Intermolecular Cross-Correlations in the Dielectric Response of Glycerol - arXiv.org
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Intermolecular Cross-Correlations in the Dielectric Response of Glycerol
Jan Philipp Gabriel1,2,,a) Parvaneh Zourchang1 , Florian Pabst1 , Andreas Helbling1, Peter Weigl1 , Till Böhmer1 ,
and Thomas Blochowicz1,b)
1)
Institut für Festkörperphysik, Technische Universität Darmstadt, 64289 Darmstadt,
Germany.
2)
Arizona State University, School of Molecular Sciences, Tempe, AZ 85281,
United States
(Dated: 17 March 2020)
We suggest a way to disentangle self- from cross-correlation contributions in the dielectric spectra of glycerol.
arXiv:1911.10976v2 [cond-mat.soft] 13 Mar 2020
Recently it was demonstrated for monohydroxy alcohols that a detailed comparison of the dynamic suscep-
tibilities of photon correlation and broadband dielectric spectroscopy allows to unambiguously disentangle a
collective relaxation mode known as the Debye process, which could arises due to supramolecular structures,
and the α-relaxation, which proves to be identical in both methods. In the present paper, we apply the
same idea and analysis to the paradigmatic glass former glycerol. For that purpose we present new light
scattering data from photon correlation spectroscopy measurements and combine these with literature data
to obtain a data set covering a dynamic range from 10−4 − 1013 Hz. Then we apply the above mentioned
analysis by comparing this data set with a corresponding set of broadband dielectric data. Our finding is
that even in a polyalcohol self- and cross-correlation contributions can approximately be disentangled in that
way and that the emerging picture is very similar to that in monohydroxy alcohols. This is further supported
by comparing the data with fast field cycling NMR measurements and dynamic shear relaxation data from
the literature, and it turns out that, within the described approach, the α-process appears very similar in all
methods, while the pronounced differences observed in the spectral density are due to a different expression of
the slow collective relaxational contribution. In the dielectric spectra the strength of this peak is reasonably
well estimated by the Kirkwood correlation factor, which supports the view that it arises due to dynamic
cross-correlations, which were previously often assumed to be negligible in dielectric measurements.
I. INTRODUCTION glycerol, which is slower than the α-relaxation.17 This is
a remarkable observation regarding the fact that only one
In the study of supercooled liquids, glycerol has a single peak is observed in dielectric spectroscopy.
prominent position as one of the pet systems, probably In terms of complexity, monohydroxy alcohols with
due to its very low tendency to crystallize and also be- only one OH-group per molecule should in some sense
cause of its large dipole moment, which make it a good be in between van der Waals liquids and polyalcohols.
candidate particularly for dielectric investigations1–6 . Many investigations were carried out on monohydroxy al-
But in fact, glycerol has been studied intensively with cohols, to single out the influence of H-bonds in this seem-
a great number of experimental techniques to answer ingly simple situation.22 In contrast to van der Waals liq-
fundamental questions of glass and fluid dynamics, in- uids and polyalcohols many monohydroxy alcohols show
cluding, besides dielectric spectroscopy, nuclear mag- a clear two-peak structure in the dielectric loss. At lower
netic resonance,7–9 dynamic light scattering,10,11 neutron frequencies than the α-relaxation, a peak with mostly a
scattering12–14 and many other techniques.15–20 In terms single-exponential or Debye-like relaxation shape is ob-
of possible interactions, however, glycerol is by no means served in the spectrum. This peak is attributed to the
a “simple” liquid, and thus its status as a “fruit fly” of dynamics of transiently hydrogen-bonded supramolecu-
glass research has recently been questioned.21 And in- lar chains.23 As the permanent dipole moments are pref-
deed, glycerol as a polyalcohol is more complicated than a erentially oriented along the H-bonded structures, the
typical van der Waals liquid, because of three OH-groups, dielectric Debye process mainly reflects intermolecular
which are able to form H-bonds in the liquid. At first cross-correlations. Accordingly, in many monohydroxy
glance, the spectral shape of a dynamic susceptibility in alcohols the relaxation strength is significantly larger
polyalcohols is hardly different from that of a van der than what is expected from uncorrelated single-molecule
Waals liquid: For example the dielectric loss shows a pri- dipole moments and the amount is quantified by the
mary process which is usually identified as the collective Kirkwood correlation factor.24 In previous investigations
structural or α-relaxation7 , which is usually thought to of monohydroxy alcohols it was demonstrated that self-
be related to the viscosity. However, recently a dynamic and cross-correlation contributions can well be separated
shear study revealed an additional relaxation process in experimentally by comparing photon correlation with di-
electric data, where in the majority of cases the former
turns out to reflect the self-correlation part of the spec-
trum 25–29 . We note that a similar analysis was also suc-
a) Electronic mail: Jan.Gabriel@fkp.physik.tu-darmstadt.de cessfully applied to a diol (ethylene glycol), in the pio-
b) Electronic mail: thomas.blochowicz@physik.tu-darmstadt.de neering work of Fukasawa et al.30 , who were able to dis-2
tinguish the above mentioned contribtions in the high fre- for a few reference measurements to ensure matching
quency regime, using dielectric and Raman spectroscopy. temperatures and correlation times between literature
Assuming that monohydroxy alcohols are systems with data and the data of our own laboratory. The PCS ex-
intermediate complexity between van-der-Waals liquids periments were performed under a scattering angle of
and complex polyalcohols, the question arises whether 90◦ in a setup already described earlier in detail.32–34
polyalcohols really show a spectrum that is qualitatively The measured intensity autocorrelation function g2 (t) =
different from monohydroxy alcohols in that it does hIs (t)Is (0)i/hIs i2 was converted into the electric field au-
not show a cross-correlation contribution in the dielec- tocorrelation function g1 (t) = hEs∗ (0)Es (t)i/h|Es |i2 by
tric spectrum or whether such a contribution is simply using the Siegert relation for partial heterodyning as de-
merged with the α-relaxation. The two peak structure scribed in more detail by Pabst et al. 3435 .
recently observed in shear mechanical data of glycerol17 In order to allow for a direct comparison of BDS and
and also the results obtained in ethylene glycol30 might light scattering data, both data sets are used in the same
be a hint that the latter is the case in polyalcohols and representation in the frequency domain, i.e. the dielectric
that self- and cross-correlation contributions are sim- loss ε′′ (ω) is compared with the imaginary part of the
ply harder to disentangle than in monohydroxy alcohols. complex light scattering susceptibility χ′′ (ω), which is
Conceptionally one might imagine a less directed total calculated from g1 (t) through Fourier transformation:36
dipole moment in the network structure of polyalcohols
Z ∞
than in the linear chain structure of monohydroxy alco- ′′
hols. χ (ω) ∝ ω g1 (t) cos(ωt) dt (1)
0
In the present work our approach will be to apply a
procedure similar to the one used for the analysis of By using the Filon rule of integration37 the transforma-
the dielectric loss in monohydroxy alcohols25–28 . For tion can be carried out for discrete datasets on logarith-
that purpose we present a broadband light scattering mic scales, resulting in a spectral representation of the
data set of glycerol, where our own photon correlation depolarized dynamic light scattering data as generalized
data are merged with Tandem Fabry-Perot and Raman susceptibility χ′′ (ω). Because PCS itself is not able to de-
data from the literature to cover a dynamic range from termine absolute relaxation strengths, χ′′ (ω) needs to be
10−4 − 1013 Hz. By comparison with broadband dielec- renormalized after Fourier transformation. This can be
tric data we suggest a way to disentangle self- and cross- achieved at least to reasonable approximation by com-
correlation contributions in the dielectric data. Further bining these data with TFPI measurements, as shown
support for this approach is derived from the discussion further below. The latter are either normalized to a tem-
of nuclear magnetic resonance (NMR) fast field cycling perature dependent absolute scattering intensity or, as
measurements and dynamic shear data, both from the e.g. applied by Brodin et al.,10 by using a particular Ra-
literature. man line.
When comparing BDS and light scattering susceptibil-
ities, one has to keep in mind that, although both reflect
II. EXPERIMENTAL BACKGROUND molecular reorientation, BDS observes a correlation func-
tion of a vectorial quantity, the molecular dipole moment,
Samples of glycerol (Karl Roth, >99.7%), were used while the PCS observable is connected with a tensorial
from a new bottle and filtered into a photon correlation quantity, the anisotropic molecular polarizability.36,38
spectroscopy (PCS) sample-cell by using a 200 nm hy- This leads to reorientational correlation functions that
drophilic syringe filter, while the dielectric samples were are expressed in terms of Legendre polynomials of rank
prepared from the same bottle without further purifica- ℓ as:
tion. Everything was prepared as quickly as possible to
minimize unwanted water contamination. Φℓ (t) = hPℓ (cos θ(t))i, (2)
In terms of temperature measurements all tempera-
ture environments were carefully calibrated to achieve with ℓ = 1 for BDS and ℓ = 2 for light scattering,
an overall accuracy of ±0.5 K. Broadband dielectric with θ(t) being the angle between the positions of the
spectroscopy (BDS) was performed using a Novocontrol respective molecular axis at times 0 and t. If the op-
Alpha-N High Resolution Dielectric Analyzer in combi- tical anisotropy and the permanent dipole moment are
nation with a time domain dielectric setup, reported in mainly located at the same molecular entity and the
detail in Ref. 31 and an Agilent E49991A Impedance An- dynamic processes under consideration are isotropic to
alyzer. Combined data sets of the complex dielectric sus- good approximation, then relations between Φ1 and Φ2
ceptibility ε∗ (ω) were obtained, covering the frequency can be established depending on the geometry of the un-
range of 10−4 − 108 Hz. derlying process. In case of random angle jump of the
Light scattering experiments were performed in molecules the correlation function becomes independent
vertical-horizontal (VH) depolarized geometry. In the of ℓ,38 and under certain conditions, also small angle
high frequency range a Tandem Fabry-Perot interferom- based reorientation geometries can lead to approximately
eter was used (TFPI, J.R. Sandercock, 3 · 108 − 1012 Hz) ℓ-independent correlation functions.393
1 2
10 10 BDS
PCS
ε’(ν)
1
TFPI
10
0
10
cross-correlation
χ’’(ν)
1
323 K 10
362 K
413 K self-correlation
χ’’(ν)
190 K 0
10
-1
200 K 10 sum of correlations
210 K
220 K
230 K -1
240 K 10
250 K
260 K glycerol - 190 K
-2 -2
10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
ν/Hz ν/Hz
FIG. 1. Generalized light scattering susceptibilities of PCS FIG. 2. Common fitting procedure for BDS and light scatter-
and TFPI measurements of glycerol. High frequency data are ing spectra of glycerol at 190 K. The solid line shows the fit
taken from Ref. 10. The normalization and fits are explained composed of self- and cross-correlation contributions (dashed
in the text. lines). High frequency data taken from3 at 185 K and 195 K
III. RESULTS AND DATA ANALYSIS
same time, the freedom in this procedure is rather lim-
ited and the uncertainty can be estimated to be around
Fig. 1 shows selected autocorrelation functions of the 10%.
electric field g1 (t) from PCS, which were Fourier trans-
Fig. 2 shows glycerol data obtained by PCS, TFPI,
formed to yield generalized susceptibility spectra between
Raman and BDS, all at T = 190 K. The light scatter-
190 and 260 K, together with TFPI data from Brodin
ing data are normalized in intensity relative to the BDS
et al.10 The TFPI data are in agreement with our own
data by superimposing the high-frequency wing of the
reference TFPI measurements with respect to peak po-
α-process in both methods. The reason for choosing
sition and spectral shape at a given temperature. We
this particular normalization is the observation in sev-
describe the depolarized light scattering spectra of glyc-
eral monohydroxy alcohols that α- and β-relaxation in
erol by an α-relaxation with high-frequency wing contri-
both PCS and BDS perfectly superimpose and that this
bution by using an extended generalized gamma (GGE)
procedure allows to single out the Debye contribution in
distribution.40 For comparing PCS with BDS data, a rea-
the dielectric spectrum of monohydroxy alcohols.22,26,27
sonable normalization for the light scattering is needed.
The same idea is now applied for the polyalcohol glycerol,
This is achieved by first normalizing the measured TFPI
where such a superposition would allow to single out slow
spectral densities S(ω, T ) with respect to the intensity
cross-correlation contributions in the dielectric spectra
of a Raman line. Then the generalized susceptibility is
assuming that the self part of the correlation function is
obtained by dividing by the Bose factor, which in the
identical in both methods as in monohydroxy alcohols.
classical limit leads to41–43 :
The resulting combined light scattering and BDS data
1 S(ω) ω set, which shows the spectra of each method at the same
χ′′ (ω) = ≈ S(ω, T ) (3) temperature, is seen in Fig. 3. We note that the scal-
~ n(ω, T ) + 1 kB T
ing factor used to superimpose light scattering with the
Here, the prefactor 1/T mimics a Curie law, which is well dielectric data is determined at the lowest temperature
known behavior for the relaxation strength in dielectric and is used for the entire data set at all temperatures.
spectroscopy. In order to combine TFPI with PCS data In the intermediate frequency range reasonable overlap is
to produce a broadband light scattering data set, Fourier achieved up to the highest temperatures. We also men-
transformed correlation functions g1 (t) are multiplied by tion, that in Fig. 3 all data, light scattering or dielectric,
1/T and then the entire PCS data set is shifted in inten- below 1 GHz are from our own lab to ensure as far as
sity relative to the TFPI data so that the high frequency possible identical temperatures, while the high-frequency
wing of χ′′ (ω) from PCS smoothly extrapolates to the low dielectric data are taken from Schneider et al. 3 and are
frequency flank of the susceptibility minimum observed slightly shifted in relaxation strength to match our own
in the GHz–THz range. The result of this procedure is BDS results. The high frequency light scattering data
shown in Fig. 1. We note that a single, temperature inde- are taken from Ref. 10 and merged with the PCS data
pendent shift factor is applied for the whole data set. As set as described above.
both, the peak hight and the high frequency wing have to Concerning the fits displayed in Figs. 2 and 3, the PCS
evolve in a continous fashion for all temperatures at the data are again described by the Fourier transform of a4
190 K 200 K 210 K 220 K 230 K 240 K
4 4
(∆εα+∆εc-c)/∆εα
250 K 260 K
323 K 3 3.5
gK
gK, (∆εα+∆εc-c)/∆εα
362 K
413 K
2 3
1 2.5
10 1
2
0
1.5
-1 1
-2
log(τ)
0.5
-3
χ’’(ν)
0 0
10 -4 200 300
T/K
400
-5
-6 BDSGGE
-7 BDSKWW+GGE
-1
10 -8 PCSGGE
-9
DDLS -10 TFPIGGE
BDS -11
2.5 3 3.5 4 4.5 5 5.5
-4 -3 -2 -1 0 1 2 3 4
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
5 6 7 8 9 10 11 12 1000K/T
ν/Hz
FIG. 4. Time constants for glycerol obtained by PCS,
FIG. 3. Combination of dielectric and light scattering spectra TFPI, Raman and BDS. The inset shows the temperature
of glycerol from Fig. 1. Dielectric permitivity spectra were dependent Kirkwood correlation factor gk compared to the
composed of low frequency data from this work with high amount of cross-correlations approximated by the ratio of
frequency data from Lunkenheimer et al.3 The light scatter- (∆ǫα + ∆ǫc-c )/∆ǫα obtained from the combined fits of the
ing data from Fig. 1 were shifted with respect to the dielec- BDS data.
tric data with a common factor determined at 190K by over-
lapping the high-frequency wing of the α-relaxation in both
methods. larger objects, i.e. transient chains, are thought to av-
erage over the dynamically heterogeneous environment
during reorientation.23
GGE distribution and the BDS data are described by the In order to crosscheck the applied procedure one can
corresponding PCS fit at the respective temperature plus now use the relaxation strength of the self and the cross-
a Kohlrausch-William-Watts (KWW) stretched exponen- correlation part in the spectrum and compare this with
tial function to take account of the BDS cross-correlation the Kirkwood correlation factor, which quantifies the
(c-c) part: amount of cross-correlations in a sample with interact-
ing dipoles.24,46 If the differences on the timescale of
β
ΦBDS (t) = ∆εα · ΦPCS (t) + ∆εc-c · e−( τc-c )
t
(4) the microscopic dynamics are neglected, and further,
if one assumes that the cross-correlations leading to
with relaxation strength ∆εc-c and the stretching param- gK > 1 are reflected dynamically mainly in the relax-
eter being approximately β ≈ 0.85 at all temperatures. ation strength ∆εc-c , then a suitable measure for the
Thus, the BDS spectra split into a broad self-correlation amount of cross-correlations would be the ratio of the
part and a more narrow cross-correlation part. Com- total relaxation strength over the α-relaxation strength
pared to monohydroxy alcohols the latter contribution (∆ǫα + ∆ǫc-c )/∆ǫα . The result is shown in the inset of
is slightly more stretched, and it should be noted that Fig. 4. We note that the area under the peak of the micro-
in some monohydroxy alcohols the Debye-like relaxation scopic dynamics in the light scattering spectra in Fig. 1
also appears to be slightly broadened44 , in particular comprises about 10% of the whole area under χ′′ (ω). As
when the latter is close to the α-relaxation indicating this area is disregarded in the simple estimate for the
rather small supramolecular structures that comprise cross-correlations in the spectrum, we include it in the
very few molecules only25–27,45 . determination of the indicated uncertainties. Now, this
The PCS, TFPI, Raman and BDS time constants ratio can be compared with the Kirkwood/Fröhlich cor-
shown in Fig. 4 are similar at high temperatures and relation factor:24,46
separate slightly at low temperatures. This result is inde- 9kB ε0 M T (εs − ε∞ )(2εs + ε∞ )
pendent of the exact procedure of analysis, either fitting gk = (5)
ρNA µ2 εs (ε∞ + 2)2
the dielectric loss independently with one GGE function
or using the PCS fits plus an extra KWW for the dielec- Here, kB is Boltzmann’s factor, NA is Avogadro’s num-
tric data. We note that in the latter approach, the sim- ber and ε0 is the permittivity of the vacuum. The static
ilarity of both timescales τc-c and τα is consistent with permittivity εs was directly extracted from the dielectric
the broadening of the cross-correlation part. In what- data. Determination of ε∞ , however, is not as straight
ever way this cross-correlation contribution is interpreted forward. One way is to take ε∞ ≈ 1.05 n2 following the
in terms of physical mechanism, its close similarity with literature47 , another approach is to take ε′ (ω) at the high-
the α-relaxation time scale indicates that to some extent est frequencies reported in Ref. 3 for one temperature
dynamic heterogeneities are reflected in that process, in T = 295 K and consider the temperature dependence by
contrast to the case of most monohydroxy alcohols, where using the temperature dependence of the squared refrac-5
1
tive index. Both approaches lead to slightly different 10
PCS
values, which were used to determine the uncertainties FFC
for gK . The refractive index n and density ρ were taken
from Mirjana et al. 48 and Leron et al. 49 in the tem-
χ’’(ν), a.u.
perature range of 288 − 323 K and linearly extrapolated
0
to lower temperatures. Finally a molecular dipole mo- 10
ment of µ = 2.76 D4 and a molecular mass for glycerol
of M = 92.09 g/mole were used. The inset of Fig. 4
demonstrates very good agreement of the values and the diluted
temperature dependence of both quantities in the range
-1
of 190 − 260 K, where a detailed comparison of the data 10
is possible.
-3 -2 -1 0 1 2 3 4 5 6 7
10 10 10 10 10 10 10 10 10 10 10
ν/νmax
IV. DISCUSSION
FIG. 5. A comparison of the generalized light scattering sus-
ceptibility from PCS with corresponding proton field cycling
In order to support the conclusions drawn from the (FFC) data from Ref. 8 and field cycling data from a dilution
above analysis in the following we compare our re- experiment from Ref. 52.
sults with some literature data, namely fast field cycling
NMR measurements and dynamic shear relaxation spec-
troscopy. It is critical for our analysis, as we are aim- different, when, e.g., in 2 H-NMR experiments particular
ing at separating self- from cross-correlation contribu- parts of the molecule are deuterated, like particular OH-
tions in the dielectric spectra, that the light scattering and CH-groups as done by Döß et al.,7 because then the
spectra are unaffected by cross-correlations. Although dynamics of different molecular entities becomes distin-
this may not be true in general, as in some cases a cor- guishable. By contrast, in the proton field cycling exper-
responding Kirkwood correlation factor can also be mea- iment as well as in light scattering, the involved interac-
sured in light scattering,50 in many systems indeed light tions average over the whole molecule and thus produce
scattering proves to be rather insensitive towards cross- the same spectral density in good approximation, see also
correlations, in particular when the structural molecu- supplement of Ref. 53.
lar anisotropy is not too big. In the case of glycerol, Although it is clear in that way that light scattering re-
this notion is further supported by NMR field cycling flects the self-part of the correlations, it is non-trivial that
experiments: By measurements of frequency dependent these should be the same in terms of spectral shape and
spin-lattice relaxation times one can access the spectral timescale as the corresponding dielectric self correlation
density of an orientational self-correlation function based function. Even if one assumes that both to first approx-
on the nuclear dipole-dipole interaction of protons.51 The imation reflect the reorientation of the whole molecule,
field cycling technique in that case measures the rotation there is still the different rank Legendre polynomials in-
and translation of molecules due to the fact that there volved in each correlation function. However, spectral
are intra- and inter-molecular proton-proton couplings. shapes and timescales which are identical within exper-
The masterplot of the generalized susceptibilities in Fig. 5 imental limits are observed when comparing BDS and
demonstrates that the PCS data are identical with the PCS data in the range of α- and β-relaxation for many
field cycling data taken from Gainaru et al. 8 in the re- monohydroxy alcohols, which leads to the conclusion that
gion of the maximum in χ′′ (ω) and at higher frequencies. the slow dynamics in monohydroxy alcohols is most likely
The only difference is given by the translational contri- governed by processes that involve large reorientation an-
butions on the low frequency flank of the field cycling gles as is the case, e.g., for random jump dynamics as
data originating from inter-molecular proton-proton in- compared to rotational diffusion.25–27,45 Drawing on the
teractions. In the case of proton NMR one can even observation in monohydroxy alcohols the same assump-
replace some protonated glycerol molecules by deuter- tion was made in the context of the present analysis.
ated glycerol and thus reduce the signal from the inter- Interestingly, when light scattering and dielectric data
molecular coupling by dilution as demonstrated by Meier are scaled on top of each other in the region of α-process
et al. 52 . This removes the translational part in the spec- and high frequency wing as shown in Fig. 3, then in the
trum and leaves only a pure orientational self-correlation. THz region the light scattering susceptibility shows about
As both NMR and light scattering probe reorientation a factor three larger intensity than the dielectric loss. In
by a tensorial quantity, which leads to an ℓ = 2 cor- fact, this is exactly what is expected from general con-
relation function in both cases, the observed identity in siderations for ℓ = 1 and ℓ = 2 correlation functions, if
both shape and timescale demonstrates that indeed cross- reorientational motions are restricted to very small an-
correlational contributions are absent in light scattering gles. In that case it can be shown that:54–56
spectra of glycerol in the region of the α-relaxation. We
note here, that of course correlation functions become χ′′ℓ=2 (ω) ≈ 3 · χ′′ℓ=1 (ω) (6)6
Previously it was argued that this relation can be ap- 0
10 M’’
plied for the dynamics in the region of the high-frequency G’’
wing, when the peak maximum of χ′′ℓ=2 (ω) and χ′′ℓ=1 (ω)
M’’, G’’, a.u.
are scaled on top of each other.8,9 If such scaling is ap-
-1
plied, however, it can be estimated from Fig. 3 that the 10
resulting difference in the THz dynamics, where the as-
sumption of small angle restricted reorientation is most
likely valid, would increase to about a factor of ten, in- -2
10
consistent with Eq. 6. By contrast, the scaling applied glycerol - 200 K
in Fig. 3 leads to an overall consistent picture up to the
THz regime.
In monohydroxy alcohols the appearance of the Debye BDS - network and local
contribution is related to the formation of supramolecu-
χ’’, ε’’, J’’-F0/ω, a.u.
1
10
lar structures, which lead to cross-correlations of molec- SC - network and local
ular dipole moments that produce an additional peak in
ε′′ . By contrast, in polyalcohols the structures formed
will most likely be network structures. How these are re- DDLS - local
0
lated to cross-correlations of molecular dipole moments 10 Debye
is far less obvious. It should be noted however, that
recently theoretical models suggest, that also without
particular interactions like hydrogen bonds, simply the
dipole-dipole interactions in a polar liquid may lead to -1
cross-correlations that produce a separate slow relaxation 10 -2 -1 0 1 2 3 4 5 6
10 10 10 10 10 10 10 10 10
peak in the dielectric loss, similar to the Debye process ν/Hz
in monohydroxy alcohols57 . Thus, the cross-correlations
observed in the dielectric loss of glycerol need not neces- FIG. 6. PCS (blue), BDS (orange), and dynamic shear (pur-
sarily be due to the hydrogen bonding network 58 . Fur- ple) data of glycerol at 200 K. The uper figure shows the mod-
ther investigations of strongly dipolar but non-hydrogen ulus representation of BDS data from this work and dynamic
bonding liquids will shed more light on this question. shear modulus measurements from Ref. 17. Open symbols
With the present analysis at hand, which suggests how show a shifted spectrum for better comparison of shape. The
to distinguish self- from cross-correlation contributions lower figure shows a comparison of the light scattering sus-
in the dielectric spectra, it is worthwhile to take a look ceptibility, the dielectric permittivity, and the relaxation part
of the shear compliance (SC) without the fluidity contribu-
at shear mechanical relaxation data, which by mere vi-
tion. The fit of the shear data (black line) is separated into a
sual inspection clearly show a bimodal spectral shape in Debye (dasehd line) and a Cole-Davidson (dash-dotted line)
the case of glycerol. In Fig. 6 the spectral shape of the contribution.
BDS measurements in modulus representation M ′′ (ω)
is compared to the dynamic shear modulus G′′ (ω) of
glycerol from Jensen et al. 17 . The comparison is made Davidson function with a shape parameter of βCD = 0.43
at 200 K and both techniques have surprisingly similar and an additional slower Debye contribution and both
spectral shape and deviate significantly from a simple functions approximately have the same intensity. For the
peak structure. The difference in time constant might shear data this result is independent of any amplitude
be due to a difference of G∞ and M∞ = 1/ε∞ val- scaling. Thus, Fig. 6 demonstrates, what can be identi-
ues, which change the time constants in modulus rep- fied as the α-relaxation is actually rather similar in all
resentation. In order to eliminate the influence of G∞ three experimental methods, while in a slower collective
and M∞ , we change the representation to a compliance contribution each method seemingly shows very different
representation J ∗ (ω) = J ′′ (ω) − iJ(ω) = 1/G∗ (ω).59 aspects of the dynamics in glycerol: While light scatter-
Similar to the complex conductivity in dielectric spec- ing pronounces the local aspect of the α-relaxation on a
troscopy σ̂(ω) = iω ε̂(ω), where the low frequency limit molecular level, as cross-correlations most probably im-
σ̂(ω → 0) = σDC is often subtracted to reveal the re- posed by the H-bonding network do not play a significant
laxational contribution in the dielectric data, one can role for the relaxation of the optical anisotropy, for the
subtract the low-frequency limit of the complex fluid- dielectric relaxation cross-correlations are significant and
ity F ∗ (ω) = iω J ∗ (ω), i.e., F ∗ (ω → 0) = F0 , from the also for the macroscopic shear response a slow collective
imaginary part of the compliance. relaxation mode seems to be important.
′′
Jrelax (ω) = J ′′ (ω) − F0 /ω (7) It is remarkable that like in glycerol, one can ob-
serve a slow contribution in the shear relaxation in
′′
Thus, Jrelax (ω) becomes directly comparable to the BDS nearly all monohydroxy alcohols 60 . By contrast, the self-
permittivity and the light scattering susceptibility. In correlation in PCS is free of any Debye-like contribution
Fig. 6 the shear compliance data are described by a Cole- in glycerol, while for certain monohydroxy alcohols, es-7
pecially secondary alcohols like 5-methyl-2-hexanol 26, a CONFLICTS OF INTEREST
weak Debye-like contribution can be identified. The rea-
son for this difference is still an open question. Most There are no conflicts to declare.
probably, it arises depending on the average lifetime of
the supramolecular structures and on how much restric-
tion they impose on the reorientation probed by the ACKNOWLEDGEMENTS
α-relaxation. If the restriction is significant and the
α-relaxation becomes slightly anisotropic, a small slow The authors are grateful to Ernst Rössler, Bayreuth,
mode in the self-part of the correlation function may be for providing the original data from Ref. 10, to Peter
seen, as is observed in light scattering, while otherwise Schneider, Augsburg, for providing the data from Ref. 3,
the selfcorrelations are unaffected and a slow mode is and to Tina Hecksher, Roskilde, for providing the origi-
only observed if cross-correlations play a significant role, nal data from the Ref. 17. We are also grateful to Catalin
like in dielectric spectroscopy. Further verification of this Gainaru, Dortmund, for fruitful discussions and his sug-
picture will be subject of future work. gestion to use Eq. 7 when comparing dielectric permit-
tivity with shear relaxation data. Furthermore, financial
support by the Deutsche Forschungsgemeinschaft under
Grant No. BL 1192/1 and 1192/3 is gratefully acknowl-
edged.
V. CONCLUSIONS
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