Thermodynamics of electron attachment to pyrimidine and styrene in supercritical ethane

Article abstract of DOI:10.1021/jp990717c

The reaction of excess electrons with pyrimidine and styrene was studied in supercritical ethane. The equilibrium constant for attachment was large when the solute was pyrimidine and small for styrene, although their electron affinities are comparable. At pressures above 100 bar, the rate constant for electron attachment to pyrimidine (k_a) was time resolved using the short pulse of the laser-electron accelerator facility (LEAF). The rate constant, k_a, is large and nearly independent of pressure and temperature; thus, the volume of activation is close to zero. At lower pressures, the equilibrium constants for this reaction were derived from the changes in the mobility of excess electrons. The free energy is a function of the polarization energy, which was evaluated with a compressible continuum model. The small equilibrium constant in the case of styrene is attributed to a smaller polarization energy. Values of ΔV_r, obtained from changes of ΔG_r with pressure, range from -9.0 to -0.4 L/mol. The observed volume changes are compared to electrostriction volumes calculated by the model. Electron attachment occurs with a large decrease in entropy associated with clustering of ethane molecules around the ion formed. Observed values of ΔS_r are comparable to expected values calculated from ΔS_r = (α/χ_T)ΔV_r.

Full text of DOI:10.1021/jp990717c

J. Phys. Chem. B 1999, 103, 9205-9210
9205
Thermodynamics of Electron Attachment to Pyrimidine and Styrene in Supercritical
Ethane
Richard A. Holroyd*
Chemistry Department, BrookhaVen National Laboratory, Upton, New York 11973
Masaru Nishikawa
Faculty of Engineering, Kanagawa Institute of Technology, 1030 Shimo-Ogino, Astugi 243-0292, Japan
Kengo Itoh
Department of Pure and Applied Science, UniVersity of Tokyo, Tokyo, 153-8902, Japan
ReceiVed: February 26, 1999; In Final Form: May 23, 1999
The reaction of excess electrons with pyrimidine and styrene was studied in supercritical ethane. The equilibrium
constant for attachment was large when the solute was pyrimidine and small for styrene, although their electron
affinities are comparable. At pressures above 100 bar, the rate constant for electron attachment to pyrimidine
a
(k ) was time resolved using the short pulse of the laser-electron accelerator facility (LEAF). The rate constant,
k
a
, is large and nearly independent of pressure and temperature; thus, the volume of activation is close to
zero. At lower pressures, the equilibrium constants for this reaction were derived from the changes in the
mobility of excess electrons. The free energy is a function of the polarization energy, which was evaluated
with a compressible continuum model. The small equilibrium constant in the case of styrene is attributed to
a smaller polarization energy. Values of ∆V
to -0.4 L/mol. The observed volume changes are compared to electrostriction volumes calculated by the
model. Electron attachment occurs with a large decrease in entropy associated with clustering of ethane
r
, obtained from changes of ∆G with pressure, range from -9.0
r
molecules around the ion formed. Observed values of ∆S
) (R/ø )∆V
r
are comparable to expected values calculated from
∆
S
r
T
r
.
Introduction
CO2, the present results provide a test of the effect of ion radius.
Earlier it was predicted that the partial molar volume of ions in
Solvated electrons in aqueous solution readily react with
aromatic hydrocarbons such as styrene and substituted pyrim-
idines, like uracil and thymine. Electrons in alkane solvents
4
supercritical fluids is largely independent of ion radius. Because
5
styrene has an electron affinity of -0.25 eV, which is
1
6
comparable to that for pyrimidine, -0.33 eV, we had expected
also react fast with these solutes. The rate constant for
it to react similarly.
1
3
attachment to pyrimidine in 2,2,4-trimethylpentane is 3 × 10
-1
-1
2
m
s
at 293 K, and that for attachment to styrene in the
12
-1 -1
3
Experimental Section
same solvent is 8.3 × 10
m
s
at 298 K. Furthermore,
electron attachment is reversible in both cases; that is, the anion
formed readily gives the electron back to the hydrocarbon
solvent. The equilibrium constants have been measured in 2,2,4-
trimethylpentane, and ∆Gr is -0.70 eV for attachment to
pyrimidine at 298 K and -0.48 eV for attachment to styrene.
These reactions occur with a large decrease in entropy that is
associated with the change in solvent density around the ions.
Here, we report the first study of the reactivity of aromatic
compounds, styrene and pyrimidine, with excess electrons in
supercritical ethane. For pyrimidine, the reaction is
Samples of ethane (MG Industries, scientific grade) were
purified by passage through a Pall filter (GLPV2C2H6VMM4).
The quantity of ethane needed was then measured, by liquid
volume at 195 K, and condensed into the pressure cell, which
4
is described elsewhere. The lifetime and mobility of excess
electrons in the purified ethane was first checked under the
various experimental conditions. Generally, the electron lifetime
was on the order of 10 µs. The pyrimidine (Aldrich 99%) and
styrene (Aldrich 99+%) were degassed at 195 K several times
prior to use. GC/MS analysis showed the pyrimidine to be free
of electron-attaching impurities, and no impurities were found
in the styrene. Solutions of these solutes in ethane were prepared
by measuring a known pressure of the vapor in a calibrated
volume, maintained at 306 K, and then condensing the sample
into the conductivity cell, cooled to 77 K.
-
-
e + pyrimidine T pyrimidine
(1)
From equilibrium measurements, we obtain not only the free
energy of reaction but also the volume change, ∆Vr, from
changes in ∆Gr with pressure. As was shown in a study of
4
electron attachment to CO2, the change in volume is largely
The results reported here were obtained by pulse conductivity
in one of two ways. Individual rate constants for electron
attachment (ka) and detachment (kd) were determined using the
fast X-ray pulse of the LEAF facility. The currents from the
due to the large negative partial molar volume of ions in
supercritical fluids because of extensive clustering of solvent
molecules around the anion. Because pyrimidine is larger than
1
0.1021/jp990717c CCC: $18.00 © 1999 American Chemical Society
Published on Web 06/19/1999

9206 J. Phys. Chem. B, Vol. 103, No. 43, 1999
Holroyd et al.
Figure 2. Free energy of reaction for attachment to pyrimidine versus
pressure at (b) 33, (9) 37, and (2) 45 °C. Data are from mobility
measurements. Solid lines are polynomial fits.
TABLE 1
T (K)
P (bar)
K
4
(m-1)
r
∆G (eV)
3
3
06
10
82.5
94.5
2600
2000
-0.21 ( 0.02
-0.20 ( 0.02
Figure 1. Data obtained at LEAF for reaction 1 in supercritical ethane.
a) Rate constant for electron attachment to pyrimidine versus pressure
(
the equilibrium was studied by measuring changes in the
mobility of excess electrons. The mobility decreased in propor-
tion to the concentration (between 6 and 17 µm) of pyrimidine
present. The electron mobility in supercritical ethane is high,
at (O) 33, (0) 37, and (4) 45 °C. (b) Rate constant for electron
-
detachment from pyrimidine versus pressure and temperature. Symbols
as in part a. (c) Free energy for reaction 1 versus pressure and
temperature. Symbols as in part a. Solid lines are quadratic fits.
2
generally between 20 and 70 cm /(V s) under these conditions.
cell were amplified using an EG&G preamplifier (model 5185)
and recorded using a 1.5 GHz LeCroy 9362 oscilloscope.
Electron mobilities, which lead to equilibrium constants for
electron attachment, were determined with the X-ray pulse of
the 2 MeV van de Graaff. During measurements, the sample
temperature was controlled to 0.05 K using an Omega (CN77530-
C2) temperature controller.
The effect on the mobility depends on pressure. At 310 K, the
presence of 17 µm pyrimidine reduces the mobility from 24.3
2
to 3.4 cm /(V s) at 98 bar. The same concentration reduces the
2
mobility from 67.9 to 46.9 cm /(V s) at 52 bar.
The pyrimidine acts as a temporary trap for electrons. Values
of the equilibrium constant, K1, were derived from the observed
mobilities using eq 3, where µo is the electron mobility in pure
ethane under the same conditions.
Density and compressibility values for ethane (Tc ) 32.3 °C
and Pc ) 48.84 bar) were calculated using an equation of state
7
-1
developed by Younglove. Volumes of electrostriction and
µ ) µ (1 + K [Pyr])
(3)
0
1
energies of polarization in SC ethane were calculated according
4
to a compressible continuum model described elsewhere.
In this way, values of the free energy of reaction were obtained,
and they are shown in Figure 2. At all three temperatures, ∆Gr
decreases sharply as the pressure increases.
Results
Styrene. Styrene was found to be much less reactive toward
electrons than pyrimidine. Consequently large concentrations
Pyrimidine. Rate constants for electron attachment and
detachment were determined using the short pulse of LEAF.
Typical current traces exhibited a fast decay followed by an
equilibrium current, the height of which depended on conditions.
(from 8 to 73 µm) of styrene were used. At the highest
concentration, reductions in mobility of 10-20% were obtained
from which values of the equilibrium constant for reaction 4
were estimated. The use of large quantities of styrene caused a
4
Analysis of such decays, by the method outlined earlier, led
to values of ka and kd for reaction 1. The rate constants are
independent of the concentration of pyrimidine, which was
varied from 0.15 to 1 µm. As shown in Figure 1a, the attachment
rate constant, ka, is large and is nearly constant, changing little
with pressure and temperature. In contrast, the detachment rate
constant, kd (Figure 1b), increases with increasing temperature
and decreases with increasing pressure. Values of the free energy
for attachment to pyrimidine, obtained using the equation
-
-
e + styrene T styrene
(4)
reduction in the lifetime of the electron to as low as 2 µs due
to the presence of an unidentified impurity. This required drift
time measurements at higher voltages, and since the mobility
is slightly field dependent in ethane, the results shown in Table
1
are upper limits for the values of K4 and the free energies
∆
G ) -RT ln(k /k )
(2)
have a large uncertainty.
r
a
d
An attempt made to detect this reaction at LEAF gave
negative results. However, if the rate constant for attachment
are shown in Figure 1c as a function of pressure at three
temperatures, 306, 310, and 318K.
At lower pressures, the detachment rate becomes too fast,
precluding analysis in terms of individual rate constants. Here,
1
3
-1 -1
is ∼10
m
s
like pyrimidine, then based on the results in
Table 1 the lifetime of the styrene anion would be of the order
of nanoseconds, making observation impossible this way.

Thermodynamics of Electron Attachment in Ethane
J. Phys. Chem. B, Vol. 103, No. 43, 1999 9207
-
TABLE 2: Free Energy Changes for e + Pyrimidine T
-
Pyrimidine
P (bar) ∆G
r
(eV)
V
0
(eV) E(Pcc-) (eV) ∆G
T ) 306 K
r
t
(gas) - E (eV)
5
6
7
8
0
0
0
5
-0.287
-0.318
-0.333
-0.359
-0.399
-0.174
-0.176
-0.172
-0.164
-0.151
-0.932
-0.968
-0.982
-0.997
-1.025
0.47
0.47
0.48
0.47
0.47
1
30
T ) 310 K
5
6
7
8
5
0
0
5
-0.278
-0.297
-0.317
-0.344
-0.386
-0.172
-0.179
-0.176
-0.17
-0.919
-0.944
-0.965
-0.983
-1.015
0.47
0.47
0.47
0.47
0.47
1
30
-0.156
T ) 318 K
7
8
00
30
60
0
5
-0.279
-0.307
-0.324
-0.364
-0.387
-0.178
-0.177
-0.174
-0.165
-0.156
-0.922
-0.953
-0.971
-0.994
-1.010
0.46
0.47
0.47
0.46
0.47
Figure 3. Diagram of the free energy (indicated by horizontal lines)
for electron attachment to various solute molecules in TMP and TMS
at 298 K and 1 bar and in supercritical ethane at 310 K and 100 bar.
Data are from this work and refs 2, 3, and 8.
1
1
1
Discussion
form here. The density F(r) at each point is calculated from P
7
using the equation of state (EOS). Several iterations are required
Energetics. In supercritical ethane, electron reaction with
pyrimidine is much more favorable than reaction with CO2. This
is in part due to the large value of ka that is 2 orders of magnitude
larger than ka for CO2. The rate constants for electron detach-
ment from the corresponding anions are comparable. Thus, the
free energies for reaction 1 are lower than the free energies for
the corresponding reaction with CO2 in ethane. This is illustrated
for a pressure of 100 bar and a temperature of 310 K in Figure
to obtain a constant F(r).
In the compressible continuum model proposed by Luo and
1
0
Tucker, the local density profile F(r) is calculated in a similar
but slightly different way. We determined F(r) so that E(r), P(r),
and ꢀ(r) all become consistent. They used an equation thermo-
1
1
dynamically derived by Frank, which relates F(r) and E(r)
their eq 4) and made F(r), E(r), and ꢀ(r) consistent without
(
referring to P(r) explicitly. However, both methods are equiva-
lent. In fact, Frank’s eq 13, on which their eq 4 is based together
with other thermodynamical relations, is equivalent to our (A-
3. This figure also shows values of the free energies of electron
attachment reactions to pyrimidine and styrene as well as CO2
in two nonpolar liquids, tetramethylsilane (TMS) and 2,2,4-
trimethylpentane (TMP). The reactions are most favorable in
TMP; the free energy of reaction is shifted higher in TMS, and
the shift is a nearly constant value of 0.24 eV for each of these
reactions. The free energies shift even higher in supercritical
ethane. The shifts from TMP to ethane, for the conditions stated,
are 0.34 eV for pyrimidine and 0.38 eV for CO2. It would be
reasonable, based on this correlation, to expect a similar shift
for styrene, which leads to a predicted free energy of -0.12
eV at 100 bar and 310 K for reaction 4, in fair agreement with
the approximate value found. Thus, despite the similar electron
affinities of styrene and pyrimidine, the free energies for
attachment in solution are quite different. This difference is
ascribed to the magnitude of the polarization energy of the
negative ion in solution (see below).
1). Their eq 4 corresponds to our eq 5 and the equation of state.
The polarization energy is then calculated from
∞
-
2 2
2
E(P ) ) 2π
∫
ꢀ ꢀ(r)[E(r)] r dr - e /8πꢀ r
(6)
0
0 ion
rion
where rion is the radius of the ion. For pyrimidine, rion is
estimated to be 0.257 nm from Bondi’s volume increments.
A small energy of compression is added to E(P ) to give the
total polarization energy in this model, E(P cc).
12
-
-
Values of the polarization energy calculated this way are
shown in Table 2 as a function of pressure at each of the three
temperatures studied. The stability of the ion increases with
-
pressure. This change in E(P cc) accounts for most of the change
in the free energy of reaction, ∆Gr, which changes from about
As shown in the earlier study of electron attachment to CO2,
evaluation of the polarization energy of ions in supercritical
ethane must take into account the extensive clustering around
ions. To do this, we utilize a compressible continuum model.
In this model, the electric field, E(r), at a distance r from the
ion gives rise to a pressure P.
-
0.28 eV at the lowest pressures studied to about -0.4 eV at
the highest.
The free energy of reaction depends as well on the energy of
the electron in the fluid, V + E , according to the equation
4
,9
0
t
-
∆
G ) ∆G + E(P ) - (V + E )
(7)
r
g
cc
0
t
r
dꢀ(r)
2
2
P ) P + (ꢀ(r) - 1)ꢀ [E(r)] /2 -
∫
ꢀ [E(r)] /2
dr
The free energy of electron attachment to pyrimidine in the gas
phase, ∆Gg, can be calculated from the data using eq 7. Values
∞
0
0
( dr
)
∞
1
3
(5)
of V0 for ethane have been measured as a function of density,
4
and Et is assumed, as before, to be small. Values of ∆Gg - Et
were calculated and, as shown in the final column of Table 2,
are quite constant, the average value being 0.47 ( 0.01 eV.
This value corresponds to an electron affinity of pyrimidine of
-0.52 eV, which differs from the reported value of -0.33 eV.
A similar difference was found for the reaction of electrons with
Where ꢀ(r) is the dielectric constant as a function of r, P∞ is
the background pressure, and ꢀ0 is the permittivity of a vacuum.
The third term gives a negligibly small contribution and was
ignored previously. Although it was checked that the calculations
made earlier4 agree within 1% with those obtained by taking
this third term into account, we used the analytically accurate
,9
4
CO2 in supercritical ethane.

9208 J. Phys. Chem. B, Vol. 103, No. 43, 1999
Holroyd et al.
-
Figure 5. Density distribution around a pyrimidine ion as a function
of distance: solid line at 306 K and 48 bar; dashed line at 318 K and
5
9 bar; dotted line at 310 K and 120 bar.
changes are given by the difference
Figure 4. Volume changes for electron attachment to pyrimidine in
SC ethane. Points are experimental values of ∆V at (b) 33, (9) 37,
and (2) 45 °C. Lines calculated by compressible continuum model:
r
-
∆
Vh ) Vh (pyr ) - Vh (pyr)
(10b)
r
(
solid line) 33 °C; (dashed line) 37 °C; (dotted line) 45 °C.
The partial molar volumes of neutral aromatic compounds in
supercritical fluids are small and positive at high pressures but
large and negative at pressures where the compressibility (øT)
is a maximum. Data specifically for pyrimidine in ethane are
not available. Some generalizations are possible based on earlier
studies. The partial molar volume of a solute, Vh (s), in a
supercritical fluid can be represented by an equation of the type15
Calculations for styrene (rion ) 0.296 nm)12 indicate the
magnitude of the polarization term is 0.12 eV less than that for
pyrimidine. This term accounts in large part for the smaller
equilibrium constant for eq 4.
Volume Changes. There is essentially no change in the rate
of attachment of electrons to pyrimidine, ka, either with
temperature or pressure, indicating the activation energy as well
1
4
Vh (s) ) aø + b
(11)
q
T
as the activation volume, ∆Va , are both close to zero. The latter
is evaluated from
When b is taken as the molar volume of the solute and a is
a negative term dependent on temperature, experimental data
on partial molar volumes for various solutes can be represented
qualitatively with eq 11. Thus, in general, Vh (s) is expected to
be slightly positive at high pressures, where øT is small, and
large and negative at pressures near the compressibility maxi-
mum.
The first and most important volume term in eq 10b is that
due to electrostriction by the ion which was calculated using
the compressible continuum model outlined above. This involves
integrating the density of the ethane clustered around the ion,
q
∆
V ) -RT d ln k /dP
(8)
a
a
1
6
q
The activation volumes for detachment, ∆Vd , evaluated by an
equation analogous to eq 8, are equal in magnitude, but opposite
in sign, to the reaction volumes discussed below. The values
q
of ∆Vd decrease with increasing pressure. These results contrast
with those found for electron attachment to CO2 in ethane where
q
∆
Va is approximately 50% of ∆Vr. However, the results are
similar to those obtained for attachment to pyrimidine in liquid
2
q
TMS in that ∆Va is near zero. It may be concluded that for
electron attachment to pyrimidine the activated state is close to
the reactants.
∞
V(r)
2
Vel ) 4π
∫
[F(r)
∫
dV]r dr
(12)
rion
V∞
The overall volume changes in reaction 1 are evaluated from
the slopes of the lines in Figures 1c and 2 using the equation
The calculated density as a function of distance from the ion
is shown for some conditions of pressure and temperature in
Figure 5. A common feature of all these curves is the gradual
decrease in density with distance. The curves indicate that there
must be a full first shell of ethane molecules around the ion,
while subsequent shells have vacancies, the number of which
increase with distance from the ion. The enhanced density
around the ion extends as far out as 1.7 nm. Calculated volumes
of electrostriction, from eq 12, are shown by the lines in Figure
∆
V ) d∆G /dP
(9)
r
r
The points in Figure 4 show the values of ∆Vr obtained this
way. The values decrease with decreasing pressure and the
minimum values observed are -8.7, -6.4, and -4.4 L/mol at
33, 37, and 45 °C, respectively. Even lower values are expected
at lower pressures, but this could not be verified because reaction
4
and are in fair agreement with observed values of ∆Vr, but at
1
is too unfavorable there.
high pressure the points fall consistently below the calculated
values. While at low pressures the points are above the
calculated lines.
The observed volume changes are associated with electros-
triction (clustering) of ethane molecules around pyrimidine
anions. Actually ∆Vr is the difference between the partial molar
volume of products and reactants,
These deviations can be attributed to the Vh (pyr) term in eq
0b. At high-pressure Vh (pyr) is expected to be approximately
1
equal to the molar volume of pyrimidine, which is 0.079 L/mol
(see eq 11). This positive value of Vh (pyr) contributes to the
negative deviations observed at high pressure (Figure 4). At
low pressures, the term containing the compressibility domi-
nates, making Vh (pyr) negative. A recent IR study confirmed
-
-
∆Vr ) Vh (pyr ) - Vh (pyr) - Vh (e )
(10a)
-
but V(e ) is presumed to be small because the electron is quasi-
free, as evidenced by the high mobility. Thus, the volume
4

Thermodynamics of Electron Attachment in Ethane
J. Phys. Chem. B, Vol. 103, No. 43, 1999 9209
TABLE 3: Volume Changes (in L/mol) for e- + S T S-
S ) pyrimdine
rion ) 0.257 nm)
S ) CO
(rion ) 0.23 nm)
2
(
P (bar)
∆V
r
(exptl)
V
el
∆V
r
(exptl)
V
el
T ) 306 K
-0.51
-0.80
-1.04
-1.6
1
10
-0.70
-0.82
-1.29
-1.76
-8.71
-0.88
-1.06
-1.12
-2.24
-9.4
-0.52
-0.82
-1.06
-1.62
-13.1
80
70
60
50
-13.0
T ) 310 K
-0.50
1
20
-0.80
-0.90
-1.19
-1.41
-2.31
-6.4
-0.87
-1.07
-1.26
-1.95
-3.03
-9.7
-0.51
-0.79
-0.99
-1.38
-2.76
-8.86
90
80
70
60
55
-0.77
-0.97
-1.36
-2.72
-8.71
the existence of enhanced local density around aromatic
compounds in a supercritical solvent (CO2).17 Thus, experi-
Figure 6. Free energy for electron attachment to pyrimidine versus
temperature at various pressures (in bar) as indicated on the graph.
mental values of ∆Vr are expected to be above the predicted
values of Vel at low pressures, as we observe at the lowest
pressures studied (Figure 4). At even lower pressures, larger
deviations are possible. The predicted minimum values of Vel
are -60.4, -19.5, and -10.4 L/mol at 33, 37, and 45 °C,
respectively. Experimental values are not available for com-
parison.
TABLE 4: Entropy and Enthalpy Changes for e-
+
-
Pyrimidine h Pyrimidine
P
∆H
r
∆S
r
∆V a
r
R
T
/ø
∆Sel
(
bar) (kcal/mol) (cal/(K mol)) (L/mol) (cal/(L K)) (cal/(K mol))
5
6
7
85
120
5
5
5
-60b
-173b
-120.8
-90.0
-78.5
-77.6
-6.39
-1.86
-1.33
-1.04
-0.80
32.0
50.1
59.2
66.0
82.9
-204.6
-93.2
-78.7
-68.6
-66.3
-44.5
-35.3
-32.0
-32.8
4
It was predicted in an earlier paper that the increase in density
around an ion due to electrostriction should not be very sensitive
to ion radius. We show in Table 3, a comparison of experimental
reaction volumes for electron attachment to pyrimidine and to
CO2 under various conditions. Calculated values of electros-
triction are shown for the same conditions. There is little effect
of ion radius on the calculated values of Vel. The calculated
values of Vel and the experimental values of ∆Vr show the same
trend for both molecules, indicating that electrostriction by the
ions is the principal source of volume change. However, as
discussed above, the partial molar volume of the neutrals must
be considered. This can be seen by comparing the difference
between the reaction volumes for electron attachment to CO2
and pyrimidine. That difference is in reality the volume change
for the reaction
a
b
Experimental volume changes observed at 310 K These values
are based on data at only two temperatures
changes from ∼-173 cal/(K mol) at 55 bar to -78 cal/(K mol)
at 120 bar. There is a corresponding large change in ∆H .
r
The large entropy changes are associated with the large
density increases (clustering) around the ions. It was shown in
studies of electron attachment in liquids that the entropy of
electrostriction, ∆S , is related to the volume change by
el
∆S ) (R /ø )∆V
r
(14)
el
T
T
where RT ) (1/V) dV/dT. The ratio RT/øT depends on P, T, and
F and will thus have various values depending on distance from
the ion. However, to evaluate the validity of eq 14 in super-
critical fluids, the values of RT and øT were computed here from
the EOS. Values of ∆Sel were then calculated using eq 14 and
the corresponding experimental values of ∆Vel and are shown
in the last column of Table 4. The calculated values show the
same trend with pressure as shown by the experimental values
and account for most of the entropy change. Thus eq 14 appears
to be valid in supercritical fluids and provides a way to estimate
the entropy change.
-
-
2
pyrimidine + CO T pyrimidine + CO
(13)
2
4
An earlier paper showed no evidence for clustering around
neutral CO2, and since the calculated electrostriction volumes
of the two ions are similar, any volume change is attributed to
Vh (pyr). The values of ∆Vr for pyrimidine (col 2) are generally
less than ∆Vr for CO2 (col 4), indicating Vh (pyr) is negative.
Above 60 bar, this difference is small, amounting to a few tenths
of a liter per mole. This is also reflected in the free energy of
reaction 13, which (by difference) is about 0.18 eV, changing
only slightly with pressure above 60 bar. However, at lower
pressures, there are significant differences and the volume
change for reaction 13, ascribed to Vh (pyr), is as much as -3
L/mol at 55 bar and 310 K.
Summary. This and the previous paper on CO24 have
provided both experimental and theoretical information about
the thermodynamics of electron capture reactions in supercritical
ethane. The results are consistent with calculations of a
compressible continuum model. Sharp minima in ∆Vr are
predicted to occur near the compressibility maxima at each
temperature. To obtain data at the minima, attachment reactions
more exoergic than that for pyrimidine will have to be studied.
Entropy Changes. The large volume changes due to elec-
trostriction are necessarily accompanied by large entropy
changes. Entropy decreases occur when electrons attach to
molecules in the liquid phase,2 and the effect is expected to
be magnified in supercritical fluids. In Figure 6, values of ∆Gr
are plotted versus temperature. The slopes of the lines, equal
to -∆Sr, increase as the pressure decreases. Entropy and
enthalpy changes are shown in Table 4. The value of ∆Sr
,3,8
Appendix A
Equation 5 was derived by considering the force balance
exerted on a small volume element dx dy dz, whose center is
placed at (x,y,z).

9210 J. Phys. Chem. B, Vol. 103, No. 43, 1999
Holroyd et al.
This volume element takes the force from the pressure P
ꢀ (ꢀ - 1)
2
∂
P
r
0
r
∂E
∂r
)
∂
2
dx
2
dx
x
P x -
- P x +
dy dz,
Acknowledgment. The authors thank James Wishart and
Steven Howell for the operation of LEAF and thank Harold
Schwarz for help in implementing data acquisition. This research
was carried out at Brookhaven National Laboratory and sup-
ported under Contract DE-AC02-98-CH10886 with the U.S.
Department of Energy through its Division of Chemical
Sciences, Office of Basic Energy Sciences. K.I. and M.N. are
supported by a Grant in Aid for Scientific Research from the
Ministry of Education, Science and Culture, Japan.
(
( (
)
(
))
2
dy
dy
2
dz
2
P y -
- P y +
dz dx,
(
(
)
(
))
dz
2
P z -
- P z +
dx dy
(
(
)
(
)
)
∂
P
x
∂P
∂y
∂P
∂z
)
-
dx dy dz,
dy dz dx,
dz dx dy
(
)
∂
∂
P ∂P ∂P
)
)
-
,
,
dx dy dz
(
)
References and Notes
∂
x ∂y ∂z
(
1) Hart, E. J.; Gordon, S.; Thomas, J. K. J. Phys. Chem. 1964, 68,
-(gradP) dx dy dz
1271.
(
(
2) Chen, P.; Holroyd, R. A. J. Phys. Chem. 1996, 100, 4491.
3) Holroyd, R. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 298. This
rate constant has been converted to molal units, which are used throughout
this work.
On the other hand, this volume element also takes the force
from the electric field E, as it is polarized and has a dipole
moment of ꢀ0(ꢀr - 1)E dx dy dz.
(4) Nishikawa, M.; Itoh, K.; Holroyd, R. A. J. Phys. Chem. 1999, 103,
5
50.
(
5) Burrow, P. D.; Michejda, J. A.; Jordan, K. D. J. Am. Phys. Soc.
1976, 98, 6392.
(6) Mathur, D.; Hasted, J. B. Chem. Phys. 1977, 16, 347.
7) Younglove, B. A.; Ely, J. F. J. Phys. Chem. Ref. Data 1987, 16,
∂
Ex
∂Ey
∂Ez
∂Ex
∂y
∂Ey
ꢀ0
(ꢀ - 1) dx dy dz E
r
x
+ Ey
+ Ez
, Ex
+
(
∂
x
∂x
∂x
(
∂
Ey
∂Ez ∂Ex
∂Ez
∂z
577.
(8) Holroyd, R. A.; Gangwer, T. E.; Allen, A. O. Chem. Phys. Lett.
975, 31, 520.
(9) Nishikawa, M.; Holroyd, R. A.; Itoh, K. J. Phys. Chem. 1998, 102,
189.
(10) Luo, H.; Tucker, S. C. J. Phys. Chem. 1996, 100, 11165.
Ey
+ Ez
, Ex
+ Ey
+ Ez
)
∂
y
∂y
∂z
∂z
1
2
grad(E )
4
)
ꢀ (ꢀ ) 1) dx dy dz
0 r
2
(
11) Frank, H. S. J. Chem. Phys. 1955, 23, 2023.
(
12) Bondi, A. Physical Properties of Molecular Crystals, Liquids and
Because the sum of these two forces must be zero, the relation
Glasses; Wiley: New York, 1968; p 450ff.
13) Nakagawa, K.; Itoh, K.; Nishikawa, M. IEEE Trans. Electr. Insul.
1988, 23, 509.
(
2
grad(E )
(14) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys Chem.
gradP ) ꢀ (ꢀ - 1)
(A-1)
0
r
2
1986, 90, 2738.
(15) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206.
(16) Liu, H.; Macedo, E. A. Ind. Eng. Chem. Res. 1995, 34, 2029.
(17) Wada, N.; Saito, M.; Kitada, D.; Smith, R. L., Jr.; Inomata, H.;
is obtained. Equation 5 was derived by integrating this equation
for the special case of spherical symmetry.
Arai, K.; Saito, S. J. Phys. Chem. B 1997, 101, 10918.