Accepted Manuscript
Title: Dielectric spectroscopy study of water dynamics infrozen bovine milk
Author: Daniel Agranovich Paul Ben Ishai Gil Katz DrorBezman Yuri Feldman
PII: S0927-7765(16)30031-5DOI: http://dx.doi.org/doi:10.1016/j.colsurfb.2016.01.031Reference: COLSUB 7608
To appear in: Colloids and Surfaces B: Biointerfaces
Received date: 5-9-2015Revised date: 21-12-2015Accepted date: 19-1-2016
Please cite this article as: Daniel Agranovich, Paul Ben Ishai, Gil Katz,Dror Bezman, Yuri Feldman, Dielectric spectroscopy study of waterdynamics in frozen bovine milk, Colloids and Surfaces B: Biointerfaceshttp://dx.doi.org/10.1016/j.colsurfb.2016.01.031
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Dielectric spectroscopy study of water dynamics in frozen bovine milk
Daniel Agranovich1, Paul Ben Ishai1, Gil Katz2, Dror Bezman2 and Yuri Feldman1, ‡
1The Hebrew University of Jerusalem, Department of Applied Physics, Israel 2Afimilk, Kibbutz Afikim, Israel
‡ Dielectric Spectroscopy group Department of Applied Physics The Hebrew University Edmond J. Safra Campus - Givat Ram 9190401 Jerusalem, Israel Tel: +972-2-6586187 E-mail: [email protected]
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Graphical abstract
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Highlights
• Interfacial dynamics in quenched bovine milk was studied by dielectric spectroscopy; • Dielectric relaxation process related to the water-lactose complexes was identified; • A presence of bulk hexagonal and cubic ices was determined; • An interfacial effect possibly on the surface of casein micelles was observed; • An intriguing structural – dynamic transition around 200 K was detected.
Abstract
Bovine milk is a complex colloidal liquid exhibiting a multi-scaled structure. It is of
particular importance, both commercially and scientifically, to investigate both its dynamic and
structural properties. In the current study we have employed the broadband dielectric spectroscopy
(BDS) technique in the frequency range of 10-1 – 106 Hz and the temperature range of 176 – 230
K in order to examine the molecular structure and dynamics of quenched bovine milk. Four
dielectric relaxation processes were identified. Three of them are associated with water in its
different forms: water-lactose complexes, bulk hexagonal and cubic ices. The fourth process is
attributed to domain wall relaxations linked to the presence of micro-cracks in the ice structures.
In addition, the first process, attributed to water-lactose complexes, obeys the Meyer-Neldel
compensation law and can be taken as evidence of differing interfaces of these complexes with the
bulk water of the milk, mediated by the lactose concentration. Furthermore, an intriguing structural
– dynamic transition around 200 K was observed. Considering the mentioned above, we conclude
that our results emphasize the structural and dynamical significance of water in bovine milk.
Keywords Dielectric Spectroscopy, Bovine milk, Dielectric relaxation, Water, Ice, Lactose.
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1. Introduction
Bovine milk has been a mainstay of the human diet for thousands of years. Nowadays, its
production and distribution in the form of milk, cheese or butter constitutes a significant
component of the food industry. Yet, losses due to spoiling and bovine infections run into billions
of dollars annually [1-3]. Consequently, there is a growing requirement for real-time milk quality
monitoring. This, in turn, necessitates the profound scientific understanding of milk’s structure
and dynamics. Strikingly, despite its importance and a plethora of research, milk is still poorly
understood.
Milk is a complex colloidal liquid exhibiting a multi-scaled structure. It is composed of
water (~87.%), lactose (~4.8%), fat (~3.6%), proteins (~3.3%) - mainly casein (~2.6%), inorganic
species (0.7%) and miscellaneous components [4]. Naïvely stated milk is a water-based emulsion
of fat globules interspersed with casein micelles and smaller moieties. This view, however, cannot
take into consideration the subtle interplay between the different constituents, their dynamic nature
or the overall molecular structure. Primarily, the state of water in bovine milk is very intriguing.
The water in milk is found in numerous phases and particularly forms various types of hydration
layers. It is, however, unclear what the interactions involved are; withal the exact microscopic
structure is unknown.
The main goal of this research was to achieve a deep insight into the different states and
the dynamics of water in bovine milk and to pick apart its interplay with the various milk
components.
In order to clarify these issues we have utilized Dielectric Spectroscopy (DS)[5]. DS is
particularly useful in this case since it provides a unique possibility to study the dynamics of
complex materials. DS probes the sample response to an impinging electrical field. This response
is correlated with interaction of the electric field with permanent and induced dipoles, and various
charge carriers, which present in the sample. The advantage of DS is that the broad frequency band
available to probe the sample allows one to selectively focus on a various length scales in an
enormously wide range. The dynamics may be further investigated by varying the temperature of
the system.
Although it might be desirable to measure milk in its liquid state, there exist a number of
obstacles to a dielectric measurement of this state. First, the high conductivity impedes the analysis
of low frequency relaxations and contributed to a significant Electrode Polarization [6], a further
artifact masking low frequency relaxations. Second, in the liquid state interfacial and hydration
water around the various structures in the liquid cannot be isolated in the spectra.
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In contrast, measuring at the low temperatures allows the examination of various types of
hydration water and the interactions involved. Therefore, we have rapidly cooled bovine milk
samples to a solid phase and then reheated them gradually, revealing the temperature dependence
of processes contributing to the dielectric relaxation. In addition, the study of frozen milk may also
assist a better understanding in the future of the influence of freeze-drying procedures on various
dairy products.
We have additionally compared the measurement results of the raw milk sample with the
fat reduced and the casein reduced milk samples produced from the same batch. This was done in
order to isolate dielectric effects arising from different types of hydration water in the bulk sample.
Based on the broadband dielectric spectroscopy (BDS) measurement results, we will
discuss in this work the interpretation of the dielectric spectra of quenched bovine milk and the
observed states of water.
2. Materials and methods
2.1. Sample preparation: Raw milk samples obtained from arbitrary selected individual Israeli
Holstein cows were provided by Afimilk Ltd. (Kibbutz Afikim, Israel) and the Volcani
Institute of Agricultural Research (Beit Dagan, Israel). Skimmed milk was prepared by
centrifugation at 3200 g for 7 min at 10 and subsequent supernatant removal. Casein
reduction was performed using the ultracentrifugation method [7] as follows: the raw milk
sample was divided into two test tubes; a sample from tube 1 was used to prepare skimmed
milk as indicated above. The remainder was subsequently centrifuged at 100,000 g for
1 hr at 25 and the pellet was discarded. The sample from tube 2 was left overnight at
4 (Stokes' Law predicts that fat globules will float due to the differences in densities
between the fat and plasma phases of milk), then the fat was collected, its concentration
was evaluated using the Gerber technique [8] and the proper amount was added to tube ,1
in order to achieve the same fat content as in the “parent” raw milk sample. The reported
amount of casein sedimentation by method of ultracentrifugation is ~90% [7].
Table 1 summarizes the origin and classification of the measured milk samples as
well as concentrations of various milk constituents in the measured samples as detected
by laboratory analysis, performed by the Central milk components laboratory, ICBA –
Israeli Cattle Breeder’s Association. The numbers indicate various milk samples
originated from different donor cows. Altough the exact amount of casein was unavailble,
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it was formerly establilshed that caseins represent about 80% of the total protein in bovine
milk [7].
2.2. Experimental technique: Dielectric measurements in the frequency range from 0.1 Hz to
1 MHz were performed using a Broadband Dielectric Spectrometer (Novocontrol BDS 40
spectrometer based on an Alpha impedance analyzer, Novocontrol Technologies GmbH)
with automatic temperature control (Quatro Cryosystem, Novocontrol Technologies
GmbH). In terms of the loss tangent, tan , the accuracy of the measurement is 10-4. The
measurements were conducted utilizing a three-electrode cylindrical sample holder (BDS
1307, Novocontrol) that avoids the errors related to thermal expansion of the samples,
prevents liquid leakage and minimizes the effects of fringing fields by using a guard
electrode[9]. The empty cell and stray capacities were 1.095 pF and 2.269 pF respectively,
sample height was 5 mm, inner and outer electrode diameters were 20 mm and 26.5 mm
respectively. We have used standard experimental setting recommended by Novocontrol.
The applied voltage was 1 Vrms (the resultant field strength remains in the linear regime).
The samples were cooled to 176 K at a rate of 10 K/min and then gradually heated and
measured with a temperature step of 3 K up to 230 K. The heating time between adjacent
temperature points was 2 min and the stabilization time on each temperature point before
measurement was 1 min.
3. Results and discussion
The temperature and frequency dependence of dielectric losses for a typical raw milk
sample is shown in Figure 1. In the temperature range of 176-230 K, four dielectric relaxation
processes can be identified.
Figures 2a and 2c depict two isothermal slices (at 176 K and 200 K respectively) of
dielectric loss spectra for various measured milk samples obtained from different cows. Figures
2b and 2d depict a representative isothermal slice of raw milk at 200 K in terms of permittivity
and dielectric losses, respectively; the raw data is represented by dots and the fittings are
represented by lines. The experimental spectra, both real and imaginary parts of the complex
dielectric permittivity, were fitted simultaneously. All the observed processes showed Cole-
Cole dependence (i.e., ∗ ∆). The left Jonscher function was used
to represent the tail of the fifth, low frequency process. The overall relaxation term is given by:
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∆
1, 1
where is the relaxation time (i.e., 1/2 ), ∆ is the dielectric strength and is the
Cole-Cole broadening parameter of the process, is the high frequency limit of the dielectric
permittivity. The fitting parameters, which are not discussed in details in the article are specified
in the supplementary material. It must be noted that since raw milk is a remarkably complex
material that exhibits a multitude of relaxation processes, the dielectric strength and the broadening
parameters are susceptible to a degree of uncertainty. Therefore, throughout the current work we
consider mainly the relaxation times.
The temperature dependences of the relaxation times for all the observed processes are well
described by the Arrhenius law:
exp , 2
where is the relaxation time, is the activation energy, R is the gas constant and T is the
temperature. The results are summarized in the supplementary Table S1.
As was already mentioned, the major milk constituents are lactose, fat and protein (mainly
casein). Therefore, the next logical step was to examine the individual contribution of the main
constituents to the total relaxation pattern. In order to do so, a raw milk sample from a particular
cow was divided into three parts; the first part was treated to obtain skimmed milk, the second part
was treated to obtain casein reduced milk and the third part was remained untreated. The samples
were measured the same day and the dielectric spectra were compared. The idea was to eliminate
separately each of the main milk components.
We, however, were able to reduce only the amount of fat and the majority of proteins
(casein). Figure 3 compares the temperature dependencies of the relaxation times of processes I-
II for the mentioned above samples. It must be noted that casein/fat removal is accompanied by a
rise in the effective conductivity and consequently a strong elevation in electrode polarization
effect [6]. This considerably enlarged the fitting uncertainties. As a result, in skimmed milk only
the processes designated I and II could be properly resolved. In casein reduced milk the combined
effects of conductivity and electrode polarization left on the first process resolvable.
It was determined that there is no apparent difference between raw milk and fat-reduced milk
in terms of activation energies and relaxation times for processes I-II (Figure 3). The same can be
said regarding the comparison of process I in raw milk and process I in casein-reduced milk (Figure
3). Hence, we may infer that fat globules most likely do not play a part in the dynamics
characterized by the first two processes. Casein micelles probably do not contribute to process I.
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We will further try to provide the plausible explanations regarding the relaxation
mechanisms behind each of the observed processes.
First and second processes
We will first refer to the second process. Figure 4a represents the relaxation times
temperature dependence of process II in quenched bovine milk.
By detailed examination of process II in terms of the time scales and the activation energy
(~21 kJ/mol) we have concluded that this process might be associated with the bulk hexagonal (Ih)
ice. It is worth noting that there are some deviations of the relaxation times compared to previously
reported values for relaxation times of Ih ice [10-12]. These variations may be related to a
distinction between experimental settings employed by different studies (e.g., sample cells,
protocols etc.). We have therefore conducted an additional measurement of pure ice in the same
sample cell under analogous conditions and compared it with the results obtained for various milk
samples. The comparison reveals a pronounced resemblance between the dynamics of process II
in milk and the dynamics of Ih ice (Figure 4a, solid line).
In the 176-230 K temperature range the dominant relaxation mechanism in bulk ice is
assigned to ionic defects [13, 14]. The observed red shift of the relaxation times for different milk
samples with respect to the bulk ice may be caused by the higher structural heterogeneity in these
samples, which in turn restricts proton movement [13]. Furthermore, as may be expected, there is
no distinguishable difference between the activation energies and relaxation times for second
process in raw and fat-reduced milk (Figure 3).
It was demonstrated above, that reduction of casein or fat content have shown only a
minimal influence on the first process. On the other hand, the dynamics similar to process I may
be observed in numerous hydrogen-bond forming systems. For instance, an analogous process
was observed in frozen aqueous solutions of BSA [15] and in water-glycerol mixtures [16]. In the
latter case, in the framework of the proposed model, the corresponding process was attributed to
interfacial ice-like water [16] and was associated with the thin layer between bulk ice and
water/glycerol matrix. The relaxation times temperature dependence of process I are depicted in
Figure 4b (symbols), together with the relaxation times of the process linked to the interfacial ice-
like water observed in water-glycerol mixtures (solid line) [16]. This process exhibits a noticeable
similarity with process I in milk in terms of both the time scales and the activation energy (~27.5
kJ/mol).
Assuming that fat and casein do not participate in relaxation described by the first process
in bovine milk, we tentatively relate this process to the interaction of water with lactose. In this
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case water and lactose form analogous complexes such as the interfacial ice-like water previously
observed in water-glycerol mixtures. As was already pointed out, lactose is one of the main solid
(after desiccation) components in milk together with fat globules and casein micelles. Although,
lactose is present in milk at relatively low concentration (around 4.6% w/w in average), it strongly
interacts with water, forming a water clustered structure with ~123 affected water molecules per
lactose molecule [17-19]. Furthermore, the phase diagram of lactose-water solution is nearly
identical to the phase diagram of whole milk [20, 21]. In particular, lactose governs the glass
transition of most concentrated liquid milk products [4]. The glass transition temperature in this
case is almost the same as that of a lactose-water mixture of the same water activity, [4]. Where
is established by the measurement of partial vapor pressure of water in the relevant substance.
A typical value of water activity for bovine milk is 0.995 , where is the mole fraction
of water in the solution. This idea is further supported by the fact that hydrolysis of lactose to
glucose and galactose in milk powders is accompanied by a significant change in properties of the
powder [21]. Taking into account the aforementioned, it is natural to link the first process with
water-lactose complexes.
Figures 5a and the supplementary Figure S1 depict the dielectric strength and the Cole-
Cole parameter respectively as a function of temperature for process I. Since changes very
slowly in the relevant temperature range, the static dielectric permittivity exhibits approximately
the same temperature dependence as the dielectric strength. As can be observed in Figure 5a, for
all the measured milk samples the static dielectric permittivity of process I decreases with
temperature. In virtue of this behavior, which is usually typical for liquids [22], we may assume a
liquid-like nature of the first process. In addition, it is worth noting that there is an apparent, both
structural and dynamic transition around 200 K for the majority of the measured samples (Figures
5a and S1). This is manifested in the distinct change of the slope around the abovementioned
temperature for both ∆ that reflects the molecular structure of the system [23], and α that related
to the system dynamics [23]. Some further insight can be gained by studying the parameters
derived from fitting the relaxation times to equation (2). Figure 5b demonstrates that the logarithm
of pre-factor, 0, has a linear dependence on the activation energy,
ln a ∆ . (3)
This behavior is frequently described as Meyer-Neldel compensation and is prevalent in
solid state systems [24, 25], it has also been noted in some glass forming systems [26], but to the
best of our knowledge it is the first time that it is observed in a system like milk. It can be
understood as follows; assuming a simple two state system to represent the exchange of a water
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molecule from the lactose/water construct with the surrounding bulk, the characteristic relaxation
time will be proportional to the probability, P, of the same exchange, which is governed by the
Helmholtz free energy, ∆ ,
∝ exp∆
→ exp∆ ∆
exp∆exp
∆ , (4)
where ∆ is the entropy contribution, k is Boltzmann’s constant and is the high temperature
limit of the relaxation time. In essence the pre-factor of equation (2) contains both the entropy
contribution and . Meyer-Neldel compensation implies that ∆ ∆ and ln .
The exchange of a water molecule in the shell around the lactose molecule leads to a rearrangement
in the same shell and so incurs an entropy cost. The nature of this interaction involves many
neighbors and is described by the parameter b; the entropy measure for rearrangement of the shell
due to molecular exchange. In figure 5b it is clear that the samples used in this study can be split
up into those with a lactose concentration of less than 5 g/100ml and those with more. The relevant
values of (in seconds) and b (in kJ-1) are (6.02.6) × 10-6 and 0.460.07 respectively for
concentrations > 5 g/100ml; and (2.40.9) × 10-6 and 0.430.06 for concentrations < 5 g/100ml.
The differing energy costs in this case imply that there is a difference in the nature of the interfacial
layer around the lactose molecule depending on the concentration. The higher energy cost for
lactose concentrations above 5 g/100ml suggests a more ordered shell. This would make sense if
one assumes that the overall radius of influence of each lactose molecule is lessened, due to the
higher concentration and the presence of other moieties in the solution. Interestingly, artificially
reducing the concentration of casein in sample 8802 moves the sample from the higher
concentration group to the lower concentration group. This point requires further investigation.
Third process
While one would expect to note in this frequency range interfacial processes linked to
moieties such as fat globules or casein micelles, we can assign process III to relaxations related to
the presence of micro-cracks in the ice structures of the milk. A similar process was noted in the
measurement of pure water frozen in the same sample cell and under the same temperature protocol
as used for the milk samples. The relaxation times for both data sets are shown in Figure 6a. Similar
relaxations have also been associated with cracks in ice crystals [27-29] and there were also reports
of processes related to the interfacial polarization (IP) in various saline ices [30]. In Figure 6a the
relaxation times and activation energies are in a good agreement, whereas the slight differences
might be caused due to discrepancy between the character of the interfaces in these systems.
However, it should be noted that one cannot entirely rule out a contribution from other interfaces
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in the sample. Nevertheless, it is problematic to calculate exactly the dielectric strength of the third
process and estimate correctly its contribution to the total relaxation pattern. This is because of
uncertainties, both in the thickness and in the value of conductivity of the interfacial layer. The
activation energy for process III is relatively low (~15.3 – 18.5 kJmol-1 for all the measured milk
samples)
Fourth process
Figure 6b depicts the relaxation times temperature dependence of process IV for various
raw milk samples. This process may be presumably attributed to the presence of cubic ice (Ic) in
quenched milk.
As may be seen on Figure 6b, there is a noticeable similarity in terms of activation energy
between the fourth process in milk and ice Ic process measured by Gough et al. [31], and analogous
results for cubic ice were reported recently [32]. The adiabatic calorimetry measurements of Ic ice
performed by Yamamuro et al. [33] provide further support to this idea, revealing comparable
values of activation energy, around 40 kJmol-1, and .
In a pure water system, cubic Ic ice phase is metastable and it readily transforms to the ice
Ih phase when warmed above 143 K. The reverse transformation has never been observed [34].
However, crystallographic observations of various quenched organic and ionic solutions [34], as
well as various hydrated protein powders [35], have revealed the existence of ice Ic. The ice Ic
phase, formed by quenching of the abovementioned aqueous solutions, transformed to ice Ih above
200 K, which was clearly higher than that observed in the pure water system. Furthermore, it was
found that ice Ic formed in the quenched disaccharide solutions is stable under anomalously high
temperatures (up to ~240 K) [34]. That bovine milk can be considered as a disaccharide (lactose)
solution and the explicit similarity between the relaxation of cubic ice and the dynamics of process
IV, point towards the fourth process in quenched milk being associated with the formation of Ic
ice.
4. Conclusions
In this study we have identified four dielectric relaxation processes in frozen bovine milk
and were able to relate each one of them to a known physical process, all of which are associated
in some way to water: process I is the relaxation caused by molecular exchange of water between
the water/lactose cluster and its surrounding bulk; process II is related to the presence of ice Ih in
the frozen milk and is usually assigned to defect migration in the same ice; process III is caused
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by interfacial relaxations originating from the presence of micro cracks in the same ice; and process
IV is due to the existence of another metastable form of ice structure , namely ice Ic.
Of the four processes only process I can be directly associated with a certain constituent of
milk. Furthermore, the existence of Meyer-Neldel compensation for this same process leads to
some interesting conclusions about the nature of water/lactose clusters in milk. As competition for
water increases there exists a critical concentration above, which the nature of hydration around
the lactose molecule changes and water becomes even more ordered around the lactose molecule.
The full implications of this are still to be investigated. A more detailed classification of milk may
reveal features of these processes not yet appreciated.
5. Acknowledgements
This work was supported by the “Nitzan” grant No. 12-09-0003 of Israeli Ministry of
Agriculture.
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6. References
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[22] H. Fröhlich, Theory of dielectrics; dielectric constant and dielectric loss, Clarendon Press, Oxford,, 1949. [23] A. Puzenko, P. Ben Ishai, Y. Feldman, Cole-Cole Broadening in Dielectric Relaxation and Strange Kinetics, Physical Review Letters, 105 (2010). [24] A. Yelon, B. Movaghar, Microscopic Explanation of the Compensation (Meyer-Neldel) Rule, Physical Review Letters, 65 (1990) 618-620. [25] R. Metselaar, G. Oversluizen, The Meyer-Neldel Rule in Semiconductors, J Solid State Chem, 55 (1984) 320-326. [26] J.C. Dyre, A Phenomenological Model for the Meyer-Neldel Rule, Journal of Physics C-Solid State Physics, 19 (1986) 5655-5664. [27] Delpenni.U, A. Loria, Mantovan.S, E. Mazzega, Polarization Phenomena Induced by Cracks in Ih Ice Crystals, Nuovo Cimento B, B 24 (1974) 108-120. [28] G.P. Johari, E. Whalley, The Dielectric-Properties of Ice Ih in the Range 272-133-K, Journal of Chemical Physics, 75 (1981) 1333-1340. [29] O. Worz, R.H. Cole, Dielectric Properties of Ice .I., Journal of Chemical Physics, 51 (1969) 1546-&. [30] R.E. Grimm, D.E. Stillman, S.F. Dec, M.A. Bullock, Low-Frequency Electrical Properties of Polycrystalline Saline Ice and Salt Hydrates, J Phys Chem B, 112 (2008) 15382-15390. [31] S.R. Gough, D.W. Davidson, Dielectric Behavior of Cubic and Hexagonal Ices at Low Temperatures, Journal of Chemical Physics, 52 (1970) 5442-&. [32] K. Amann-Winkel, C. Gainaru, P.H. Handle, M. Seidl, H. Nelson, R. Bohmer, T. Loerting, Water's second glass transition, P Natl Acad Sci USA, 110 (2013) 17720-17725. [33] O. Yamamuro, M. Oguni, T. Matsuo, H. Suga, Heat-Capacity and Glass-Transition of Pure and Doped Cubic Ices, J Phys Chem Solids, 48 (1987) 935-942. [34] T. Uchida, S. Takeya, M. Nagayama , K. Gohara, Freezing Properties of Disaccharide Solutions: Inhibition of Hexagonal Ice Crystal Growth and Formation of Cubic Ice, in: E. Borisenko (Ed.) Crystallization and Materials Science of Modern Artificial and Natural Crystals, InTech2012, pp. 203-224. [35] G. Sartor, A. Hallbrucker, E. Mayer, Characterizing the secondary hydration shell on hydrated myoglobin, hemoglobin, and lysozyme powders by its vitrification behavior on cooling and its calorimetric glass->-liquid transition and crystallization behavior on reheating, Biophysical journal, 69 (1995) 2679-2694.
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Fig.1 Broadband dielectric spectroscopy measurement of typical raw bovine milk sample; dielectric losses as a function of frequency and temperature
Fig.2 Typical dielectric spectra of bovine milk. Dielectric losses as a function of frequency for various measured milk samples obtained from different cows; isothermal slices at (a) 200 K and (c) 176 K. The different numbers indicate various milk samples originated from different donor cows. In addition, a representative isothermal slice of raw milk at 200 K in terms of (b) permittivity and (d) dielectric losses is indicated: the raw data (dots) and the fittings (lines)
Fig.3 Relaxation times temperature dependence of the first and second processes for raw, skimmed and casein reduced milk samples
Fig.4 (a) Relaxation time as a function of the reverse temperature for process II in milk compared with ice measured under similar conditions; (b) Relaxation time as a function of the reverse temperature for process I in milk compared with water-glycerol mixture (21.2% w/w). The different numbers indicate various milk samples originated from different donor cows. “Skim” refers to a fat reduced sample and “Casein (-)” refers to a casein reduced sample
Fig.6 (a) Relaxation time as a function of the reverse temperature for process III in milk compared with the process attributed to the interfacial polarization in pure ice. The different numbers indicate various milk samples originated from different donor cows. “Skim” refers to a fat reduced sample; (b) Relaxation dynamics of the fourth process in milk compared with ice Ic measured by Gough [27]. In addition, calorimetric measurements of ice Ic performed by Yamamuro [29] are provided
Fig.5 (a) The dielectric strength as a function of temperature and (b) the pre-factor of the relaxation times, 0, as a function of the activation energy, Ea , for process I. The different numbers indicate various milk samples originated from different donor cows. The scale for the pre-factor is log10. The samples in frame (b) are grouped by the lactose concentrations and the straight lines indicate the fit according to the Meyer Neldel compensation law
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Table 1 - Concentration of main milk constituents in the measured samples
Sample # Fat† 0.066
Protein† 0.047
Lactose† 0.092
3061 1.190 2.970 4.5803212 1.090 3.245 5.5658696 4.220 3.545 5.525 8428 5.140 4.330 4.910 8802 4.180 3.620 5.250 8802 (skimmed) 0.080 3.730 5.510 †the values are in [gr/100 ml]
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