Structural and thermodynamic characterization of polyphenylbenzenes

Article abstract of DOI:10.1021/jp207593s

The thermodynamic and structural study of a series of polyphenylbenzenes, from benzene, n(Ph) = 0, to hexaphenylbenzene, n(Ph) = 6, is presented. The available literature data for this group of compounds was extended by the determination of the relevant thermodynamic properties for 1,2,4- triphenylbenzene, 1,2,4,5-tetraphenylbenzene, and hexaphenylbenzene, as well as structural determination by X-ray crystallography for some of the studied compounds. Gas phase energetics in this class of compounds was analyzed from the derived standard molar enthalpies of formation in the gaseous phase. The torsional profiles relative to the phenyl-phenyl hindered rotations in some selected polyphenylbenzenes, as well as the gas phase structures and energetics, were derived from quantum chemical calculations. In the ideal gas phase, a significant enthalpic destabilization was observed in hexaphenylbenzene relative to the other polyphenylbenzenes, due to steric crowding between the six phenyl substituents. A relatively low enthalpy of sublimation was observed for hexaphenylbenzene, in agreement with the decreased surface area able to establish intermolecular interactions. The apparently anomalous low entropy of sublimation observed for hexaphenylbenzene is explained by its high molecular symmetry and the six highly hindered phenyl internal rotations. For the series of polyphenylbenzenes considered, it was shown that the differentiation in the entropy of sublimation can be chiefly ascribed to the torsional freedom of the phenyl substituents in the gas phase and the entropy terms related with molecular symmetry.

Full text of DOI:10.1021/jp207593s

ARTICLE
pubs.acs.org/JPCA
Structural and Thermodynamic Characterization of
Polyphenylbenzenes
†
†
‡
‡,§
||
Carlos F. R. A. C. Lima, Marisa A. A. Rocha, Andr ꢀe Melo, Lígia R. Gomes, John N. Low, and
,
†
Luís M. N. B. F. Santos*
†
Centro de Investiga c- ~a o em Química, Departamento de Química e Bioquímica, Faculdade de Ci ^e ncias da Universidade do Porto,
P-4169-007 Porto, Portugal
‡
REQUIMTE - Departamento de Química e Bioquímica, Faculdade de Ci ^e ncias, Universidade do Porto, Rua do Campo Alegre,
P-4169-007, Porto, Portugal
§
CIAGEB - Faculdade de Ci ^e ncias da Sa ꢀu de, Escola Superior de Sa ꢀu de da UFP, Universidade Fernando Pessoa, P-4200-150 Porto,
Portugal
Department of Chemistry, University of Aberdeen, Meston Walk, Old Aberdeen, AB24 3UE, Scotland
S Supporting Information
b
ABSTRACT: The thermodynamic and structural study of a
series of polyphenylbenzenes, from benzene, n(Ph) = 0, to
hexaphenylbenzene, n(Ph) = 6, is presented. The available
literature data for this group of compounds was extended by
the determination of the relevant thermodynamic properties for
1
,2,4-triphenylbenzene, 1,2,4,5-tetraphenylbenzene, and hexa-
phenylbenzene, as well as structural determination by X-ray
crystallography for some of the studied compounds. Gas phase
energetics in this class of compounds was analyzed from the
derived standard molar enthalpies of formation in the gaseous
phase. The torsional profiles relative to the phenylꢀphenyl
hindered rotations in some selected polyphenylbenzenes, as well as the gas phase structures and energetics, were derived from
quantum chemical calculations. In the ideal gas phase, a significant enthalpic destabilization was observed in hexaphenylbenzene
relative to the other polyphenylbenzenes, due to steric crowding between the six phenyl substituents. A relatively low enthalpy of
sublimation was observed for hexaphenylbenzene, in agreement with the decreased surface area able to establish intermolecular
interactions. The apparently anomalous low entropy of sublimation observed for hexaphenylbenzene is explained by its high
molecular symmetry and the six highly hindered phenyl internal rotations. For the series of polyphenylbenzenes considered, it was
shown that the differentiation in the entropy of sublimation can be chiefly ascribed to the torsional freedom of the phenyl
substituents in the gas phase and the entropy terms related with molecular symmetry.
1
. INTRODUCTION
these molecules, make dispersive interactions the more promi-
nent ones in inter and intramolecular contacts. van der Waals
interactions are the main component of the so-called aromatic
Polyphenylbenzenes are benzene derivatives with the general
formula presented in Figure 1. The phenyl substituents may have
other groups attached to them and are distributed around a
central benzene ring. In this work, polyphenylbenzenes bearing
simple phenyl substituents, from benzene, n(Ph) = 0, to hex-
aphenylbenzene, n(Ph) = 6, are considered.
10,11
interactions,
which also include a significant electrostatic
contribution that confers some orientational preferences to
aromatic complexes. Hence, these types of interactions can have
a noticeable influence on the structure and stability of aromatic
compounds, as for example polyphenylbenzenes.
The way phenyl substituents are distributed around the central
benzene ring can induce some interesting structural changes at
the supramolecular and molecular levels. These changes are
reflected in thermodynamic differentiation, which can be easily
perceived in the sublimation equilibrium and in gas phase
Polyphenylbenzenes possess the ability to form conducting
1
,2
polymers and have some applications in the fields of organic
light emitting diodes (OLEDs) and nonlinear optical devices,
field-effect transistors, ultraviolet organic lasers, catalysis, and
enzyme simulation among others. Some polyphenylbenzene
derivatives have biological activities, behaving as immune sup-
pressants, antioxidants, antithrombosis, and anticoagulants.
3,4
5
6,7
8
9
The atomic constitution of polyphenylbenzenes (only H and
C) precludes the establishment of significant bond dipoles and
local charge build ups. This fact, together with the relative size of
Received: August 8, 2011
Revised:
September 11, 2011
Published: September 13, 2011
r 2011 American Chemical Society
11876
dx.doi.org/10.1021/jp207593s
|J. Phys. Chem. A 2011, 115, 11876–11888

The Journal of Physical Chemistry A
ARTICLE
sublimed under reduced pressure. The compounds 1,2,4-triphe-
nylbenzene and 1,2,4,5-tetraphenylbenzene were synthesized by
12,13
the Suzuki-Miyaura cross-coupling methodology.
1
,2,4-Triphenylbenzene. A 150 mL solution of K CO (120
2
3
mmol) in water was added to a solution of 1,2,4-tribromoben-
zene (15 mmol), phenylboronic acid (100 mmol), and palladium
acetate (2 mol %) in 150 mL of DMF. The resultant solution was
stirred at 90 ꢀC for 9 h. The crude product was extracted with
ethyl acetate. The organic phase was washed with water and
NaOH(aq) 1 M and evaporated yielding a brown oil. A white
solid began to precipitate with the addition of a few drops of
ethanol (yield (%) = 81) The compound was purified by
recrystallization with hexane and dichloromethane, and by sub-
limation under reduced pressure (mp = 118.8ꢀ120.4 ꢀC).
Figure 1. Schematic structure of the polyphenylbenzenes considered in
this work (n = 0ꢀ6).
1
,2,4,5-Tetraphenylbenzene. A 160 mL solution of K CO
2 3
(
5
140 mmol) in water was added to a solution of 1,2,4,
-tetrabromobenzene (15 mmol), phenylboronic acid (120 mmol),
and palladium acetate (2 mol %) in 180 mL of DMF. The
resultant solution was stirred at 90 ꢀC for 9 h. The crude product
was extracted with hot toluene and filtered over Celite. The
resulting organic phase was washed with water and NaOH(aq)
Figure 2. Schematic structure of the compounds studied in this work.
From left to right: 1,2,4-triphenylbenzene (124tPhB), 1,2,4,5-tetraphe-
nylbenzene (1245TPhB), and hexaphenylbenzene (HPhB).
1
M, and evaporated. The resulting precipitate was washed with
energetics. In this work, special emphasis is given to the
energetic/structural relationships in this family of compounds,
focusing essentially in thermodynamic and X-ray crystallographic
data. In this way, the literature data on polyphenylbenzenes was
enriched by the measurement of the solid phase standard molar
ether and filtered yielding a white solid (yield (%) = 82). The
compound was washed with boiling methanol and purified by
1
sublimation under reduced pressure (mp = 272.8ꢀ274.3 ꢀC). H
NMR (300 MHz, CDCl , 300 K, TMS): δ = 6.98 (s, 2H), δ =
3
6.96 (m, 20 H).
o
enthalpies of formation, Δ H (cr), by combustion calorimetry,
The identity of 124tPhB and 1245TPhB was confirmed by the
X-ray crystal structures obtained and the purity of all the three
compounds checked by gas chromatography, using an HP 4890
apparatus equipped with an HP-5 column, cross-linked, 5%
diphenyl and 95% dimethylpolysiloxane, showing a %(m/m)
purity greater than 99.9% in all cases.
f
m
g
cr
o
m
and the derivation of the standard molar enthalpies, Δ H , and
entropies, Δ S , of sublimation by a Knudsen/quartz crystal
g o
cr m
effusion technique, for the three polyphenylbenzenes illustrated
in Figure 2. Gas phase standard molar enthalpies of formation,
o
m
Δ H (g), were derived by the combination of the previous
f
results. X-ray crystallography was used to determine molecular
structure in the solid phase, whereas quantum chemistry was
employed for the derivation of gas phase geometries, torsional
profiles, and thermodynamic properties. In conjuction with the
relevant literature data on this subject, a comprehensive thermo-
dynamic and structural characterization of polyphenylbenzenes was
made, emphasizing the observed structural/energetic relationships,
and the origins of enthalpic and entropic differentiation.
The polyphenylbenzenes considered in this study are abbreviated
as follows: ortho-terphenyl, o-dPhB; meta-terphenyl, m-dPhB; para-
terphenyl, p-dPhB; 1,2,3-triphenylbenzene, 123tPhB; 1,2,4-triphe-
nylbenzene, 124tPhB; 1,3,5-triphenylbenzene, 135tPhB; 1,2,4,
2.2. Crystallographic Measurements. Crystal data, data
acquisition conditions, and refinement parameters for 124tPhB
and 1245TPhB are listed in the Supporting Information. Crystals
of 124tPhB and 1245TPhB suitable for X-ray diffraction were
obtained by slow evaporation from hexane and CH Cl solu-
2
2
tions, respectively. The intensity data was collected in a Bruker-
Nonius CCD diffractometer. Data collection, cell refinement,
and data reduction were made with the software package of the
1
4
14
diffractometer: SMART for data collection and SAINT for
cell refinement and for data reduction. Absorption correction
15
was performed with SADABS. The structures were solved and
refined using the software: OSCAIL and SHELXL97. Mo-
lecular graphics were produced by ORTEPIII and PLATON.
16
17
18
19
5
-tetraphenylbenzene, 1245TPhB; and hexaphenylbenzene, HPhB.
The properties of most chemical systems are a result of an
The complete set of structural parameters in CIF format is
available as an Electronic Supplementary Publication from the Cam-
bridge Crystallographic Data Centre (CCDC 736467 and 703163).
124tPhB crystallized in the orthorhombic system; space group
Pbca from the systematic absences. 1245TPhB crystallized in the
triclinic system; space group P-1 assumed and confirmed by the
analysis. The H atoms were treated as riding atoms with CꢀH-
(aromatic) = 0.95 Å with U (H) = 1.2U (C).
entangled ensemble of physicalꢀchemical effects that are hard to
isolate and quantify individually. However, the nature and
behavior of relatively simple chemical systems, like the poly-
phenylbenzenes studied in this work, are governed by a limited
number of those effects, making their proper isolation, charac-
terization, and quantification easier. Therefore, the systematic
study of simple and interrelated compounds becomes of funda-
mental importance for the exploration and consolidation of
chemical trends and laws.
iso
eq
2.3. Combustion Calorimetry. 1,2,4,5-Tetraphenylbenzene.
The standard molar enthalpy of combustion, Δ H , at T =
o
m
c
2
98.15 K, was measured in an isoperibol static bomb combustion
calorimeter with a twin valve bomb of internal volume of 0.290
dm , formerly used at the National Physical Laboratory, Ted-
2. EXPERIMENTAL SECTION
3
2
.1. Synthesis, Purification, and Characterization of the
dington, U. K., and was used mainly as previously described,
Studied Compounds. Hexaphenylbenzene was commercially
obtained from Sigma-Aldrich, washed with boiling acetone, and
although a few changes in technique, due to different auxiliary
20,21
equipment, were applied.
1
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dx.doi.org/10.1021/jp207593s |J. Phys. Chem. A 2011, 115, 11876–11888

The Journal of Physical Chemistry A
ARTICLE
Samples in pellet form were weighed in an analytical balance
of 298.420 ( 0.001 K by a TRONAC temperature controller,
model PTC-40. For data acquisition, a 6 1/2 digits multimeter
(Keithley, model 2000) interfaced to a PC was used to measure
the resistance of the thermistor every 10 s, in four-wire measure-
ment mode. The charging, firing circuit, and voltage measurement
across the 2000 μF discharger condenser are done automatically
by means of a set of Advantech acquisition/automation modulus,
series 4000. Real time recording and displaying of data is
with a resolution of 0.01 mg and ignited in oxygen at a pressure of
3
3
.04 MPa, with a volume of 1.00 cm of water added to the bomb.
From a weighed acrylic vessel, water was added to the calori-
meter, and for each experiment a correction to the energy
equivalent for the deviation from 2900.0 g of the mass of water
added has been taken into account. Calorimetric temperatures
ꢀ
5
were measured with a resolution of 1 ꢁ 10 K with an S10 four
wire calibrated ultrastable thermistor (Thermometrics, standard
serial No. 1030) and recorded by a 7 1/2 digits nano-ohm meter
2
2
achieved with a modified version of the LABTERMO software.
ꢀ
1
The energy equivalent of the calorimeter, ε(calor)/J K
=
(
Hewlett-Packard model 34420A), interfaced to a PC type
1945.77 ( 0.08 (0.004%), was obtained from a total of 36
calibration experiments, made with benzoic acid (Calorimetric
Standard NIST 39j).
22
computer, using the program LABTERMO v3.0. Temperature
measurements were automatically collected every 10 s and the initial
temperature of the combustion experiments was very close to
The amount of carbon soot, when formed, is determined
gravimetrically, and this is considered for the total energy
involved in the combustion process based on the value of
2
98.15 K.
The energy equivalent of the calorimeter was determined from
0
ꢀ1 23
the combustion of benzoic acid (Calorimetric Standard NIST 39j),
having a massic energy of combustion under bomb conditions of
Δ u (C) = ꢀ33 kJ g
. The densities of 124tPhB, 1245TPhB,
c
and HPhB were taken from the crystallographic data presented in
this work as 1.21, 1.25, and 1.17 g cm , respectively. The values
ꢀ
1
23
ꢀ3
ꢀ
(26434.0 ( 3.0) J g , as previously described. The electrical
ꢀ
1
energy for the ignition was determined from the change in the
potential difference across a 1400 μF condenser on discharge
through a platinum ignition wire. For the cotton thread fuse
of (∂u/∂p) at T = 298.15 K, were assumed to be ꢀ0.2 J g
T
ꢀ
1 27,28
MPa
.
The corresponding energetic correction usually
leads to insignificant errors in the final combustion results.
(
empirical formula CH1 O0.843), the massic energy of com-
Standard state corrections were calculated for the initial and
.686
0
ꢀ1 24
29
bustion is assigned to Δ u = ꢀ16240 J g
.
Corrections for
final states by the procedures given by Hubbard et al. and by
c
ꢀ
1
30
nitric acid formation were based on ꢀ59.7 kJ mol for the molar
Good and Scott. The relative atomic masses used were those
ꢀ
3
31
energy of formation of 0.1 mol dm HNO (aq) from O (g),
recommended by the IUPAC Commission in 2005.
3
2
25
N (g), and H O(l). The amount of nitric acid was determined
by titration against NaOH. During the combustion experiments,
the sample purity, as well as combustion completeness was
supported by a CO recovery analysis. From 16 calibration
experiments, the energy equivalent of the calorimeter, ε(calor)/
2.4. Knudsen/Quartz Crystal Effusion. The vapor pressures
of the three studied compounds as a function of temperature
were measured by the combined Knudsen/quartz crystal effusion
2
2
32
apparatus recently developed in our laboratory. This technique
is based on the simultaneous gravimetric and quartz crystal
microbalance mass loss detection, enabling the use of a tempera-
ture-step methodology, and having the advantages of smaller
sample sizes and effusion times and the possibility of achieving
temperatures up to 650 K. For the measurement of pressures
lower than 0.1 Pa a flow-concentrator device, placed between the
oven and the quartz crystal, was used. Like a typical Knudsen
effusion experiment, the system is kept at high vacuum, enabling
free effusion of the vapor from the cell, and the oven is kept at a
fixed temperature, T. During the effusion experiment, the rate of
mass loss from the Knudsen effusion cell, dm(cell)/dt, is
proportional to the rate of change of the mass deposited in the
quartz crystal, dm/dt, as shown by eq 1
2
ꢀ1
(
J K ), was found to be {15546.3 ( 1.8 (0.012%)} for an
average mass of water added to the calorimeter of 2900.0 g; the
quoted uncertainty refers to the standard deviation of the mean.
1
,2,4-Triphenylbenzene and Hexaphenylbenzene. The stan-
o
dard molar enthalpies of combustion, Δ H , at T = 298.15 K,
were measured in an isoperibol mini-bomb combustion calorimeter.
The mini-bomb is made of stainless steel with 0.46 cm wall
thickness and 18.185 cm of internal volume. The internal fittings
located on the head of the mini-bomb (electrodes, crucible
support and sheet) are all made of platinum.
The samples were pressed in the form of pellets and placed in
the platinum crucible, and their apparent mass weighed on a
Mettler Toledo, model UMT2, microbalance with a sensitivity of
c
m
26
3
ꢀ
7
dmðcellÞ
dt
dm
dt
Aq df
(
10 g. The electrical discharge for the ignition was made via a
¼
g
¼ g
ð1Þ
Sq dt
2
0
cm long platinum wire (Goodfellow, mass fraction 0.999, Φ =
.080 mm) tied in both electrodes terminals and bent down to a
where g is a geometric factor of the mass detection, A is the area
q
“
V” shape toward the pellets. A platinum sheet with an inverted U
of the quartz crystal, S is the mass sensitivity of the crystal, and
q
shape was placed above the crucible assembly to concentrate the
heat, thus helping to prevent the formation of carbon residues.
Ultrapure water (0.050 cm ) was added to the bomb before
adjusting the head with an O-ring to the body of the mini-bomb
by means of a retaining screw-ring. The bomb was purged four
times and filled with ultrapure oxygen up to a pressure of 3.04
MPa. The bomb was then placed in its support, equipped with an
electrical contact for electrical discharge, and introduced into the
cylindrical copper block, which contains a bean type thermistor
df/dt is the rate of change of the resonance frequency of the
quartz crystal. Taking W = ꢀS /(A g), where W is defined as the
3
q
q
effective mass sensitivity coefficient, eq 1 becomes
df
dt
dmðcellÞ
dt
¼ ꢀ W
ð2Þ
To derive the vapor pressure, p, the value of W must be known
for each compound. This value can be determined by weighing
the total mass loss of the Knudsen cell, Δm(cell), during an
independent experiment, and using eq 3
(
R = 4 kΩ, at T = 298.15 K) for temperature measurement.
Helium (mass fraction 0.9999) was used to fill the block up to 0.2
MPa, after purging, in order to improve heat conduction between
the bomb and the block. The calorimetric system is surrounded
by a thermostatic water bath, maintained at a constant temperature
Δf
W ¼ ꢀ
ð3Þ
ΔmðcellÞ
1
1878
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The Journal of Physical Chemistry A
ARTICLE
where Δf is the total change in the crystal’s resonance frequency
in the whole experiment. The vapor pressures at each tempera-
ture are therefore obtained from eq 4
ꢀ
ꢁ
1
=2
df
1
2πRT
p ¼ ꢀ
ð4Þ
dt woAoW MM
where M is the molar mass of the effusing vapor, R is the gas
M
constant, A is the area of the effusion orifice, and w is the
o
o
transmission probability factor, which is usually calculated by means
of eq 5, where l is the length of the effusion orifice and r its radius
wo ¼ f1 þ ð3l=8rÞgꢀ
1
ð5Þ
In this technique only one effusion cell is used, with l = 0.0125
2
mm and r = 0.500 mm, giving A = 0.7854 mm and w = 0.9907.
Figure 3. View of 124tPhB with our numbering scheme. Displacement
o
o
2
.5. Calvet Microcalorimetry. The enthalpy change due to
ellipsoids are drawn at the 30% probability level.
the heating of the sample in the crystalline phase from T = 298.15
o
o
K to the temperature T, {H (cr, T) ꢀ H (cr, 298.15 K)} was
m
m
measured for each compound using a similar methodology to
that described by Bernardes et al. The values of Δ
33
T
o
H (cr)
2
98.15K
m
were determined for 124tPhB, 1245TPhB, and HPhB, using a
high temperature Calvet microcalorimeter, SETARAM model
34
HT1000D, described in the literature. Samples of about 4ꢀ6
mg each were placed into thin capillary tubes, sealed at one end,
and dropped simultaneously with the corresponding blank tube,
at room temperature (T = 298.15 K), into the hot reaction zone
of the calorimeter, at a fixed temperature, T.
From the previous results, the standard molar heat capacities of
o
p,m
the crystalline phase, C (T , cr) were derived for each compound,
m
where Tm is the mean temperature between 298.15 K and the
calorimeter hot zone temperature, T, which was very close to the
mean temperature of the corresponding sublimation experiments,
carried out in the Knudsen/quartz crystal apparatus. The micro-
calorimeter was calibrated with anthrancene at the respective tem-
perature of the experiments for 124tPhB and with sapphire at the
respective temperature of the experiments for 1245TPhB and HPhB.
Figure 4. View of 1245TPhB with our numbering scheme. Displace-
ment ellipsoids are drawn at the 30% probability level.
3. RESULTS
The calibration constants were found to be k(anthrancene, T =
3.1. Structural Characterization. The X-ray structure deter-
m
3
31.8 K) = 0.9849 ( 0.0071, k(sapphire, T = 372.6 K) = 1.0099 (
mination for 124tPhB and 1245TPhB confirmed the expected
molecular structures. A search made in the literature revealed
41
m
0.0007, and k(sapphire, T = 399.6 K) = 1.0068 ( 0.0064.
m
40
2
.6. Computational Details. All theoretical calculations were
that the crystalline structures for 1245TPhB, and for HPhB
35
performed using the Gaussian 03 software package. The full
geometry optimizations were performed using the M €o ller-Ples-
set perturbation theory with a second order perturbation (MP2)
and the correlation consistent basis set cc-pVDZ, and density
functional theory (DFT) with the hybrid exchange correlation
functional (B3LYP) and the 6-311++G(d,p) basis set. The spin-
component-scaled MP2 approach (SCS-MP2) was also used
for the calculation of electronic energies. The B3LYP/6-311+
+
frequencies calculations. The torsional potential profiles respect-
ing the phenylꢀphenyl (Ph-Ph) internal rotation in ortho-
terphenyl (σ = 2) and para-terphenyl (σ = 2) were calculated
at the MP2/cc-pVDZ level of theory, with full optimization of the
remaining hyperspace potential. The contributions of these
hindered rotors to S (g) were estimated by a 1D hindered rotor
analysis using the formalism introduced by Broadbelt and co-
have been previously determined. Nevertheless the details of
molecular conformation and supramolecular structures for these
molecules were not presented by their authors, and so they will
be discussed here. The molecular structure for 124tPhB is shown
in Figure 3. The present data for 1245TPhB compares well with
40
that of the structure previously published which was collected
at 93 K in spite of the fact that the present structure determina-
tion has a data completeness of 87% at θ = 25ꢀ. The molecular
structure for 1245TPhB is shown in Figure 4. The main bond
lengths for the compounds are within the expected range for
polyaromatics. The distances found for CꢀC bonds of the
phenyl rings show values within the typical range of 1.384(13)
corresponding to the mean value for the CarꢀCar bond in
36
G(d,p) and MP2/cc-pVDZ levels of theory were used for
int
int
42
aromatic compounds. Nevertheless, a systematic elongation
of the CarꢀCar bonds on the central ring, which is more
pronounced in HPhB, is observed. The dihedral angles between
the mean planes of each of the phenyl rings with respect to the
mean plane of the central benzene ring differ significantly
between the studied compounds. The list of those angles is
presented in Table 1.
0
37ꢀ39
workers and the program CALCTHERM.
In this context
the torsional potentials were fitted by a Fourier series, the
hindered rotor Schr €o dinger equation solved numerically, and
the thermodynamic quantities calculated accordingly.
1
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The Journal of Physical Chemistry A
ARTICLE
Table 1. Dihedral Angles (ꢀ) between Mean Planes of Central
Ring and Attached Rings
dihedral angles/ꢀ
a
c
attachment atom position
124tPhB
1245TPhB
HPhB
b
C1
C2
C3
C4
C5
50.66(5)
47.78(4)
40.50(12)
65.96(12)
88.59(10)
75.53(10)
87.95(12)
82.17(11)
65.14(10)
76.50(10)
b
42.03(5)
40.50(12)
65.96(12)
C6
a
b
In the central ring. For 1245TPhB C1 and C2 are centrosymetrically
related to C4 and C5. The corresponding values in ref 40 are
9.97(14)ꢀ and 66.01(14)ꢀ.
c
3
Figure 5. View of the supramolecular structure of 124tPhB, showing
Table 2. Intermolecular Interactions (Å, ꢀ) in the Studied
a
the CꢀH π intermolecular interactions. Hydrogen atoms not in-
Compounds
3 3 3
volved in the motifs are not included.
compound
DꢀH 3 3 3
A
H
A
D
A
DꢀA 3 3 3
A
3 3 3
3 3 3
the calorimetric fluid is helium instead of water. The meaning
of all of the terms presented in eq 6 is explained in the
Supporting Information. The products of combustion in the
experiments consist of a gaseous phase and an aqueous
i
124tPhB
C(22)ꢀH(22) 3 π(1)
2.86 3.5378(10)
2.90 3.7165(10)
2.98 3.6653(10)
2.78 3.636(3)
2.85 3.782(3)
2.80 3.699(3)
129
145
130
150
166
157
3 3
ii
C(43)ꢀH(43) π(11)
3
3 3
iii
C(46)ꢀH(46) π(11)
3
3 3
iv
1
245TPhB C(14)ꢀH(14) π(31)
3
3 3
mixture for which the thermodynamic properties are known.
b
v
o
HPhB
C(13)ꢀH(13) π(1)
The values of Δ u refer to the reactions represented by
3
3 3
c
vi
C(43)ꢀH(43) π(1)
eqs 7ꢀ9, for 124tPhB, 1245TPhB, and HPhB, respectively
3
3 3
a
π(31) is the centroid of the C31ꢀC36 ring, π(1) is the centroid of the
C24H18ðcrÞ þ 57=2O2ðgÞ f 24CO2ðgÞ þ 9H2OðlÞ
C1ꢀC6 ring, and π(11) is the centroid of the C11ꢀC16 ring. Symmetry
codes: i = 1 ꢀ x, 1 ꢀ y, 1 ꢀ z; ii = 3/2 ꢀ x, 1 ꢀ y, ꢀ1/2 + z; iii = 3/2 ꢀ x,
ð7Þ
ꢀ
1/2 + y, z; iv = 1 ꢀ x, ꢀy, 1 ꢀ z; v = 1/2 + x, 3/2 ꢀ y, z; vi = ꢀ1/2 + x,
b
1
/2 ꢀ y, z. Atom labels corresponding to our numbering scheme.
C H ðcrÞ þ 71=2O ðgÞ f 30CO ðgÞ þ 11H OðlÞ
3
0
22
2
2
2
Most phenyl dihedral angles in HPhB are at least 10ꢀ higher
ð8Þ
ð9Þ
than those in 124tPhB and 1245TPhB. This can result from the
steric hindrance imposed by neighboring substituents. It is
interesting to note that, in each structure, the rings exhibiting
C H ðcrÞ þ 99=2O ðgÞ f 42CO ðgÞ þ 15H OðlÞ
4
2
30
2
2
2
lower dihedral angles are those participating in the CꢀH
π
3
3 3
o
interactions involved in the supramolecular structures. These
Table 3 lists the set of individual Δ u values obtained for each
c
o
supramolecular structures are stabilized by weak CꢀH
π
studied compound, as well as the mean Δ u and corresponding
3
3 3
c
interactions: three in 124tPhB and two in 1245TPhB and HPhB.
Their geometric parameters are summarized in Table 2 and the
interactions are depicted in Figures 5ꢀ7.
standard deviation of the mean. Table 4 lists the derived standard
0
molar energies of combustion, Δ U (cr), the standard molar
c
m
0
enthalpies of combustion, Δ H (cr), and the standard molar
enthalpies of formation, Δ H (cr), of the crystalline solids. In
c
m
0
f m
3
.2. Combustion Calorimetry. The detailed results for com-
bustion calorimetry are presented in Supporting Information.
The internal energy for the isothermal bomb process, ΔUIBP, was
calculated according to eq 6
accordance with the normal thermochemical practice, the un-
0 0
certainties assigned to Δ H (cr) and Δ H (cr) are twice the
c
m
f m
overall standard deviation of the mean and include the uncer-
tainties in calibration and in the auxiliary quantities used. To
0
f m c m
0
ΔUIBP ¼ ꢀ fεðcalorÞ
þ cpðH2O, lÞΔmðH2OÞgΔTad
þ ðTi ꢀ 298:15Þεi
derive Δ H (cr) from Δ H (cr), the standard molar enthalpies
of formation of H O(l) and CO (g) at T = 298.15 K, ꢀ285.830 (
2
2
ꢀ
1
43
0.042 and ꢀ393.51 ( 0.13 kJ mol , respectively, were used.
.3. Knudsen/Quartz Crystal Effusion. For the three com-
pounds considered in this work, the standard molar enthalpies,
3
þ ð298:15 ꢀ Ti ꢀ ΔTadÞεf ꢀ ΔUðignÞ
ð6Þ
g
cr
o
m
g o
cr m
Δ H , and entropies, Δ S , of sublimation at the mean
where Δm(H O) is the deviation of the mass added to the
2
temperature, ÆTæ, of the sublimation experiments were derived
using the integrated form of the ClausiusꢀClapeyron equation
calorimeter from 2900.0 g, the mass assigned to ε(calor), and
ΔTad is the calorimeter adiabatic temperature change cor-
rected for the heat exchange and the work of stirring,
calculated with the LABTERMO program using the Re-
gnaultꢀPfaundler method, and applying a second order
fitting for the initial and final periods, as reported by Santos
ln p ¼ a ꢀ b=T
where a is a constant and b = Δ H (ÆTæ)/R. Figure 8 presents a
comparative plot of ln p = f (1/T) for the three studied
ð10Þ
g
cr
m
2
2
et al. For the mini-bomb calorimeter Δm(H O) = 0 since
compounds. The detailed sublimation results are given as
2
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The Journal of Physical Chemistry A
ARTICLE
Table 3. Individual Values of Standard Massic Energies of
0
Combustion, Δ u , for the Three Polyphenylbenzenes
c
a
Studied, at T = 298.15 K
124tPhB
1245TPhB
HPhB
o
ꢀ1
c
Δ u /J g
ꢀ39976.93
ꢀ39983.03
ꢀ39971.66
ꢀ39972.94
ꢀ39975.38
ꢀ39981.19
ꢀ39974.03
ꢀ
39980.77
ꢀ39855.82
ꢀ39871.87
ꢀ39852.69
ꢀ39864.78
ꢀ39860.52
ꢀ39870.12
ꢀ39862.04
ꢀ39859.00
ꢀ39884.59
ꢀ39864.89
ꢀ39861.96
ꢀ39863.20
ꢀ39875.18
ꢀ39861.41
ꢀ39866.63
ꢀ
39854.46
39869.96
ꢀ
o
ꢀ1
ÆΔ
c
u æ/J g
ꢀ
39977.0 ( 1.5
ꢀ39862.5 ( 2.7
ꢀ39866.1 ( 2.7
a
0
Error in ÆΔ u æ given as the standard deviation of the mean.
c
Figure 6. View of the supramolecular structure of 1245TPhB, showing
the CꢀH 3 π intermolecular interactions. Hydrogen atoms not in-
3 3
Table 4. Derived Standard Molar Energies of Combustion,
volved in the motifs are not included.
0
Δ U (cr), Standard Molar Enthalpies of Combustion,
c
m
0
Δ H (cr), and Standard Molar Enthalpies of Formation,
c
m
0
Δ H (cr), in the Crystalline State, at T = 298.15 K, for the
f
m
Studied Compounds
0
m
ꢀ1
0
m
ꢀ1
0
f m
ꢀ1
Δ
c
U
(cr)/kJ mol
Δ
c
H
(cr)/kJ mol
Δ H (cr)/kJ mol
1
24tPhB
245TPhB ꢀ15247.6 ( 4.4
ꢀ21316.4 ( 5.9
ꢀ12249.2 ( 3.1
ꢀ12260.4 ( 3.1
ꢀ15261.2 ( 4.4
ꢀ21335.0 ( 5.9
243.6 ( 4.4
311.8 ( 5.9
520.1 ( 8.0
1
HPhB
Figure 7. View of the supramolecular structure of HPhB, showing the
CꢀH 3 π intermolecular interactions. Hydrogen atoms not involved
3 3
in the motifs are not included.
g
o
Supporting Information. The values of Δ H at ÆTæ are deter-
cr
m
mined by the parameter b of the ClausiusꢀClapeyron equation
Figure 8. Plots of ln p = f (1/T) for one experiment of each compound
obtained by the Knudsen/quartz crystal effusion technique.
g
cr m
g
cr m
and the values of Δ S , at p(ÆTæ) and at ÆTæ, Δ S (ÆTæ, p(ÆTæ)),
are calculated as
where T = (ÆTæ + 298.15)/2. The standard molar entropies of
m
g
g
g o
Δ SmðÆTæ, pðÆTæÞÞ ¼ Δ HmðÆTæÞ=ÆTæ
ð11Þ
sublimation, Δcr
following equation:
S
m
, at T = 298.15 K, were calculated by the
cr
cr
g
o
g
cr
o
m
g
The standard molar enthalpies of sublimation, Δ H , at T =
98.15 K were determined by eq 12
cr
m
Δ S ð298:15 KÞ ¼ Δ S ðÆTæ, pðÆTæÞÞ
cr
m
2
g
0
þ Δ C ðT Þ lnð298:15=ÆTæÞ
cr p, m
m
g
cr
o
m
g
Δ H ð298:15 KÞ ¼ Δ H ðÆTæÞ
0
cr
m
ꢀ R lnðp =pðÆTæÞÞ
ð13Þ
g
0
þ ð298:15 ꢀ ÆTæÞΔ C ðT Þ
cr p, m
m
o
5
where p = 10 Pa. The standard molar Gibbs energies
g
cr
o
m
ð12Þ
of sublimation, Δ G , at T = 298.15 K, were calculated using
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Table 5. Standard Molar Enthalpies, for the Crystalline Phase, from T = 298.15 K to the Temperature, T, Programmed in the
ARTICLE
T
o
m p,m m
o
Calvet Microcalorimeter, Δ2
H (cr), and the Derived C (T , cr)
98.15K
T
298.15K
o
m
ꢀ1
o
ꢀ1
ꢀ1
T/K
m
T /K
Δ
H
(cr)/kJ mol
m
Cp,m(T , cr)/J K mol
1
1
24tPhB
365.43
446.98
500.99
331.8
372.6
399.6
26.9 ( 0.5
84.9 ( 1.3
399.8 ( 7.8
570.4 ( 8.7
818.4 ( 8.6
245TPhB
HPhB
166.0 ( 1.5
Table 6. Standard Molar Enthalpies, Entropies and Gibbs
Energies of Sublimation, at T = 298.15 K, for the Studied
Compounds
g
cr
0
m
ꢀ1
g
cr
0
m
ꢀ1
ꢀ1
g
0
ꢀ1
Δ
H
/kJ mol
Δ
S
/J K mol
cr m
Δ G /kJ mol
1
1
24tPhB
132.8 ( 0.7
161.4 ( 1.6
175.5 ( 2.1
239.7 ( 2.0
257.5 ( 4.2
245.4 ( 5.2
61.3 ( 0.9
84.6 ( 2.0
245TPhB
HPhB
102.3 ( 2.6
eq 14
g
cr
o
m
g
o
Δ G ð298:15 KÞ ¼ Δ H ð298:15 KÞ
cr
m
Figure 9. Three hindered rotations considered in this work. The
g
o
associated barrier height increases in the order P1 < P2 < P3.
ꢀ
298:15Δ S ð298:15 KÞ
ð14Þ
ð15Þ
cr
m
g
cr p,m
0
The values of Δ C (T ), were calculated as
m
g
0
o
p, m
o
p, m
Δ C ðTmÞ ¼ C ðTm, gÞ ꢀ C ðTm, crÞ
cr p, m
o
p,m
The values of C (T , g) were calculated by computational
m
thermochemistry at the B3LYP/6-311++G(d,p) level of theory
44
using the scaling factor of 0.9688 for the fundamental frequen-
o
p,m
ꢀ1
ꢀ1
cies calculations: C (124tPhB, g) = 372.9 ( 5.0 J K mol
,
o
p,m
ꢀ1
ꢀ1
o
p,m
C
(1245TPhB, g) = 523.2 (5.0 J K mol ,andC (HPhB,g) =
ꢀ1
ꢀ1
ꢀ1
ꢀ1
7
81.9 ( 5.0 J K mol (the error of (5.0 J K mol was
o
p,m
assumed as an upper bound). The values of C (T , cr) were derived
m
T
o
from the values of Δ2
H (cr) measured by Calvet microcalori-
98.15K
m
metry. Table 5 lists the enthalpy change due to the heating of the
sample in crystalline phase from T = 298.15 K to the programmed
temperature, T, in the Calvet microcalorimeter and the derived
o
o
o
Figure 10. Potential energy profiles for the Ph-Ph torsion in p-dPhB
(P1) (b), o-dPhB (P2) (2), and the central phenyl substituent in
123tPhB (P3) (9), calculated at the MP2/cc-pVDZ level of theory.
C
(T , cr). Considering the values of C (T , g) and C (T , cr)
m p,m m p,m m
g o g o
p,m
obtained, the Δ C (T ) values were calculated as Δ C -
cr p,m
m
cr p,m
ꢀ
1
ꢀ1
g
cr p,m
g o
cr p,m
(
124tPhB) = ꢀ26.9 ( 9.3 J K mol , Δ C (1245TPhB) =
ꢀ1
ꢀ1
o
ꢀ
47.2 ( 10.0 J K mol , and Δ C (HPhB) = ꢀ36.5 (
ꢀ1 ꢀ1
o
5
9
.9 J K mol . Table 6 lists the derived standard (p = 10 Pa)
and all the other points were scaled relative to the o-dPhB
profile.
molar enthalpies, entropies and Gibbs energies of sublimation,
at T = 298.15 K, for the three polyphenylbenzenes.
The above-mentioned profiles were used for the calculation of
S (g), at T = 298.15 K, taking σsym = 1 for all cases, at the B3LYP/
0
3
.4. Computational Results. The results for the total electro-
nic energies obtained from the optimized structures of the
selected compounds, as well as the detailed results for the internal
rotation torsional profiles are presented as Supporting Informa-
tion. Figure 9 illustrates the three different hindered rotations
considered in this work. The torsional profiles for the Ph-Ph
torsion in p-dPhB (profile 1, P1), o-dPhB (profile 2, P2), and for
the central phenyl substituent in 123tPhB (profile 3, P3),
calculated at the MP2/cc-pVDZ level of theory, are presented
in figure 10. The Ph-Ph torsional profile for m-dPhB is expected
to be very similar to p-dPhB, as supported by the fact that a
large resemblance in the profiles of p-dPhB (this work) and
6-311++G(d,p) and MP2/cc-pVDZ levels of theory using,
4
4
46
respectively, the scaling factors of 1.0161 and 0.9379 for
3
7ꢀ39
entropy correction, and the program CALCTHERM.
The
0
values of S (g) corrected for hindered rotation, considering the
two Ph-Ph internal rotors in terphenyls, were calculated for
o-dPhB (using P2), m-dPhB (using P1), p-dPhB (using P1) and
an hypothetic o-dPhB (using P3) where the torsional profile
obtained for the central Ph substituent in 123tPhB (P3) was used
for describing the two Ph-Ph hindered rotations. These results
are presented in table 7. Note that for very high rotational
0
barriers, S (g) approaches the value derived within the harmonic
4
5
biphenyl, is observed. For the central phenyl substituent
of 123tPhB only the structure corresponding to the Ph-Ph
dihedral of 0ꢀ (presumably the maximum) was calculated
oscillator (HO) approximation. Table 8 shows the derived
0
HR
hindered rotor entropy contributions, S (g), associated to each
hindered rotor profile considered in this work, P1, P2, and P3.
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The Journal of Physical Chemistry A
ARTICLE
0
Table 7. Calculated S (g), at T = 298.15, for ortho, meta, and
Table 9. Selected Standard Molar Thermodynamic Quanti-
ties, at T = 298.15 K, for the Polyphenylbenzenes Considered
in This Work
para-Terphenyl, Taking into Account the Harmonic Oscilla-
tor (HO), P1, P2, and P3 Torsional Profiles, at the B3LYP/
6
-311++G(d,p) and MP2/cc-pVDZ Levels of Theory
g
0
g
0
0
Δ
cr
H
m
/
Δ
cr
S
m
/
Δ
f
H
m
(g)/
ꢀ1
a
ꢀ1
ꢀ1
ꢀ1
0
ꢀ1
ꢀ1
n(Ph)
kJ mol
J K mol
kJ mol
S (g)/J K mol
4
7,48
b
b
benzene
0
1
2
2
2
3
3
3
4
6
44.7 ( 0.2
140.6
82.9 ( 0.9
182.0 ( 0.7
285.5 ( 3.6
279.9 ( 3.9
284.4 ( 3.5
376.7 ( 5.3
376.4 ( 4.5
366.8 ( 4.9
473.2 ( 6.1
695.6 ( 8.3
molecule
torsional profile
MP2
B3LYP
4
9
biphenyl
81.5 ( 0.2
103.0 ( 0.4
118.6 ( 0.7
125.6 ( 0.8
134.1 ( 1.1
132.8 ( 0.7
147.8 ( 0.7
161.4 ( 1.6
175.5 ( 2.1
180.3 ( 0.5
210.6 ( 1.3
233.1 ( 2.2
224.3 ( 2.2
245.1 ( 3.2
239.7 ( 2.0
254.0 ( 2.0
257.5 ( 4.2
245.4 ( 5.2
o-dPhB
2 x HO
512.0
523.7
510.4
514.4
534.5
514.6
534.3
490.7
503.1
489.8
492.2
513.0
493.3
512.9
50
o-dPhB
2
2
x P2
x P3
50
m-dPhB
50
p-dPhB
m-dPhB
p-dPhB
2 x HO
x P1
2 x HO
x P1
51
1
1
1
1
23tPhB
24tPhB
35tPhB
2
51
2
245TPhB
HPhB
a
b
n(Ph) is the number of phenyl substituents in the benzene ring.
Derived hypothetical values: they refer to conditions of temperature
Table 8. Calculated Hindered Rotor Entropy Contributions,
0
HR
S
(g), at T = 298.15 K, at the B3LYP/6-311++G(d,p) and
and pressure at which benzene is a liquid.
MP2/cc-pVDZ Levels of Theory, Respecting the P1, P2, and
P3 Hindered Rotor (HR) Profiles
0
ꢀ1
ꢀ1
S
HR(g)/J K mol
HR profile
MP2
B3LYP
mean
P1
P2
P3
28.6
23.4
16.8
28.6
23.8
17.2
28.6
23.6
17.0
0
Despite the discrepancy in individual values of S (g) when
comparing the B3LYP and MP2 methods, it is worth noting
0
HR
the very nice agreement in the S (g) values.
4. DISCUSSION
Table 9 lists the relevant thermodynamic quantities for
g
0
m
Figure 11. ΔcrH , at T = 298.15 K, as a function of the number of
polyphenylbenzenes. The standard molar enthalpies of forma-
0
m
phenyl substituents in benzene, n(Ph), for the species with ortho related
phenyl rings. HPhB is clearly an outlier.
tion in the gas phase, Δ H (g), at T = 298.15 K, for the studied
f
compounds, were calculated according to eq 16
0
m
0
4.1.2. Contribution of Entropy. A very poor correlation is
observed between Δ S and the number of phenyl substituents,
Δf H ðg, 298:15 KÞ ¼ Δf H ðcr, 298:15 KÞ
m
g 0
cr m
g
cr
0
m
þ Δ H ð298:15 KÞ
ð16Þ
n(Ph), as shown in Figure 12. Moreover, HPhB clearly has an
g
cr m
0
abnormally low Δ S .
One factor that can impose some entropic differentiation is
molecular symmetry. HPhB is a highly symmetric molecule belong-
ing to the D6d space group, which has associated an external
symmetry number, σsym, of 12. The influence of molecular
4
.1. Sublimation Thermodynamics. 4.1.1. Contribution of
Enthalpy. In this series of compounds, the expected increse in
g
cr
0
m
Δ H , as the number of phenyl groups increases is observed.
However, as illustrated in Figure 11, HPhB deviates consider-
ably from the linear trend obtained by plotting Δ H against
52ꢀ63
g
cr
0
m
symmetry on entropy is still a matter of debate in the literature.
Strictly speaking, only entropy differences can be measured
experimentally, and thus it is very hard to evaluate the real
influence of molecular symmetry in the different phases of
matter. In the case of entropies of sublimation, entropic differ-
entiation due to symmetry can either be ascribed to a higher
the total number of phenyl substituents, n(Ph), for polyphe-
nylbenzenes with at least one ortho relation. Another obser-
vation that can be drawn from Table 9 is that the compounds
g
0
with ortho substituents tend to have lower Δ H , indicating a
cr
m
significant decrease of the cohesive energy as more surface
area is buried from the intermolecular environment. This
situation is driven to a limit in HPhB, where none of the
phenyl substituents have free π-faces able to establish significant
0
0
S (cr), a lower S (g), or a combination of both to varying extents.
Quantitatively, the influence of symmetry on both phases is
g
0
m
always on the direction of: higher symmetry f lower ΔcrS , by a
intermolecular interactions (dispersive and CꢀH
π), which
factor that should be proportional to R ln(σsym). However, these
perspectives are fundamentally quite different. More symmetry
leads to more ways of allocating the molecule in a given free space
of the crystal lattice. In the condensation process the molecule
strikes a structured lattice in a random orientation, and the
3
3 3
g
0
results in the observed lower than expected Δ H . As
cr
m
mentioned in section 3.1 HPhB only establishes two CꢀH
π
3
3 3
intermolecular interactions per molecule, a small number considering
its molecular size.
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The Journal of Physical Chemistry A
ARTICLE
0
0
in this work that symmetry may affect both S (cr) and S (g) its
g 0
cr m
influence on Δ S shall be more correctly described as cR
ln(σsym), where c is a factor of proportionality.
Another origin of entropic differentiation in these compounds
is the vibrational freedom of the phenyl substituents, with respect
to the phenylꢀphenyl torsion. The three hindered rotations
illustrated in figure 9 can be clearly distinguished: the phenyl
substituent with no ortho neighbors (e.g., the two phenyls in p-
dPhB), one ortho neighbor (e.g., the two phenyls in o-dPhB) and
two ortho neighbors (e.g., the central phenyl substituent in
1
23tPhB). It was expected, on the basis of simple stereochem-
istry, and verified computationally (figure 10) that the barrier
height increases in the direction of 0, 1, and 2 ortho neighbors. A
higher rotational barrier implies a more hindered torsional
motion, and thus an associated decrease in vibrational entropy,
as can be inferred from table 8. This differentiation will be
predominantly noted in the gas phase, since in the crystal lattice
these high-amplitude vibrational modes are much more re-
stricted due to molecular packing. This can be pictured in the
sublimation process as a number of frozen torsional modes in the
crystalline state becoming free to rotate in the gas phase to
different extents, depending on the number of ortho neighbors.
In this perspective, a phenyl with no ortho neighbors will be freed
to a higher extent than one with two ortho neighbors, resulting in
a more pronounced increase in entropy for the former, and
g
cr m
0
Figure 12. Δ S , at T = 298.15 K, as a function of the number of phenyl
substituents in benzene, n(Ph).
probability of effectively condensing or bouncing off is affected
by that orientation. A molecule will crystallize more easily if it
strikes the solid surface with the orientation that it will adopt in
that specific point of the crystal lattice. Symmetry increases the
likelihood of a successful strike by increasing the number of
correct molecular orientations, in an analogous way that geo-
metric factors influence reaction kinetics. Put it simply, higher
molecular symmetry should increase the sticking coefficient in
the condensation process. Hence, higher symmetry can be
associated with a faster condensation process, contributing for
a lower volatility. This can be understood thermodynamically in
terms of the so-called concept of residual entropy, which is a
g
0
consequently raising Δ S relative to the latter. This contribu-
cr m
tion in polyphenylbenzenes can be quantified based on the calcu-
lated P1, P2, and P3 hindered rotor profiles shown in Figures 9 and
0
HR
1
0, and the respective hindered rotor entropies, S (g), presented
0
in Table 8. The following assumptions were made:
nonthermal contribution to S (cr), and arises because symmetry
1
- The 1D hindered rotor profiles for each phenyl substituent
increases the number of equivalent ways into which the crystal
phase can be realized. This is so because in the crystal phase each
molecule and atom can be considered distinguishable since a
specific and unique set of geometrical coordinates can be
in polyphenylbenzenes have an additive contribution to
0
S (g) and are based on the ones calculated for o-dPhB and
p-dPhB, namely P1, P2, and P3.
2
- Meta substituents were treated as para substituents, since
64,65
ascribed to each of them, irrespective of their identity.
On
0
0
S (m-dPhB, g) ≈ S (p-dPhB, g), as shown in Table 7, and
the other hand, σsym is introduced in the expression for the
rotational molecular partition function in order to correct for an
overcounting of the microscopically indistinguishable rotational
states that are not allowed by the Pauli exclusion principle in a
symmetric molecule. This arises from the parity restrictions of
the molecular wave function for fermions, which must be
antisymmetric with respect to the interchange of identical nuclei
the corresponding torsional profiles should be very alike.
The previous considerations about symmetry and hindered
g
0
cr m
rotation suggest that an additive estimation model for Δ S can
be employed in this class of compounds. This model takes
symmetry and hindered rotation into account and can be
mathematically described by eq 17
6
6,67
g
cr
0
m
in the molecule.
In this way higher symmetry can also lead to
Δ S ðmodelÞ ¼ a þ bnðPhÞ ꢀ cR lnðσ
Þ
sym
0
a decrease of S (g). The real situation should follow the following
reasoning: in the crystal phase more symmetry leads to a larger
number of allowed permutations of the atoms compatible with a
0
HR
þ S ðg, P1Þnðm=p-PhÞ
0
þ S ðg, P2Þnðo-PhÞ
HR
0
þ S ðg, P3Þnðcentral-PhÞ
ð17Þ
0
HR
given macrostate (higher S (cr)), whereas in gas phase some of
those permutations are forbidden by quantum mechanical re-
quirements (lower S (g)) when the molecules do not possess
where a, b, and c are fitting parameters, n(Ph) is the total number
of phenyl substituents relative to the central benzene ring, and
n(m/p-Ph), n(o-Ph), and n(central-Ph) are respectively the
number of phenyl rings with 0, 1, and 2 ortho relations in
0
ways so as to render those requirements less important. For
instance, the polyphenylbenzenes studied in this work are
relatively big and flexible molecules, and hence rotationalꢀvibra-
tional coupling may easily occur and partially or fully compensate
for the entropic penalty associated to symmetry in the gas phase.
For each compound considered in this work, σsym, correspond-
ing to the number of unique orientations of the rigid molecule
that only interchange identical atoms, was taken from the analysis
of the X-ray crystal structures, contained in this work and in the
literature. This was done approaching the observed solid phase
structure to the molecular geometry that corresponds to the
closest point group with highest symmetry. Since it is considered
0
0
a given molecule. The values of S (g,P1), S (g,P2), and
HR
HR
0
HR
S
(g,P3) were taken as the mean values presented in Table 8.
0 0
Increased symmetry will increase S (cr) and/or lower S (g),
g
cr m
0
thus, decreasing Δ S , hence the “ꢀ” sign in the respective
0
term. Less hindered rotations will increase S (g), thus increasing
g
cr m
0
Δ S , hence, the “+” sign in the corresponding terms.
For each polyphenylbenzene studied in this work, Table 10
presents the molecular symmetry point group and the correspond-
ing σsym, and the number of phenyl groups with 0, 1, and 2 ortho
neighbors, n(m/p-Ph), n(o-Ph), and n(central-Ph), respectively.
1
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The Journal of Physical Chemistry A
ARTICLE
Table 10. Molecular Symmetry Point Group and Associated
External Symmetry Number, σsym, and the Number of Phenyl
Groups with 0, 1, and 2 ortho Relations, n(m/p-Ph), n(o-Ph),
and n(central-Ph), Respectively, for Each Studied
Polyphenylbenzene
point group
σsym n(m/p-Ph) n(o-Ph) n(central-Ph)
6
8
benzene
D
6h
12
0
1
0
2
2
0
1
3
0
0
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
1
0
0
0
6
6
9
bBiphenyl
D
2
4
2
7
0
o-dPhB
C
C
C
C
C
C
C
2
7
1
m-dPhB
s
1
7
2
p-dPhB
2h
2
2
1
23tPhB
2
1
24tPhB
1
1
7
3
1
35tPhB
2
2
Figure 13. Schematic representation of the model used in this work for
1
245TPhB
2h
2
g
0
4
1
the calculation of Δcr
m 1 2
S , at T = 298.15 K, in polyphenylbenzenes, c + c = c
HPhB
D
6d
12
(in eq 17).
The references of the X-ray crystallographic structures used to
determine the symmetry point groups are shown near the
compound’s name.
By the least-squares method the values for the fitting para-
ꢀ1
ꢀ1
ꢀ1
ꢀ1
meters in eq 17 are a = 171.1 J K mol , b = 0.3 J K mol
,
and c = 1.4, giving an average error between the experimental and
g
cr m
0
ꢀ1
ꢀ1
estimated Δ S values of 2.8 J K mol , which corresponds
approximately to 1% deviation (since 123tPhB was found to be
an outsider it was not included in the fitting). The contributions
g
cr m
0
for Δ S considered within this model are schematically repre-
sented in Figure 13.
In this figure the Δ S term on the left corresponds to the
g 0
cr m
hypothetical situation were entropic differentiation is only due to
the number of Ph substituents. The other two terms (symmetry
and hindered rotation) are then considered in order to reproduce
g
0
the experimental Δ S values by the present model. It is
cr m
interesting to note that b ≈ 0 in eq 17, which can indicate that
virtually no entropic differentiation would be observed if only the
g
cr m
0
molar mass was considered. In this case, Δ S could be chiefly
ascribed to the translational and rotational (neglecting symmetry
considerations) contributions, which have a smaller dependency
on molar mass. The fact that c = 1.4 suggests that symmetry
g
0
Figure 14. Plot of Δcr
S
m
(model) versus the experimental values of
Δ S for the studied polyphenylbenzenes, at T = 298.15 K. 123tPhB
cr m
0
0
g 0
influences both S (cr) and S (g) to varying extents. This also
suggests that symmetry shall not be fully active in differentiating
entropically both phases, since c < 2. A partial influence of
symmetry on entropy can be understood in terms of continuous
ꢀ1
(
7), was not considered in the fitting. An average error of (3 J K
ꢀ
1 g 0
m
mol was considered for ΔcrS (model). Legend: benzene (1), biphe-
nyl (2), o-dPhB (3), p-dPhB (4), m-dPhB (5), 124tPhB (6), 123tPhB
(7), HPhB (8), 135tPhB (9), and 1245TPhB (10).
54,63
symmetry numbers, as stated by other authors.
Since internal
dynamics causes the molecules to incessantly interconvert be-
tween many more or less symmetric, transient and equilibrium
structures, a fractional symmetry number seems more adequate
to describe the real average situation, particularly when consider-
ing compounds with high molecular flexibility like most poly-
phenylbenzenes studied in this work. The value of c in eq 17
translates the average contribution of symmetry concerning all
the compounds included in the fitting and is not necessarily the
same for all of them, given, for instance, the different degree to
which each molecule can distort from its equilibrium structure.
the Ph-Ph hindered rotations in this class of compounds are key
g
0
factors influencing the differentiation in Δcr
S , with higher
m
symmetry and a more pronounced hindered phenyl internal
g
0
rotation contributing for a decrease of Δcr
From Figure 14 one can see that 123tPhB presents a low
S .
m
g
cr m
0
Δ S (model). From the rationale presented thus far one can
conclude that the model described by eq 17 should include at
least one additional positive term respecting this compound.
This indicates that in 123tPhB some unknown factor is increas-
g
0
g
0
m
0
0
Figure 14 plots the values of Δ S (model) versus the experi-
ing ΔcrS , either by decreasing S (cr) or increasing S (g).
cr m
g 0
cr m
mental values of Δ S for the polyphenylbenzenes studied in
Unfortunately, despite of the efforts, we could not obtain suitable
crystals for X-ray diffraction, and no crystal structure was found in
the literature. A lower thermodynamic stability of the solid phase
this work.
The good agreement obtained is a strong indication that
molecular symmetry and the vibrational entropy associated with
0
(which can derive from a lower S (cr)) could explain the
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The Journal of Physical Chemistry A
ARTICLE
Figure 16. General homodesmotic reaction scheme used for the evalua-
tion of the total substituent interaction enthalpy in polyphenylbenzenes.
Table 11. Experimental and Calculated (B3LYP/6-311+
o
m
+
G(d,p) and SCS-MP2) Values of ΔHRH (g), at T = 298.15
K, for the Individual Homodesmotic Reactions Presented in
Figure 16
0
m
Figure 15. Δ H (g), at T = 298.15 K, as a function of the number of
f
o
ꢀ1
phenyl substituents in benzene, n(Ph), for the species with ortho-related
HR m
Δ H (g)/kJ mol
phenyl rings. HPhB is an outlier.
DFT
SCS-MP2
exp.
difficulties in the crystallization process. However, this is not
reflected in the melting points of the triphenylbenzene isomers:
m.p.(123tPhB) ≈ 158 ꢀC, m.p.(124tPhB) ≈ 120 ꢀC, and m.
p.(135tPhB) ≈ 173 ꢀC. In principle, a significant decrease in
o-dPhB
m-dPhB
p-dPhB
ꢀ15.4
ꢀ0.6
0.4
ꢀ0.9
1.2
ꢀ4.4 ( 3.0
1.2 ( 3.4
1.1
ꢀ3.3 ( 2.9
3.5 ( 4.6
1
1
23tPhB
24tPhB
ꢀ33.2
ꢀ15.2
ꢀ1.2
ꢀ30.7
ꢀ1.3
1.4
0
S (cr) should lead to a considerably lower melting point of
3.8 ( 3.6
1
23tPhB relative to its isomers. In gas phase, the most obvious
0
135tPhB
245TPhB
HPhB
3.7
13.4 ( 4.1
6.1 ( 5.1
explanation for an increased S (g) of 123tPhB is an ill description
of the vibrational motions, including internal rotations. Substan-
tial vibrational coupling may occur and free the Ph-Ph hindered
1
2.7
ꢀ18.1 ( 6.7
0
rotations to some extent, thus raising S (g).
4
.2. Gas Phase Energetics. A linear trend was obtained when
molecules. The fact that for 135tPhB the DFT result is
more negative than the MP2 one may indicate that
correlation energy is a source of stabilization in this
molecule.
0
ploting Δ H (g) versus the number of phenyl substituents,
n(Ph), for polyphenylbenzenes with at least one ortho relation,
as depicted in Figure 15.
f
m
HPhB is an outlier in the correlation, showing a marked increase
2. Meta relations have a more pronounced stabilizing effect.
3. The intramolecular interactions between ortho-related
phenyl rings are significantly overestimated by DFT in
the direction of increased steric repulsion. In reality, the
existence of ortho substituents does not have such a
noteworthy destabilizing effect, possibly indicating the
existence of a considerable van der Waals attractive term
(which would be ill described by B3LYP), characteristic of
an intramolecular π π interaction between the two
0
in ΔH (g), which is associated with some additional destabilization
f
m
in this molecule. The homodesmotic reaction presented in Figure 16,
concerning the breaking of the phenylꢀphenyl bonds in the poly-
phenylbenzenes to yield only biphenyls, is a good way to measure the
total interaction enthalpy between the phenyl substituents in a given
o
polyphenylbenzene. When ΔHRH (g) < 0, this interaction has an
m
o
m
enthalpic destabilizing effect, and when ΔHRH (g) > 0, it has a
stabilizing effect. The computational and experimental results ob-
3
3 3
o
tained for ΔHRH (g) are presented in Table 11.
adjacent phenyl rings.
m
0
m
The values of Δ H (cr) for all of the compounds presented in
4. In general SCS-MP2 accounts well for the energetics of
gaseous polyphenylbenzenes, with higher deviations being
observed for bigger molecules.
f
Table 9 were determined by combustion calorimetry. Thus, in
o
m
the calculation of the uncertainties in ΔHRH (g), the contribu-
tions of the uncertainties of CO (g) and H O(l) in the overall
5. HPhB clearly has an additional destabilizing effect, possibly
related to the fact that the phenyl substituents do not
possess the ability to relieve strain by increasing the
distance between the ortho groups. This can be achieved
in the other polyphenylbenzenes with ortho relations,
where the molecular compactness is not enough to restrain
a geometrical relaxation. This fact is supported by the X-ray
crystal structures for the studied polyphenylbenzenes. Like
mentioned in section 3.1, the Ph-Ph dihedral angles in
HPhB tend to be higher, which may be related with
enhanced steric hindrance. As well a more pronounced
elongation of the C ꢀC bonds in the central ring is
2
2
uncertainties cancel out, and can be ignored. It was assumed that
o
ΔHREel,m ≈ Δ H (g, 298.15 K), where ΔHREel,m is the molar
HR
m
energy of the homodesmotic reaction derived using the values of
Eel(0 K) for each species, calculated by B3LYP/6-311++G(d,p)
and SCS-MP2/cc-pVDZ. The corrections to ZPE and thermal
enthalpy were neglected since they are generally of little sig-
nificance in an homodesmotic approach.
Despite the fact that all of the studied compounds are aromatic,
aromaticity is not expected to be an important source of energetic
differentiation among them, since there are no apparent reasons
for aromaticity to be significantly enhanced or disrupted in any of
these molecules. The five main observations that can be drawn
ar
ar
observed. The CꢀCꢀC angle, αCCC, schematized in
Figure 17, is about 120ꢀ for phenyl rings with no ortho
relation (e.g., 135tPhB), slightly higher, ∼123ꢀ, for ortho-
phenyls (e.g., 1245TPhB), and ∼120ꢀ in HPhB. For HPhB
the centroid-centroid distance between two ortho-phenyls,
from the results obtained are the following:
o
m
1
. ΔHRH (g) tends to be more positive as more phenyl
substituents are present, indicating the existence of some
sort of through-space stabilizing interaction in these
1
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The Journal of Physical Chemistry A
ARTICLE
and HPhB, computational data, and optimized geometries. This
material is available free of charge via the Internet at http://pubs.
acs.org.
’
AUTHOR INFORMATION
Corresponding Author
*
fc.up.pt.
Fax: +351 220402659. Fax: +351 220402836. E-mail: lbsantos@
Figure 17. Relevant geometrical parameters in the crystalline state,
obtained by X-ray crystallography, for a general polyphenylbenzene with
an ortho relation.
’
ACKNOWLEDGMENT
Thanks are due to Funda c- ~a o para a Ci ^e ncia e Tecnologia
dCt-Ct, is about 4.3 Å, whereas for the other ortho-poly-
phenylbenzenes it is ∼4.7 Å. These facts indicate that ortho
rings tend to relieve some strain by increasing αCCC, and
that this cannot be achieved in HPhB, due to its molecular
compactness. Because this phenomenon is multiplied by six
(
(
FCT) and Programa Operacional Ci ^e ncia e Inova c- ~a o 2010
POCI 2010) supported by the European Community Fund
FEDER for the financial support to Project POCI/QUI/61873/
2004. C.F.R.A.C.L. and M.A.A.R. also thank FCT and the
European Social Fund (ESF) under the third Community
Support Framework (CSF) for the award of Ph.D. Research
Grants SFRH/BD/29394/2006 and SFRH/BD/60513/2009,
respectively.
0
in HPhB, a substantial increase in Δ H (g) is observed.
f
m
Recently, an interesting review paper concerning twisted
74
acenes presented a survey on their structures and properties.
Twisted acenes are compounds with unusual geometries, and
some of them are structurally related to polyphenylbenzenes,
particularly with HPhB. However, the X-ray and computationally
optimized geometries of the polyphenylbenzenes studied in this
work do not show any significant geometry twisting, and thus,
this interesting phenomenon needs not be considered for the
rationalization of structure and energetics in this case.
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