.316 (s, 18 H), 1.304 (s, 9 H), 1.299 (s, 9
H). 13C NMR (125 MHz, CDCl3; 293 K): aromatic region, expected,
24 resonances, found, 24 resonances at 151.0, 150.9, 150.4, 148.2,
148.0, 146.2, 145.4, 141.85, 141.80, 138.0, 130.3, 129.8, 129.3, 129.0,
128.0, 127.6, 127.4, 127.2, 126.8, 125.24, 125.18, 125.13, 122.4, 122.0;
aliphatic region, 86.0, 81.4, 81.1, 52.1, 34.52 (br), 34.49, 31.31, 31.29,
31.28. IR (cm-1): 3557 (O-H), 3458 (O-H), 1567 (Ar), 1084 (C-
O-C). A small amount of an unknown impurity was present: 1H, 2.270
(s); 13C, 125.5, 30.3.
resonances at 130.4, 129.7, 127.9, 127.3, 127.2, 125.1; aliphatic region,
86.1 (q), 81.2 (q), 52.1, 34.5 (q), 31.3. H NMR (500 MHz, C6D6,
1
1H-1H fast COSY cross-peaks in aromatic region; 293 K): 7.850 (bs,
4 H, 7.451, 7.150), 7.451 (bs, 4 H, 7.850, 7.150), 7.328 (d, J ) 8, 4 H,
7.282), 7.282 (d, J ) 8, 4 H, 7.328), 7.174 (d, J ) 8, 4 H, 7.039),
7.150 (bs, 4 H, 7.850, 7.451), 7.039 (d, J ) 8, 4 H, 7.174), 2.821 (s,
6 H), 2.150 (bs, 2 H), 1.341 (s, 18 H), 1.324 (s, 18 H). 13C{1H} DEPT
(135°) NMR (125 MHz, C6D6; 293 K): aromatic quaternary region,
expected, 7 resonances, found, 6 resonances at 150.9 (q), 149.5 (q),
146.7 (q), 143.3 (q), 139.9 (q), 122.9 (q); aromatic nonquaternary region,
expected, 7 resonances, found 7 resonances at 131.1, 130.9, 128.67,
128.3, 128.0, 126.1, 125.7; aliphatic region, 86.9 (q), 81.6 (q), 52.3,
34.9 (q), 34.8(q), 31.72, 31.66. An additional resonance at 128.64 ppm
was assigned to C6D5H. IR (cm-1): 3433 (O-H), 1567 (Ar), 1080
(C-O-C).
Diol 6C. The product was changed from white to brown solid at
308 °C and melted and became a brown liquid at 320-322 °C. FABMS
(3-NBA) cluster m/z (% RA for m/z ) 200-1520): at (M - OCH3)+.
1260.9 (25), 1261.9 (23), 1262.9 (68), 1263.9 (52), 1264.9 (98), 1265.9
(67), 1266.9 (73), 1267.9 (43), 1268.9 (27), 1269.9 (13); at (M - OH)+,
1274.9 (21), 1275.9 (18), 1276.9 (66), 1277.9 (50), 1278.9 (100), 1279.9
(68), 1280.9 (76), 1281.9 (47), 1282.9 (31), 1283.9 (16). 1H NMR (500
MHz, EM ) -1.22, GB ) 0.48, CDCl3, 1H-1H COSY cross-peaks in
aromatic region; 293 K): 7.517 (t, J ) 1.5, 4 H, 7.468, 6.488), 7.468
(t, J ) 1.5, 4 H, 7.517, 6.488), 7.359 (d, J ) 9, 4 H, 7.033), 7.260 (d,
J ) 9, 4 H, 6.907), 7.033 (d, J ) 8, 4 H, 7.359), 6.907 (d, J ) 9, 4 H,
7.260), 6.488 (t, J ) 1.5, 4 H, 7.517, 7.468), 2.800 (s, 2 H), 2.685 (s,
6 H), 1.318 (s, 18 H), 1.310 (s, 18 H). 13C NMR (125 MHz, CDCl3;
293 K): aromatic region, expected, 14 resonances, found, 14 resonances
at 151.1, 150.5, 147.9, 145.7, 142.3, 138.0, 129.9, 128.9, 128.1, 127.50,
127.42, 125.10, 125.02, 122.3; aliphatic region, 85.7, 81.4, 51.8, 34.55,
34.42, 31.31 (EM ) -2.88, GB ) 0.48), 31.28. IR (cm-1): 3566 (O-
H), 3453 (O-H), 1566 (Ar), 1082 (C-O-C). A small amount of an
unknown impurity was present: 1H, 2.270 (s); 13C, 125.5, 30.3.
Tetrabromocalix[4]arene Tetraethers 7. A 100 mL flask with
sidearm was charged with NaH (0.300 g of 60% dispersion in mineral
oil, 7.722 mmol). After removal of mineral oil with pentane under
nitrogen flow, THF (15 mL) was added. The reaction mixture was
cooled with an ice bath, and then diol 6A (1.669 g, 1.287 mmol) in
THF (30 mL) was added. The resultant, stirred suspension was allowed
to attain ambient temperature over a priod of ∼2 h. Subsequently,
iodomethane (1.30 mL, 20.6 mmol) was added at 0 °C. The reaction
mixture was allowed to attain ambient temperature overnight. After
the usual aqueous workup (ether, MgSO4), the white or light yellow
solid was crystallized from ether/MeOH to give pure product 7A as
indicated below. An analogous procedure was used to obtain 7C-E.
The calculated isotopic intensities at (M - OCH3)+ in FABMS of
7A-E are as follows: C71H73O3Br4, 1289.2 (14), 1290.2 (11), 1291.2
(61), 1292.2 (46), 1293.2 (100), 1294.2 (70), 1295.2 (80), 1296.2 (49),
1297.2 (31), 1298.2 (15).
Tetraether 7A. From diol 6A (1.669 g), 1.042 g (62%) of 7A as
white powder was obtained. The product was softened at 305 °C and
melted and became a brown liquid at 324-326 °C. Anal. Calcd for
C72H76O4Br4: C, 65.27; H, 5.78. Found: 64.98; H, 5.89. FABMS
(3-NBA) cluster m/z (% RA for m/z ) 200-1460): at (M - OCH3)+,
1289.2 (25), 1290.2 (20), 1291.2 (70), 1292.2 (52), 1293.2 (100), 1294.2
(69), 1295.2 (73), 1296.2 (46), 1297.2 (30), 1298.2 (15). 1H NMR (500
MHz, CDCl3, EM ) -0.68, GB ) 0.46, CDCl3, 1H-1H COSY cross-
peaks in aromatic region; 293 K): 7.504, 7.500 (d, J ) 1.5, d, J )
1.5, 8 H, 6.848, 6.434), 7.278 (d, J ) 9, 8 H, 7.034), 7.034 (d, J ) 9,
8 H, 7.278), 6.848 (bs, 2 H, 7.504, 7.500), 6.834 (bs, 2 H, 7.504, 7.500),
2.861 (s, 12 H), 1.312 (s, 36 H). (COSY cross-peaks are not resolved
for the J ) 1.5 multiplets.) 13C NMR (125 MHz, CDCl3; 293 K):
aromatic region, expected, 12 resonances, found, 12 resonances at 150.4,
146.3, 145.7, 137.8, 130.1, 129.3, 128.9, 128.4, 126.4, 124.8, 121.9,
121.8; aliphatic region, 86.1, 52.2, 34.5, 31.3. IR (cm-1): 1563 (Ar),
1086 (C-O-C).
Tetraether 7C. From 3.5:1 mixture of diols 6B,C (0.102 g, 0.079
mmol), 0.110 g of yellow viscous solid was obtained. PTLC (10%
benzene in hexane) of 0.032 g of the crude mixture gave 0.0268 g
(88%) of 7D,C (3.6:1) as a clear viscous solid.
From 1:8 mixture of diols 6B,C (20.0 mg, 0.016 mmol), 15.7 mg
(74%, single spot in TLC, 3% ether in hexane) of 7D,C (1:8) as yellow
viscous solid was obtained. Treatment with ether/MeOH did not
improve the purity of the product.
1H NMR (500 MHz, CDCl3, EM ) -1.30, GB ) 0.46, 1H-1H
COSY cross-peaks in aromatic region; 293 K): 7.466 (d, J ) 1.5, 8
H, 7.010), 7.322 (d, J ) 9, 8 H, 7.131), 7.131 (d, J ) 9, 8 H, 7.322),
7.010 (t, J ) 1.5, 4 H, 7.466), 2.883 (s, 12 H), 1.323 (s, 36 H). 13C
NMR (125 MHz, CDCl3; 293 K): aromatic region, expected, 8
resonances, found, 8 resonances at 150.63, 146.04, 137.9, 129.73,
128.96, 127.2, 124.94, 121.74; aliphatic region, 86.10, 52.15, 34.53,
31.32. IR (cm-1): 1566 (Ar), 1083 (C-O-C).
Diol 6D. The product was softened at 187 °C and melted and became
a yellow liquid at 223-225 °C. FABMS (3-NBA) cluster m/z (% RA
for m/z ) 200-2700): at (M - OCH3)+, 1261.2 (35), 1262.2 (34),
1263.2 (76), 1264.2 (57), 1265.2 (95), 1266.2 (70), 1267.2 (80), 1268.2
(53), 1269.2 (36), 1270.2 (24); at (M - OH)+, 1275.2 (25), 1276.2
(21), 1277.2 (68), 1278.2 (55), 1279.2 (100), 1280.2 (70), 1281.2 (82),
1
1282.2 (50), 1283.2 (35), 1284.2 (18). H NMR (500 MHz, EM )
-1.20, GB ) 0.80, CDCl3; 293 K): 7.497 (t, J ) 2, 2 H), 7.478 (t, J
) 2, 2 H), 7.465 (t, J ) 2, 4 H), 7.332 (d, J ) 9, 2 H), 7.320 (d, J )
9, 4 H), 7.200 (d, J ) 9, 2 H), 7.012 (d, J ) 8, 2 H), 6.974 (d, J ) 8,
4 H), 6.925 (d, J ) 9, 2 H), 6.599 (t, J ) 1.5, 2 H), 6.551 (t, J ) 1.5,
2 H), 2.865 (s, 3 H), 2.775 (s, 3 H), 2.736 (s, 2 H, D2O exch), 1.328
(s, 9 H), 1.326 (s, 18 H), 1.297 (s, 9 H). 13C{1H} DEPT (135°) NMR
(125 MHz, CDCl3; 293 K): aromatic quaternary region, expected, 12
resonances, found, 11 resonances at 151.0 (q), 150.6 (q), 148.0 (q),
147.9 (q), 145.66 (q), 145.61 (q), 142.4 (q), 138.8 (q), 138.2 (q), 122.35
(q), 122.32 (q); aromatic nonquaternary region, expected, 12 resonances,
found 10 resonances at 130.2, 130.0, 129.4, 128.4, 127.8, 127.36,
127.29, 125.1, 125.0, 124.8; aliphatic region, 86.14 (q), 86.11 (q), 81.3
(q), 52.05, 52.03, 34.55 (q), 34.45 (q), 31.3. IR (cm-1): 3570 (O-H),
3463 (O-H), 1567 (Ar), 1082 (C-O-C).
Diol 6E. The product was yellow solid at 160 °C and melted and
became a clear liquid at 197-200 °C. Anal. Calcd for C70H72O4Br4:
C, 64.83; H, 5.60. Found: 65.30; H, 5.94. FABMS (3-NBA) cluster
m/z (% RA for m/z ) 280-2400): at (M - OCH3)+, 1261.1 (23),
1262.1 (20), 1263.1 (66), 1264.1 (52), 1265.1 (100), 1266.1 (66), 1267.1
(76), 1268.1 (45), 1269.1 (38), 1270.1 (22); at (M - OH)+, 1275.1
(19), 1276.1 (17), 1277.1 (54), 1278.1 (38), 1279.1 (80), 1280.1 (57),
1281.1 (66), 1282.1 (41), 1283.1 (29), 1284.1 (15). 1H NMR (500 MHz,
1
CDCl3, H-1H fast COSY cross-peaks in aromatic region): 293 K,
7.498 (bs, 4 H, 7.360, 6.730), 7.360 (bs, 4 H, 7.498, 6.730), 7.327 (d,
J ) 8, 4 H, 6.960), 7.286 (d, J ) 8, 4 H, 7.052), 7.052 (d, J ) 8, 4 H,
7.286), 6.960 (d, J ) 8, 4 H, 7.327), 6.730 (bs, 4 H, 7.498, 7.360),
2.953 (s, 6 H), 2.669 (s, 2 H, D2O exch), 1.341 (s, 18 H), 1.324 (s, 18
H). 13C{1H} DEPT (135°) NMR (125 MHz, CDCl3; 293 K): aromatic
quaternary region, expected, 7 resonances, found, 7 resonances at 150.9
(q), 150.3 (q), 148.1 (q), 145.0 (q), 142.1 (q), 138.7 (q), 122.1 (q);
aromatic nonquaternary region, expected, 7 resonances, found 6
Tetraether 7D. From diol 6D (0.348 g, 0.268 mmol), 0.299 g (84%)
of 7D as white powder was obtained. The product was softened at 152
9
J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004 6983

A R T I C L E S
Rajca et al.
°C, melted at 168-170 °C, and became a clear liquid at 178 °C. From
other reactions, 0.573 g (63%) and 0.773 g (83%) of 7D as white
powder after treatment with ether/MeOH were obtained from 0.909 g
(0.698 mmol) and 0.914 g (0.705 mmol) of diol 6D, respectively. The
product was softened at 189 °C and melted and became clear liquid at
197-200 °C. Anal. Calcd for C70H72O4Br4: C, 65.27; H, 5.78. Found:
65.16; H, 5.25. FABMS (3-NBA) cluster m/z (% RA for m/z ) 200-
2600): at (M - OCH3)+, 1289.2 (22), 1290.2 (18), 1291.2 (67), 1292.2
(52), 1293.3 (100), 1294.2 (71), 1295.2 (77), 1296.2 (50), 1297.2 (29),
quenching product 8-H (40.7 mg, 23%); homocoupling product 10 (24.7
mg, 7%); tricoupling product 12 (1.8 mg, 1%). Another isolation of
10, without treatment with ether/MeOH, gave 16.4 mg (9%) of clear
oil.
24-Ether 1-(OMe)24: softening at 186 °C and melting at 200-201
°C (clear liquid). Anal. Calcd for C504H592O24: C, 86.06; H, 8.48.
Found: 86.60; H, 8.22. FABMS (3-NBA) cluster m/z (% RA for m/z
) 3200-7400): at (M - OCH3)+, 6998.5 (35), 6999.5 (52), 7000.5
(74), 7001.5 (90), 7002.5 (100), 7003.5 (75), 7004.5 (71), 7005.5 (49),
7006.5 (31); calcd for C503H589O23 at (M - OCH3)+, 6998.5 (11), 6999.5
(32), 7000.5 (61), 7001.5 (88), 7002.5 (100), 7003.5 (96), 7004.5 (78),
1
1298.3 (15). H NMR (500 MHz, EM ) -1.20, GB ) 0.85, CDCl3,
1H-1H FastCOSY cross-peaks in aromatic region; 293 K): 7.522 (t, J
) 2, 2H, 7.409, 7.037), 7.502 (t, J ) 2, 2 H, 7.409, 6.965), 7.409 (t,
J ) 2, 2H, 7.522, 7.037), 7.409 (t, J ) 2, 2H, 7.502, 6.965), 7.312 (d,
J ) 9, 4 H, 7.145), 7.312 (d, J ) 9, 2 H, 7.010), 7.268 (d, J ) 9, 2 H,
7.060), 7.145 (d, J ) 8, 4 H, 7.312), 7.060 (d, J ) 8, 2 H, 7.268),
7.037 (t, J ) 2, 2H, 7.522, 7.409), 7.010 (d, J ) 9, 2 H, 7.312), 6.965
(t, J ) 2, 2H, 7.502, 7.409), 2.935 (s, 3 H), 2.919 (s, 6 H), 2.895 (s,
3 H), 1.334 (s, 9 H), 1.329 (s, 18 H), 1.314 (s, 9 H). 13C{1H} DEPT
(135°) NMR (125 MHz, CDCl3): 293 K, aromatic quaternary region,
expected, 12 resonances, found, 12 resonances at 150.53 (q), 150.49
(q), 150.40 (q), 146.3 (q), 146.1 (q), 145.9 (q), 145.8 (q), 138.23 (q),
138.17 (q), 137.7 (q), 121.84 (q), 121.67 (q); aromatic nonquaternary
region, expected, 12 resonances, found 12 resonances at 130.3, 129.84,
129.80, 129.5, 128.88, 128.76, 128.35, 127.6, 127.4, 125.04, 124.93
(overlapped with 7C in mixtures), 124.8; aliphatic region, 86.09 (q),
86.04 (q), 52.4, 52.21, 52.12, 34.53 (q) (overlapped with 7C in
mixtures), 34.51 (q), 31.35. IR (cm-1): 1564 (Ar), 1081 (C-O-C).
1
7005.5 (56), 7006.5 (35). H NMR (500 MHz) spectra for 1-(OMe)24
were obtained in C6D6 (293-348 K), toluene-d8 (293-383 K), and
tetrachloroethylene (293-383 K). The best resolved spectra were
obtained in benzene-d6, and only those are listed below. 1H NMR (500
MHz, C6D6): 293 K, 8.10-7.00 (br m, 196 H), 3.264 (s, 12 H), 2.947
(s, 48 H), 2.869 (s, 12 H), 1.211 (s, 144 H), 1.205 (s, 144 H), 1.062 (s,
36 H); 328 K, 8.10-7.00 (br m, 196 H), 3.265 (s, 12 H), 2.949 (s, 48
1
H), 2.885 (s, 12 H), 1.214 (s, 288 H), 1.086 (s, 36 H). H NMR (500
1
MHz, EM ) -1.20, GB ) 0.90, benzene-d6, H-1H COSY cross-
peaks in aromatic region; 348 K): 7.97 (br, 4 H), 7.90 (br, 8 H), 7.817
(d, J ) 2, 16 H, 7.673), 7.673 (t, J ) 2, 8 H, 7.817), 7.636 (d, J ) 9,
8 H, 7.260), 7.455 (d, J ) 9, 32 H, 7.227), 7.448 (d, J ) 8, 32 H,
7.219), 7.423 (d, J ) 8, 8 H, 7.352), 7.352 (d, J ) 8, 8 H, 7.423),
7.260 (d, J ) 9, 8 H, 7.636), 7.227 (d, J ) 9, 32 H, 7.455), 7.219 (d,
J ) 9, 32 H, 7.448), 3.262 (s, 12 H), 2.952 (s, 48 H), 2.896 (s, 12 H),
1.220 (s, 288 H), 1.106 (s, 36 H). 13C{1H} DEPT (135°) NMR (125
1
MHz, EM ) -0.90 Hz, GB ) 1.90 Hz, C6D6, H-13C HMQC-GS
Tetraether 7E. From diol 6E (0.291 g, 0.225 mmol), 0.112 g (38%)
of 7E as white crystals was obtained. Mp: 295-298 °C. Other reactions
from diol 6E (0.345 g, 0.266 mmol; 0.102 g, 0.079 mmol) gave 0.254
g (61%) and 0.058 g (57%), respectively, of 7E as white solids. The
product was softened at 304 °C and melted and became brown liquid
at 312-314 °C. Anal. Calcd for C72H76O4Br4: C, 65.27; H, 5.78.
Found: C, 65.29; H, 5.26. FABMS (3-NBA) cluster m/z (% RA for
m/z ) 240-2500): at (M - OCH3)+, 1289.2 (20), 1290.2 (17), 1291.2
(65), 1292.2 (50), 1293.2 (100), 1294.2 (70), 1295.2 (78), 1296.2 (46),
cross-peaks in aromatic nonquaternary region; 348 K): aromatic
quaternary region, expected, 10 resonances, found, 9 resonances at 150.3
(q), 150.0 (q), 145.02 (q), 144.98 (q), 143.8 (q), 143.2 (q), 142.8 (q),
140.6 (q), 140.5 (q); aromatic nonquaternary region, expected, 10
resonances, found 9 resonances at 131.2 (7.352), 130.0 (7.673), 129.6
(7.455, 7.448), 128.8 (7.636), 127.9 (7.817), 127.5 (br, 7.90), 127.0
(7.423), 125.7 (7.260), 125.1 (7.227, 7.219); aliphatic region, 88.5 (q),
88.1 (q), 87.9 (q), 52.90, 52.87, 52.6, 34.9 (q), 31.99, 31.96 (EM )
-0.9, GB ) 1.0). Note: the 13C resonance at 125.1 ppm corresponds
to two resonances at 125.15 and 125.13 (EM ) -0.77 and GB ) 0.40)
at 293 K. IR (cm-1): 1595 (ArH), 1082 (C-O-C). GPC/MALS: Table
4s, Supporting Information.
1
1297.2 (31), 1298.2 (14). H NMR (300 MHz, EM ) -1.30, GB )
0.85, CDCl3; 293 K): 7.456 (d, J ) 2, 8 H), 7.322 (AB, J ) 9, 8 H),
7.147 (t, J ) 2, 4 H), 7.119 (AB, J ) 9, 8 H), 2.932 (s, 12 H), 1.338
1
1
(s, 36 H). H NMR (500 MHz, C6D6, H-1H COSY cross-peaks in
aromatic region; 293 K): 7.699 (d, J ) 1.5, 8 H, 7.553), 7.553 (bs, 4
H, 7.699), 7.301 (d, J ) 9, 8 H, 7.226), 7.226 (d, J ) 9, 8 H, 7.301),
2.783 (s, 12 H), 1.149 (s, 36 H). 13C{1H} DEPT (135°) NMR (125
MHz, C6D6; 293 K): aromatic quaternary region, expected, 4 reso-
nances, found, 4 resonances at 150.8 (q), 146.7 (q), 140.2 (q), 122.5
(q); aromatic nonquaternary region, expected, 4 resonances, found 4
resonances at 131.6, 129.3, 128.4, 126.2; aliphatic region, 86.9 (q),
52.3, 34.8 (q), 31.7. IR (cm-1): 1565 (Ar), 1083 (C-O-C).
Octaether 2-(OMe)8. A procedure analogous to that for 1-(OMe)24
was used. t-BuLi (0.189 mL of 1.855 M solution in pentane,66 0.351
mmol) was added to bromoether 9 (76.7 mg, 0.165 mmol) in THF
(1.5 mL) in a heavy-wall Schlenk vessel at -78 °C. After 2 h at -78
°C, the reaction mixture was warmed to -20 °C for 10 min and then
recooled to -78 °C. Following addition of ZnCl2 (0.17 mL of 1.03 M
solution in ether, 0.175 mmol), the reaction mixture was allowed to
attain ambient temperature. In a Vacuum Atmospheres glovebox,
Pd(PPh3)4 (6.0 mg, 5.2 µmol) and tetrabromocalix[4]arene tetraether
7E (36.5 mg, 27.5 µmol) were added to the reaction mixture.
Subsequently, the reaction mixture was heated at 100 °C for 3 days.
Following the usual workup, column chromatography (preheated silica
at 200 °C overnight, 3-5% ether in hexane) and treatment with ether/
MeOH, 8.7 mg (12%) of 2-(OMe)8 as a white powder was obtained.
(The purity of fractions corresponding to 2-(OMe)8 was checked with
1H NMR before combining and filtering through the cotton plug.)
Similarly, 6.6 mg (10%) of homocoupling side product 11 was obtained
as a white powder.
24-Ether 1-(OMe)24. t-BuLi (0.136 mL of 1.855 M solution in
pentane,66 0.253 mmol) was added to bromopentaether 8 (0.186 g,
0.117 mmol) in THF (1.3 mL) in a heavy-wall Schlenk vessel at -78
°C. After 2 h at -78 °C, the reaction mixture was allowed to attain
-20 °C for 10 min and then recooled to -78 °C. Following the addition
of ZnCl2 (0.13 mL of 1.03 M solution in ether, 0.134 mmol), the
reaction mixture was allowed to attain ambient temperature. In a
Vacuum Atmospheres glovebox, Pd(PPh3)4 (5.0 mg, 4.3 µmol) and
tetrabromocalix[4]arene tetraether 7E (25.9 mg, 19.5 µmol) were added
to the reaction mixture. Subsequently, the reaction mixture was stirred
at 100 °C for 3 days. Following the usual aqueous workup, two
consecutive purifications by column chromatography (4-8% ether in
hexane) and treatments with MeOH/ether gave 24-ether 1-(OMe)24 as
a white powder (54.7 mg, 40%). Three additional reactions, each starting
from 0.2-0.400 g of bromopentaether 8, gave 24-ether in 28, 13, and
16% yields.
A second reaction yielded 23.6 mg (16%) of 2-(OMe)8 as a white
powder; it was performed on a double scale using t-BuLi (0.45 mL of
1.5 M solution in pentane, 0.675 mmol), bromoether 9 (150 mg, 0.322
mmol) in THF (3.0 mL), and tetraether 7E (75.0 mg, 56.7 µmol).
A third reaction yielded 21.7 mg (16%) of 2-(OMe)8 as a white
powder; it was carried out using t-BuLi (0.45 mL of 1.5 M solution in
pentane, 0.675 mmol), bromoether 9 (150 mg, 0.322 mmol) in THF
(3.0 mL), and tetraether 7E (70.1 mg, 52.9 µmol).
The following side products were isolated by column chromatog-
raphy and treated with ether/MeOH to give white powders: dendrimer
9
6984 J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004

Organic Spin Clusters
A R T I C L E S
both resonances for THF-d7 remain relatively sharp. 13C NMR (125
MHz, pulse delay ) 0.1 s, acquisition time ) 0.5 s, 7 × 104 scans,
THF-d8; 293 K): aromatic region, expected, 24 resonances, found, 10
resonances at 152.4, 149.2, 145.6, 144.3, 132.3, 125.6, 120.9, 120.3,
119.3, 118.2; aliphatic region, 85.8 (Ar3C), 34.2, 32.6, 32.4 (30.7, imp).
Polyradicals 1 and 2. Samples for Magnetic Measurements. 24-
Ether 1-(OMe)24 (0.50-1.60 mg, 70-230 nmol) was placed in a glass
reaction vessel, equipped with coarse glass frit, two high-vacuum PTFE
stopcocks, and a 5-mm o.d. quartz tube with thin bottom 6 cm from
the end of the tube (Figure 13). The vessel containing polyether was
heated overnight under vacuum; i.e., part of the vessel containing
polyether was immersed in an oil bath at 60 °C and the rest of the
vessel was heated at 200 °C using heating tape. Subsequently, the vessel
was transferred to a glovebox and a small drop of Na/K alloy was
added. Following attachment of the vessel to vacuum line, Na/K was
allowed to come in contact with polyether, and THF-d8 (0.06-0.08
mL, 99.95% D) was immediately vacuum-transferred from sodium/
benzophenone. After 3-5 days of stirring at 10 °C, the reaction mixture
was filtered under temperature gradient into the quartz tube. (An
alternative procedure was based upon preparation of carbopolyanion
in a glovebox equipped with oven/antechamber.) Iodine (99.999%,
ultradry) was vacuum-transferred in small portions to the reaction
mixture at -103 to -106 °C, until the final yellow-brown color of 1
appeared. The tube was flame sealed (total length of about 20 cm) and
stored in liquid nitrogen prior to insertion to SQUID magnetometer.
Analogous procedures were used for octaradical 2 and tetraradical 3.
The dilute sample of 2 was prepared using a previously reported method,
in which the measured amount of polyradical is not known.21
Samples for SANS Measurements. The procedure was based upon
10-30 mg of 24-ether 1-(OMe)24; quartz cylindrical cells with 2-mm
and 5-mm optical paths were used (Figure 13).
Figure 13. Vessel for preparation of polyanions and polyradicals for
SQUID magnetometry (tube A), ESR spectroscopy (tube B), SANS
(cylindrical cell C), and NMR spectroscopy (sample tube not shown): (a)
sample compartment with Teflon-coated magnetic stirbar; (b) glass frit
(course); (c) Pyrex-to-quartz seal; (d) thin bottom (∼6 cm from the end of
the tube). Solv-seal joints and Kontes (or Chemglass) vacuum stopcocks
are used.
Approximately twice the volume of THF-d8, compared to the samples
for magnetic measurements, was used for generation of carbopolyanion.
For polyradical generation, iodine and THF-d8 were vacuum transferred
in small portions until the desired color and volume in the cell were
attained. Subsequently, the cells were flame sealed; the quartz seal,
above the cylindrical part of the cell, had to be <2 cm long to provide
an adequate fit to the SANS sample holder.
Octaether 2-(OMe)8: softening at 201 °C and melting at 226-229
°C. Anal. Calcd for C184H208O8: C, 86.75; H, 8.23. Found: 85.39; H,
7.99. FABMS (3-NBA) cluster m/z (% RA for m/z ) 700-4300): at
(M - OCH3)+, 2514.6 (65), 2515.6 (100), 2516.6 (95), 2517.6 (65),
2518.5 (40); calcd for C183H205O7, 2514.6 (45), 2515.6 (95), 2516.6
Quenching Studies. 1-H24. A cylindrical SANS cell, containing 124-
(prepared from 29.56 mg, 4.20 µmol, of 1-(OMe)24) in THF-d8, was
immersed under argon-bubbled MeOH (100 mL) at room temperature.
The cell was cracked, and the brown mixture was leaking out to be in
contact with MeOH to form a white precipitate. Following the usual
aqueous workup with hexane, PTLC (25% chloroform in hexane), and
treatment with ether/MeOH, 10.9 mg (41%) of the less polar (F1) and
2.6 mg (10%) of the more polar (F2) fractions of 1-H24 were obtained
as white powders. Although the Rf values for F1 and F2 are significantly
1
1
(100), 2517.6 (70), 2518.6 (35). H NMR (500 MHz, C6D6, H-1H
COSY cross-peaks in aromatic region; 293 K): 8.06 (br, 4 H, 7.95),
7.95 (br, 8 H, 8.06), 7.627 (d, J ) 8, 8 H, 7.218), 7.533 (d, J ) 8, 16
H, 7.265), 7.472 (d, J ) 8, 8 H, 7.439), 7.439 (d, J ) 8, 8 H, 7.472),
7.265 (d, J ) 8, 16 H, 7.533), 7.218 (d, J ) 8, 8 H, 7.627), 3.132 (s,
12 H), 3.035 (s, 12 H), 1.211 (s, 72 H), 1.060 (s, 36 H). 13C{1H} DEPT
(135°) NMR (125 MHz, C6D6, 1H-13C HSQC-GS cross-peaks in
aromatic nonquaternary region; 293 K): aromatic quaternary region,
expected, 8 resonances, found, 7 resonances at 150.1 (q), 150.0 (q),
145.3 (q), 144.3 (q), 142.3 (q), 140.54 (q), 140.47 (q); aromatic
nonquaternary region, expected, 8 resonances, found 8 resonances at
130.4 (8.06, br), 130.1 (7.472), 129.5 (7.533), 128.8 (7.627), 127.5
(7.95), 127.3 (7.439), 125.8 (7.218), 125.3 (7.265); aliphatic region,
88.0 (q), 52.6, 52.4, 34.78 (q), 34.72 (q), 31.8. IR (cm-1): 1595 (ArH),
1081 (C-O-C). GPC/MALS: Table 4s, Supporting Information.
Carbopolyanion 124- for NMR or SANS Studies. Polyether
1-(OMe)24 (11.40 mg, 1.62 µmol) was placed in a glass reaction vessel,
equipped with a 5-mm NMR sample tube or a quartz cylindrical cell
(Figure 13). Carbopolyanion was generated by following the procedure
for polyradical 1, which is described in the following paragraph. After
the solution of carbopolyanion was filtered into the NMR tube or SANS
cell, the sample vessel was flame sealed and stored in liquid nitrogen
1
different on silica, their H NMR spectra are almost identical.
F1: softening at 194 °C and melting at 204-206 °C (clear liquid).
1H NMR (500 MHz, CDCl3; 293 K): 7.25-6.65 (m, 196 H), 5.45-
5.35 (m, 4 H), 5.219, 5.178 (s, s, 19 H), 1.35-1.05 (m, 325 H). 13C
NMR (125 MHz, CDCl3; 293 K): aromatic region, expected 20
resonances, found 18 resonances at 148.5, 144.5 (br), 143.7 (br), 142.5,
141.34, 141.26, 140.5 (br), 138.4, 129.5, 128.86, 128.83, 128.6, 128.4,
126.6, 126.2 (br), 125.5, 125.3-124.8 (br), 124.9; aliphatic region, 56.7
(br), 56.4 (br), 55.9, 34.3, 31.1. IR (cm-1): 1595 (ArH). GPC/MALS:
Table 4s, Supporting Information. SANS (THF-d8): see main text.
F2: softening at 190 °C and melting at 204-206 °C (yellow liquid).
1H NMR (500 MHz, CDCl3; 293 K): 7.23-6.60 (m, 196 H), 5.45-
5.35 (m, 4 H), 5.217, 5.178 (s, s, 18 H), 1.37-1.00 (m, 317 H). IR
(cm-1): 1595 (ArH).
2-H8. A small portion of polyradical 2 in THF (prepared from 9.4
mg of octaether 1-(OMe)8) was transferred to a quartz tube for magnetic
measurements, and the remaining polyradical was stirred with Na/K at
-95 to -78 °C for several hours and then quenched with MeOH. The
usual aqueous workup, followed by PTLC (2.5% ether in hexane), gave
1
for subsequent studies. H NMR (500 MHz, THF-d8): 293 K, 7.40-
6.10 (m, 196 H), 1.164 (s, 320 H); 193 K, 7.8-5.3 (bm), 1.4-0.9 (bm),
9
J. AM. CHEM. SOC. VOL. 126, NO. 22, 2004 6985

A R T I C L E S
Rajca et al.
2-H8 as glassy solid (6.1 mg, 70%) with softening at 190 °C and melting
at 202-205 °C (yellow liquid). FABMS (3-NBA) cluster m/z (% RA
for m/z ) 2288-2333, S/N ≈ 2.5/1): 2305.5 (65), 2306.5 (85), 2307.5
(95), 2308.5 (100), 2309.5 (85), 2310.5 (65); calcd for C176H193 (M +
H)+, 2306.5 (50), 2307.5 (100), 2308.5 (98), 2309.5 (65), 2310.5 (30).
1H NMR (500 MHz, CDCl3; 293 K): 7.5-6.7 (m, 60 H), 5.8-4.4 (8
H), 1.35-1.1 (m, 107 H). IR (cm-1): 1594 (ArH).
at the four 4-biphenyl-substituted sites gave the following values of xi
and Si: xi ) p4, 4p3(1 - p), 6p2(1 - p)2, 4p(1 - p)3, (1 - p)4, and
8[p3(1 - p) + 3p2(1 - p)2 + 3p(1 - p)3 + (1 - p)4] and Si ) 2 +
10p, 1.5 + 8p, 1 + 6p, 0.5 + 4p, 2p, and p, where i ) 1, 2, ... 6.
Because in eq 2 the Brillouin functions were not explicitly multiplied
by values of spin, Si, fractions xi included Si. Therefore, spin-average
spin Ss should be defined as shown in eq 4.51
SQUID Magnetometry. A Quantum Design (San Diego, CA)
MPMS5S (with continuous temperature control) was used. The sample
tubes were inserted to the magnetometer at low temperature under
helium atmosphere and then evacuated and purged with helium, as
described elsewhere. Following the measurements, sample tubes were
stored at ambient temperature for several weeks, until they were
diamagnetic in the 1.8-150 K range. Such samples were carefully
reinserted to the magnetometer, with the sample chamber at 200 or
290 K. Then the temperature was slowly lowered to 10 K to condense
the solvent and to freeze the sample. The identical sequence of
measurements, as for the original sample, was carried out. The resultant
data were used for the point-by-point correction for diamagnetism.
Numerical Curve Fitting for Magnetic Data. The SigmaPlot for
Windows software package was used for numerical curve fitting. The
reliability of a fit is measured by the parameter dependence, which is
defined as follows: dependence ) 1 - ((Variance of the parameter,
other parameters constant)/(Variance of the parameter, other param-
eters changing)). Values close to 1 indicate overparametrized fit.
Up to four variable parameters, J/k (spin coupling constant in
Kelvins), N (number of moles of polyradical), Θ (mean field parameter
for small intermolecular magnetic interactions), and Mdia (correction
for diamagnetism), are used for fitting MT vs T data over wide range
of T. In 1, Θ does not affect the fits and it is omitted (Θ ) 0), as the
intermolecular magnetic interactions are essentially negligible. With
the exception of one sample of 1, in which Mdia was more than 1% of
the total diamagnetism after point-by-point correction, Mdia ) 0 was
set. Thus, no more than three variable parameters were used. Equations
for magnetization, M(T,H), are obtained using the standard statistical
mechanical procedures for energy eigenvalues, derived from Heisenberg
Hamiltonian.26,46-48
Ss ) ΣiSixi/Σixi
(4)
For polyradical 1, eq 4 could be simplified: Ss ) 12p/(9 - 8p).
The second percolation model, used in this work, was based on
eq 5:
M ) 11180NΣiAiB(Si)
(5)
Coefficients Ai and spin values Si are optimized through two variable
parameters, q and p. Parameter p was defined as in the first percolation
model. Parameter q was the probability that a biphenylene moiety
mediates ferromagnetic (vs antiferromagnetic) coupling. This model
was quantitative, using number of moles (N) of polyradical (or
polyether) as an input; Msat was not a variable parameter. Configurations
with 0-4 defects at the four 4-biphenyl-substituted sites and 0-4
antiferromagnetic couplings across four biphenylene coupling units were
enumerated, leading to 1280 spin systems; however, only 10 spin values
(Si, i ) 0-9) were unique. Elucidation of all values of Si and coefficients
Ai for 24-radical 1 followed general methods as reported elsewhere.28a
Acknowledgment. This research was supported by the
National Science Foundation (Chemistry Division) and the
National Center for Neutron Research (beam time on NG3,
Grant Nos. 1781 and 2471). We thank Drs. Richard Schoemaker
and Ronald Cerny for their help with NMR spectral determina-
tions and mass spectral analyses. We thank Drs. Maren Pink
and Victor G. Young, Jr., of the X-ray Crystallographic
Laboratory at the University of Minnesota for the structure
determination of compound 7E. S.R. thanks the European
Molecular Biology Laboratory (Hamburg, Germany) for the
ATSAS program package for numerical fitting of SANS data.
M vs H data at low temperatures (T ) 1.8, 3, 5, 10 K) were analyzed
with Brillouin functions as described in the text.
For 1, an alternative procedure for analysis of the M vs H data
involved fitting of the M vs H/T data to linear combinations of Brillouin
functions (Β(Si)) weighed with fractions (xi) of spin systems with spin
Si. Two different percolation models were used to obtain values of xi
and Si.
Supporting Information Available: An experimental section
(materials and special procedures, NMR spectroscopy and other
analyses, characterization data for 8-H, 8-D, 10, 11, and 12-
(OMe)19, SANS instrumental setup and sample handling,
numerical curve fitting for the SANS data), Tables 1s-4s
(summary of NMR data for 6 and 7, summary of GPC/MALS
data), Figures 1s-6s (FAB MS for 2-(OMe)8 and 12-(OMe)19,
summary plot of GPC/MALS data, selected NMR spectra for
2-(OMe)8, SANS plots for polyradical 1 and polyanion 124-),
and an X-ray crystallographic file for 7E in CIF format. This
material is available free of charge via the Internet at
http://pubs.acs.org.
The first percolation model, which was employed in the preliminary
communication,22 used eq 3.
M/Msat ) ΣiΒ(Si)xi/Σixi
(3)
The model assumed ferromagnetic coupling between all nearest
neighbor arylmethyls. Two variable parameters, p and Msat, were used.
Parameter p was the probability that triarylmethyl site had an intact
radical. Because the value of Msat was a variable parameter, this model
was not quantitative. Enumeration of configurations with 0-4 defects
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