Hydrophilic-to-hydrophobic volume ratios as structural determinant in small-length scale amphiphilic crystalline systems: Silver salts of phenylacetylene nitriles with pendant oligo(ethylene oxide) chains

Article abstract of DOI:10.1021/ja0006651

A series of 13 silver salts of phenylacetylene nitriles with pendant oligo(ethylene oxide) side chains have been crystallized, and their structures have been determined by single-crystal X-ray methods. All the organic molecules are amphiphilic in that they contain either a hydrophobic rigid linear or 3-fold planar phenylacetylene backbone to which are attached four to six rather plastic hydrophilic oligo(ethylene oxide) side chains. Six of the crystal structures have one-dimensional coordination networks based on Ag-N and Ag-O bonding, while the remainder are two-dimensional. Considering the hydrophilic and hydrophobic portions of these crystals as separate components of the crystal structure, five of the crystal structures contain parallel columns of hydrophobic moieties within a matrix of hydrophilic groups, four contain layers of hydrophilic and hydrophobic portions stacked one on top of the other, two have perforated lamellar structures and two are bicontinuous. Volume ratios of hydrophilic to hydrophobic portions prove a strong determinant as to which crystal topology is adopted for a given crystal composition. Such volume ratios can be calculated from knowledge of the molecular structure alone. A comparison is made to similar columnar and lamellar structures found in block copolymers and liquid crystalline systems. Finally, a similar breakdown of crystal topology as a function of volume ratios is found for aromatic-oligo(ethylene oxide) molecules in the Cambridge Structural Database.

Full text of DOI:10.1021/ja0006651

8376
J. Am. Chem. Soc. 2000, 122, 8376-8391
Hydrophilic-to-Hydrophobic Volume Ratios as Structural Determinant
in Small-Length Scale Amphiphilic Crystalline Systems: Silver Salts
of Phenylacetylene Nitriles with Pendant Oligo(ethylene Oxide)
Chains
Zhengtao Xu, Y.-H. Kiang, Stephen Lee,* Emil B. Lobkovsky, and Nathan Emmott
Contribution from the Department of Chemistry and Chemical Biology, Baker Laboratory,
Cornell UniVersity, Ithaca, New York 14853-1301
ReceiVed February 23, 2000. ReVised Manuscript ReceiVed May 20, 2000
Abstract: A series of 13 silver salts of phenylacetylene nitriles with pendant oligo(ethylene oxide) side chains
have been crystallized, and their structures have been determined by single-crystal X-ray methods. All the
organic molecules are amphiphilic in that they contain either a hydrophobic rigid linear or 3-fold planar
phenylacetylene backbone to which are attached four to six rather plastic hydrophilic oligo(ethylene oxide)
side chains. Six of the crystal structures have one-dimensional coordination networks based on Ag-N and
Ag-O bonding, while the remainder are two-dimensional. Considering the hydrophilic and hydrophobic portions
of these crystals as separate components of the crystal structure, five of the crystal structures contain parallel
columns of hydrophobic moieties within a matrix of hydrophilic groups, four contain layers of hydrophilic
and hydrophobic portions stacked one on top of the other, two have perforated lamellar structures and two are
bicontinuous. Volume ratios of hydrophilic to hydrophobic portions prove a strong determinant as to which
crystal topology is adopted for a given crystal composition. Such volume ratios can be calculated from knowledge
of the molecular structure alone. A comparison is made to similar columnar and lamellar structures found in
block copolymers and liquid crystalline systems. Finally, a similar breakdown of crystal topology as a function
of volume ratios is found for aromatic-oligo(ethylene oxide) molecules in the Cambridge Structural Database.
Introduction
materials, which include porosity43-62 potentially useful in
separation and catalysis, magnetism,63-67 electronic33,68-70 and
optical properties,71 and even moderately high Tc superconduc-
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* Author to whom correspondence should be addressed.
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10.1021/ja0006651 CCC: $19.00 © 2000 American Chemical Society
Published on Web 08/22/2000

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8377
tivity,72,73 and in part by the promise of accessing the full
panoply of organic molecular synthesis in the optimization of
these aforementioned properties. One of the chief impediments
in this undertaking is that the actual physical properties depend
to a great extent not just on the molecular shape but the
crystalline packing and that it is, in general, difficult to envision
exactly this crystal packing from a knowledge of the shape and
stoichiometry of the molecular building blocks alone.
local packing environment around any given molecule from
which one may at times infer suggestions as to the global crystal
structure. For example, Robson and others80-84 have found that
there is often a strong analogy between the extended networks
adopted by organic extended solids and common inorganic
crystal structure types. The development of further methods in
correlating molecular shape to crystalline topology nevertheless
remains an essential problem in the field.
At the current time the most standard approach to rationalize
crystal structure has been to detail non-isotropic intermolecular
forces.74-79 This often leads to a clear picture of the optimal
By comparison, the situation for large-length scale organic
systems such as block copolymers and liquid crystals is much
firmer.85-88 Over the last several decades a clear picture of
crystalline topologies has emerged. In such systems there are
generally two components (e.g., hydrophilic and hydrophobic
fractions) which separate on a nanometer length scale. The
resultant principal structure types include the spherical, colum-
nar, bicontinuous, perforated lamellar, and lamellar topologies
where the topology is defined by the interface between the two
components. Furthermore, on the basis of the volume ratio of
the two components and the degree of interfacial incompatibility
one can predict the evolution of the adopted crystalline
topologies.
In this contribution we study the usefulness of such large-
length scale interfacial concepts in the rationalization of
coordination bonded extended solids. In particular, we examine
these interfaces as one approaches crystalline cell axes only an
order of magnitude larger than the individual atomic bonds. We
have prepared 13 crystalline compounds based on rigid hydro-
phobic phenylacetylene nitrile cores to which nonrigid hydro-
philic oligo(ethylene oxide) side chains have been covalently
attached. These molecules are then joined together through
coordination bonds to silver ions. We find a direct analogy
between the topology of these crystal structures and those found
in the block copolymer and liquid crystalline literature. Crystal
types adopted are of the columnar, perforated lamellar, lamellar,
and bicontinuous types. The type adopted appears to be optimal
in terms of both the hydrophobic-to-hydrophilic volume ratio
and the local bonding requirements of the individual molecules.
A study of crystal structures found in the Cambridge Structural
Database (CSD) reveals the interface structure types reported
in this paper tracks closely those found in other related non-
coordination bonded organic solids.
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Experimental Section
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8378 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
Scheme 1
the organic molecules is outlined in Scheme 1. Powder X-ray diffraction
data were recorded on an INEL MPD diffractometer (XRG 3000, CPS
120 detector) at 25 mA and 35 kV for Cu KR1; λ ) 1.54056 Å, with
a silver behenate and elemental silicon standard. Lattice constants were
fitted to powder data by a least-squares method. HRMS were collected
on a Micromass 70-4F spectrometer. Electrospray ionization mass
spectra were collected on a Micromass QUATTRO spectrometer. 1H-
and 13C NMR were performed on a Bruker AF-300 spectrometer at 25
°C.
Single-crystal X-ray data were collected on a Bruker SMART
diffractometer equipped with a CCD area detector using Mo KR
radiation. Single-crystal diffraction data were collected at 173 K. All
structure solutions were obtained by direct method and refined using
full-matrix least-squares with Shelxl 97. Tables of bond distances, bond
angles, anisotropic thermal factors, observed and calculated structure
factors, and powder data appear in the Supporting Information. All
crystals were grown without any precautions taken to exclude water
or air. Hydrophobic and hydrophilic cell volume and molecular closest
contacts were calculated using the Cerius2 suite of programs from MSI.89
4-Bromo-2,6-dimethyl-benzonitrile (2). A suspension of 4-bromo-
2,6-dimethyl-aniline 1 (10.0 g, 0.05 mmol) in 13 mL of HCl (12 M)
and 5 mL of H2O was stirred and heated to 90-95 °C in a round-
bottom flask for 1.5 h. The mixture was then cooled to 0-5 °C with
an ice-water cold bath. A solution of sodium nitrite (3.75 g, 0.054
mmol) in H2O (15 mL), previously cooled to 0-5 °C, was added
dropwise to the reaction mixture. Stirring was continued for 30 min
after the addition of sodium nitrite. When the presence of free nitrous
acid was confirmed (starch-KI paper), the diazonium salt mixture was
carefully neutralized with sodium carbonate and then transferred to an
ice-jacketed addition funnel.
salt mixture was then added to the copper(I) cyanide solution over a
period of 15 min, the reaction temperature being carefully maintained
at 0-5 °C. Afterward, the mixture was stirred at 0-5 °C for 30 min,
at room temperature for 2 h and then heated to 50 °C without stirring
and cooled to room temperature. The reaction mixture, after mixing
with an additional 30 mL of toluene, was then filtered to remove the
red precipitate formed during the reaction.
The filtrate was placed in a separatory funnel, and the two layers
were separated followed by extraction of the aqueous layer with toluene
(2 × 60 mL). The combined organic layer was washed with water,
dried over anhydrous MgSO4, and concentrated in vacuo to give a dark-
colored solid. Recrystallization from hexanes provided 2 (8.3 g, 79%
yield) as a brownish solid: 1H NMR (300 MHz, CDCl3) δ 7.32 (s,
2H), 2.51 (s, 6H); 13C NMR (75 MHz, CDCl3) δ 144.1, 130.8, 127.4,
116.9, 112.7, 20.8.
4-Bromo-2,6-bis-bromomethyl-benzonitrile (3). A 100-mL round-
bottom flask was charged with 2 (2.1 g, 7.6 mmol), N-bromosuccin-
imide (4.27 g, 24.0 mmol), benzene (40 mL), benzoylperoxide (38 mg,
0.16 mmol), and a magnetic stirrer. After refluxing at 90-95 °C for
30 h, the reaction mixture was cooled to room temperature and filtered.
The filtrate was washed with acidic NaHSO3 solution (pH 2), water
and then dried over anhydrous Na2SO4. Removal of solvent on a rotary
evaporator led to a white solid residue. Flash column chromatography
(silica gel, 4H 25 cm) using 2:1 hexanes/CH2Cl2 as eluent yielded 3
(1.8 g, 50% yield) as a white solid: 1H NMR (300 MHz, CDCl3) δ
7.65 (s, 2H), 4.57 (s, 4H); 13C NMR (75 MHz, CDCl3) δ 143.9, 133.6,
128.3, 118.9, 114.4, 28.4.
4-Bromo-2,6-bis-(2-methoxy-ethoxymethyl)-benzonitrile (4a). To
a sodium hydride sample (50 mg, 2.05 mmol, 60% dispersion in mineral
oil) in a 25-mL round-bottom flask equipped with a magnetic stirrer
was added a 3:1 THF/2-methoxyethanol mixture. After hydrogen gas
stopped forming, a solution of 3 (0.35 g, 0.95 mmol) in anhydrous
Toluene (35 mL) was added to a newly prepared copper(I) cyanide
solution90 at 0-5 °C. With vigorous mechanical stirring, the diazonium
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Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8379
THF (5 mL) was added. The reaction mixture was stirred for 15 min
at room temperature, and then mixed with 5 mL of HCl (0.05 M). The
mixture thus obtained was then poured into ice water, extracted with
ether, dried over anhydrous MgSO4, and evaporated under reduced
pressure. The residue was a reddish viscous liquid from which pure 4a
(0.24 g, 70% yield) was isolated by flash column chromatography eluted
by CH2Cl2 and then CH2Cl2/ethyl acetate (10:1): 1H NMR (300 MHz,
CDCl3) δ 7.69 (s, 2H), 4.70 (s, 4H), 3.74-3.71 (m, 4H), 3.62-3.59
(m, 4H), 3.39 (s, 6H); 13C NMR (75 MHz, CDCl3) δ 144.4, 130.7,
128.6, 118.8, 115.2, 72.0, 70.8, 70.5, 59.4.
4-Bromo-2,6-bis-(2,5,8-trioxanonyl)-benzonitrile (4b). 4b was
synthesized in 68% yield in the same procedure as for 4a. The eluent
for column chromatography was CH2Cl2/ethyl acetate (5:1): 1H NMR
(300 MHz, CDCl3) δ 7.68 (s, 2H), 4.69 (s, 4H), 3.76-3.67 (m, 8H),
3.67-3.61 (m, 4H), 3.58-3.52 (m, 4H), 3.36 (s, 6H); 13C NMR (75
MHz, CDCl3) δ 144.5, 130.6, 128.6, 115.1, 108.4, 72.2, 70.9, 70.9,
70.8, 70.4, 59.3.
4-Bromo-2,6-bis-(2,5,8,11-tetraoxadodecyl)-benzonitrile (4c). 4c
was synthesized in 65% yield in the same procedure as 4a. The eluent
for column chromatography was CH2Cl2/ethyl acetate (1:1): 1H NMR
(300 MHz, CDCl3) δ 7.69 (s, 2H), 4.71 (s, 4H), 3.74-3.71 (m, 8H),
3.69-3.63 (m, 12H), 3.57-3.52 (m, 4H), 3.36 (s, 6H); 13C NMR (75
MHz, CDCl3) δ 144.5, 130.6, 128.6, 115.1, 108.4, 72.2, 71.0, 70.9,
70.8, 70.7, 70.4, 59.3.
mixture was then cooled to room temperature, poured into ice-water,
and extracted with ether (2H 15 mL). The organic phase was dried
over anhydrous MgSO4, filtered, and evaporated down to a viscous
residue. Flash column chromatography eluted by a 30:1 CH2Cl2/THF
mixture afforded 6a (0.12 g, 55% yield) as a yellowish solid: 1H NMR
(300 MHz, CDCl3) δ 7.77 (s, 4H), 4.80 (s, 8H), 3.81-3.73 (m, 8H),
3.68-3.59 (m, 8H), 3.40 (s, 12H); 13C NMR (75 MHz, CDCl3) δ 143.9,
143.4, 126.7, 115.6, 110.4, 72.0, 71.1, 70.8, 59.4; HRMS (FAB, NBA)
m/z 557.2866 [(M + 1)+; calcd for C30H41N3O8, 557.2863].
4,4′-Dicyano-3,3′,5,5′-tetrakis-(2,5,8-trioxanonyl)-biphenyl (6b).
6b was synthesized in 45% yield with the same procedure as for 6b.
Column chromatography eluted by 5:1 CH2Cl2/THF and then 3:1 CH2-
Cl2/THF afforded the product as a slightly yellow, viscous liquid: 1H
NMR (300 MHz, CDCl3) δ 7.72 (s, 4H), 4.80 (s, 8H), 3.83-3.76 (m,
8H), 3.76-3.70 (m, 8H), 3.69-3.62 (m, 8H), 3.57-3.50 (m, 8H), 3.34
(s, 12H); 13C NMR (75 MHz, CDCl3) δ 144.0, 143.5, 126.8, 115.6,
110.4, 72.2, 71.1, 70.9, 70.8, 59.3. ESMS (methanol) m/z 755.5 (M +
Na)+.
2,6-Bis-(2-methoxy-ethoxymethyl)-4-trimethylsilyl-benzonitrile (7a).
A heavy-walled Schlenk tube equipped with a magnetic stirrer was
charged with (4a) (0.95 g, 2.6 mmol), copper(I) iodide (5 mg, 0.026
mmol), bis(triphenylphosphine)palladium(II) chloride (29.9 mg, 0.052
mmol), triphenylphosphine (68 mg, 0.26 mmol), and triethylamine (10
mL). The tube was carefully evacuated by a vacuum manifold until
the solution started boiling and then back-filled with nitrogen. After
being thus purged 5 times, trimethylsilylacetylene (0.80 mL, 5.6 mmol),
previously stored under nitrogen, was added to the flask under nitrogen
via syringe. The tube was then sealed with a septum and stirred at 70
°C for 15 h. The reaction mixture was then allowed to cool to room
temperature and was filtered through a fritted glass funnel. The filtrate
was evaporated to dryness under reduced pressure on a rotary evaporator
on silica gel (9:1 CH2Cl2:ethyl acetate) to yield 7a as a waxy solid
(0.63 g, 62%): 1H NMR (300 MHz, CDCl3) δ 7.60 (s, 2H), 4.70 (s,
4H), 3.75-3.72 (m, 4H), 3.64-3.62 (m, 4H), 3.41 (s, 6H) 0.26 (s,
9H); 13C NMR (75 MHz, CDCl3) δ 142.3, 130.6, 127.9, 115.2, 109.4,
103.3, 99.2, 71.7, 70.6, 70.4, 59.0, -0.28.
1,3,5-Tris{[4-cyano-3,5-bis(2-methoxy-ethoxymethyl)phenyl]-
ethynyl}benzene (5a). A Schlenk tube was charged with 4a (0.28 g,
0.77 mmol), 1,3,5-triethynylbenzene (34 mg, 0.23 mmol), triphen-
ylphosphine (9 mg, 0.034 mmol), bis(triphenylphosphine)palladium-
(II) chloride (4.5 mg, 6.4H 10-3 mmol), copper(I) iodide (2 mg, 0.01
mmol), and triethylamine (8 mL). The tube was carefully evacuated
by a vacuum manifold until the solution started boiling and then back-
filled with nitrogen. After being thus purged five times, the tube was
sealed with a plug and stirred at 80 °C for 12 h. The reaction mixture
was cooled to room temperature, poured into water, and extracted with
CH2Cl2 (2H 10 mL). The combined organic layer was dried over
anhydrous MgSO4, filtered, and evaporated down to a viscous liquid.
Purification by flash column chromatography using a 4:1 CH2Cl2/ethyl
acetate mixture afforded 5a (0.18 g, 80% yield) as a yellowish solid:
1H NMR (300 MHz, CDCl3) δ 7.68 (s, 9H), 4.75 (s, 12H), 3.82-3.73
4-Trimethylsilyl-2,6-bis-(2,5,8-trioxanonyl)-benzonitrile (7b). 7b
was synthesized with the same procedure as that for 7a in the amount
of 0.74 g (80% yield). Flash column chromatography eluted by a 5:1
CH2Cl2/ethyl acetate mixture yielded 7b as a viscous liquid: 1H NMR
(300 MHz, CDCl3) δ 7.54 (s, 2H), 4.67 (s, 4H), 3.71-3.68 (m, 8H),
1
(m, 12H), 3.68-3.60 (m, 12H), 3.42 (s, 18H); H NMR (300 MHz,
acetone-d6) δ 7.88 (s, 3H), 7.78 (s, 6H), 4.76 (s, 12H), 3.78-3.74 (m,
12H), 3.61-3.58 (m, 12H), 3.33 (s, 18H); 13C NMR (75 MHz, CDCl3)
δ 142.9, 135.2, 130.6, 127.6, 123.8, 115.4, 109.9, 91.4, 89.9, 72.0, 70.8,
70.8, 59.4; HRMS (FAB, NBA) m/z 982.4497 [(M + 1)+; calcd for
C57H64N3O12, 982.4490].
3.65-3.62 (m, 4H), 3.55-3.52 (4H, m), 3.35 (s, 6H) 0.22 (s, 9H); 13
C
NMR (75 MHz, CDCl3) δ 142.4, 130.5, 127.8, 115.1, 109.2, 103.3,
99.0, 71.9, 70.5, 70.4, 70.3, 59.0, -0.32.
4,4′-Dicyano-3,3′,5,5′-tetrakis-(2-methoxy-ethoxymethyl)tolan (8a).
7a (0.45 g, 1.7 mmol), potassium carbonate (0.08 g, 0.58 mmol), a
methanol/dichloromethane 1:6 solution (14 mL), and a magnetic stirrer
were placed in a heavy-walled Schlenk flask and stirred under nitrogen
for 2 h. This mixture was transferred to another heavy-walled Schlenk
flask previously charged with 7a (0.43 g, 1.2 mmol), triphenylphosphine
(31 mg, 0.12 mmol), bis(dibenzylideneacetone)palladium(0) (13 mg,
0.024 mmol), and triethylamine (4 mL). The flask was then purged
with nitrogen in the same way as for 7a and sealed with a Teflon cap.
After stirring at 70 °C for 12 h, the reaction mixture was allowed to
cool to room temperature and was filtered through a glass funnel. The
filtrate was evaporated under reduced pressure on a rotary evaporator,
and the residue was purified by column chromatography on silica gel
(3:1 CH2Cl2/ethyl acetate) to yield 8a as a yellow solid (0.51 g, 73%):
1H NMR (300 MHz, CDCl3) δ 7.67 (s, 4H), 4.74 (s, 8H), 3.77-3.74
(m, 8H), 3.64-3.61 (m, 8H), 3.41 (s, 12H); 13C NMR (75 MHz, CDCl3)
δ 142.7, 130.3, 127.1, 115.1, 109.7, 91.7, 71.8, 70.5, 59.1; HRMS (EI,
70 eV) m/z 580.2777 [M+; calcd for C32H40N2O8, 580.2785].
4,4′-Dicyano-3,3′,5,5′-tetrakis-(2,5,8-trioxanonyl)tolan (8b). 8b
was synthesized with the same procedure as for 8a in the amount of
0.52 g (47% yield). Flash column chromatography eluted by a 2:1 CH2-
Cl2/ethyl acetate mixture yielded 8b as a yellowish solid: 1H NMR
(300 MHz, CDCl3) δ 7.66 (s, 4H), 4.73 (s, 8H), 3.77-3.72 (m, 16H),
3.68-3.65 (m, 8H), 3.57-3.54 (m, 8H), 3.36 (s, 12H); 13C NMR (75
MHz, CDCl3) δ 143.1, 130.6, 127.3, 118.9, 115.4, 110.0, 92.0, 72.2,
70.9, 70.8, 70.6, 59.3; HRMS (EI, 70 eV) m/z 756.3816 [M+; calcd
for C40H56N2O12, 756.3833].
1,3,5-Tris{[4-cyano-bis-(2,5,8-trioxanonyl)phenyl]ethynyl}-
benzene (5b). 5b was synthesized in 92% yield with the same procedure
as 5a. Flash column chromatography using ethyl acetate followed by
a 10:1 ethyl acetate/ethanol mixture furnished 5b as a yellowish solid:
1H NMR (300 MHz, CDCl3) δ 7.69 (s, 3H), 7.65 (s, 6H), 4.75 (s, 12H),
3.78-3.72 (m, 24H), 3.68-3.65 (m, 12 H), 3.57-3.54 (m,12H), 3.33
(s, 18H); 13C NMR (75 MHz, CDCl3) δ 143.0, 135.1, 130.5, 127.5,
123.8, 115.4, 109.8, 91.3, 89.9, 72.2, 70.9, 70.8, 70.8, 59.4; HRMS
(ESMS, Methanol) m/z 1263.63281 [(M + NH4)+; calcd for C69H91N4O18,
1263.63284].
1,3,5-Tris{[4-cyano-3,5-bis(2,5,8,11-tetraoxadodecyl)phenyl]-
ethynyl}benzene (5c). 5c was synthesized in 85% yield with the same
procedure as for 5a. Flash column chromatography using ethyl acetate
followed by a 10:1 ethyl acetate/ethanol mixture afforded 5c as a
yellowish viscous liquid: 1H NMR (300 MHz, CDCl3) δ 7.69 (s, 3H),
7.65 (s, 6H), 4.75 (s, 12H), 3.80-3.72 (m, 24H), 3.70-3.66 (m, 24H),
3.66-3.61 (m,12H), 3.55-3.50 (m, 12H), 3.33 (s, 18H). 13C NMR
(75 MHz, CDCl3) δ 143.0, 135.0, 130.3, 127.4, 123.8, 115.2, 109.8,
91.2, 89.9, 72.8, 72.7, 71.5, 71.4, 70.9, 70.8, 70.2, 58.7; HRMS (FAB,
NBA) m/z 1510.7656 [(M + 1)+; calcd for C81H112N3O24, 1510.7636].
4,4′-Dicyano-3,3′,5,5′-tetrakis-(2-methoxy-ethoxymethyl)-biphen-
yl (6a). A Schlenk flask was charged with bis(pinacolato) diborane
(0.219 g, 0.863 mmol), 4a (0.284 g, 0.785 mmol), tetrakis(triphen-
ylphosphine)palladium (28 mg, 0.024 mmol), potassium acetate (0.23
g, 2.32 mmol), and DMSO (5 mL). The flask was degassed, back-
filled with nitrogen, and then heated to 80-85 °C for 2 h. The reaction

8380 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
X-ray Quality Single Crystal of 8a‚AgOTf (9). A solution of 8a
(5.0 mg, 8.6 µmol) in benzene (1.5 mL) was mixed with a solution of
silver triflate (2.2 mg, 8.6 µmol) in benzene (1.5 mL). No precipitate
formed immediately after mixing. Slow evaporation of the solvent over
3 days produced colorless, needlelike single crystals suitable for X-ray
analysis. X-ray powder diffraction of the bulk sample (see Supporting
Information) showed only one crystal phase which corresponds to the
single-crystal structure.
a 23 mg m-xylene solution of silver tetrafluoroborate (1.1%, 0.05 M).
Colorless needlelike single crystals were obtained as the final product.
X-ray powder diffraction showed only one single-crystal phase which
corresponds to the pattern generated by the solved single-crystal
structure.
X-ray Quality Single Crystal of 6a‚1.25AgSbF6‚1.25C6H6 (19).
The same method was applied as for 15. The three solutions used were
a 20 mg benzene-d6 solution of 6a (1.8%, 0.032 M), a 40 mg benzene-
d6 solution, and a 23 mg m-xylene solution of silver tetrafluoroborate
(1.2%, 0.031 M). Blocks of colorless single crystals were obtained as
the final product. X-ray powder diffraction showed only one single-
crystal phase which corresponds to the pattern generated by the solved
single-crystal structure.
X-ray Quality Single Crystal of 5a‚AgOTf (20). The same method
was applied as for 15. The three solutions used were a 40 mg benzene-
d6 solution of 5a (1.5%, 0.015 M), a 60 mg benzene-d6 solution, and
a 40 mg m-xylene solution of silver triflate (0.4%, 0.013 M). Blocks
of colorless single crystals were obtained as the final product. X-ray
powder diffraction showed only one single-crystal phase which
corresponds to the pattern generated by the solved single-crystal
structure.
X-ray Quality Single Crystal of 8a‚AgPF6 (10). A 500 mg benzene
solution of 8a (2.0% by weight, 0.030 M) was mixed with a 500 mg
benzene solution of silver hexafluorophosphate (0.89%, 0.030 M). A
white precipitate formed immediately. Enough acetone was added to
dissolve all of the precipitate. Slow evaporation at room temperature
over 3 weeks yielded colorless needlelike crystals suitable for X-ray
analysis.
X-ray Quality Single Crystal of 8a‚AgSbF6 (11). The same method
was applied as for 10. The solutions used were a 500 mg benzene
solution of 8a (2.0%, 0.030 M) and a 500 mg benzene solution of silver
hexafluoroantimonate (1.2%, 0.030 M). Colorless needles of single
crystals were obtained as the final product.
X-ray Quality Single Crystal of 8b‚AgSbF6‚H6O (12). The same
method was applied as for 10. The solutions used were a solution of
8b (10 mg, 0.013 mmol) in benzene (1.5 mL) and a solution of AgSbF6
(4.5 mg, 0.013 mmol) in benzene (1.5 mL). Slow evaporation of the
solvents over 3 days yielded colorless, needlelike single crystals suitable
for X-ray analysis. X-ray powder diffraction of the bulk sample showed
only one crystal phase which corresponds to the single-crystal structure.
X-ray Quality Single Crystal of 5b‚4AgOTf (21). The same method
was applied as for 15. The three solutions used were a 30 mg benzene-
d6 solution of 5b (11%, 0.07 M), a 60 mg benzene-d6 solution, and a
90 mg m-xylene solution of silver triflate (2.5%, 0.085 M). Blocks of
colorless single crystals were obtained as the final product. X-ray
powder diffraction showed only one single-crystal phase which
corresponds to the pattern generated by the solved single-crystal
structure.
X-ray Quality Single Crystal of 6b‚4AgOTf (13). A 20 mg
benzene-d6 solution of 6b (4.9%, 0.063 M), a 40 mg benzene-d6
solution, and a 75 mg m-xylene solution of silver triflate (1.8%, 0.063
M) were sequentially placed one beneath the other in a 2 mm diameter
glass tube. The tube was then sealed. Slow diffusion at ambient
temperature over 1 week yielded needlelike crystals which, however,
were too small for single-crystal X-ray analysis. A small cleft was cut
at the tip of the tube to allow slow evaporation of the solvents for
further crystallization. Colorless needles of crystals of X-ray quality
were collected after another 2 weeks. X-ray powder diffraction showed
only one single-crystal phase which corresponds to the pattern generated
by the solved single-crystal structure.
Results
Single-Crystal Structure of 8a‚AgOTf (9). The crystal
structure of 9 is illustrated in Figure 1a. In this structure the
silver atoms are bonded to two ligand nitrogen atoms in a nearly
linear fashion at Ag-N distances of 2.12 and 2.14 Å. The silver
atoms are also coordinated to one triflate counterion with a
Ag-O distance of 2.44 Å. In addition, there is a rather weak
Ag-Ag bond: this Ag-Ag distance of 3.23 Å is slightly shorter
than twice the 1.72 Å silver van der Waal radius.91 Considering
only Ag-N and Ag-O bonds, the silver atom coordination is
T-shaped. It is interesting to note that although molecule 8a
contains eight oxygen atoms, none of them are coordinated to
silver.
As each silver atom is bonded to two ligand nitrogen atoms
and vice versa, each ligand molecule is bonded to two silver
atoms, and the resulting topology contains one-dimensional (1-
D) infinite chains alternating between silver atoms and ligand
8a molecules. As one may see in Figure 1a, a unit cell contains
two such 1-D infinite chains running along [1 0 -2]. Parallel
chains exhibit π-π interactions at an average plane-to-plane
distance 3.6 Å. Thus, considering just Ag-N and Ag-O
coordination bonds the network is one-dimensional, while if
π-π interactions are also included, the overall net is two-
dimensional (2-D).
X-ray Quality Single Crystal of 6b‚2AgBF4‚H2O (14). The same
method was applied as for 10. The solutions used were a 20 mg
m-xylene solution of 6b (1.3%, 0.015 M) and a 17 mg m-xylene solution
of silver tetrafluoroborate (0.78%, 0.036 M). Blocks of colorless crystals
were collected as the final product. X-ray powder diffraction showed
only one single-crystal phase which corresponds to the pattern generated
by the solved single-crystal structure.
X-ray Quality Single Crystal of 6b‚AgBF4‚C6H6‚H2O (15). A 20
mg benzene-d6 solution of 6b (4.9%, 0.065 M), a 40 mg benzene-d6
solution, and a 55 mg m-xylene solution of silver tetrafluoroborate
(1.4%, 0.065 M) were sequentially placed one beneath the other in a
2 mm diameter glass tube. The tube was then sealed. Slow diffusion at
ambient temperature over 1 week yielded blocks of colorless crystals
suitable for X-ray analysis.
X-ray Quality Single Crystal of 6b‚2AgSbF6 (16). The same
method was applied as for 10. The solutions used were a 20 mg
m-xylene solution of 6b (1.3%, 0.015 M) and a 22 mg m-xylene solution
of silver hexafluoroantimonate (1.1%, 0.028 M). Colorless needles of
single crystal were obtained as the final product. X-ray powder
diffraction showed only one single-crystal phase which corresponds to
the pattern generated by the solved single-crystal structure.
Single-Crystal Structure of 8a‚AgPF6 (10). The Ag atom
in this structure is bonded to two 8a molecules through Ag-N
bonds 2.14 and 2.22 Å long and with an N-Ag-N angle of
145.1°. One side chain from a third 8a molecule then chelates
the Ag atom through two Ag-O bonds 2.58 and 2.50 Å long.
The resultant overall coordination is sawhorse-like with the two
nitrogen atoms sitting on a bent horizontal bar and the two
oxygen atoms at the fulcra.
X-ray Quality Single Crystal of 6a‚2AgOTf‚0.5 m-xylene (17).
The same method was applied as for 13. The solutions used were a 20
mg benzene-d6 solution of 6a (1.8%, 0.032 M), a 40 mg benzene-d6
solution, and a 13 mg m-xylene solution of silver triflate (1.3%, 0.046
M). Blocks of colorless single crystals were obtained as the final
product.
Like 9, the structure contains infinite chains of alternating
organic molecules and Ag(I) ions, and the infinite chains stack
to form a 2-D sheet (Figure 1b). The interplanar π-π distance
X-ray Quality Single Crystal of 6a‚2AgBF4 (18). The same method
was applied as for 15. The three solutions used were a 20 mg benzene-
d6 solution of 6a (1.8%, 0.032 M), a 40 mg benzene-d6 solution, and
(91) Bondi, A. J. Phys. Chem. 1964, 68, 441.

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8381
Figure 1. Stereoviews of crystal structures of (a) 8a‚AgOTf (9), (b) 8a‚AgPF6 (10), (c) 8a‚AgSbF6 (11), (d) 8b‚2AgSbF6‚2H2O (12), (e) 6b‚
4AgOTf (13), (f) 6b‚2AgBF4‚H2O (14), (g) 6b‚AgBF4‚C6H6‚H2O (15), (h) 6b‚2AgSbF6 (16), (i) 6a‚2AgOTf‚0.5 m-xylene (17), (j) 6a‚2AgBF4
(18). Counterions: red, Ag: brown, N: light blue, O: blue, C: green. For the sake of clarity, disorder in atom positions has been removed.
is roughly 3.4 Å. The overall coordination network is 2-D due
to the chelation of the oxygen atoms to the Ag ions across the
neighboring chains.
Single-Crystal Structure of 8a‚AgSbF6 (11). This structure
bears close resemblance to 10 in both its overall coordination
topology and the way the organic molecules and the metal ions

8382 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
are packed, Figure 1c. The local coordination geometry of the
silver ion, however, shows some differences. While the two
Ag-N bonds continue to form in a similar fashion (bond
lengths, 2.179 and 2.248 Å; bond angle, 149.1°), there are three
oxygen atoms coordinated to each silver atom at distances
ranging from 2.48 to 2.73 Å. The overall coordination of the
silver atom is a distorted trigonal bipyramid.
hydrogen atom could be located by Fourier difference maps
0.99 Å from the oxygen site.
The Ag-6b-Ag units stack along the b axis (π-π distance,
3.5 Å) to form a columnar structure. Like 12, two of the side
chains from each 6b molecule chelate Ag atoms which lie above
and below it in the columnar stack. The remaining two side
chains chelate silver atoms from neighboring columns. The
resultant coordination network is therefore a 2-D sheet consisting
of the columns linked by these latter Ag-O bonds, as shown
in Figure 1f. Disorder in the possible water molecules as well
as in the BF4 units has been removed from this drawing.
Single-Crystal Structure of 6b‚3AgBF4‚C6H6‚H2O (15).
There are three crystallographically non-equivalent Ag atoms
in this structure. Ag1 is bonded in a distorted square pyramid
to one nitrogen atom and four oxygen atoms. One of the oxygen
atoms is from an adventitious water molecule, while the other
three are derived from side chains of the 6b molecule. The
hydrogen atoms of this adventitious water molecule were also
found by Fourier difference maps. The Ag1-N distance is 2.25
Å while the Ag1-O distances range from 2.39 to 2.51 Å. The
Ag2 atom is bonded to one nitrogen atom and three side chain
oxygen atoms at a distance range similar to that of Ag1. In
addition, Ag2 weakly interacts with a benzene molecule with
the closest Ag-C distance being 2.76 Å. The nitrogen atom,
the oxygen atoms, and the closest carbon atom together form a
distorted square pyramid around Ag2. Ag3 is coordinated to
five side chain oxygen atoms in a distorted square pyramid at
Ag-O distances ranging from 2.36 to 2.77 Å. The same benzene
molecule that is bonded to Ag2 also interacts with Ag3, the
closest Ag-C distances being 2.48 Å. Including this Ag-C
interaction, Ag3 has a distorted octahedral coordination environ-
ment.
Single-Crystal Structure of 8b‚2AgSbF6‚2H2O (12). There
are two crystallographically non-equivalent Ag atoms in the unit
cell. Ag1 is coordinated to one nitrogen from a 8b molecule,
three oxygen atoms on one side chain of another 8b molecule,
and one oxygen atom from a water molecule. The hydrogen
atoms of this adventitious water molecule were located through
the Fourier electron density difference map. The overall
coordination of Ag1 is a distorted square pyramid with an Ag-N
distance of 2.25 Å and Ag-O distances ranging from 2.42 to
2.55 Å. Ag2 is coordinated to one nitrogen atom and five oxygen
atoms in a distorted octahedron with an Ag-N bond length of
2.21 Å and the Ag-O distances ranging from 2.40 to 2.87 Å.
The nitrogen atom and two of the oxygen atoms are derived
from the same 8b molecule, while the remaining three oxygen
atoms reside on one side chain of another 8b molecule.
As Figure 1d shows, the two nitrogen ends of each 8b
molecule are respectively capped by Ag1 and Ag2. Such Ag1-
8b-Ag2 units then stack along the a axis with an interplanar
distance of 3.3 Å. One of the Ag atoms of each Ag1-8b-Ag2
unit is bonded to a side chain from the 8b molecule just above
it in the stacking sequence, while the other is bonded to a side
chain of the 8b molecule just underneath. The resulting structure
is a 1-D column of 8b molecules and silver atoms connected
through Ag-N, Ag-O bonds and π-π interactions.
Single-Crystal Structure of 6b‚4AgOTf (13). There are two
crystallographically non-equivalent Ag atoms in this structure.
Ag1 is coordinated to one nitrogen from a 6b molecule, three
oxygen atoms on one side chain of another 6b molecule, and
one oxygen atom from a triflate ion. The overall coordination
is a distorted square pyramid with an Ag-N distance of 2.184
Å and Ag-O distances ranging from 2.31 to 2.68 Å. Ag2 is
coordinated to five oxygen atoms in a distorted square pyramid
at distances ranging from 2.40 to 2.65 Å. Three of the oxygen
atoms reside on one side chain of a 6b molecule, while the
other two are from two different triflate ions. One of the triflate
ions is bonded exclusively to Ag2, and the other one has close
contacts with both Ag1 and Ag2 at Ag-O distances of
respectively 2.31 and 2.62 Å.
Similar to that of 12, the coordination network of 15 is 1-D
and consists of columns of Ag1-6b-Ag2 units stacked along
the a axis (π-π distance, 3.5 Å), Figure 1g. Each Ag1 or Ag2
atom is chelated by side chains of 6b molecules which are either
directly above or directly beneath the Ag atom in the columnar
stacking sequence. Each column is further strengthened by both
the Ag3 atoms as well as the cocrystallized benzene molecule.
The overall coordination network is two-dimensional.
Single-Crystal Structure of 6b‚2AgSbF6 (16). In this
structure the silver atom is coordinated in a distorted square
pyramid to one nitrogen atom at Ag-N distance of 2.16 Å and
four oxygen atoms at Ag-O distances ranging from 2.27 to
2.60 Å. Two of the oxygen atoms and the nitrogen atom are
derived from the same 6b molecule. The other two oxygen
atoms sit on one side chain of another 6b molecule.
As seen in Figure 1h, the Ag-6b-Ag units stack along the
b axis at π-π distance of 3.6 Å. Two of the side chains on
each Ag-6b-Ag unit chelate one Ag atom from above and
one from beneath, as is found in 12-15. The resulting structure
is a 1-D column of 6b molecules connected through Ag-N,
Ag-O bonds and π-π interactions.
Single-Crystal Structure of 6a‚2AgOTf‚0.5 m-xylene (17).
The silver atom in this structure is coordinated to two 6a
molecules via two Ag-N bonds at distances of 2.14 and 2.14
Å and two triflate ions via two Ag-O bonds at distances of
2.49 and 2.50 Å. The overall coordination around the Ag atom
is sawhorse-like with the two nitrogen atoms along the slightly
bent horizontal bar and the two oxygen atoms at the fulcra (O-
Ag-O angle, 114.8°; N-Ag-N angle, 155.9°).
Like 12, each organic molecule is capped by two Ag atoms,
and the aromatic rings of the 6b molecules stack in a columnar
fashion along the a axis, Figure 1e. The interplanar π-π
distance is around 3.5 Å. Again like 12, the two Ag1 atoms on
each Ag-6b-Ag unit are bonded to oxygen atoms from the
side chain of an organic molecule lying either just above it or
beneath it in the columnar sequence. The Ag-6b-Ag units in
the column are also linked by a triflate ion. The resultant overall
coordination network is one-dimensional.
Single-Crystal Structure of 6b‚2AgBF4‚H2O (14). The Ag
atom in this structure is bonded to one nitrogen atom at Ag-N
distance of 2.19 Å and five oxygen atoms at Ag-O distances
ranging from 2.32 to 2.79 Å. The overall coordination resembles
a distorted octahedron. The nitrogen atom, two of the oxygen
atoms, and the other three oxygen atoms are respectively
furnished by three different 6b molecules. Also located through
Fourier difference maps was an additional site near an inversion
center. We assigned this site to be the oxygen of a water
molecule, a suggestion supported by the fact that a possible
As Figure 1i shows, the structure consists of infinite chains
of alternating 6a molecules and Ag(I) ions, a structural motif
also found in 9-11. Triflate ions link these infinite chains into

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8383
pairs, as each triflate ion is coordinated to silver ions on two
neighboring chains. The resultant coordination network is a
double-stranded infinite chain. There are additional π-π
interactions both within each double-stranded chain and between
the double chains. The closest π-π distance is 3.6 Å, and the
shortest Ag-π distance is 3.6 Å. Including these π-π interac-
tions the overall net structure is two-dimensional.
Single-Crystal Structure of 6a‚2AgBF4 (18). There are two
crystallographically non-equivalent Ag atoms in this structure.
Each is coordinated to one nitrogen atom and three oxygen
atoms in a sawhorse-like geometry. The Ag-N distances for
Ag1 and Ag2 are 2.20 and 2.21 Å, respectively. The Ag-O
distances for the two Ag atoms range from 2.30 to 2.61 Å.
The coordination network is very similar to that of 14. The
Ag1-6a-Ag2 units stack along b axis in a columnar structure,
Figure 1j. Half of the side chains form linkages to intracolumnar
Ag atoms, while half form intercolumnar linkages. The overall
coordination network is therefore two-dimensional.
Single-Crystal Structure of 6aA‚1.25AgSbF6‚1.25C6H6
(19). 19 crystallized in the P1h space group with a unit cell
volume of over 17 000 Å3. In the final refinement, the aromatic
rings of 6a were restrained to be planar and the aromatic bonds
of 6a were restrained to all have the same bond length. The
fluorine atoms of the SbF6 anions related by pseudosymmetry
were restrained to to have the same anisotropic displacement
parameters. Two-fifths of the silver atoms in the final structure
(Ag2, Ag8, Ag9, and Ag3) are coordinated to one nitrogen and
four oxygen atoms in a square pyramid with Ag-N distances
ranging from 2.16 to 2.18 Å and Ag-O bonds from 2.36 to
2.61 Å. As Figure 2k shows, the remaining silver atoms are
either coordinated in a linear fashion to two nitrogen atoms or
are coordinated in a sawhorse-like geometry with two end
nitrogen atoms at distances ranging from 2.10 to 2.18 Å and
two fulcrum oxygen atoms at distances ranging from 2.54 to
2.69 Å.
As Figure 3c illustrates, a fundamental building block of this
structure is a rigid rod, some 65 Å long with two end Ag atoms,
each with only a single Ag-N bond and then alternating in the
interior of the rod linear doubly coordinate 6a molecules and
silver sites. The overall rod contains a tetramer of 6a molecules
and two capping and three interior silver sites. Each of these
tetrameric rods stacks parallel to one another to form a planar
sheet with stacked π rings 3.8 Å apart. Neighboring tetramers
stack in such a way as to place the end silver atoms in close
proximity to more central aromatic rings of the neighboring
tetramers. The end silver atoms are bonded to some of the
oxygen atoms of the side chain of the neighboring tetramers.
The overall coordination environment is therefore two-
dimensional. Fairly large cavities are created by the staggered
nature of adjacent tetramers. These cavities are in turn filled
with solvent benzene molecules. The solvent benzene molecule
lies parallel to the tetramer in such a way as to make π-π
distances of roughly 3.8 Å. This overall crystal structure may
be viewed as intermediate between the doubly capped structures
found for 12-16 and 18 and the infinite Ag-organic chains
found for 9-11 and 17.
Figure2. Stereoviewsofcrystalstructuresof(k)6a‚1.25AgSbF6‚1.25C6H6
(19), (l) 5a‚AgOTf (20), (m) 5b‚4AgOTf (21). Counterions: red, Ag:
brown, N: light blue, O: blue, C: green. For the sake of clarity,
disorder in atom positions has been removed.
given sheet. The remaining side, unobstructed by the triflate
ion, is π-π stacked (interplanar distance, 3.3 Å) to another
single sheet. The two sheets are so oriented that the silver atom
of one sheet directly faces the central aromatic ring of the 5a
molecule of the other sheet. These bilayers thereafter stack (π-π
distance, 3.6 Å) so that the triflate ions lie at the corners of the
hexagonal pores of a neighboring bilayer. The stacking of
bilayers produces distorted hexagonal channels filled with the
side chains and triflate ions. Considering only Ag-O and Ag-N
bonds, the overall coordination network is two-dimensional. The
inclusion of π-π interaction results in a three-dimensional (3-
D) structure.
Single-Crystal Structure of 5b‚4AgOTf (21). The dataset
for 21 proved to be of rhombohedral symmetry with systematic
extinctions compatible with R3, R3h, R32, R3m, and R3hm. The
first two of these space groups have Laue class 3h, while the
last three have Laue class 3hm. As Rint was fairly uniform for all
five space groups, we proceeded to solve the crystal structure
in the higher Laue class. Initial refinement was carried out in
R3hm. In this space group the rigid framework of the 5c molecule
as well as those of two silver sites could be located. The Ag1
site was three-coordinate to nitrogen in a trigonal planar fashion.
Ag2 proved to be coordinated neither to the nitrogen atoms of
5c nor to any triflate ions but instead only to the oxygen atoms
derived from the side chains of 5c molecules. Furthermore the
Single-Crystal Structure of 5a‚AgOTf (20). The silver atom
in this structure is trigonally coordinated to three 5a molecules
via three Ag-N bonds (all Ag-N distances, 2.24 Å). The triflate
ion is weakly bonded at the apical position of a trigonal pyramid
with a Ag-O distance of 2.51 Å.
As shown in Figure 2l, the crystal structure consists of slightly
distorted honeycomb sheets based on alternating 5a molecules
and Ag(I) ions. The triflate ions lie on only one side of any

8384 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
these disordered triflate ions is shown per site in Figure 2m. In
the final refinement these disordered triflate ions were restrained
to have a chemically reasonable triflate geometry.
Finally, it may be noted in Figure 2m that each of the
hexagonal sheets lie parallel to one another. Interplanar distances
alternate between 3.5 and 7.3 Å. The first distance is that
generally expected for π-π aromatic interaction. Indeed,
honeycomb nets separated at this shorter distance shows the
typical slightly staggered parallel arrangement of aromatic rings.
Such honeycomb nets are also paired up to form bilayers similar
to those found in 21. The 7.3 Å gap between neighboring
bilayers is due to the larger spatial requirement of the tri(ethylene
oxide) side chains.
Discussion
Crystal Structures. The 13 crystal structures reported above
display a slightly bewildering array of crystal types. If we restrict
our attention to the structures involving silver together with
molecules 6a-b and 8a-b, molecules all with a rigid linear
backbone capped at both ends with nitrile groups and also all
with four oligo(ethylene oxide) chains pendant to this backbone,
we find even here a real variation in structure. Considering
Ag-N concatenation, the various units observed range from
infinite chains of alternating organic molecules and silver ions
as is found in 9-11 and 17 to oligomers as in 19, to single
organic molecules capped by Ag ions as in 12-16 and 18. These
three basic types are illustrated in Figure 3.
Figure 3. The three basic Ag-N concatenation motifs in 9-21. (a)
The monomeric unit in 6a‚2AgBF4 (18). (b) The infinite chain in 6a‚
2AgOTfA‚0.5 m-xylene (17). (c) The tetrameric unit in 6a‚1.25AgSbF6‚
1.25C6H6 (19). Ag: large gray, N: black medium, C: small gray, O:
small black spheres.
Ag2 site as well as one of the coordinating oxygen atoms lies
on the mirror plane found in the R3hm space group. Hence, the
solution in R3hm automatically leads to a complex disorder of
the side chains around Ag2. However, if one removes this mirror
plane, lowering the space group to R32, all disorder of the side
chains is removed. It therefore seemed preferable to finish the
crystal structure refinement in R32. It should be noted that, as
it is only the side chains of 5c which break the R3hm symmetry
and as these side chains have atoms with large Debye-Waller
factors, it is difficult to ascertain the correct space group. A
less disordered model being preferable, we chose to refine this
crystal structure in R32. All refinements in R32, R3h, or R3hm,
however, bear the following geometric features in common.
The three 3-fold symmetric phenylacetylene arms of the
molecule 5c are capped by the Ag1 atom. Each Ag1 atom lies
on a 6c site with C3 symmetry and is coordinated to three
nitrogen atoms at a bonding distance of 2.30 Å. The molecules
5c together with the Ag1 atoms are therefore assembled into a
honeycomb net with alternating vertices occupied by Ag1 atoms
and the centroid aromatic rings of molecules 5c. The oxygen
atoms of the side chains are in turn coordinated to the Ag2 site.
Each Ag2 site is coordinated to five oxygen atoms with Ag-O
distances ranging from 2.46 to 2.72 Å. As Figure 2m shows,
these side chains together with the Ag2 sites form hexagonal
rosettes whose center is the 3-fold symmetric Ag1 site. In the
final refinement the side chain oxygen-carbon and carbon-
carbon bond lengths were restrained to be respectively 1.43 and
1.53 Å.
There are three triflate sites in the crystal. Of these, two are
disordered. Particularly complex is the disordered model chosen
for the triflate ion nearest Ag1. These triflate ions lie between
two Ag1 atoms with a distance from Ag1 to Ag1 of 7.32 Å.
Furthermore, these Ag1 sites lie both on the same 3-fold axis.
Were one to place the 3-fold axis of the triflate ion on this
crystallographic 3-fold axis, due to the short Ag1-Ag1 distance,
either the oxygen or the fluorine atoms of the triflate ions would
approach Ag1 sites at chemically unreasonable distances. We
found a chemically more reasonable solution, in which the 3-fold
axis of the triflate ion is canted with respect to the crystal-
lographic 3-fold axis. The result is a 6-fold disordered triflate
ion with Ag1-O distances of 2.59 and 2.64 Å. A single one of
If in addition we add Ag-O coordination, there is an even
greater range of structural variations. In 8a‚AgOTf (9), for
example, the Ag-organic molecule infinite chains illustrated
in Figure 3 are not cross-linked by any Ag-O bonds and the
coordination network remains 1-D, while in the compositionally
similar 8a‚AgPF6 (10) similar infinite chains are linked together
through Ag-O bonds to form a 2-D coordination network. Even
less clear are the factors which cause 6b‚2AgBF4‚H2O (14) to
have a 2-D coordination network and yet the slightly more
silver-rich 6b‚AgBF4‚C6H6‚H2O (15) to be 1-D. In the case of
the latter two compounds, both systems have a rich environment
of Ag-O bonds. However, for 15 these Ag-O bonds are
between organic molecules and silver atoms already connected
through the Ag-N-based infinite chains, while for 14 these
Ag-O bonds bridge adjacent Ag-N-based infinite chains to
each other.
This is not to say that one cannot a posteriori rationalize
these structural results. To a good extent one can. The following
rules generally hold. The chief factor in the crystal topologies
is the Ag-N coordination. If each Ag is coordinated to only a
single N then perforce the structure will contain Ag-organic
molecule-Ag monomer units. This is the case in 12-16 and
18. If, however, the Ag atoms are two-coordinate to nitrogen
atoms, the Ag-N coordination environment is linear, and the
resulting structures contain infinite chains of alternating silver
atoms and organic molecules. This is the case in 9-11 and 17.
The determining factor as to whether one or the other environ-
ment is adopted appears to be the stoichiometric ratios of silver
ions to organic molecules. In the infinite chain structures 9-11
and 17, this ratio is 1:1 while for the monomeric structures the
ratio is always greater than 2:1. Only in the case of intermediate
stoichiometry as is found in the 5:4 ratio of 19 does one find
the intermediate tetrameric structure.
These results suggest that, as may be expected, the strongest
coordination bonds in these systems are between silver and
nitrogen. All nitrogen atoms are therefore coordinated to silver

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8385
atoms. As such, a one-to-one ratio of silver ions to the ditopic
ligands 6a-b and 8a-b results in an average silver-to-nitrogen
coordination of two. The linear N-Ag-N is the coordination
geometry lowest in energy, and disproportionation of the silver-
nitrogen linkage does not occur. As molecules 6a-b and 8a-b
are themselves linear, the result is the formation of infinite
chains of alternating ligands and silver ions. Similarly, there is
energetic preference for two silver atoms singly bonded to
nitrogen rather than one silver atom two-coordinate to nitrogen.
Therefore, when organic molecule-to-silver ratios exceed 1-to-
2, one finds monomeric units rather than more complicated
structures.
The dimensionality of the coordination network is further
complicated by the Ag-O bonds. The following two general
rules, however, hold. If the number of side chain oxygen atoms
is greater, as is found in molecules 6b and 8b, as opposed to
6a and 8a, then the overall coordination network is 1-D rather
than 2-D. Also if the crystal contains coordinating counterions
such as the triflate ions or adventitious water, one finds 1-D
networks. Thus, 9, 12-13, and 15-17 all contain either the
long side chain molecules 6b or 8b, a triflate ion, or water
molecules and have 1-D coordination networks, while 10-11,
14, and 18-19 contain none of the above molecular units and
have 2-D coordination networks. The only exception to this
general rule is the crystal structure 14, and here the exception
is caused by a disordered water molecule which has only been
tentatively assigned as such.
We may account for these trends in the following way. As
described previously, Ag-N coordination by itself leads to the
formation of monomeric, tetrameric units or linear infinite
chains. Hence, whether the overall coordination is one or two-
dimensional depends on the Ag-O linkages. Both the oxygen
atoms of the triflate ion and the water molecules form stronger
bonds to the silver ions and hence they preferentially coordinate
to the metal atoms over the ether oxygen atoms of the various
organic side chains. As stronger bonds are formed, there tend
to be fewer Ag-O bonds in these former systems, and as these
oxygen atoms do not have to bridge the silver atom the new
organic ligands, they do not cause an increase in the dimen-
sionality of the coordination network. Similarly the more
oxygen-rich molecules 6b and 8b are able each by themselves
to more readily satisfy the coordination requirements of the
silver ions. A single 6b or 8b can furnish two or three
coordinating oxygen atoms, again reducing the need for Ag ions
to further cross-link to other organic molecules. Again, the result
is a reduced dimensional system.
Figure 4. Experimentally determined phase diagram for PS-PI
(polystyrene-polyisoprene)diblock copolymers.86 s: spheres, c: col-
umns, l: layers, bi: bicontinuous, pl: perforated layers.
In these examples, we can predict with some confidence as
we interpolate between existing results. Where our predictive
powers break down is where we need to extrapolate to
significantly new crystal types. Our rules discussed so far allow
the former and not the latter type of predictions.
In recent years, however, just such an extrapolative scheme
has been developed for large-length scale heterogeneous mol-
ecules as are found in amphiphilic and block copolymer
systems.92-94 The types of systems studied involve mixtures of
two different chemical components. Components are chosen
which on their own would phase-separate. However, by the
addition of amphiphilic surfactants or by the direct joining of
the two different polymer types, a mixture of the two compo-
nents is enforced. It has been found in such cases that an almost
universal phase diagram is produced.89,93 Key factors are the
volume ratio of the two components and the driving force of
Interfacial Model. The goal of systematic structural studies
is however not just the rationalization of determined structures
but also the prediction of structural properties in new as yet
undetermined families of structures. It is here that we can see
a breakdown of the aforementioned generalizations. For ex-
ample, if we were to substitute for the silver ions another metal
ion, introduce a kink in the rigid backbone of the phenylacety-
lene unit, or even just extend the side chains to a significantly
longer length, it would be difficult for us to predict even the
dimensionality of the overall coordination network. Predictions
we can make with confidence are of a simpler sort. Consider,
for example, the heretofore unprepared 8b‚AgOTf or 6a‚
2AgPF6. Following our previously established rules, we expect
for the former compound a structure with an infinite linear chain
of 8b-Ag ions and an overall 1-D coordination network of
Ag-N and Ag-O bonds. In the latter system we expect a
compound composed of Ag-6a-Ag monomeric units linked
together by Ag-O bonds into a 2-D network.
segregation, usually characterized by the parameter øN.95
A
typical example is shown in Figure 4.
At low volume ratios, spheres of one component form inside
the main body of the second body. At slightly higher volume
ratios, the spheres turn into columns, while at the volume ratio
of 1:1 lamellar structures are found. Finally, between the
columnar and lamellar regions a more complex type of structure
appears, involving either a bicontinuous form or a perforated
layer structure. Principal driving forces for this structure map
(92) Thomas, E. L.; Lescanec, R. L. Phase Morphology in Block
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525.

8386 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
are the minimization of the interfacial area between the two
chemical components or alternatively the curvature requirements
of this interface.
are layers of alternating hydrophobic and hydrophilic ligands.
Finally, 19 and 20 are bicontinuous. In the case of 20, we find
columns of hydrophilic moieties partially separated by a
pseudohexagonal network of hydrophobic aromatic groups.
However, the hydrophilic columns are not isolated but are in
close contact with one another. In the case of 19, the structure
is lamellar, but again there are close contacts between all next
nearest neighbor layers through perforations in each individual
lamella. For both 20 and 19, the result of these closest contacts
are the formation of one continuous hydrophobic and one
continuous hydrophilic domain. In accordance with the literature,
they are therefore termed bicontinuous.114,115
To date very little effort has been spent to see if this overall
general map is useful in the prediction and rationalization of
extended networks in coordination solids although significant
efforts have been made to apply the concepts of minimal
surfaces to solid-state crystal chemistry.96-99 Nor at the outset
is it clear that this generic framework will be useful for extended
coordination networks. The type of systems studied to date have
been at nanometer scales ranging up to 1000 Å in unit cell axes.
At such large distances, the individual vagaries caused by
anisotropic chemical bonds will be minimized. As we approach
5-10 Å, the typical unit cell lengths found in many extended
coordination networks, even the concept of the interface is less
well defined. Nevertheless, many coordination networks con-
tinue to adopt structures reminiscent of those found in Figure
4.49,70,100-113
We have prepared the crystals 9-21 in order to test the utility
of this generic framework (see Table 1). In each of the
crystallized extended networks, the organic molecules clearly
divide into a phenylacetylene backbone which is strongly
hydrophobic and oligo(ethylene oxide) side chains which are
correspondingly hydrophilic. Joining these molecules together
are silver salts. While the anion portion of the salt is certainly
hydrophilic, the case of the silver ion is less clear. Silver ions
coordinated solely to oxygen atoms are acting in a hydrophilic
manner. However, silver ions bound to softer ligands such as
nitrile groups and which in addition show weak bonding to
π-aromatic clouds are less hydrophilic. We will consider the
first sort of silver ions to be hydrophilic and the latter to be
intermediate in their hydroaffinity. Similarly, we will consider
nitrile groups to be of intermediate hydrophilicity. As for the
included benzene and water molecules, they are treated as
hydrophobic and hydrophilic, respectively. In the Figures 5 and
6 we redisplay these 13 structures using green to indicate the
hydrophilic portions of the crystal, red for hydrophobic portions,
and brown for those portions intermediate in hydroaffinity.
It may be seen that all 13 structures have topologies in
correspondence with the generic structures previously shown
in Figure 4. Of course, in comparing Figure 4 to Figures 5 and
6 there are noticeable differences. In Figure 3, the columnar
structure has only two lattice axes and the layer structure, only
a single lattice axis, while in Figures 5 and 6 all of the structures
correspond to normal crystal unit cells with three cell axes and
three cell angles. Furthermore, in Figure 4 the columnar structure
has hexagonal symmetry, while in Figure 5 this 6-fold symmetry
is lost. Even more complex are the bicontinuous systems. Here,
in the block copolymer literature, tremendous effort is made to
distinguish between different bicontinuous systems such as the
gyroid and the double diamond forms.116-118 If crystal symmetry
is no longer preserved, the boundaries become more indistinct.
Rather than trying to keep these different groups separate, in
Figure 5 we topologically group them into a single bicontinuous
family. Nevertheless, the correspondence between the crystal
structures reported in this work and the crystal topologies found
for generic biphasic heterogeneous systems is striking.
If the overall picture of biphasic separation is to prove useful,
we need to find the factors which cause the columnar, lamellar,
or bicontinuous topologies. As mentioned earlier, it is thought
that the two chief factors are the volume ratios and the overall
energy of segregation. In our case we are dealing with highly
hydrophobic aromatic rings and equally hydrophilic oligo-
(ethylene oxide) moieties. We are clearly within the high
segregation limit. We therefore turn to the hydrophilic-to-
hydrophobic ratio. At the same time we need to choose a useful
algorithm to rigorously classify a given crystal as of columnar,
lamellar, perforated lamellar, or bicontinuous type.
The 13 structures divide into three basic families. For 12-
14, 16, and 18 we find columns of the hydrophobic moieties in
a mixture of hydrophilic groups. For 9-11, 15, 17, and 21, there
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We chose the following method for calculating volume ratios.
We consider first the hydrophilic atoms. We place at each
hydrophilic atom a sphere with a radius corresponding to the
given atom’s van der Waals radius and calculate the volume of
the union of these spheres (The van der Waals radii are
standard91 and are given in the Supporting Information). We
carry out the same procedure for the hydrophobic atoms. We
then take the ratio of the two volumes. To verify that our
findings are invariant to reasonable definitions of hydrophobicity
and hydrophilicity, we performed these same calculations under
a range of assumptions. In particular we considered the carbon
adjacent to both the aromatic rings and the first oxygen of the
side chain to be hydrophobic in one set of calculations and
hydrophilic in another. As for the nitrile groups and the silver
ions bonded to nitrile groups, we considered them both
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Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8387
Table 1. Crystal Data and Structure Refinements for Compounds 9-21
9
10
11
12
formula
mol wt
T (K)
wavelength (Å)
system
space group
a (Å)
b (Å)
c (Å)
R (deg)
â (deg)
γ (deg)
V (Å3)
C33H40AgF3N2O11S
837.60
C32H40AgF6N2O8P
833.50
C32H40AgF6N2O8Sb
924.28
C40H58Ag2F12N2O13Sb2
1462.12
173(2)
173(2)
173(2)
173(2)
0.71073
0.71073
0.71073
0.71073
monoclinic
P21/n
13.5024(6)
9.8307(4)
38.919(2)
90
94.853(1)
90
5147.6(4)
4
1.887
1.891
triclinic
triclinic
triclinic
P1h
P1h
P1h
8.0147(1)
15.1807(1)
15.93250(1)
108.696(1)
98.906(1)
93.080(1)
1802.96(3)
2
11.2529(2)
13.4468(2)
14.1345(2)
104.016(1)
104.434(1)
111.615(1)
1788.19(5)
2
11.3394(3)
12.231
15.0405(4)
101.335(1)
110.647(2)
106.036(1)
1773.09(7)
2
Z
F
calc (g/cm3)
1.543
0.693
1.548
0.690
1.731
1.397
abs coeff (mm-1
θ range (deg)
limiting indices
)
2.28-23.26
-8 e h e 8
-16 e k e 16
-17 e l e 10
5093/0/448
8718
1.75-23.26
-12 e h e 12
-12 e k e 14
-15 e l e 15
5060/0/451
8092
1.83-18.84
-10 e h e 8
-11 e k e 11
-13 e l e 13
2741/0/241
4924
2.10-26.37
-16 e h e 14
-12 e k e 9
-45 e l e 48
10422/0/642
28323
data/restraints/params
measd reflns
unique reflns
abs correction
GOF on F2
Rint
5093
5060
2741
10422
SADABS
1.006
SADABS
1.062
SADABS
1.731
SADABS
0.891
0.0461
0.0357
0.0735
0.0683
R1
wR2
0.0587 (I > 2σ(I))
0.060 (I > 2σ(I))
0.1084 (I > 2σ(I))
0.0411 (I > 2σ(I))
0.1515 (I > 2σ(I))
0.1574 (I > 2σ(I))
0.2942 (I > 2σ(I))
0.0949 (I > 2σ(I))
13
14
15
16
formula
mol wt
T (K)
wavelength (Å)
system
space group
a (Å)
b (Å)
c (Å)
R (deg)
â (deg)
γ (deg)
V (Å3)
C21H28Ag2F6NO12S2
880.30
173(2)
0.71073
monoclinic
P21/n
7.3265(3)
26.101(1)
15.9343(3)
90
94.473(2)
90
3037.8(2)
4
1.925
C38H56Ag2B2F8N2O13
1138.21
173(2)
0.71073
monoclinic
P2/n
17.709(1)
7.5134(6)
18.067(1)
90
110.527(2)
90
2251.2(3)
2
1.679
C44H64Ag3B3F12N2O13
1413.01
173(2)
0.71073
triclinic
C19H28AgF6NO6Sb
710.04
173(2)
0.71073
monoclinic
C2/c
24.744(2)
7.3484(7)
27.940(3)
90
91.706(2)
90
5077.9(8)
8
1.858
P1h
12.3839(2)
14.4048(2)
16.5943(3)
104.869(1)
99.550(1)
99.507(1)
2753.61(8)
2
Z
F
calc (g/cm3)
1.704
1.157
abs coeff (mm-1
θ range (deg)
)
1.522
0.966
1.913
2.02-20.82
-7 e h e 7
-26 e k e 25
-11 e l e 15
3176/0/227
9836
3176
SADABS
1.181
2.00-23.25
-19 e h e 18
-8 e k e 8
-15 e l e 20
3213/9/320
8778
3213
SADABS
0.989
1.50-20.81
-12 e h e 12
-12 e k e 14
-16 e l e 13
5680/0/684
9610
5680
SADABS
0.976
2.17-24.80
-17 e h e 28
-8 e k e 8
-32 e l e 32
4309/0/307
11867
4309
SADABS
1.048
limiting indices
data/restraints/params
measd reflns
unique reflns
abs correction
GOF on F2
Rint
0.1151
0.0823
0.0537
0.0893
R1
wR2
0.0784 (I > 2σ(I))
0.1949 (I > 2σ(I))
0.0587 (I > 2σ(I))
0.1261 (I > 2σ(I))
0.0587 (I > 2σ(I))
0.1345 (I > 2σ(I))
0.0626 (I > 2σ(I))
0.0873 (I > 2σ(I))
17
18
19
20
21
formula
mol wt
T (K)
wavelength (Å)
system
space group
a (Å)
b (Å)
c (Å)
R (deg)
â (deg)
γ (deg)
V (Å3)
C35H45AgF3N2O11S
866.66
173(2)
0.71073
triclinic
P1h
8.7526(6)
14.835(1)
15.073(1)
97.790(2)
97.586(2)
92.184(2)
1919.0(2)
2
C30H40Ag2B2F8N2O8
946.00
173(2)
0.71073
monoclinic
P21/c
17.4924(6)
7.1943(1)
28.4848(9)
90
95.601(2)
90
3567.6(2)
4
C300H380Ag10F60N16O64Sb10
8670.40
173(2)
0.71073
triclinic
P1h
19.4111(3)
27.8506(4)
33.0801(3)
98.636(1)
91.473(1)
102.486(1)
17231.2(4)
2
C58H59AgF3N3O15S
1235.01
173(2)
0.71073
triclinic
C85H111Ag4F12N3O36S4
2538.49
173(2)
0.71073
rhombohedral
R32
22.4670(4)
22.4670(4)
36.1131(5)
90
90
120
15786.5(5)
6
P1h
8.7564(1)
18.2486(2)
19.5099(3)
104.3780(2)
99.1780(7)
102.2930(8)
2875.40(6)
2
Z

8388 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
Table 1. (Continued)
17
18
19
20
21
F
calc (g/cm3)
1.500
1.761
1.190
1.671
1.427
1.426
0.466
1.602
0.915
abs coeff (mm-1
θ range (deg)
)
0.654
2.35-20.82
-8 e h e 8
-14 e k e 13
-15 e l e 15
3910/18/303
7119
1.17-20.82
-17 e h e 13
-7 e k e 7
-26 e l e 28
3715/0/259
11485
3715
SADABS
1.039
0.0885
0.0952 (I > 2σ(I))
0.2270 (I > 2σ(I))
0.62-19.78
-18 e h e 17
-26 e k e 18
-30 e l e 31
30210/4636/1968
51478
30210
SADABS
1.197
0.0751
0.1352 (I > 2σ(I))
0.3619 (I > 2σ(I))
1.11-24.71
-10 e h e 10
-21 e k e 14
-22 e l e 22
9561/0/428
14621
9561
SADABS
1.173
0.0379
0.0653 (I > 2σ(I))
0.1678 (I > 2σ(I))
1.54-23.26
-24 e h e 17
-24 e k e 24
-34 e l e 40
5051/157/245
20721
5051
SADABS
2.334
0.0742
0.1564 (I >2σ(I))
0.3684 (I >2σ(I))
limiting indices
data/restraints/params
measd reflns
unique reflns
abs correction
GOF on F2
Rint
3910
SADABS
1.070
0.1306
R1
wR2
0.1063 (I > 2σ(I))
0.2515 (I > 2σ(I))
a R1 ) ∑||Fc| - |Fo||/∑|Fo|. b wR2 ) [∑[w(Fo2 - Fc2)]2/∑[w(F2o)2]]1/2
.
hydrophobic and of intermediate character (in this latter case
they are not considered in either volume grouping).
should have closest contacts between layers, while the other
component should not. Finally, in bicontinuous systems, both
components should by themselves form one continuous domain.
The only undetermined factor is the definition of the closest
contact itself. Here again we based our definition on van der
Waals radii. While the sum of the van der Waals radii prove
slightly too small for this purpose, if we choose a close contact
distance as being one less than 1.15 to 1.30 times the sum of
the two atoms’ van der Waals radii, the resulting structure
assignments correspond to the structure type which is expected
by visual inspection. Furthermore, only 10% of the structures
change their classification in changing the cutoff parameter from
1.15 to 1.30.
In Table 2 we list under a variety of different definitions of
hydrophilicity, hydrophobicity and close contact, the breakdown
of structure type as a function of hydrophilic to hydrophobic
volume ratios. As may be seen under each of these different
definitions, the hydrophilic to hydrophobic volume ratio proves
to be a critical component in separating columnar- from layer-
type structures.
For example in choosing sp3 carbon atoms adjacent to the
aromatic rings to be hydrophilic and CN-Ag units to be
hydrophobic, we find four distinct regions of structure type.
We find for volume ratios between 21 to 28% columnar
structures, from 29 to 34% a combination of columnar and
perforated layer structures, from 35 to 38% layer structures, and
finally at 40% bicontinuous structures. Similar evolution of
structure type as a function of volume ratios is found for each
alternate definition of hydroaffinity. As may be seen in Table
2, the predominant change due to alternate definitions of
hydroaffinity is not in the separation of structure types but the
actual numerical value assigned to the volume ratios. With the
exception of 18 and possibly 21 one may correctly order the
13 structures by volume ratio from columnar, to lamellar, to
bicontinuous structures. For 18 this exception depends on the
exact definition of hydroaffinity. If we define the sp3 carbon
atoms adjacent to the aromatic rings to be hydrophobic, 18
converts from columnar to the perforated layer type and is no
longer exceptional. This picture is confirmed by Figure 5f, in
which it may be seen that 18 is poised between the columnar
and lamellar types. For crystal 21, the volume ratio on the crystal
data places this perforated layer structure near the volume ratio
of the other perforated layer structure, 15. The molecular model
data strongly suggests that this volume ratio is significantly
lower in value; we discuss this point further below.
As a final test, we created de novo models for the molecules
and ions found in each crystal structure. Bond distances are
standard119 and are given in the Supporting Information. sp3,
sp2, and sp sites were assumed to be respectively perfectly
tetrahedral, trigonal planar, and linear. These latter calculations
therefore did not rely on crystal data beyond knowledge of the
unit cell chemical composition. In columns A and D of Table
2, we compare the volume ratios found from both the molecular
models and actual crystal data. We assumed in both cases that
all sp3 carbon atoms adjacent to oxygen atoms are hydrophilic
and the CN-Ag units are hydrophobic. As may be seen, the
volume ratios obtained from molecular composition and crystal
structure are in substantial agreement.
Deviation is greatest for 21. Crystal 21 is in many ways the
weakest crystal solution reported in this paper with an R1 and
wR2 of respectively 15.6 and 36.8%. Several of the outermost
side chain atoms could not be located in the structure, nor with
such large Debye-Waller factors were any solvent molecules
found. Therefore, both exact molecular composition of the unit
cell and locations of the exact oligo(ethylene oxide) side chains
are undetermined. The difference in the two calculations
represents the uncertainty as to the actual hydrophilic-to-
hydrophobic volume ratio.
We now turn to the assignment of structure topology. This
proved to be somewhat difficult. At first, one might think that
we need only examine the surfaces of the two components
derived by the above volume calculations. However, such
surfaces are often very complex. The complexity may be
understood when we recall that the Kitaigorodsky ratio, that is,
the ratio between the portion of the cell occupied by the atoms
and the volume of the unit cell itself, generally lies between 70
and 75%.120 Some quarter of the cell volume belongs neither
to the hydrophobic or hydrophilic portions. It is presumably
this 25% void which greatly adds to the complexity of the
overall surface morphology.
Much more useful has proven to be close contacts between
neighboring atoms. In the case of a columnar structure, the minor
component, which constitutes the columns themselves, should
not have closest contacts between neighboring column atoms.
Similarly, in the lamellar structures neither component should
have close contacts which traverse the complementary layer.
In the perforated layer structure one of the two components
(119) March, J. AdVanced Organic Chemistry, 4th ed.; Wiley: New York,
1992; p 21.
(120) Kitaigorodsky, A. I. Molecular Crystals and Molecules; Academic
Press: Inc.: New York, 1973; pp 18-21.
Figure 5 illustrates nicely the overall evolution of structures.
We have ordered the 12 structures in Figure 5 by their
hydrophobic-to-hydrophilic volume ratios. In Figure 5a the

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8389
Figure 5. Hydrophobic and hydrophilic portions of 9-20. (a) 13. (b) 16. (c) 12. (d) 14. (e) 15. (f) 18. (g) 11. (h) 9. (i) 17. (j) 10. (k) 20. (l) 19.
Structures are ordered in increasing hydrophobicity. Red: hydrophobic, green: hydrophilic, brown: intermediate. See text for definitions of
hydroaffinity.
pseudohexagonal columns of the hydrophobic portion of 13 are
clear. As we increase this volume ratio these columns begin to
approach one another, until by Figure 5, parts e and f, the
perforated layers are evidenced. At higher volume ratios true
layer structures are found until at even higher ratios bicontinuous
structures appear. Taken together one sees isolated hydrophobic
channels grow in size until they become sufficiently large, and
it is the hydrophilic portions which begin to form in more
isolated pockets.
Of particular interest are structures 20 and 21. Unlike the
structures previously discussed, the rigid phenylacetylene
backbones in these crystals arise from 3-fold symmetric planar
groups. In each organic molecule there are three rigid pheny-
lacetylene groups extending out from the central aromatic ring
and each of these three groups is capped with a nitrile group.
We have recently shown that such molecules tend to enforce a
3-fold trigonal planar coordination environment for the silver
ions and that this combination of 3-fold symmetric silver ions
and 3-fold symmetric organic molecules leads to a honeycomb
pattern in which the walls of the channel are derived from a
phenylacetylene-silver network and the interior of the channels
contain cocrystallized solvent molecules. References 24, 25, and
44 contain some 20 examples of this pattern. The distinct
energetic preference is therefore for the columnar-type structure,
where the columns are composed of solvent molecules and the
matrix is the phenylacetylene-silver host.
In 20 and 21 we have further attached six oligo(ethylene
oxide) side chains to the phenylacetylene backbone. In these

8390 J. Am. Chem. Soc., Vol. 122, No. 35, 2000
Xu et al.
compatible. The crystal structure resolves this difference by
forming close contacts between columns. The resultant perfo-
rated columnar structure is therefore bicontinuous, a structure-
type much more compatible with the 40% volume ratio.
Interestingly, the other crystal with an equally high volume ratio,
19, also forms a bicontinuous structure, but here the bicontinuous
domains are based on a lamellar structure in which each layer
type is perforated to allow for close contacts.
For 21 the volume ratio is either 29% (column A, Table 2),
quite near the crossover from the columnar to lamellar structure
type, or 24%> (column D, Table 2), more properly in the
columnar region of structures. The local geometry requirements
of 3-fold coordination planar molecules and 3-fold coordinate
silver ions is not compatible with the columnar structure. 21
forms in the perforated layer structure, a structure expected to
be found near the crossover point.
It is interesting to speculate what would occur if one really
opposed local geometry requirements to overall surface area
issues. We can think of two such limiting cases. If we were to
prepare a linear phenylacetylene nitrile compounds with ex-
tremely long oligo(ethylene oxide) side chains, we could prepare
systems with extremely low volume ratios, but for which the
local π-π stacking forces would favor the continued formation
of π-stacked columns.121 While Figure 4 would suggest the
formation of a spherical structure, there is a good likelihood
that a columnar structure would still be maintained. Similarly,
if side chains of large length are added to the 3-fold symmetric
phenylacetylene nitriles, the volume ratio suggests the formation
of a columnar structure, but the local geometry requirements
could require the continued formation of the perforated layer
structure. Our results for crystal 21 suggest but do not prove
that this local geometry requirement is preeminent.
A study of long-chain aliphatic carboxylic acid structures
shows that in such extreme cases, although the interfacial surface
areas are important, the exact volume percentage ranges shown
in Figure 4 are no longer maintained.122,123 Thus, for long
aliphatic chain carboxylic acids, while the overall interface
between the hydrophilic acid group and the hydrophobic
aliphatic chains are quite flat, presumably due to a minimization
of hydrophilic-to-hydrophobic contact, only lamellar structures
are found. This result appears to be independent of the aliphatic
chain length and hence is independent of the hydrophilic-to-
hydrophobic volume ratio. In these crystals, the energy require-
ment of the perfect interdigitation of the aliphatic chains seems
to prevent the formation of columnar or spherical structures.
Crystal Database. The previously described crystal structures
suggest within the family of phenylacetylene nitrile compounds
with pendant oligo(ethylene oxide) side chains a reasonably
sharp evolution of amphiphilic structure types is observed as a
function of the hydrophilic-to-hydrophobic volume ratios. We
therefore searched the Cambridge Structural Database (CSD)
to see if this evolution of structures was to be found in this
much larger crystal set. In Figure 7 we illustrate the core unit
of our search as well as two illustrative examples of the
molecules uncovered. We considered molecules containing only
carbon, oxygen, and hydrogen atoms and further required that
all sp3 carbon atoms were adjacent to an oxygen atom. None
of the thus revealed structures were phenylacetylene-type
molecules with pendant oligo(ethylene oxide) side chains. In
fact, no pendant side chains were found. Rather the two main
Figure 6. Hydrophobic and hydrophilic portions of 5b‚4AgOTf (21).
(a) View down the [1 0 0] direction. (b) View down the c axis of a
single bilayer perforated by hydrophilic moieties. Red: hydrophilic,
green: hydrophobic, brown: intermediate. See text for definitions of
hydroaffinity.
Table 2. Topologies of Compounds 9-21 under Different
Definitions of Hydrophilicity and Hydrophobicity
Aa
Bb
Cc
Dd
vol ratio
vol ratio
vol ratio
vol ratio
compd (%) topologye (%) topology (%) topology (%)
13
16
12
14
21
15
18
11
9
17
10
20
19
21.0
23.6
26.0
26.9
29.0 PL
30.5 PL
34.3
34.8
34.9
35.9
36.0
C
C
C
C
26.2
30.6
32.8
33.0
34.7 PL
37.9 PL
40.0 PL
44.6
44.3
43.1
45.9
49.1 IC
48.7 BI
C
C
C
C
15.7
17.1
20.4
19.4
25.0 PL
25.2 PL
26.0
29.0
28.4
31.2
29.8
C
C
C
C
20.6
24.9
26.3
26.5
23.5
30.8
33.5
34.9
35.1
37.1
35.3
40.6
40.3
C
L
L
L
L
C
L
L
L
L
L
L
L
L
39.7 BI
41.0 BI
35.3 BI
35.6 BI
a sp3 carbon atoms next to aromatics: hydrophilic; CN-Ag units:
hydrophobic; data: crystal structure. b sp3 carbons next to aromatics:
hydrophobic; CN-Ag units: hydrophobic; data: crystal structure. c sp3
carbons next to aromatics: hydrophilic; CN-Ag units: intermediate;
data: crystal structure. d sp3 carbon atoms next to aromatics: hydro-
philic; CN-Ag units: hydrophobic; data: molecular model. e Closest
contacts are set at 1.15 times the sum of van der Waals radii. C: column,
PL: perforated layer, L: layer, BI: bicontinuous, IC: inverse column.
systems we are therefore able to partially control the amount
of material outside the original honeycomb phenylacetylene
matrix. For 20, the honeycomb structure is sufficiently capacious
to allow all the mono(ethylene oxide) side chains to lie within
the channels. Hence, the original solvent-based columnar
structure is retained. For 21, the tri(ethylene oxide) side chains
are too large and the honeycomb channels split apart into bilayer
hexagonal sheets with the excess side chain molecules filling
the layer between these sheets. In Figures 2 and 6 we show
views of the bilayers for both 20 and 21. The side chains are
safely contained within the channel in 20 but are excessively
large for 21. Structures 20 and 21 are thus crystals where the
trigonal planar nature of both the ligands and metal ions highly
restrict the possible crystalline topologies. It is therefore unclear
whether these structures will conform to the interfacial model
described above.
(121) Shetty, A. S.; Zhang, J. S.; Moore, J. S. J. Am. Chem. Soc. 1996,
118, 1019.
(122) Abrahamsson, S.; Lunde´n, B. M. Acta Crystallogr., Sect. B 1972,
28, 2562.
In 20 the volume ratio in column A of Table 2 is 40%. The
local geometry requirements point to a hexagonal columnar
structure with hydrophilic regions separated by a hydrophobic
matrix. As Figure 4 shows these two requirements do not seem
(123) Taga, T.; Miyasaka, T. Acta Crystallogr., Sect. C 1987, 43, 748.

Crystal Topology as a Function of Volume Ratios
J. Am. Chem. Soc., Vol. 122, No. 35, 2000 8391
outlined in the previous section and use the criterion of 1.3 times
the sum of the van der Waals radii as a close contact. Again
only 10-15% of the structures change their classification in
changing this value from 1.3 to 1.15.
As Table 3 shows, there is a clear evolution of structure types
as one traverses the possible values of volume ratios. Further-
more, the results of Table 3 are in substantial agreement with
the qualitative picture presented in Figure 4. The progression
of structures proceeds from spherical to columnar, perforated
lamellar, lamellar, bicontinuous, inverse perforated lamellar,
inverse columnar. and finally inverse spherical. One distinction
between the results in Table 3 and Figure 4 are for the
bicontinuous phases. While in Figure 4 the bicontinuous phase
is found at lower volume ratios than the lamellar phase, in Table
3 these two phases occupy the same general volume ratio region.
This result may be understood if we note that both the
bicontinuous and lamellar structure types are self-complemen-
tary, that is to say that the regions of space occupied by the
hydrophobic and hydrophilic components are topologically
similar. Therefore, unlike the perforated layer and inverse
perforated layer structures, the bicontinuous structures which
flank the lamellar phase in Figure 4 are actually in the same
topological family and not two different families. With the
broadening of the boundaries, as is found in Table 3, these two
groups diffuse into one another, causing the bicontinuous phases
to be found at volume ratios such as those of the authentic layer
phases.
Taken together these crystal structures show that hydrophilic-
to-hydrophobic volume ratios are a significant factor in the final
crystal structure adopted. There are, of course, a number of other
important variables. For example, as Table 3 shows, there is
one columnar structure where the volume ratio is less than 10%.
We might have supposed that only spherical structures would
have been found at such low ratios. An examination of this
structure, which is shown in the Supporting Information, shows
that the columns in question are π-π stacks of parallel aromatic
rings. Thus, the energetic stability of such stacks outweighs the
minimization of hydrophobic-to-hydrophilic contact.
Figure 7. Representative molecules from CSD search. Top: tranal10,
a functionalized sugar molecule; bottom: cenpam, a crown ether. Bold
lines represent the CSD search fragment.
Table 3. Correlation between Structure Types and
Hydrophobic-to-Hydrophilic Volume Ratiosa
hydrophobic-to-hydrophilic
volume ratios (%)
S
C
PL BI
L
IPL IC IS
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
-
-
2
-
-
-
-
-
-
1
1
8
-
-
1
-
-
-
2
-
-
-
3
5
1
-
-
-
-
-
-
-
-
3
1
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
1
9
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
a Structural classification is based on closest contacts defined as less
than 1.3 times the sum of the van der Waals radii. S: sphere, C:
column, PL: perforated layer, BI: bicontinuous, L: layer, IPL: inverse
perforated layer, IC: inverse column, IS: inverse sphere.
types found were either crown ether or sugar molecules to which
aromatic groups have been attached. Although these molecules
therefore contain certain common features with the crystals
previous described in this paper, they are sufficiently different
to test the extrapolative ability of the overall amphiphilic phase
diagram shown in Figure 4. It is therefore gratifying to see that
of the 38 structures found all but three were of spherical,
columnar, perforated lamellar, lamellar, or bicontinuous types.
Of the three exceptions, one structure has overly large voids,
suggesting that solvent molecules have not been located, a
second by inspection clearly appears to be bicontinuous, and
only the last structure fundamentally does not correspond to
the previously discussed topological types.
If we are to use volume ratios as an aid in the prediction of
desired structural topologies, it therefore appears wisest to
consider those fortunate compounds where both surface effects
and local geometry predispose the molecules to pack in one
unique and obvious manner. It is our belief in such cases that
the judicious use of the generic amphiphilic phase diagram and
the concomitant restriction to synthetic targets of columnar,
lamellar, perforated lamellar, or bicontinuous structure type can
be an aid in translating molecular structure to crystal structure.
We show these molecules and their corresponding crystal
structures in the Supporting Information. The compounds are
classified as spherical, columnar, perforated lamellar, lamellar,
bicontinuous, inverse perforated lamellar, inverse columnar, and
inverse spherical. In the latter three structures, the minor
component is hydrophilic, and the major component is hydro-
phobic. We used the same criterion as described in the previous
section to assign volume ratios and structure types. In particular,
we considered all aliphatic carbon atoms bonded to oxygen
atoms to be hydrophilic. In Table 3, we divide the structures
by types and volume ratios. Included in Table 3 are the 13
crystal structures reported in this paper. For the sake of
simplicity we report volume ratios for only one set of criteria.
We assume that all sp3 carbon atoms bonded to oxygen atoms
are hydrophilic. For structure type assignment we use the method
Acknowledgment. This work was supported by the National
Science Foundation (Grant DMR-9812351). We thank Ms.
Susan Wilson for assisting in the calculation of volume ratios.
Supporting Information Available: Figures of the mol-
ecules from CSD search and their corresponding crystal
structures; tables of crystal refinement data, bond distances, bond
angles, anisotropic thermal factors for compounds 9-21 and
van der Waals radii and bond lengths used in molecular
modeling. Experimental and calculated powder diffraction data
for the crystalline compounds (PDF). This material is available
free of charge via the Internet at http://pubs.acs.org.
JA0006651