Polyphenyl macrocyclic oligophenylenes

Article abstract of DOI:10.1021/ja0541985

The Diels-Alder reaction of tribenzohexadehydro[12]annulene (12) and 3,4-diphenyl-2,5-dimethylcyclopentadienone (13) at 300 °C gave the triple adduct 2,3,10,11,18,19-hexaphenyl-1,4,9,12,-17,20-hexamethylhexa-o-phenylene (6b) in 13% yield. NMR and X-ray an

Full text of DOI:10.1021/ja0541985

Published on Web 09/07/2005
Polyphenyl Macrocyclic Oligophenylenes
Qiuling Song, Christopher W. Lebeis, Xianfeng Shen, Douglas M. Ho, and
Robert A. Pascal, Jr.*
Contribution from the Department of Chemistry, Princeton UniVersity,
Princeton, New Jersey 08544
Received June 24, 2005; E-mail: snake@chemvax.princeton.edu
Abstract: The Diels-Alder reaction of tribenzohexadehydro[12]annulene (12) and 3,4-diphenyl-2,5-
dimethylcyclopentadienone (13) at 300 °C gave the triple adduct 2,3,10,11,18,19-hexaphenyl-1,4,9,12,-
17,20-hexamethylhexa-o-phenylene (6b) in 13% yield. NMR and X-ray analysis indicated that 6b adopts
a screw conformation (C2) rather than a crown conformation (C3), and computational studies seem to rule
out any interconversion of the two. Palladium-catalyzed coupling of 1,2-bis(4-bromophenyl)-3,4,5,6-
tetraphenylbenzene (17) and the corresponding bis(boronic acid) 18 gave a mixture of linear and cyclic
oligomers of hexaphenylbenzene containing two to six hexaphenylbenzene subunits. A macrocyclic tetramer
was isolated from this mixture in 5% yield, and X-ray analysis showed it to be the “supertetraphenylene”
7 (C168H112) that contains a large central cavity and packs to form highly solvated, porous crystals. The
difficulties encountered in the purification of 7 led to the development of alternative, more highly selective
syntheses that give the pure macrocycle more easily but in essentially the same overall yield.
Chart 1
Introduction
“Polyphenylene nanostructures” are of great current interest,
but the term embraces an enormous variety of molecules
differing greatly in their structures, properties, and representation
in the literature. Judging from recent reviews,1,2 large linear or
dendrimeric polyphenylenes are the most common forms,
followed by large “graphenes” (planar, highly condensed,
polycyclic aromatic hydrocarbons) that are themselves prepared
by dehydrogenation of dendrimeric polyphenylenes. Much less
common are cyclic oligophenylenes: medium or large rings
constructed entirely from benzene subunits connected by single
bonds.
We are particularly interested in molecules with the topology
of the cyclic o-phenylenes, tetra-o-phenylene (1, Chart 1), and
hexa-o-phenylene (2).3 These molecules are substructures of the
hypothetical carbon allotrope “cubic graphite”,4 and their conical
cavities suggest that they might be used as hosts in molecular
association or as building blocks for porous solids. Indeed,
compound 1 forms a variety of crystalline solvates,5 and Mu¨ller
et al. have prepared the octaphenyl derivative 4 that also
encapsulates solvent in the crystal.6 However, larger cavities,
able to accommodate more complex or numerous guests, would
be more interesting, and in this work we explore the chemistry
of larger, macrocyclic oligophenylenes. We report the synthesis
and structure of a highly substituted derivative of hexaphenylene
(6), computational studies of the conformational preferences and
interconversion of the hexaphenylenes, and several syntheses
and the structure of “supertetraphenylene” 7,7 in which each
benzene ring of 1 is replaced by a hexaphenylbenzene.
(1) Berresheim, A. J.; Mu¨ller, M.; Mu¨llen, K. Chem. ReV. 1999, 99, 1747-
1785.
(2) Watson, M. D.; Fechtenko¨tter, A.; Mu¨llen, K. Chem. ReV. 2001, 101, 1267-
1300.
(3) Inasmuch as this paper deals only with the ortho isomers, henceforth, tetra-
o-phenylene and hexa-o-phenylene will be named simply “tetraphenylene”
and “hexaphenylene”.
(4) Gibson, J.; Holohan, M.; Riley, H. L. J. Chem. Soc. 1946, 456-461.
(5) (a) Huang, N. Z.; Mak, T. C. W. J. Chem. Soc., Chem. Commun. 1982,
543-544. (b) Wong, H. N. C.; Man, Y.-M.; Mak, T. C. W. Tetrahedron
Lett. 1987, 28, 6359-6362.
(6) Mu¨ller, M.; Iyer, V. S.; Ku¨bel, C.; Enkelmann, V.; Mu¨llen, K. Angew.
Chem., Int. Ed. Engl. 1997, 36, 1607-1610.
(7) One synthesis and the structure of 7 has been reported in a preliminary
communication: Shen, X.; Ho, D. M.; Pascal, R. A., Jr. Org. Lett. 2003,
5, 369-371.
9
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J. AM. CHEM. SOC. 2005, 127, 13732-13737
10.1021/ja0541985 CCC: $30.25 © 2005 American Chemical Society

Polyphenyl Macrocyclic Oligophenylenes
A R T I C L E S
Table 1. Computational Data for Macrocyclic Oligophenylenes
compda
symm
E (MMFF) (kcal/mol)
E (AM1) (kcal/mol)
E (HF/3-21G) (au)b
E (B3LYP/6-31G(d)) (au)b
1
4
7
D2d
C2
D2
C2 (∼D2)
D3d
D2
C2
114.65
111.64
350.11
357.82
757.93 (0.0)c
758.52 (0.6)
810.78 (3.0)c
807.75 (0.0)
2
3
16
181.35 (0.0)
203.45 (22.1)
176.67 (0.0)
195.67 (19.0)
267.62 (91.0)d
-1369.571478 (0.0)c
-1369.552311 (12.0)
-1369.397073 (109.4)e
-1386.293677 (0.0)c
-1386.284023 (6.1)
5a
6a
C3
C2
626.60 (40.5)
586.08 (0.0)
611.68 (22.0)
589.68 (0.0)
-4108.579855 (35.0)
-4108.635638 (0.0)
5b
6b
C3
C2
409.02 (0.0)
410.06 (1.0)
344.40 (0.0)
351.12 (6.7)
-2972.008288 (4.3)
-2972.015212 (0.0)
-3008.433571 (5.2)
-3008.441843 (0.0)
8
D3
Ci
C2 (∼D2)
1136.80 (20.7)
1121.05 (15.8)
1116.09 (0.0)
9
a Formulas: C24H16 (1); C36H24 (2,3); C72H48 (4); C108H72 (5a,6a); C78H60 (5b,6b); C168H112 (7); C252H168 (8,9). b 1 au ) 627.503 kcal/mol. c The relative
energy of the isomeric compounds (in kcal/mol) is given in parentheses. d Zero-point energy corrections give a ∆E of 90.1 kcal/mol. e Zero-point energy
corrections give a ∆E of 107.9 kcal/mol.
Results and Discussion
the proposed structures are consistent with the products observed
in subsequent reactions with the less sterically encumbered
cyclopentadienone 13.
Synthesis of Substituted Hexaphenylenes. Mu¨ller et al.
prepared the octaphenyl-tetraphenylene 4 by Diels-Alder
reaction of bisalkyne 10 with tetracyclone 11, and because of
the strain in 10, this reaction required a temperature of only
150 °C.6
A similar reaction of tetracyclone with tribenzohexadehydro-
[12]annulene (12) might produce a dodecaphenylhexaphenylene
(5a or 6a, see Table 1), but higher temperatures would be
required. When compounds 11 and 12 were heated overnight
in refluxing nitrobenzene (210 °C), no addition products were
observed. However, when 11 and 12 were heated in phenyl ether
at 300 °C (sealed tube), a mixture of monoadducts was observed.
The 1H NMR spectrum of this material was extremely complex,
but mass spectrometry (MS) analysis showed prominent ions
at m/z 656 and 658. The former corresponds to the simple
Diels-Alder adduct of 11 and 12, and the latter might arise by
Bergman cyclization of the initial adduct followed by hydrogen
abstraction. Although these products were not well characterized,
When 3,4-diphenyl-2,5-dimethylcyclopentadienone8 (13) and
12 were heated for 5 h at 300 °C in diphenyl ether, monoadducts
(8) Cyclopentadienone 13 is a dimer at room temperature but dissociates to
the monomer upon heating.
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A R T I C L E S
Song et al.
Diels-Alder addition, which may explain the observation of
only this conformation. The 12 substituents on 6b largely project
away from the hexaphenylene core, which differs little from
the X-ray structure of the parent hydrocarbon 3,13 but the
substitution pattern gives rise to an unusual twisted, T-shaped
morphology with no large molecular cavity.
Computational Studies of Cyclic Oligophenylenes. We
were somewhat disappointed to obtain the screw isomer 6b,
for it is the crown isomer 5b that contains a large cavity formed
by the “crowning” phenyls. Might 6b be converted to 5b?
Aromatic hydrocarbons are relatively stable compounds, and
high temperatures could be employed for the isomerization. For
this reason, we used computational methods to examine the
interconversion of hexaphenylene atropisomers, a process that
seems not to have been considered previously by theorists.
Two questions must be asked. First, which of the isomers in
each pair is more stable, and second, what is the barrier to
interconversion? We examined the isomeric pairs 2 and 3 and
5b and 6b at four levels of theory (Table 1).11 At all levels, the
crown isomer 2 is more stable than 3, but the difference drops
from an estimated 22.1 kcal/mol by molecular mechanics
(MMFF) to 6.1 kcal/mol by density functional theory (B3LYP/
6-31G(d)14). In contrast, the results for 5b and 6b are scattered,
but the higher level calculations favor 6b by 4-5 kcal/mol. No
doubt the steric strain from colliding substituents at carbons 1,
4, 9, 12, 17, and 20 (the “equatorial” sites) in 5b nearly balances
the face-to-face repulsion of the benzene rings in 6b, and even
relatively high levels of theory can have difficulties assessing
nonbonded interactions accurately.15 Notably, in the case of the
dodecaphenylhexaphenylenes 5a and 6a, the screw isomer is
strongly favored: the “equatorial” phenyls are simply too
crowded in the crown isomer.
The question of interconversion is more difficult. In Wittig’s
original work,9 compound 2 was heated at 480 °C for 24 h
without detectable conversion to 3, and 3 was heated at 470 °C
for 8 h without conversion to 2! (Some decomposition was
observed in both cases, of course.) We examined the intercon-
version at both the AM116 and HF/3-21G17 levels of theory.
Extensive searches for any intermediates in the interconversion
were unsuccessful. Instead, only a single bona fide transition
state (16) was located at each level of theory,11 and small
perturbations to these structures cause them to evolve smoothly
to either 2 or 3 upon optimization. At the AM1 level, the
transition state is more than 90 kcal/mol above the ground state
2 and 71 kcal/mol above 3; at HF/3-21G, these values increase
to a daunting 109 and 97 kcal/mol! The two calculated transition
states are similar; both have C2 symmetry, and they result from
pulling two adjacent phenylene groups past each other. The HF/
Figure 1. Two views of the molecular structure of compound 6b. Thermal
ellipsoids are drawn at the 50% probability level, and hydrogen atoms have
been omitted for clarity.
and the desired triple Diels-Alder adduct were observed. The
mass spectrum of the monoadduct fraction exhibited a prominent
molecular ion at m/z 534, corresponding to the Bergman
cyclization product 15. An exact mass measurement confirmed
the formula as C42H30. However, this same material had very
1
complex H and 13C NMR spectra; the 19 strong peaks in the
13C NMR spectrum are consistent with the Cs-symmetric
structure 15, but a more complex, less intense subspectrum
indicated that a less symmetric isomer is also present.
The triple adduct from the reaction of 12 and 13 showed a
fast-atom bombardment (FAB) MS molecular ion at m/z 997
(12C7713CH60), as expected for a hexaphenylhexamethylhexa-
phenylene. However, hexaphenylenes may exist in either a
“crown” conformation (2 and 5, Chart 1) or a “screw” confor-
mation (3 and 6), which do not interconvert under normal
conditions.9 The 1H NMR spectrum of the triple adduct showed
three methyl resonances, the number expected for the C2-
symmetric screw isomer 6b (see Table 1), and the X-ray
structure (Figure 1) confirms that assignment. Indeed, the
molecule lies on a special position in the X-ray structure and
possesses crystallographic C2 symmetry.
(11) Molecular mechanics (MMFF) and semiempirical molecular orbital (AM1)
calculations were performed by using SPARTAN 5.0, and ab initio (HF/
3-21G) and density functional (B3LYP/6-31G(d)) calculations were
performed by using GAUSSIAN 98. In both programs, the default
thresholds for wave function and gradient convergence were employed.
Transition states were located by using the QST3 option in GAUSSIAN
98, and they were verified by analytical frequency calculations.
(12) Halgren, T. A. J. Comput. Chem. 1996, 17, 490-519.
For hexaphenylene itself, the crown isomer 2 is thought to
be more stable than the screw isomer 3, but both are formed in
each of the two literature syntheses of hexaphenylene.9,10
However, MMFF calculations11,12 suggest that the immediate
precursor of 6b, a double adduct of 13 to 12, strongly prefers
a C2 conformation that would lead directly to 6b upon the third
(13) Irngartinger, H. Acta Crystallogr., Sect. B 1973, 29, 894-902.
(14) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (b) Lee, C.; Yang,
W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789. (c) Miehlich, B.; Savin,
A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200-206.
(15) (a) Pascal, R. A., Jr. J. Phys. Chem. A 2001, 105, 9040-9048. (b) Pascal,
R. A., Jr.; Hayashi, N.; Ho, D. M. Tetrahedron 2001, 57, 3549-3555.
(16) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am.
Chem. Soc. 1985, 107, 3902-3909.
(9) Wittig, G.; Ru¨mpler, K.-D. Liebigs Ann. Chem. 1971, 751, 1-16.
(10) Simhai, N.; Iverson, C. N.; Edelbach, B. L.; Jones, W. D. Organometallics
2001, 20, 2759-2766.
(17) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; John Wiley & Sons: New York, 1986; pp 63-100.
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Polyphenyl Macrocyclic Oligophenylenes
A R T I C L E S
Scheme 1 a
Figure 2. Calculated (HF/3-21G) transition state (16) for the interconversion
of 2 and 3.
3-21G transition state is illustrated in Figure 2. It is amusing to
note that the π system of the interior macrocycle adopts a
Mo¨bius topology. Given that a barrier of even 71 kcal/mol
corresponds to a half-life of 6 h at 600 °C, the successful
interconversion of hexaphenylene atropisomers is highly un-
likely, and the methyl substituents in 5b and 6b will only make
the barrier higher!
a (a) (i) n-BuLi, ether, (ii) B(OMe)3, (iii) H3O+; (b) (Ph3P)4Pd, toluene,
EtOH, K2CO3; (c) 4-bromobenzaldehyde, (Ph3P)4Pd, toluene, aq. NaHCO3;
(d) NaBH4, EtOH; (e) Ph3PBr2, MeCN; (f) (i) Ph3P, xylenes, (ii) n-BuLi,
THF, (iii) 20; (g) 11, Ph2O, 300 °C; (h) 4-bromostyrene, (Ph3P)4Pd, toluene,
aq. NaHCO3; (i) Grubbs 2, CH2Cl2.
Both 7 and (the presumed) 8 are freely soluble in common
organic solvents, but after many trials only compound 7 gave
satisfactory crystals. Its hepta(nitrobenzene) solvate was obtained
from nitrobenzene-ethylene glycol, an unusual solvent com-
bination (subsequently, nitrobenzene-2-methoxyethanol was also
found to give the same crystal form). The molecular structure
of 7 is illustrated in Figure 3. It is one of only four crystal
structures of very large (>150 carbons) hydrocarbon macro-
cycles.21 In the crystal, 7 lies on a general position and thus
possesses C1 symmetry, but its conformation is nearly C2 or
(less closely) D2 symmetric. Both MMFF and AM1 calculations
find C2 and D2 symmetric structures that differ only slightly in
energy (Table 1), and optimization of the X-ray geometry leads
rapidly to the C2 structure. The molecule contains two large,
V-shaped clefts and a central channel between them. The width
of the channel is approximately 6 Å, and from it the clefts open
to a width of 15 Å. These spaces are occupied by disordered
nitrobenzene molecules in the crystal. In addition, the molecules
of 7 are stacked in a manner that forms large, infinite channels
in the crystal (Figure 4), a common feature in our structures of
large polyphenyl molecules.18,22
Synthesis of “Supertetraphenylene” 7. The substitution of
tetraphenylene and hexaphenylene with many phenyl groups
gives reasonably large molecules, but a more ambitious approach
is to replace each benzene ring in 1 and 2 with a larger, 6-fold
symmetric substructure such as hexaphenylbenzene. The result-
ing molecules, 7 and 8 (or perhaps 9, Chart 1), have very large
internal cavities, and might be expected to stack in crystals to
form highly porous solids.18,19 There are three synthetic ap-
proaches to such molecules, and they are illustrated for 7 in
Scheme 1.
In the most direct approach, dibromohexaphenylbenzene 17
was converted to the bis(boronic acid) 18, and equimolar
quantities of the two were subjected to a Suzuki coupling
reaction.20 Such a procedure might yield both compounds 7 and
8 or even larger macrocycles composed of an even number of
hexaphenylbenzene subunits. In the event, a 35% yield of
nonpolar oligomers of hexaphenylbenzene, as well as a con-
siderable amount of polar material (possibly unreacted boronic
acids), was obtained. The nonpolar material was fractionated
into five components, and FABMS analysis indicated that these
five fractions contained two, three, four, five, and six hexa-
phenylbenzene units, respectively. However, the structures of
these compounds could not be assigned with complete confi-
dence on the basis of their MS, 1H NMR, and 13C NMR spectra,
so we focused our attention on crystallization of the tetramer 7
and hexamer 8.
(21) For the others, see: (a) Mu¨ller, P.; Uson, I.; Hensel, V.; Schlu¨ter, A. D.;
Sheldrick, G. M. HelV. Chim. Acta 2001, 84, 778-785. (b) Nielsen, M.
B.; Schreiber, M.; Baek, Y. G.; Seiler, P.; Lecomte, S.; Boudon, C.;
Tykwinski, R. R.; Gisselbrecht, J.-P.; Gramlich, V.; Skinner, P. J.; Bosshard,
C.; Gu¨nter, P.; Gross, M.; Diederich, F. Chem.-Eur. J. 2001, 7, 3263-
3280. (c) Ipaktschi, J.; Hosseinzadeh, R.; Schlaf, P.; Dreiseidler, E.;
Goddard, R. HelV. Chim. Acta 1998, 81, 1821-1834.
(22) (a) Qiao, X.; Padula, M. A.; Ho, D. M.; Vogelaar, N. J.; Schutt, C. E.;
Pascal, R. A., Jr. J. Am. Chem. Soc. 1996, 118, 741-745. (b) Lu, J.; Zhang,
J.; Shen, X.; Ho, D. M.; Pascal, R. A., Jr. J. Am. Chem. Soc. 2002, 124,
8035-8041. (c) Shen, X.; Ho, D. M.; Pascal, R. A., Jr. J. Am. Chem. Soc.
2004, 126, 5798-5805.
(18) Pascal, R. A., Jr.; Barnett, L.; Qiao, X.; Ho, D. M. J. Org. Chem. 2000,
65, 7711-7717.
(19) For a concise review of ordered porous materials, see: Davis, M. E. Nature
2002, 417, 813-821.
(20) Miyaura, N.; Suzuki, A. Chem. ReV. 1995, 95, 2457-2483.
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A R T I C L E S
Song et al.
Figure 5. Molecular structure of compound 20. Thermal ellipsoids are
drawn at the 50% probability level.
on FABMS analysis, it was never obtained in pure form. We
therefore sought alternative methods for the synthesis of 7 and
8. If the macrocyclic diene 23 could be prepared, a double
Diels-Alder reaction with 11, at a high enough temperature to
promote decarbonylation and dehydrogenation of the adduct,
should yield 7, and similar treatment of an analogous macro-
cyclic triene might give 8.
Three methods were used to prepare 23. In the first, a Suzuki
coupling of bis(boronic acid) 18 with 4-bromostyrene gave the
divinyl compound 19 in 97% yield. This material was subjected
to reactions with Grubbs’ first and second generation olefin
metathesis catalysts23 in attempts to generate macrocyclic olefins
containing two or three hexaphenylbenzene subunits. The first
generation catalyst gave no macrocyclic products, but the second
did form compound 23, though in only 9% yield.
Figure 3. Two views of the molecular structure of compound 7. Thermal
ellipsoids are drawn at the 50% probability level, and hydrogen atoms have
been omitted for clarity.
In the second method, a Suzuki coupling of compound 18
with p-bromobenzaldehyde gave the dialdehyde 20 in 90% yield.
The molecular structure of this highly crystalline compound is
shown in Figure 5. The aldehyde groups are on the top of a
broad hydrocarbon cleft, and they should be unencumbered for
further reaction. A McMurry coupling reaction24 was performed
with 20 as the sole carbonyl substrate, but in the best of several
trials, diene 23 was obtained in only 4% yield, and no
macrocyclic triene was ever detected.
The third method was the longest, but it gave the best, if
still mediocre, results. Dialdehyde 20 was reduced to the diol
21 in 86% yield, and this material was converted to the
dibromide 22 (91%). A double Wittig reagent was generated
from 22, and the reaction of the ylid with dialdehyde 20 gave
macrocycle 23 in 32% yield. In this case, because of the use of
two distinct precursors, it is not possible to generate a macro-
cyclic triene.
Figure 4. Crystal packing of compound 7 viewed along the b axis.
Compound 23 was then heated with tetracyclone (11) in
refluxing diphenyl ether for 24 h to give the desired polyphen-
The purification and crystallization of 7 from the Suzuki
reaction mixture is both tedious and inefficient, and although
the “superhexaphenylene” 8 was almost certainly present based
(23) Trnka, T. M.; Grubbs, R. H. Acc. Chem. Res. 2001, 34, 18-29.
(24) McMurry, J. E. Acc. Chem. Res. 1983, 16, 405-411.
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Polyphenyl Macrocyclic Oligophenylenes
A R T I C L E S
ylene 7 in 19% yield. The product was of good quality, but the
yield was low for such a reaction. The 1H and 13C NMR spectra
of diene 23 are relatively simple, and there seems to be only
one double bond isomer present, presumably the Z isomer. One
might expect such a molecule to react smoothly in a Diels-
Alder reaction, but this was not the case. With two inefficient
late steps, the overall yield of the multistep synthesis of 7 from
bis(boronic acid) 18 is only 4%. However, it is easier to obtain
pure material in this way than by the one-step Suzuki coupling
of 17 and 18, because of the straightforward purifications in
the multistep synthesis. Still, compound 7 is not yet a readily
available material!
molecules. Computational studies indicate that both 6b and 7
adopt their most stable conformations in the crystal and that
the thermal isomerization of “screw” hexaphenylenes to “crown”
hexaphenylenes is essentially precluded.
Acknowledgment. This work was supported by National
Science Foundation Grant CHE-0314873, which is gratefully
acknowledged.
Supporting Information Available: The Experimental Sec-
tion (containing the full procedures for the syntheses of
compounds 6b, 15, 18, 19, 20, 21, 22, 23, and 7 and a summary
1
of crystallographic methods and data), the H NMR spectrum
of compound 6b, 13C NMR spectra for compounds 7, 15, 19,
20, 21, 22, and 23, crystallographic information files (CIF)
containing the X-ray structural information for compounds 6b,
7, and 20, and an ASCII text file containing the coordinates of
the calculated structures of 2, 3, 5b, and 6b at the B3LYP/
6-31G(d) level and 5a, 6a, and the transition state 16 at the
HF/3-21G level. This material is available free of charge via
the Internet at http://pubs.acs.org.
Conclusion
We have described the synthesis and crystal structures of the
two new, large, polyphenyl macrocyclic oligophenylenes 6b and
7. Compound 6b is a polysubstituted derivative of the “screw”
conformer of hexaphenylene, and contains no significant internal
cavities (unlike its “crown” conformation 5b), but compound
7, a “phenylog” of tetraphenylene, contains a large internal
cavity. In the crystal structure of 7, this cavity contains seven
molecules of nitrobenzene, and the molecules of 7 stack in the
crystal to form infinite channels made up of the roughly tubular
JA0541985
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