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: yurif@mail.huji.ac.il

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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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Figure 1

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Figure 2

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Figure 3

Figure 4

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Figure 5

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Figure 6

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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]