Molecular dynamics simulations of the time dependent dipolar correlation function for esters containing substituted 1,3-dioxacyclohexane rings in their structure

Article abstract of DOI:10.1021/jp9717812

The temperature dependence of the components of the complex dielectric permittivity of cis/trans-2-phenyl-5-(acetoxymethyl)-5-ethyl-1,3-dioxacyclohexane (HEDPA), model compound of the side group of poly[(cis/ trans-2-phenyl-5-ethyl-1,3-dioxacyclohexane-5-yl)methyl acrylate] (PHEDPA), is reported. The curve describing the temperature dependence of the dielectric loss presents a prominent α absorption, centered at -45°C at 1 Hz, associated with the glass-liquid transition. No secondary absorptions are detected in the glassy state down to -120°C. The time dependence of the dipolar autocorrelation coefficient g(t) for HEDPA was simulated at different temperatures by MD procedures. Transformation of the autocorrelation coefficient from the time domain to the frequency domain permits us to evaluate the normalized components ε′/(ε₀ - ε_∞) and ε″ε″_max of the complex dielectric permittivity ε*. The simulated values of ε′/(ε₀ - ε_∞) and ε″/ε″_max, plotted as a function of log(ω/ω_max), where ω_max is the angular frequency at the maximum of the α absorption, are in rather good agreement with the experimental results obtained for HEDPA.

Full text of DOI:10.1021/jp9717812

J. Phys. Chem. B 1997, 101, 10949-10953
10949
Molecular Dynamics Simulations of the Time Dependent Dipolar Correlation Function for
Esters Containing Substituted 1,3-Dioxacyclohexane Rings in Their Structure
E. Saiz,† E. Riande,*,‡ R. D´ıaz-Calleja,§ and J. Guzma´n‡
Departamento de Qu´ımica F´ısica, UniVersidad de Alcala´, 28871 Alcala´ de Henares, Spain, Instituto de Ciencia
y Tecnolog´ıa de Pol´ımeros (CSIC), 28006 Madrid, Spain, and Departamento de Termodina´mica Aplicada,
ETSII, UniVersidad Polite´cnica de Valencia, 46022 Valencia, Spain
ReceiVed: June 2, 1997; In Final Form: September 12, 1997X
The temperature dependence of the components of the complex dielectric permittivity of cis/trans-2-phenyl-
5-(acetoxymethyl)-5-ethyl-1,3-dioxacyclohexane (HEDPA), model compound of the side group of poly[(cis/
trans-2-phenyl-5-ethyl-1,3-dioxacyclohexane-5-yl)methyl acrylate] (PHEDPA), is reported. The curve
describing the temperature dependence of the dielectric loss presents a prominent R absorption, centered at
-45 °C at 1 Hz, associated with the glass-liquid transition. No secondary absorptions are detected in the
glassy state down to -120 °C. The time dependence of the dipolar autocorrelation coefficient g(t) for HEDPA
was simulated at different temperatures by MD procedures. Transformation of the autocorrelation coefficient
from the time domain to the frequency domain permits us to evaluate the normalized components ꢀ′/(ꢀ0 -
ꢀ∞) and ꢀ′′/ꢀ′′max of the complex dielectric permittivity ꢀ*. The simulated values of ꢀ′/(ꢀ0 - ꢀ∞) and ꢀ′′/ꢀ′′max
,
plotted as a function of log(ω/ωmax), where ωmax is the angular frequency at the maximum of the R absorption,
are in rather good agreement with the experimental results obtained for HEDPA.
Introduction
The phenomenological theory of linear responses to perturba-
tion fields predicts that transformation of g(t) to the frequency
The relaxation loss response of glass-forming liquids to a
variety of weak perturbation fields (mechanical, electrical,
optical, etc.), measured at temperatures just slightly above their
glass-transition temperature, exhibits in the frequency domain
an R process followed by a faster â process. An increase in
temperature moves both the R and â absorptions to higher
frequencies, the larger shift occurring for the R process as a
consequence of its comparatively large activation energy. As
a consequence, the R and â processes tend to merge as the
temperature is increased, forming a combined Râ relaxation
process.1 In general, the R relaxation is described by the stretch
Kohlrausch-Williams-Watts (KWW) equation or decay func-
tion given by2,3
domain gives the frequency dependence of a compliance
function Γ (creep compliance J*(ω), dielectric permittivity ꢀ*-
(ω), etc). The general expression is given by9,10
Γ*(ω) - Γ
Γ0 - Γ∞
∞ ) 1 - ∞g(t) exp(-iωt) dt
(3)
∫
0
where Γ*(ω) is the complex compliance function at the angular
frequency ω and Γ0 and Γ∞ are the values of this quantity at
zero and infinite frequencies, respectively. If the relaxation
strength of the â process is negligible, the decay function g(t)
for the R relaxation can be expressed in molecular terms by9,10
µ (0)‚µ (t) +
µ (0)‚µ (t)
i j
g(t) ) exp[-(t/τ*)âh]
(1)
∑
i
i
i*j
g(t) )
(4)
where 0 < âh e 1. The exponent âh is related to the complexity
of the relaxation in such a way that the lower its value is, the
wider is the distribution of relaxation times of the R absorption.
For a process described by a single relaxation time or Debye
type peak, âh ) 1. The temperature dependence of the mean
relaxation time, τ*, in the vicinity of the glass transition
temperature is governed by the empirical Vogel-Fulcher-
Tamman-Hesse (VFTH) equation:4-6
µ (0)‚µ (0) +
µ (0)‚µ (0)
i j
∑
i
i
i*j
where µi(t) is the dipole moment of the molecule i along the
trajectory at time t.
One of the objectives of this work was to simulate, employing
molecular dynamics procedures, the dipole moment time-
correlation function g(t) for cis/trans-2-phenyl-5-(acetoxym-
ethyl)-5-ethyl-1,3-dioxacyclohexane (HEDPA), a model com-
pound of the side group of poly[(cis/trans-2-phenyl-5-ethyl-
1,3-dioxacyclohexane-5-yl)methyl acrylate]. Earlier studies
have shown that the values of the mean-square dipole moments
of several esters with substituted cyclohexane and 1,3-dioxacy-
clohexane rings in their structure, computed from the evolution
of the dipole moments along the trajectories, are in rather good
agreement with the experimental results.11-13 Another goal of
this investigation was to transform the simulated dipole moment
correlation function from the time domain to the frequency
domain in order to obtain the frequency dependence of the
components of the complex dielectric permittivity. The results
obtained are further compared with the experimental ones with
m
T - T0
τ*(T) ) A exp
(2)
[
]
where T0, located at a temperature ca. 50 K below Tg, can be
viewed as the Kauzmann temperature,7,8 that is, the temperature
at which the configurational entropy of the system vanishes and
m is believed to be related to the relative free volume of the
system.
† Universidad de Alcala´.
‡ Instituto de Ciencia y Tecnolog´ıa de Pol´ımeros (CSIC).
§ Universidad Polite´cnica de Valencia.
X Abstract published in AdVance ACS Abstracts, November 1, 1997.
S1089-5647(97)01781-1 CCC: $14.00 © 1997 American Chemical Society

10950 J. Phys. Chem. B, Vol. 101, No. 50, 1997
Saiz et al.
the aim of obtaining information on the reliability of MD
simulations to describe the R relaxation behavior of glass-
forming liquids.
Experimental Part
Synthesis of cis/trans-2-Phenyl-5-(acetoxymethyl)-5-ethyl-
1,3-dioxacyclohexane. cis/trans-2-Phenyl-5-ethyl-5-hydroxym-
ethyl-1,3-dioxacyclohexane (HEDP) was synthesized by reaction
of 2-ethyl-2-hydroxymethyl-1,3-propanediol with benzaldehyde
(1/1) using p-toluene sulfonic acid (0.5%) as catalyst. The
reaction proceeded for 4 h in refluxing toluene, under nitrogen
atmosphere, with azeotropic removal of water. The product,
HEDP, was separated from the reaction medium by distillation
and collected under vacuum. cis/trans-2-Phenyl-5-(acetoxym-
ethyl)-5-ethyl-1,3-dioxacyclohexane (HEDPA) was synthesized
at 0 °C under nitrogen by dropwise addition of acetyl chloride
into a chloroform solution of HEDP using triethylamine to
neutralize the hydrogen chloride evolved during the reaction.
The triethylamine salt was removed by filtration, and the
reaction mixture was washed several times with distilled water.
The mixture of HEDPA isomers was dried with sodium sulfate
and further distilled under vacuum (133 °C at 1.5 mbar).
Characterization of HEDP and HEDPA. 1H and 13C NMR
spectra of both HEDP and HEDPA were obtained with a Varian
apparatus operating at 200 MHz for 1H and 50.4 MHz for 13C,
using deuterated chloroform as solvent and tetramethylsilane
as an internal reference. The 13C spectra showed the purity of
both compounds. To obtain the stereochemical composition of
HEDPA, two small fractions of cis and trans isomers of HEDP
were separated by flash chromatography in a column of silica
60 (230-400 mesh ASTM), using a mixture of 1/1 ethyl acetate/
chloroform as eluent. Details of the assignment of the signals
Figure 1. Temperature dependence of the dielectric loss ꢀ′′ for
2-phenyl-5-(acetoxymethyl)-5-ethyl-1,3-dioxacyclohexane (HEDPA) at
the frequencies indicated.
where Φ is the relative free volume and B is an empirical
constant on the order of the unity, which is believed to be related
to the ratio between the critical volume required for a relaxation
process to take place and the volume of the segment or segments
intervening in the relaxation.15 The assumption that the volume
is a linear function of temperature leads eq 5 to the VFTH
expression (eq 2). Comparison of eqs 5 and 2 gives the
important relationship
1
to the H NMR spectrum of HEDP, from which the stereo-
Φg Tg - T0
chemical compositions of both HEDP and HEDPA were
obtained, are given elsewhere.13 By taking the ester residue
and the phenyl group to define the configurations, one finds
that the ratio of cis/trans is (70 ( 2) /(30 ( 2).
Dielectric Measurements. Experimental values of the loss
ꢀ′′ and real ꢀ′ components of the complex dielectric permittivity
ꢀ* of HEDPA were obtained with a three-terminal plane
condenser and a capacitance apparatus operating in the fre-
quency range 10-4-102 kHz. The experiments in the glassy
state proceeded from low to high temperature at a heating rate
of 1 °C/min. In the glass-liquid transition, ꢀ′ and ꢀ′′ were
measured under isothermal conditions.
)
(6)
B
m
which permits us to obtain the relative free volume at Tg. The
value of m was determined from the slope of the straight line
obtained by plotting the natural logarithm of the relaxation times
against 1/(Tmax - T0), as eq 2 suggests, where Tmax is the
temperature at the peak maximum of the isochrones of Figure
1. The value of T0, taken as the one that best fits the results to
a straight line, was 175 K. The glass transition temperature
was taken to be 225 K, the temperature associated with the
maximum of the isochrone at 0.1 Hz. By susbtitution of the
slope (m ) 1840) of the plot of Figure 2 into eq 6, a value of
0.027 is obtained for Φg/B. It is worth noting that this result
lies within the range 0.025 ( 0.005 reported for many
viscoelastic liquids.16
For Debye type substances, that is, for systems whose
responses are described by a single relaxation time, the complex
plane plots of ꢀ′′ vs ꢀ′ are semicircumferences whose intercepts
with the abscissa give, respectively, the relaxed ꢀ0 [)ꢀ′(0)] and
unrelaxed ꢀ∞ [)ꢀ′(∞)] dielectric permittivities. In general, the
dielectric relaxation behavior of liquids cannot be described by
a single relaxation time and the complex plane plots are arcs
that eventually become skewed arcs in polymers and other
complex liquids in which the R relaxation has a wide relaxation
time distribution. In general, these curves fit the Havriliak-
Negami equation:17,18
Experimental Results
Isochrones showing the temperature dependence of the
dielectric loss for HEDPA are plotted at several frequencies in
Figure 1. The isochrones present a prominent absorption
associated with the glass-liquid transition whose location in
the loss-temperature plane shifts, as usual, to higher temperature
with increasing frequency. This absorption, called R relaxation
process, is centered at -45 °C at 1 Hz. Subglass absorptions
were not detected in the glassy region down to -130 °C. The
R relaxation can also be observed in the plots of the values of
ꢀ′′ against frequency obtained at temperatures slightly higher
than -45 °C. This latter temperature should be very close to
the calorimetric glass transition temperature.
The mean relaxation time associated with the R process is
usually taken as the reciprocal of ω ) 2πf, where f is the
frequency in hertz. Doolittle formulated the following empirical
equation for the relaxation times:14
ꢀ0 - ꢀ∞
[1 + (iωτ0)1-Rj
ꢀ* ) ꢀ∞ +
(7)
γj
]
where 0 e Rj < 1 and 0 e γj < 1. For a Debye type relaxation
Rj ) 0 and γj ) 1. Consequently, the larger is the departure of
Rj and γj from 0 and 1, respectively, the higher is the complexity
B
Φ
τ ) A exp
(5)
[
]

Molecular Dynamics Simulations
J. Phys. Chem. B, Vol. 101, No. 50, 1997 10951
Molecular dynamics computations were performed at tem-
peratures of 300, 500, and 1000 K according to standard
procedures19 with the Sybyl molecular modeling package20
employing the Tripos force field.21 Partial charges were
computed with the MOPAC program and the AM1 procedure.22
The charges were used both to calculate the Coulombic
contributions to the force field and to evaluate the dipole
moment of each of the conformations along the trajectory. An
integration step δ ) 1 fs (i.e., 10-15s) was used for all the
calculations. Taking into account that the molecular motions
grow faster as the temperature increases, the integration cycle
was repeated 10 × 106, 5 × 106, and 2 × 106 times, respectively,
for calculations performed at T ) 300, 500, and 1000 K in order
to ensure that all the conformational space is properly sampled
even at the lowest temperature. Conformations generated along
the MD trajectories were recorded every 50 steps for T ) 1000
K and every 100 steps for T ) 500 and 300 K, thus providing
a total number of conformations N ) 10 × 104, 5 × 104, and
4 × 104, respectively, for T ) 300, 500, and 1000 K, each of
them separated by ∆ ) 100 fs (T ) 300, 500 K) or ∆ ) 50 fs
(T ) 1000 K).
Figure 2. Natural logarithm of the reciprocal of the experimental
frequencies versus the reciprocal of Tmax - T0 where Tmax is the
temperature at which the maximum of ꢀ′′ is reached for each frequency
while T0 was taken to be Tg - 50.
A common feature of the trajectories simulated at 300 K is
that the 1,3-dioxacyclohexane ring remains in the conformation
used as the starting point of the MD trajectory. For both
configurations, the trajectories starting with the ester residue in
the axial position present dipole moments significantly larger
than those starting in the alternative conformation. As shown
elsewhere,13 the average values at 300 K of the mean-square
dipole moments along the axial-axial conformation of the trans
configuration and the axial-equatorial of the cis configuration
are, respectively, µ2 ax-ax ) 14.29 D2 and µ2 ax-eq ) 9.87 D2.
For trajectories starting with the ester residue in the equatorial
Figure 3. Complex plane representation of ꢀ* (i.e., loss ꢀ′′ versus real
ꢀ′ components) for HEDPA at -35 °C.
position, µ2
) 3.73 D2 and µ2
) 3.82 D2 for the
eq-eq
eq-ax
trans and cis configurations, respectively. By taking into
account that the molar fractions of the conformations in the cis
and trans configurations with the phenyl group in the axial
position are negligible, one finds that the simulated mean-square
dipole moment of the product is 8.1 D2, in very good agreement
with the experimental result,13 7.9 D2.
Though MD simulations carried out at 300 K give a very
good account of the dipole moment of HEDPA, chair-to-chair
conformational transitions were not observed in a reasonable
computing time. However, though these transitions have no
incidence on the equilibrium mean-square dipole moment, they
strongly affect the dipole moment time-correlation function
defined by eq 4. Therefore, temperatures higher than 300 K
were used to speed up chair-to-chair inverse transitions in the
1,3-dioxacyclohexane ring.
Although the intermolecular cross-correlation terms in eq 4
will have appreciable magnitude and their signs may be positive
or negative, there are experimental and theoretical considerations
suggesting that auto- and cross-correlation terms may have the
same time dependence.1,9 By use of this assumption, g(t) can
be expressed in terms of the autocorrelation function
Figure 4. Trans configuration (equatorial-equatorial conformation)
of the 2-phenyl-5-(acetoxymethyl)-5-ethyl-1,3-dioxacyclohexane (HED-
PA) molecule. Rotational angles were taken to be 180° in their trans
orientation.
of the system. An illustrative plot of the dielectric results of
HEDPA at -35 °C is shown in Figure 3. It can be seen that
the curve is a skewed arc whose parameters are as follows: Rj
) 0.04; γj ) 0.484; τ0 ) 0.01 s.
Theoretical Analysis
The NMR analysis of HEDPA shows that this compound is
a mixture of cis and trans configurations arising from the
location of the substituents in the 1,3-dioxane ring. A schematic
representation of the trans configuration is indicated in Figure
4 where the ester residue and the phenyl group were used to
define the configuration. Chair-to-chair conformational transi-
tions can occur within each configuration through modifications
of the angles ø1 and ø2 governing the relative positions of the
substituents. The conformational space of the compound for
each configuration is governed by the rotational angles φ1, φ2,
and φ3, which define the conformations of the ethyl and ester
residue and the angles ø1 and ø2 associated with the locations
equatorial/axial of the substituents in the 1,3-dioxane ring.
µ(0)‚µ(t)
g(t) )
(8)
µ2
where µ2 is the mean-square dipole moment of the molecules.
The autocorrelation function was computed as a function of time
at 500 and 1000 K with the equation23
N-n
1
g(n∆) )
µ[i∆]‚µ[(i + n)∆]
(9)
∑
2
i)1
µ (N - n)
This equation represents an average over the N - n values of

10952 J. Phys. Chem. B, Vol. 101, No. 50, 1997
Saiz et al.
TABLE 1: Values for the τ and â Parameters of the KWW
Equation (Eq 2) Obtained through Least-Squares Fitting of
the Dipolar Correlation Function g(t) Computed from MD
Trajectories of the 2-Phenyl-5-(acetoxymethyl)-5-ethyl-
1,3-dioxacyclohexane (HEDPA) Molecule Performed at Two
Temperaturesa
config
T (K)
τ (ns)
â
104σ2
g(t) ) exp[-(t/τ)â]
ax-eq
ax-eq
eq-eq
eq-eq
500
1000
500
0.028 72
0.6450
0.5640
0.5616
0.4774
0.8
0.9
2.5
1.4
0.004 13
0.003 48
0.002 41
1000
a The σ2 parameter indicates the sum of the squared deviations of
the fitting.
The quality of the fitting could also be observed in Figures 5
and 6 where the dotted lines represent the fitted functions and
the solid lines indicate the values of g(t) actually calculated from
MD trajectories. The fitting is quite good at 500 and 1000 K.
In particular, at 500 K, the cis configuration gives âh ≈ 0.65,
while the results for the trans configuration are fitted with a
slightly smaller value of this parameter, namely, âh ≈ 0.56.
Experimental measurements carried out at constant temper-
ature allowed the determination of the real (ꢀ′) and loss (ꢀ′′)
components of ꢀ* as function of frequency. These components
Figure 5. Dipole correlation function g(t) as a function of time for
the cis configuration of the HEDPA molecule obtained at temperatures
of 500 and 1000 K. Solid lines represent values computed from MD
trajectories, while broken lines represent least-squares fittings to the
KWW function (eq 2).
are customarily written in terms of ꢀ′/(ꢀ0 - ꢀ∞) and ꢀ′′/ꢀ′′max
,
where ꢀ′′max is the loss at the maximum of the peak. The values
of ꢀ0 and ꢀ∞ are obtained from the complex plane plots as
indicated above. The normalized values of ꢀ′ and ꢀ′′ are
represented in the frequency domain in Figures 7 (real com-
ponent) and 8 (loss component).
According to eq 3, the theoretical calculation of ꢀ′/(ꢀ0 - ꢀ∞)
and ꢀ′′/ꢀ′′max can be performed by means of the following
equation:10
ꢀ′(ω) - ꢀ∞
ꢀ0 - ꢀ∞
) 1 - ∞g(t) cos(ωt) dt
∫
0
ꢀ′′(ω)
ꢀ′′max ꢀ′′max
∞g(t) sin(ωt) dt
1
)
(10)
∫
0
Values of these integrals were obtained by the method outlined
by Williams et al.:24
Figure 6. Same as for Figure 5 for the trans configuration of the
HEDPA molecule.
(-1)n-1 Γ(nâh + 1)
∞
ꢀ*(ω) - ꢀ∞
)
cos
-
∑
[
nâh
ꢀ0 - ꢀ∞
Γ(n + 1)
g obtained with all the pairs of conformations that are separated
by a time equal to n∆. The value of the correlation function
decreases rather quickly with increasing time. Thus, g(n∆) ≈
0 for values of n that are much smaller than the total number
of studied conformations N, and therefore, N - n is very large
(higher than 20 000 in all the results presented below), which
ensures a good sampling of g over all the conformational space.
Figures 5 and 6 show the value of g(t) as function of time
for two temperatures, respectively, for cis and trans configura-
tions of the HEDPA molecule. The cis configuration was
obtained by starting the MD trajectories in a configuration in
which the ester group is attached to the axial position with
respect to the dioxane ring while the phenyl group is located at
the equatorial position. For this reason, the cis configuration
is referred to as ax-eq. Conversely, the trans configuration is
obtained when the MD simulation starts with both the ester and
phenyl group occupying equatorial positions and is denoted the
eq-eq configuration.
n)1
(ωτ0)
nâhπ
(11)
(
)
]
2
for high frequencies (i.e., -1 e log(ωτ0) e +4 when âh > 0.25),
and
ꢀ*(ω) - ꢀ∞
ꢀ0 - ꢀ∞
(ωτ0)n-1
Γ(n)
∞
n + âh - 1
âh
)
(-1)n-1
Γ
×
∑
(
)
n)1
(n - 1)π
(n - 1)π
cos
+ i sin
(12)
(
)
(
)
[
]
2
2
for low frequencies. Figures 7 and 8 present the theoretical
values of the normalized loss and real components of the
complex permittivity of HEDPA as a function of log(ω/ωmax).
These results were obtained from the autocorrelation function
computed at 500 K through the â parameter of the KWW
function summarized in Table 1. Taking the values of the loss
component ꢀ′′ as an example, Figure 7 shows that both ax-eq
and eq-eq configurations, when taken independently, give good
To eliminate noises and facilitate further treatment of data,
the values of g(t) were fitted to the KWW function1-3 (eq 1).
The coefficients obtained in the fitting are summarized in Table
1, whose last column contains the sum of the squared deviations.

Molecular Dynamics Simulations
J. Phys. Chem. B, Vol. 101, No. 50, 1997 10953
temperature, provided that the computing time at the temperature
of interest is large enough for the molecules to visit all the
conformational space. The temperature would mainly affect
the value of the mean relaxation time, τ*, and as result, the
location of the relaxation curves in the frequency or time
domains. Consequently, the plot of the normalized components
of the complex dielectric permittivity vs log(ω/ωmax) should be
independent of temperature. This assumption is backed by the
good agreement between theoretical and experimental results
observed for other molecules, specifically, 2-chlorocyclohexyl
isobutyrate23 and alicyclic low molecular weight analogues of
acrylate polymers.25
In conclusion, these results show that the intramolecular
motions occurring in HEDPA give a good account of the R
relaxation of this compound. Interactions with the surroundings
shift the frequencies of the relaxation to lower values without
apparently changing the breadth of the distribution of relaxation
times in the logarithmic frequency scale, as the temperature-
time superposition principle suggests. It should be pointed out
that despite the relative simplicity of HEDPA, the exponent of
the KWW stretch function is surprisingly not much larger than
the value reported for long molecular chains.
Figure 7. Normalized values of the real component ꢀ′ of the complex
electrical permittivity ꢀ* of HEDPA. The circles indicate experimental
values measured at -35°, while the lines represent theoretical results
computed at 500 °C with MD procedures.
Acknowledgment. This work was supported by the DGI-
CYT through Grants PB94-0364 and PB96-0134-C02-01.
References and Notes
(1) Williams, G. In Dielectric Relaxation Spectroscopy of Amorphous
Polymer Systems: The Modern Approaches; Riande, E., Eds.; Keynote
Lectures in Polymer Science; CSIC: Madrid, 1995.
(2) Kohlrausch, R. Ann. Phys. 1847, 12 (3), 3931.
(3) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80.
(4) Vogel, H. Z. Phys. 1921, 22, 645.
(5) Fulcher, G. S. J. Am. Ceram. Soc. 1925, 8, 339.
(6) Tamman, G.; Hesse, W. Z. Anorg. Allg. Chem. 1926, 156, 245.
(7) Stillinger, F. H. Science 1995, 267, 1924.
(8) Kauzman, K. Chem. ReV. (Washington, D.C.) 1948, 43, 29.
(9) Williams, G. AdV. Polym. Sci. 1979, 39, 59.
(10) Riande, E.; Saiz, E. Dipole Moments and Birefringence of Polymers;
Prentice Hall: Englewood Cliffs, NJ, 1992.
(11) Saiz, E.; Riande, E. J. Chem. Phys. 1995, 103, 3832.
(12) Saiz, E.; Riande, E.; Guzma´n, J.; Iglesias, M. T. J. Phys. Chem.
1996, 100, 3818.
(13) Saiz, E.; Guzma´n, G.; Iglesias, M. T.; Riande, E. J. Phys. Chem.
1996, 100, 18345.
(14) Doolittle, A. K.; Doolittle, D. B. J. Appl. Phys. 1957, 28, 901.
(15) Turnbull, D. C.; Cohen, M. H. J. Chem. Phys. 1958, 29, 1049.
(16) Ferry, J. D. Viscoelastic Properties of Polymers; Interscience: New
York, 1980.
Figure 8. Same as for Figure 7 for the loss component ꢀ′′.
(17) Havriliak, S.; Negami, S. Polymer 1967, 8, 161; 1969, 10, 859.
(18) Havriliak, S., Jr.; Havriliak, S. J. Dielectric and Mechanical
Relaxation in Materials; Carl Hanser Verlag: New York, 1997.
(19) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids;
Clarendon Press: Oxford, 1987.
(20) Tripos Associates Inc., St. Louis, MO 63144.
(21) Clark, M.; Cramer, R. D., III; van Opdembosch, N. J. Comput.
Chem. 1989, 10, 983.
(22) MOPAC, Quantum Chemistry Program Exchange; Department of
Chemistry, Indiana University: Bloomington, IN, 47405
(23) Saiz, E.; Riande, E.; Diaz-Calleja, R. J. Phys. Chem. A 1997, 101,
7324.
(24) Williams, G.; Watts, D. C.; Dev, S. B.; North, A. M. Trans. Faraday
Soc. 1971, 67, 1323.
agreement with experimental results. Moreover, the agreement
between theory and experience is improved by taking into
account that the fractions of ax-eq and eq-eq configurations
in the experimental sample amount to ca. 0.7 and 0.3,
respectively. Performing the same kind of weighted average
with the theoretical values of ꢀ′′, one obtains the results indicated
by the thicker solid line of Figure 7 that gives an almost perfect
agreement with the experimental results.
The assumption stated above that the cross-correlation terms
in eq 4 do not alter in a significant way the time dependence of
the decay function suggests that the âh exponent obtained for
this equation in the MD simulations should be independent of
(25) Saiz, E.; Riande, E.; Diaz-Calleja, R. J. Chem. Soc., Perkin Trans.
2, in press.