Effect of hydrostatic pressure on the viscoelastic response of polyurea

Abstract

Dielectric spectroscopy is used to measure the local segmental relaxation times for the soft segments of a polyurea as a function of temper-ature and pressure. In combination with the equation of state determined for the material, we show that the relaxation times are uniquely defined by the product of temperature times specific volume, with the latter raised to the power of 2.35 AE 0.10. This superpositioning of the relaxation times enables both the local segmental and the global chain dynamics to be calculated for any combination of temperature and pressure, using only measurements at ambient pressure. Since this polyurea finds applications as a coating to mitigate the damage from impact loading, its response to high frequencies and elevated hydrostatic pressure is of some import.

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Effect of hydrostatic pressure on the viscoelastic response of polyurea
C.M. Rolanda,*, R. Casalinia,b
aNaval Research Laboratory, Chemistry Division, Code 6120, Washington, DC 20375-5342, United States
bChemistry Department, George Mason University, Fairfax, VA 22030, United States
Received 25 May 2007; received in revised form 9 July 2007; accepted 10 July 2007
Available online 15 July 2007
Abstract
Dielectric spectroscopy is used to measure the local segmental relaxation times for the soft segments of a polyurea as a function of temper-
ature and pressure. In combination with the equation of state determined for the material, we show that the relaxation times are uniquely defined
by the product of temperature times specific volume, with the latter raised to the power of 2.35 ?0.10. This superpositioning of the relaxation
times enables both the local segmental and the global chain dynamics to be calculated for any combination of temperature and pressure, using
only measurements at ambient pressure. Since this polyurea finds applications as a coating to mitigate the damage from impact loading, its
response to high frequencies and elevated hydrostatic pressure is of some import.
? 2007 Elsevier Ltd. All rights reserved.
Keywords: Polyurea; Pressure; Viscoelasticity
1. Introduction
Polyurea (PU) is the generic term for the block copolymer
formed from reaction of diisocyanates with polyamines. Com-
mercialized in 1989, PU can exhibit a wide range of mechan-
ical properties, from soft rubber to hard plastic depending on
the chemistry. The range of properties together with their rapid
reaction has led to many applications as coatings, for example
on tunnels, bridges, roofs, parking decks, storage tanks, freight
ships, truck beds, etc. More recently PU has been used in lam-
inates on buildings and vehicles to impart impact resistance to
the structure. For example, building foundations coated with
PU are more resistant to damage from a bomb blast and are
less likely to fragment (debris propelled by the blast pressure
is a leading cause of injury in bombed buildings) [1e3]. PU
coatings are also applied to military armor to increase its resis-
tance to ballistic penetration [1,4]. The mechanism of blast
and ballistic mitigation from PU laminates is not entirely un-
derstood, but contributing factors may include delayed onset
of necking of the metal substrate [5], alteration of stress waves
through the laminate [6] and substantial energy dissipation
within the PU due to a strain-induced transition from the rub-
bery to the glassy state [7]. The glass transition zone of poly-
mers is the region of greatest energy dissipation and this
transition can be induced in rubbers by sufficiently fast defor-
mation [8].
In light of the growing applications of PU for improving
impact resistance, there has been substantial effort of late to
characterize its viscoelastic behavior, including high strain
rate testing in tension [9], compression [10e12], and com-
bined bulk and shear [13,14], as well as modeling [5]. Such
efforts are essential for understanding and optimizing the per-
formance of PU coatings. When subjected to impact, the PU
coating experiences a locally elevated pressure, in addition
to the compressive strain. Since hydrostatic pressure changes
the viscoelastic response, an accurate determination of pres-
sure effects is warranted. To date studies addressing this effect
have been limited to combined volume and shear deformation
experiments, requiring subsequent deconvolution of the pres-
sure effect [13,14] . It is difficult to carry out directly mechan-
ical measurements with hydrostatic pressure as a distinct
experimental variable.
* Corresponding author. Tel.: þ1 202 767 1719; fax: þ1 202 767 0594.
E-mail address: roland@nrl.navy.mil (C.M. Roland).
0032-3861/$ - see front matter ? 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.polymer.2007.07.017
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A complicating factor in characterizing the mechanical re-
sponse of a polymer is that the temperature, T, and pressure, P,
dependences depend strongly on the viscoelastic modes that
are probed. The chain modes, as described by Rouse, repta-
tion, and various other rheological models [8,15], have
a weaker response to thermodynamic variables than do the lo-
cal segmental modes. The latter arise from intermolecularly
cooperative conformational transitions of the polymer back-
bone and serve as the mechanism of the glass transition, as
well as being the precursor to the chain motions responsible
for rubbery and flow properties. The difference in temperature
dependence of the global and local modes was discovered
more than 40 years ago [16] and has been demonstrated for
various elastomers, including polyisoprene [17], polyisobutyl-
ene [18], and amorphous polypropylene [19]. More recently
the different response to pressure of these modes has been re-
ported for polyisoprene [20], polypropylene glycol [21,22],
and polyoxybutylene [23]. If the impact of the laminate
coating causes transition of the polymer to the glassy state,
as has been demonstrated for PU in representative applications
[7], accurate characterization of the P dependence of the local
segmental dynamics is essential.
An alternative to mechanical measurements of the local seg-
mental dynamicsisdielectricspectroscopy.Thelocaldynamics
measured dielectrically are identical to the segmental motions
underlying the dynamic mechanical properties in theglass tran-
sition zone. Although dielectric relaxation times are somewhat
longer than mechanical relaxation times [17,24,25], their varia-
tion with thermodynamic conditions is expected to be the same.
Dielectric spectroscopy has three advantages over mechanical
experiments in this regard: (i) the resolution of the local modes
from the chain modes is unambiguous; (ii) the frequency range
of dielectric measurements is broader, routinely covering 9 or
moredecades;and(iii)theabsenceofmovingpartsinthedielec-
tric experiment facilitates measurements at elevated pressure.
Of course, the dielectric experiment probes only the linear re-
sponse.Inthepresentworkwemeasured dielectricallythelocal
segmental dynamics of the soft segments of a PU of interest as
a coating for blast and ballistic mitigations. The measurements
extended over a range of 232 < T (K) < 299 and pressures up to
almost 1 GPa. The calorimetric glass transition temperature of
the soft segments is ca. 182 K, whereas Tgof the PU hard seg-
ment is higher than 400 K, and thus not relevant herein [7].
We also report the equation of state (EOS) for the material, ob-
tainedfromstaticPVTmeasurements.Usingthelatter,weshow
thattherelaxationtimesforthePUsuperposeasafunctionofthe
productvariable,temperaturetimesspecificvolumewiththelat-
terraisedtothepowerof2.35.Thismastercurveenablesthedy-
namics to be obtained for any combination of T and P for
relaxation times in the range from less than 1 ms to w1 s.
2. Experimental
The polyurea was formed by reaction of Isonate 143L (Dow
Chemical) and Versalink P1000 (Air Products), in the ratio of
1:4 isocyanate to amine. Prior to measurements the sample
was annealed to a water content of 3.5%, as determined by
thermogravimetric analysis.
Dielectric spectroscopy was done using a parallel plate ge-
ometry with the sample in the form of a disk (16 mm diameter,
2 mm thick). Spectra were obtained as a function of T and P
using a Novocontrol Alpha analyzer (10?2e106Hz). For mea-
surements at ambient and elevated pressure, the sample capac-
itor assembly was contained in a Manganin cell (Harwood
Engineering), with pressure applied using an Enerpac hydrau-
lic pump in tandem with a pressure intensifier (Harwood
Engineering). Pressures were measured with a Sensotec
tensometric transducer (resolution ¼ 150 kPa). The sample as-
sembly was contained in a Tenney Jr. temperature chamber
(?0.1 K precision at the sample).
Changes in volume as a function of pressure at fixed tem-
perature were obtained with a Gnomix instrument [26], utiliz-
ing mercury as the confining fluid. The experimental range
was 10 ? P (MPa)? 200 and 299.0? T (K) ? 386.5. Samples
with w1 ml volume were cut from the same PU sheet used for
dielectric samples. The differential volume data were con-
verted to specific volumes using the value of V¼ 0.9052 g/ml,
determined at 295.9 K and ambient pressure by the buoyancy
method.
3. Results and discussion
3.1. Equation of state
The specific volume change was measured over a tempera-
ture range from 299 < T (K) <387 as a function of pressure up
to 200 MPa (Fig. 1). The Tait EOS [26] describes well the be-
havior of liquids and polymers above the glass transition:
V?T;P?¼?a0þa1T þa2T2?½1?C lnð1þP=b0expð?b1TÞÞ?
ð1Þ
Fitting the experimental data we obtain the Tait parameters in
Table 1. At ambient conditions the bulk modulus, B, equals
1500 50 100200
0.86
0.88
0.90
0.92
0.94
V [ml/g]
P [MPa]
Fig. 1. Specific volume of the polyurea at (bottom to top) T¼299.2, 309.3,
318.7, 328.0, 337.8, 347.1, 357.3, 367.0, 376.9, 387.0 K.
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2.57 GPa, with dB/dP¼ 12 ? 1. This is larger than the bulk
modulus reported by Chakkarapani et al. [13] from simulta-
neous shearandvolume
B ¼2.10 GPa. For the ambient thermal expansion coefficient
we obtain aP¼ 5.53 ? 10?4K?1. Amirkhizi et al. [12] cited
a much lower value of 2 ?10?4K?1, obtained by an unspec-
ified method. We believe the results herein are more accurate,
due to the higher accuracy of our measurement technique;
however, it should be recognized that the properties of poly-
urea are very sensitive to chemical stoichiometry [9], so that
samples prepared in different labs could show differences.
deformationexperiments,
3.2. Temperature and pressure effects on local segmental
relaxation
Dielectric relaxation spectroscopy was carried out on the
PU at ambient and elevated pressures, with representative di-
electric loss spectra shown in Fig. 2. With decreasing temper-
ature or increasing pressure, the dispersion in the dielectric
loss shifts toward lower frequency. We can define a local seg-
mental relaxation time, representing the most probable value,
as t ¼ ð2pfmaxÞ?1, where fmaxis the frequency of the peak
maximum. The isobaric data, plotted vs. inverse T in Fig. 3,
show the usual non-Arrhenius behavior. Included in the figure
are data for this same PU but with less absorbed water [7]. PU
is hygroscopic, so that its moisture content is affected by the
ambient humidity. At higher temperatures in Fig. 3, there is
no discernible effect, but with cooling the relaxation times
for the two samples show some deviation.
Amirkhizi et al. [12] reported mechanical measurements on
the PU using a Hopkinson split bar apparatus. These were car-
ried out at a constant strain rate w3000 s?1at temperatures
down to 273 K. From the data in Ref. [12], the PU remained
in the rubbery state during the high strain rate mechanical test,
which is consistent with the fact that the time scale of the defor-
mation,0.3 ms(indicatedbythehorizontallineinFig.3),islon-
gerthanthetmeasuredforthePU;thus,thechainsegmentscan
responsetotheimpulseloading.Itisonlyatfasterappliedstrain
rates, corresponding to time scales on the order of 6 ms, that the
deformationwillinvolvethelocalsegmentaldynamics,withthe
PU transitioning to a glassy state during impact [7].
At constant temperature the relaxation times increase line-
arly with pressure (Fig. 4). From mechanical experiments at
3000 s?1, Amirkhizi et al. [12] reported a pressure coefficient
of the shift factor for the chain (Rouse) modes of this material
equal to 7.2 K/GPa. From Fig. 4 we deduce a linear coefficient
of 120 ? 14 K/GPa at the frequency of the mechanical exper-
iments. Thus, the segmental modes of PU have a much stron-
ger P dependence than found previously for the chain modes
(as noted above, the PU exhibited rubbery behavior in the
mechanical experiments [12]). This difference is unsurprising,
since similar to the T dependence [16e19], the P dependence
of polymer dynamics is stronger for local modes than for chain
modes [20,21,23].
The activation volume, DV#, is the usual parameter for
quantifying this pressure dependence:
DV#¼
RT
logðeÞ
v logt
vlog P
????
T
ð2Þ
where R is the gas constant and e is Euler’s number. The im-
plied proportionality between log t and log P describes the
data in Fig. 4, but Eq. (2) is not expected to apply at sufficiently
high pressures. In the inset of Fig. 4, DV#is shown for the four
measurement temperatures, decreasing by w1/3 over the range
of T. This inverse variation of DV#with T is commonly found
[27]. The activationvolume is often interpreted as a measure of
the volume swept out by the relaxing unit; thus, its magnitude
is on the order of the repeat unit size.
Table 1
Equation of state parameters for PU above Tg
a0(ml/g)
a1(ml/gC)
4.90?10?4
a2(ml/gC2)
1.75?10?7
b0(MPa)
b1(C?1)
4.03?10?3
C
aPa(C?1)
5.53?10?4
Ba(GPa)
0.890
2200.07762.57
aT¼ 298 K; P¼0.1 MPa.
101
102
103
104
105
106
0.2
0.4
0.6
0.8
dielectric loss
frequency [Hz]
283.8 K
0.3
0.5
0.7
312.3 K
0.2
0.4
0.6
0.8
0.1 MPa
Fig. 2. Representative dielectric loss spectra: (top, from left to right)
T¼232.7, 242.4, 252.3, 262.4, 273.2, and 288.6 K; (middle, from left to right)
P¼845.0, 703.1, 517.3, 365.5, 210.9, and 22.3 MPa; (bottom, from left to
right) 730.0, 636.3, 430.8, 258.3, 107.1, and 4.9 MPa. The rise toward lower
frequency is due to dc conductivity.
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C.M. Roland, R. Casalini / Polymer 48 (2007) 5747e5752

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The activation volume concept implies that volume governs
the segmental dynamics, but this is not the case for the PU. To
show this we use the EOS (Eq. (1)) to calculate the specific
volume for each measurement condition, and plot in Fig. 5
the t vs. V. It is clear that the relaxation times are not solely
defined by V; rather changes in thermal energy amplify the
variation of t with V. Thus, a full accounting of the segmental
behavior requires quantifying the relative contribution of T
and V to the dynamics.
3.3. Thermodynamic scaling
There are various approaches to extract the distinct effects
of T and V on t. We have recently shown very generally for
non-associated liquids and polymers that the structural or local
segmental relaxation times are a single function of a product
variable [28e30]:
t ¼ fðTVgÞð3Þ
where g is a material-specific constant. This means that the re-
laxationtimesmeasuredforvariousTandPyieldamastercurve
when plotted versus the quantity TVg. The exponent is constant
withrespecttoT,P,andV,andfordifferentmaterialsvariesover
a broad range 0.14 ?g ? 8.5 [27]. We apply this scaling proce-
durehereintothepolyureadata,adjustingthevalueoftheexpo-
nent to obtain superpositioning of the t (Fig. 6). The deduced
value of g¼ 2.35 ? 0.10 israthersmall, reflecting aweakinflu-
ence of volume. The magnitude of the scaling exponent is re-
lated to the steepness of the intermolecular repulsive potential
[31,32],withthelowvalueforPUinkeepingwiththeassociated
0 200400600800 1000
-6
-5
-4
-3
-2
-1
0
270
290
310
30
36
42
48
312.3 K
298.6 K
283.8 K
267.7 K
log (τ /s)
P [MPa]
ΔV# [ml/mol]
T [K]
Fig. 4. Pressure dependence of the local segmental relaxation times at the in-
dicated temperatures. The slopes of the fitted lines yield the activation volumes
(Eq. (2)) displayed in the inset.
0.780.81 0.840.870.90
-7
-6
-5
-4
-3
-2
-1
0
312.3 K
298.6 K
283.8 K
267.7 K
0.1 MPa
log (τ /s)
V [ml/g]
Fig. 5. Local segmental relaxation times plotted versus the specific volume.
3.43.63.84.04.24.44.6
-6
-5
-4
-3
-2
-1
0
1
3.5% water
0.8% water
P = 0.1 MPa
log (τ /s)
1000/T [K-1]
Fig. 3. Temperature dependence of the local segmental relaxation times mea-
sured at ambient pressure. Also included are data from Ref. [7] for this same
PU but having a lower moisture content. The dashed horizontal line denotes
the time scale of high strain rate mechanical tests [12], for which the PU
exhibited a rubbery response.
170185 200 215230245
-7
-6
-5
-4
-3
-2
-1
0
312.3 K
298.6 K
283.8 K
267.7 K
0.1 MPa
log(τ /s)
TV2.35 [Kml2.35 /g2.35]
Fig. 6. Local segmental relaxation times plotted according to Eq. (3) with
g¼2.35.
5750
C.M. Roland, R. Casalini / Polymer 48 (2007) 5747e5752

Page 5

nature of its chain segments. For strongly hydrogen-bonded
liquids such as water, the thermodynamic scaling breaks down
entirely with g approaching unity (i.e., volume changes per se
do not affect the dynamics) [32].
3.4. Isochronal superpositioning
Usually a decrease in temperature or increase in pressure
(i.e., longer t) causes the relaxation function (distribution of
relaxation times) to systematically broaden. By judicious se-
lection of P and T, combinations can be found for which the
peak frequency for local segmental relaxation is constant;
that is, higher pressure and higher temperature compensate
to give constant t. When this is the case, it has been shown
quite generally that the peak shape (breadth) is constant
[33,34]. This means that the relaxation function of a material
at fixed t is constant, independent of temperature and pressure.
We assess conformance of the PU to this temperaturee
pressure superpositioning of the segmental dispersion at
constant t. In Fig. 7 the dielectric loss peak is shown for 6 mea-
surement conditions, for which fmaxis equal to one of two
values. The loss peak for a given fmaxremains the same, except
for the slight rise toward lower frequency due to dc conductiv-
ity. Thus, for PU the relaxation time determines the breadth of
thesegmentaldispersion(butnottheconverse,sincethebreadth
may be sensibly invariant to small changes in T or P). This peak
breadth in turn is correlated with other relaxation properties,
such as the ‘‘dynamic crossover’’ [35,36] and the ‘‘fragility’’,
or Tge normalized temperature dependence of t [37].
4. Summary
The soft-segment local segmental relaxation times and the
EOS were measured for a PU of special interest for ballistic
and other impact applications. Both temperature and pressure
affect the dynamics, with the product variable TV2.35yielding
superposition of the t. Using the obtained master curve, the re-
laxation time can be calculated for any thermodynamic condi-
tion; that is, if t is known for any T and P, via Eq. (3) it can be
calculated for any other T and P. Since as shown herein the
shape of the relaxation function is a function of t, this means
that g also uniquely defines the relaxation function. Thus, at
least in the linear viscoelastic regime, the most important
properties of the local segmental relaxation process e t and
its distribution e are governed entirely by the material con-
stant g. Although no normal mode was observed herein for
the PU, we note that it has been found that the normal model
relaxation times, reflecting the global chain dynamics, have
been found to superpose as a function of TVg, with the expo-
nent identical to the value yielding superpositioning of the lo-
cal segmental relaxation times (although the dependence per
se is weaker) [23,38,39]. This means that the chain relaxation
times, obtained from rheological measurements at ambient
pressure as a function of T, can be calculated for any arbitrary
pressure, by making use of the scaling relationship, Eq. (3).
Consideration of the effect of hydrostatic pressure can be quite
important for blast and ballistic mitigation applications.
Acknowledgements
This work was supported by the Office of Naval Research.
We thank D.P. Owen of NSWC-Caderock for preparing the
polyurea sample, K.J. McGrath for assistance with the PVT
measurements, and R.B. Bogoslovov of NRL for fruitful
discussions.
References
[1] Roland CM. In: Rubber technologist’s handbook, vol. 2. Shrewsbury,
UK: RAPRA; 2007.
[2] Davidson JS, Fisher JW, Hammons MI, Porter JR, Dinan RJ. J Struct Eng
2005;131:1194.
[3] Porter J, Dinan RJ, Hammons MI, Knox KJ. Advanced Materials,
Manufacturing, and Testing Information Analysis Center Quarterly
2002;6:47.
[4] Matthews W. Defense News 26 April 2004;32.
[5] Xue Z, Hutchinson JW. Mech Mater 2007;39:473.
[6] Bahei-El-Din YA, Dvorak GJ, Fredricksen OJ. Int J Solid Struct
2006;43:7644.
[7] Bogoslovov RB, Roland CM, Gamache RM. Appl Phys Lett 2007;90:
221910.
[8] Ferry JD. Viscoelastic properties of polymers. New York: Wiley; 1980.
[9] Roland CM, Twigg JN, Vu Y, Mott PH. Polymer 2007;48:574.
[10] Yi J, Boyce MC, Lee GF, Balizer E. Polymer 2006;47:319.
[11] Sarva SS, Deschanel S, Boyce MC, Chen W. Polymer 2007;48:2208.
[12] Amirkhizi AV, Isaacs J, McGee J, Nemat-Nasser S. Philos Mag
2006;86:5847.
[13] Chakkarapani V, Ravi-Chandar K, Liechti KM. J Eng Mater Technol
2006;128:489.
[14] Jiao T, Clifton RJ, Grunschel SE. American Institute of Physics Confer-
ence Proceedings 2006;845:809.
[15] Doi M, Edwards SF. The theory of polymer dynamics. New York: Oxford
Science; 1986.
[16] Plazek DJ. J Phys Chem 1965;6:612.
[17] Santangelo PG, Roland CM. Macromolecules 1998;31:3715.
[18] Plazek DJ, Chay IC, Ngai KL, Roland CM. Macromolecules 1995;28:
6432.
101
102
103
frequency [Hz]
104
105
106
0.4
0.6
0.8
1.0
262.4 K, 0.1 MPa
298.6 K, 314.2 MPa
312.3 K, 517.3 MPa
283.8 K, 4.9 MPa
298.6 K, 119.7 MPa
312.3 K, 210.9 MPa
ε"/ε"max
Fig. 7. Dielectric loss (normalized by the peak value) measured under condi-
tions (as indicated) for which the peak frequency is equal to a constant value
of: (solid symbols) 2560 Hz or (open symbols) 29,040 Hz. The spectra were
shifted slightly along the abscissa to superpose the peaks.
5751
C.M. Roland, R. Casalini / Polymer 48 (2007) 5747e5752

Page 6

[19] Roland CM, Ngai KL, Santangelo PG, Qiu XH, Ediger MD, Plazek DJ.
Macromolecules 2001;34:6159.
[20] Floudas G, Reisinger T. J Chem Phys 1999;111:5201.
[21] Andersson SP, Andersson O. Macromolecules 1998;31:2999.
[22] Roland CM, Psurek T, Pawlus S, Paluch M. J Polym Sci Polym Phys Ed
2003;41:3047.
[23] Casalini R, Roland CM. Macromolecules 2005;38:1779.
[24] McCrum NG, Read BE, Williams G. Anelastic and dielectric effects in
polymer solids. London: Wiley; 1967.
[25] Colmenero J, Alegria A, Santangelo PG, Ngai KL, Roland CM. Macro-
molecules 1994;27:407.
[26] Zoller P, Walsh DJ. Standard pressureevolumeetemperature data for
polymers. Lancaster, PA: Technomic; 1995.
[27] Roland CM, Hensel-Bielowka S, Paluch M, Casalini R. Rep Prog Phys
2005;68:1405.
[28] Casalini R, Roland CM. Phys Rev E 2004;69:062501.
[29] Alba-Simionesco C, Calliaux A, Alegria A, Tarjus G. Europhys Lett
2004;68:58.
[30] Dreyfus C, Aouadi A, Gapinski J, Steffen W, Matos-Lopes M,
Patkowski A, et al. Eur Phys J B 2004;42:309.
[31] Roland CM, Feldman JL, Casalini R. J Non-Cryst Solids 2006;352:4895.
[32] Roland CM, Bair S, Casalini R. J Chem Phys 2006;125:124508.
[33] Roland CM, Casalini R, Paluch M. Chem Phys Lett 2003;367:259.
[34] Ngai KL, Casalini R, Capaccioli S, Paluch M, Roland CM. J Phys Chem
B 2005;109:17356.
[35] Ngai KL, Roland CM. Polymer 2002;43:567.
[36] Casalini R, Ngai KL, Roland CM. Phys Rev B 2003;68:14201.
[37] Bo ¨hmer R, Ngai KL, Angell CA, Plazek DJ. J Chem Phys 1993;99:4201.
[38] Roland CM, Casalini R, Paluch M. J Polym Sci Polym Phys Ed
2004;42:4313.
[39] Kriegs H, Gapinski J, Meier G, Paluch M, Pawlus S, Patkowski A.
J Chem Phys 2006;124:104901.
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