Behaviour of viscosity in metaphosphate glasses
L. Muñoz-Senovilla1,2, F. Muñoz1,*
1
2
Insituto de Cerámica y Vidrio (CSIC), Kelsen 5, 28049 Madrid (Spain)
Departamento de Quıímica Inorgánica, Facultad de Ciencias, Universidad
Autónoma de Madrid, Cantoblanco 28049 Madrid (Spain)
Abstract
The experimental viscosity data of a series of alkali, alkaline-earth and zinc
metaphosphate glasses have been analysed using VFT, AM and MYEGA models.
The kinetic fragility and activation energy for viscous flow have been obtained and
studied as a function of the composition, paying special attention to the short and
intermediate range order structure as studied by Nuclear Magnetic Resonance and
Raman spectroscopy. The fragility shows an increasing tendency within the alkali
and alkaline-earth series and presents the lowest value for the Zn(PO3)2
composition. Meanwhile the modifiers influence on the local structure of the PO4
tetrahedra follows a direct relationship with their cationic potential; both static NMR
and Raman experiments showed evidence of a change in the rings versus chains
configurations at the medium range order that could have an important contribution
on the variation of activation energy. Furthermore, the molar volume and average
bond strength of the glasses have shown to play a most important role, having a
similar variation as the activation energy in the high viscosity range. However, the
low viscosity range data seem to increase with the modifier’s cationic potential, thus
suggesting a different flow mechanism when compared with the high viscosity
range.
1
Keywords: Phosphate Glasses; Viscosity; Structure; Nuclear Magnetic Resonance;
Raman Spectroscopy
*
E-mail address of the corresponding author: [email protected]
2
1. Introduction
Phosphate glasses have led to an extensive research field of glassy materials developed
for a wide range of special applications. Their particular properties, low glass transition
temperature, high thermal expansion coefficient and low optical dispersion compared
with silicate glasses, allow phosphate glasses to be employed as low temperature glass
to metal seals [1-4], high power lasers host materials [5,6], matrices for the vitrification
of nuclear wastes [7] or bio-compatible materials [8].
The viscosity affects many aspects of glass manufacturing, such as melting and fining,
devitrification, their forming and the efficiency of the internal stresses relaxation
through annealing. During melting and glass forming processes, e.g. production of
optical fibres, moulding of spherical lenses or glass to metal sealing, viscosity must
always be kept under control to ensure high-quality products. However, the viscosity of
phosphate glasses has been much less studied due to their lower and small-scale
industrial production. The rapid variation of viscosity with temperature, as well as the
pronounced devitrification tendency, may imply some difficulties to perform the
measurements. As to our knowledge, few viscosity experimental data have been
reported on phosphate glasses so far. There are several studies about how the thermal
properties and the temperature dependence of viscosity are affected by the addition of
metal oxides, such as Al2O3, ZnO, PbO or alkaline earth oxides to the batch
composition [9-14]. The crosslinking of the metal cations between phosphate chains
strengthens the glass network and influences not only glass properties but also help
improving the chemical durability. Structural relaxation studies have also been
performed on phosphate glasses and its relationship with viscous flow [15-19]. Above
the glass transition temperature, beam bending or micropenetration are those techniques
commonly used to measure viscosity. At high temperature, the methods based on
3
measuring the shear strain on the melt employing parallel plate, concentric cylinder,
sinking bar or rotational viscometers, among others, are mainly utilize [9-19].
Oscillatory shear flow experiments are also employed to determine the complex
dynamic shear viscosity (η*) in the full range of temperature in order to study its
dependence with time [20,21]. Also few experimental viscosity data belonging to
publications up to 1985, mainly of binary alkaline and alkaline-earth metaphosphate
glasses measured by fibre elongation, are compiled in the handbook of glass data [22].
One of the most interesting features of a glass forming melt is its sharp increase of
viscosity near the glass transition. In vitreous silica the variation of viscosity against the
reduced temperature (Tg/T) can be approximated to an Arrhenius equation and constant
activation energy of viscous flow can be determined [23]. In contrast, phosphate glasses
present a much stronger variation of viscosity with temperature, thus referring to them
as “fragile” glasses according to Angell’s definition [24], while silicate glasses are
classified as “strong”. Therefore, for more fragile glasses, the viscosity variation with
temperature can no longer be described by a single activation energy and the viscosity
versus temperature dependence can only be analysed with the help of empirical models,
e.g. introducing the fragility parameter as in the equation (1) [24].
m=
δlogη T
Tg
δ
T
(1)
T=T g
In this work the temperature dependence of the viscosity in a series of metaphosphate
glasses was evaluated using the three-parameter viscosity models that cover the full
range of temperatures. Vogel-Fulcher-Tamman (VFT), equation (2) [25]:
log η T = log η∞ +
A
T − T0
(2)
4
Avramov-Milchev (AM), equation (3) [26]:
log ηT = log η∞ +
τ
T
α
(3)
and Mauro-Yuanzheng-Ellison-Gupta-Allan (MYEGA), equation (4) [27]:
log ηT = log η∞ +
K
C
exp
T
T
(4)
Some previous studies have also been carried out to study the relationship between the
activation energy of viscous flow and the glass network structure in phosphate glasses
[28, 29]. Furthermore, Doremus proposed [30] another criterion for fragility based on
the ratio of the activation energy of viscous flow at high (QH) and low viscosity ranges
(QL) (equation 5) for a number of oxide melts such as silica (RD=1.38), boron oxide
(RD=5.47) or diopside melts (RD=7.26), but this has not been yet studied for phosphate
glasses.
RD =
QH
QL
(5)
He found that viscosity presents, within the ranges of low and high temperature, an
Arrhenius-type dependence, thus taking different values for the activation energy of
viscous flow. By this evaluation of fragility, all the experimental viscosity data are
involved in the analysis and not only those values near the glass transition temperature.
The aim of this work has been to get insight into the relationships between fragility,
composition and structure of phosphate glasses, as determined by means of Nuclear
Magnetic Resonance and Raman spectroscopy. A systematic study of the viscosity
behaviour in alkali, alkaline-earth and zinc metaphosphate glasses has been carried out.
The kinetic fragility of each glass has been determined by fitting the viscosity
experimental data to the three models described above, and the activation energy of
5
viscous flow, and its correlation with composition and structure, has been followed
through the Doremus ratio.
2. Experimental
2.1 Glass melting
Alkali, alkaline-earth and zinc metaphosphate glasses with compositions 50MO.50 P2O5
(M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na) were prepared by conventional
melt-quenching procedure. Reagent grade raw materials analytically pure Na2CO3,
MgO, CaCO3 and ZnO (Panreac); SrCO3 and BaCO3 (Alfa Aesar); (NH4)2HPO4 and
Li2CO3 (Sharlau, ACS), were mixed and the batches were calcined in porcelain crucibles
up to 450ºC, in a electric furnace, and then melted during 2 h at temperatures ranging
from 900ºC to 1200ºC depending on composition. The melts were poured onto brass
moulds and annealed slightly above their glass transition temperature.
2.2 Characterization of the glasses
Glass transition temperature (Tg), dilatometric softening temperature (Td) and the
Coefficient of Thermal Expansion (CTE) were determined from the thermal expansion
curves of the glasses obtained in air with a Netzsch Gerätebau dilatometer, model 402
PC/1 at a heating rate of 2K.min-1. Prismatic samples around 10 mm in length were
used for the measurements. The estimated errors in CTE and Tg are ± 2% and ± 1K,
respectively.
The density of the glasses was measured by helium pycnometry in a Quantachrome
Corp. multipycnometer on bulk samples (±0.01g.cm-3). The molar volume (Vm) of the
glasses was calculated from density measurements by using the relation:
6
Vm =
M
in cm3 . mol−1
d
(6)
where M is the molar mass and d is the density of the glass.
The average single bond strength of binary glasses (B) could be expressed by the
following equation according with the approach proposed in [31], where BM-O is the
corresponding single bond strength in each oxide and ni is the molar fraction:
B = Σni BM−O
in
kJ
mol
(7)
Fourier Transformed Infrared (FT-IR) spectroscopy was performed on mirror-like
polished glass samples around 2 mm in thickness in a PerkinElmer Spectrum 100
spectrometer operating in the transmission mode within the wave number range of 950
to 5500 cm-1. The water content of the metaphosphate glasses can be expressed in terms
of the OH absorption coefficient (rOH) that determines the relative concentration of OH
in the glasses:
rOH =
log
T3000
T5000
in cm−1
l
(8)
where T3000 and T5000 are the transmission at 3000 and 5000 cm-1 and l is the sample
thickness (in cm). T5000 serves as a background transmission and includes the Fresnel
reflection losses. To calculate the OH absolute content in ppm in the glasses the
following equation is used:
OHcontent = 30. rOH cm−1
Static and Magic Angle Spinning (MAS)
(9)
31
P Nuclear Magnetic Resonance (NMR)
spectra were recorded on a Bruker ASX 400 spectrometer operating at 161.96 MHz
(9.4T). The pulse length was 2.5 μs and 60 s delay time was used. A total number of
128 scans were accumulated with a spinning rate of 10 kHz for the MAS spectra. MAS
7
NMR spectra were fitted to Gaussian functions, in accordance with the chemical shift
distribution of the amorphous state. Solid (NH4) H2PO4 was used as secondary reference
with a chemical shift of 0.82 ppm with respect to H3PO4 (85%).
Raman spectroscopy analyses were performed on a WItec Alpha300RA Raman-AFM
confocal spectrometer with 532 nm laser wavelength excitation and 39 mW power in
the range of 220-3800 cm-1. The laser polarization angle was in x axis. Polished glass
samples around 2 mm thick were used.
The viscosity-temperature curves of the glasses were determined using the rotation and
beam-bending methods at high and low temperature ranges, respectively. The viscosity
of the melts in the range 103–101 dPa.s was determined employing a high-temperature
Haake viscometer of the cylindrical Searle type (Haake, Karlsruhe, Germany) equipped
with a ME 1700 sensor. Rotation speeds of 3 to 15 rpm were used for 15 min, following
the International Standard ISO 7884-2. Three measurements were carried out at three
different rotation speeds for each temperature within this range. The viscosity (η) was
calculated from the shear stress () and the shear rate () applied by the viscous fluid on
a rotating cylindrical platinum spindle according to the equation:
η = τ in dPa. s
(10)
Within the viscosity range 1012.5–109 dPa.s viscosity was measured by bending glass
beams heated at 2K.min-1 and using weights of 10 to 200 g. A viscometer VIS401
(Bähr Thermoanalyse, Germany) with a 40 mm open span in symmetric three point
mode was employed. The viscosity was calculated according to the standard testing
conditions DIN ISO 7884-4:
l3S w
η = 68.1
IC b
(11)
8
3. Results
3.1. Glass Properties
In order to be able to compare the results obtained through the use of the three models,
VFT, AM and MYEGA, the adjustable parameters have been expressed in terms of Tg,
as defined for a shear viscosity equal to 1012 dPa.s, the fragility and the extrapolated
infinite temperature viscosity. Mauro et al. [27] have analyzed a great amount of silicate
liquids and have approximated the viscosity at infinite temperature to about -4, obtained
by VFT fittings, -3 by MYEGA and -1.5 by AM. In this work the three adjustable
parameters are obtained by fitting the experimentally measured viscosity data to the
following equations derived from (2), (3) and (4), respectively:
log ηT = logη∞ +
13 − logη∞
2
12
Tg
m
− 1 + 13 − logη∞
T
log ηT = logη∞ + 13 − logη∞
log ηT = logη∞ + 13 − logη∞
Tg
T
Tg
T
m
13−log η ∞
m
−1
13−log η ∞
(13)
Tg
−1
T
(14)
Figure 1 plots the experimental data of viscosity and the best fits to the VFT model as
an example. The regression coefficient (r2) in all three models fits was of 0.99 or
greater. The average of viscosity at infinite temperature for this metaphosphate series
was 2.3 obtained by VFT fittings, 1.1 by MYEGA and 0.2 by AM; values which are
significantly different, and lower, compared to those obtained for silicate glasses. This
is in accordance with the more fragile character of phosphate glasses. The viscosity
range between Tg and infinite temperature is shorter, thus viscosity change needs to be
stronger. Figure 2 shows the viscosity dependence with the reduced temperature (Tg/T)
9
and best fits to MYEGA equation in all glasses, as an example among three models fits,
from which kinetic fragility has been obtained. Structure and properties of
metaphosphate glasses will be influenced mainly by the composition. We have selected
the cationic potential (Z/a) as the parameter employed to show the effect of composition
through the modifier cation. (Z/a) reflects the most important characteristics that defines
a counterion, the charge (Z), and the ionic radius (a).
Figure 3a shows the variation of Tg, as measured by dilatometry, and the glass transition
values obtained from the fits to viscosity models as a function of the cationic potential.
Both Tg values are quite similar to each other for all glass compositions, showing a
good agreement between the definition of Tg by DSC and by dilatometry. Tg increases
for alkali and alkaline-earth phosphate glasses with Z/a. For Zn(PO3)2, the value is
lower than the one expected attending to its cationic potential. Thus the relation with
Z/a is not straightforward. Figure 3b shows the Tg versus the product of the cationic
potential and the coordination number of the modifier in each composition (Z/axCNMO),
being as follows: CNNa-O=5, CNLi-O=4-5, CNBa-O=8, CNSr-O=8.2, CNCa-O=7, CNZn-
O=4.3
and CNMg-O=5.3 [32-34]. Here, a linear correlation between Tg and Z/axCNM-O
has been found. The increase of Tg with Z/axCNM-O might then be due to the rise of the
glass network strength and connectivity.
Figure 4 illustrates the average of the kinetic fragility values obtained through the three
models for each composition as a function of cationic potential. As it can be observed in
Table I where all the values are collected, they depend on the model used to determine
it. The greater the Z/a, the greater the kinetic fragility for both alkali and alkaline-earth
metaphosphate series. The zinc metaphosphate composition shows the lowest fragility,
similarly to the variation of Tg.
10
In Figure 5 the activation energy of viscous flow at low (Ealow-T) and high temperature
(Eahigh-T), calculated by fitting the experimental values to Arrhenius-type equations, is
represented separately in both temperature ranges. At low temperature, activation
energy follows a similar behaviour as fragility does with cationic potential (Fig. 4),
while at high temperature, the activation energy in general increases with the cationic
potential of the modifier, i.e. the covalent character of the M-NBO bonds. In search of
further insights to be able to explain this behaviour, we have interpreted it in terms of
molar volume and the single bond strength for each binary glass, which have both been
represented as a function of the modifier’s cationic potential in Figure 6. It can be
observed that the activation energy for viscous flow increases with the decrease of the
molar volume and with the rise of the bond strength of the glass.
Figure 7 shows the Doremus ratio as a function of the modifier cationic potential, which
increases slightly with Z/a for the alkali metaphosphate glasses and decreases for the
alkaline-earth ones. It can also be seen that the bigger the gap between the low and high
temperature activation energies, the greater the Doremus ratio. Zinc metaphosphate
glass shows now an RD value more in accordance with its cationic potential.
3.2. Structural characterization
The basic building units in phosphate glasses are the PO4 tetrahedra. These tetrahedrons
are connected through bridging oxygens to form different phosphate arrangements. The
tetrahedra are classified using the Qi terminology, established by Lippmaa et al. in
silicates [35], where ‘i’ means the number of bridging oxygens per tetrahedron.
Metaphosphate glasses have structures that are based on chains or rings made of Q2
units, i.e. two bridging (BO) and two non-bridging oxygens (NBO) per group. Those
chains and rings are linked through terminal oxygens bonded with the modifying
cations.
11
Figure 8 shows the 31P MAS NMR spectra of the metaphosphate glasses. The different
Qi tetrahedra have isotropic 31P chemical shift peaks. The peaks due to Q3 groups appear
at about -51 ppm, -22 ppm for Q2 tetrahedra while for Q1 and Q0 signals are usually at 10 ppm and 0 ppm, respectively. In the spectra, it can be observed that the main
resonance corresponds to Q2 tetrahedra at about -20 ppm, which shifts high-field with
the cationic potential of the modifier. There is also a small amount of Q1 groups due to a
non-stoichiometric composition. These units are present in the glass as terminal and
pyrophosphate groups.
From the integration of
31
P NMR peaks using dmfit software [41], the fraction of Qi
tetrahedra can be determined and the glass composition derived using equation (15) [36]
fQ2 =
2 − 3x
1−x
(15)
where x is the modifier oxide content in mol % and f(Q2) the fraction of Q2 groups.
The highest deviations from the nominal composition corresponded to Ba(PO3)2,
Ca(PO3)2, and Mg(PO3)2 with 47 mol % of P2O5, while Li2PO3 and Zn(PO3)2 present 49
mol% of P2O5; and 48 and 50 mol% for Sr(PO3)2 and Na2PO3, respectively. Since the
difference in the P2O5 molar fraction indirectly determined through
31
P MAS NMR
decomposition is not greater than 3 mol % with respect to the nominal composition, it
can be assumed that there should not be a relevant influence on the glass properties. Due
to the hygroscopic character of phosphate glasses, and in order to determine whether the
proportion of Q1 groups is due to the presence of water in the glass composition, the
water content has also been determined by FTIR spectroscopy as described in the
experimental section. The water concentration is lower than 2.10-2 wt. % ± 5.10-3 for all
glasses.
12
The inset in Figure 8 shows the variation of the isotropic 31P NMR chemical shift with
the cationic potential. It is well known that the peaks shift high-field with Z/a due to the
increase on the covalent character of M-NBO bonds that decreases the electronic
density on phosphorous atoms, thus increasing the shielding.
From the static
31
P NMR spectra, the chemical shift anisotropy (δCSA) and the
asymmetry (ηCSA) can be determined, which provides information about the
conformation of the Qn units. In this work δCSA and ηCSA have been calculated following
the Haerleben convention (16, 17, 18) [37]:
δCSA = δ33 − δISO
(16)
1
δISO = (δ11 + δ22 + δ33 )
3
(17)
δ22 − δ11
(δ33 − δISO )
(18)
ηCSA =
where δISO is the isotropic chemical shift and δ11, δ22, δ33 are the three principal
components of the tensor that describes the chemical shift interaction. The asymmetry
variation in metaphosphate series is small (ηCSA = 0.47 ± 0.04), therefore, the
composition has a little influence on this parameter for metaphosphate compositions.
Generally, δCSA is calculated from the full integration of the MAS NMR spectra using
fitting programs like dmfit [38]. However, we have observed that the fitted spectra do
not reproduce with enough accuracy the experimental ones. This might be due to the
simulation of the bands that only take into account Q2 units shape. To consider also the
contribution of Q1 and thus their influence on the anisotropy, the components of the
tensor have been determined graphically from the static 31P NMR spectra, as shown in
Figure 9 for a sodium metaphosphate glass as an example of all the spectra obtained.
Figure 10 plots the δCSA and δ33 as a function of modifier cationic potential. The increase
13
of δCSA involves an increase of the δ33 with cationic potential until a maximum at the
CaPO3 composition. It is known that δCSA values are larger in ring structures than in
phosphate chains [39,40], thus the chains to rings ratio increases with the cationic
potential up to CaPO3 composition. On the other hand, the higher the δ33 component, the
longer the P-NBO bond length and the shorter the NBO-P-NBO bond angle. This is in
accordance with the increase of the ionic character of this bond due to the increase on
modifier cationic potential. Asymmetry and anisotropy as well as the δCSA tensor values
obtained, are in agreement with the ones reported for Brow et al. [41].
Figure 11 shows the Raman spectra collected for the metaphosphate series. All the
spectra were decomposed into Gaussian contributions from 600 cm-1 to 1400 cm-1. The
spectra are all dominated by two main bands appearing at about 650-750 cm-1 and 11501250 cm-1 and attributed to the symmetric stretching modes of P-O-P and NBO-P-NBO
bonds, respectively [42,43]. The P-O bond bending mode of Q2 units appears as a broad
shape in the range of 200 cm-1 to 400 cm-1. A smaller band can be observed around
1000 cm-1, which is due to the small proportion of Q1 groups present on barium,
calcium and strontium metaphosphate glasses. The band attributed to the asymmetric
stretching mode of the NBO-P-NBO bonds in Q2 groups is located around 1280 cm-1.
In order to obtain the proportion between rings and chains in the glass network the
relative intensity was calculated following the equation (19)
where Irings and Ichains correspond to the intensities of the bands obtained from the
deconvolution of the νsym Q2 (NBO-P-NBO) band into two Gaussians, related with the
presence of rings and chains in the glass network [44]. Figure 12 shows the relative
intensity is plotted as a function of cationic potential and the inset in Fig. 12 shows the
deconvolution of νsym Q2 (NBO-P-NBO) band for Sr(PO3)2 glass as an example. The
14
proportion of chains increases with the modifier cationic potential until CaPO3 as it was
also concluded from the chemical shift anisotropy through the static 31P NMR.
Fig. 13 presents the Raman shifts of the bands attributed to the symmetric stretching
modes of P-O-P and NBO-P-NBO bonds as a function of the cationic potential. The
peak frequency of NBO-P-NBO band shifts to higher values from Na to Li and from Ba
to Mg including zinc, while the P-O-P Raman shift increases for alkali phosphate
glasses and decreases for alkaline-earth ones.
4. Discussion
By means of the NMR and Raman spectroscopy data, it has been seen that the
composition influences the atomic structure at both short and medium range orders and,
as a consequence, the main glass properties will also be influenced up to some extent by
those. The short range order structure is determined through the modifying cation
influence directly onto the P-O bonds. The increase of its cationic potential, i.e. a higher
covalence of M-O, and a higher coordination number make the glass network stronger
as this is reflected in the increase of the glass transition temperature with the product
PCxIC (Fig. 3b). However, the medium range order structure is subject to the effect of
the modifier’s cationic potential onto the organization of the tetrahedral units in rings
and chains. As seen by NMR and Raman, the increase of cationic potential increases the
proportion of chains versus rings in the glass network. Nevertheless, the results can not
be considered quantitative, and so we are not able to determine the precise proportion of
units in each of those arrangements in order to consider the right influence on the
properties.
As a macroscopic transport property, the viscosity will be affected by the organization
of the glass network and how this organization changes with temperature throughout the
15
deformation process that allows the structural arrangements to flow along the whole
temperature range. The activation energy of viscous flow, as well as the kinetic fragility,
is influenced not only by the composition and structure, but also on temperature. We
can observe how fragility does not vary in the same manner as Tg does, then it should
not depend on the same factors and in the same amount.
The activation energy varies in a different way at low and a high temperature ranges
with the cationic potential. This may imply two different mechanisms controlling the
viscous flow through a different evolution of the structure with temperature in each of
them. At low temperatures, it increases sharply for alkali glasses while it does also
increase slightly from Ba to Ca, then decreasing a bit for Mg. The Zn(PO3)2
composition shows the lowest activation energy value among all glasses.
Figure 14 plots the variation of the ratio between bond strength and molar volume and
the activation energy at low temperature range, both as a function of the cationic
potential. The higher the ratio between the bond strength and molar volume the higher is
the activation energy. It can be seen that Ea and B/Vm behave in a very similar way.
However the change between barium and magnesium glasses is much less pronounced
for the activation energy than for the BM-O/Vm ratio, which could necessitate of
additional factors affecting the variation in this series, like the medium range order in
the glass network. The zinc metaphosphate glass takes the lowest value for both the
activation energy and the BM-O/Vm ratio, thus showing the strong influence of this
parameter. As seen through the analysis of the chemical shift anisotropy and the Raman
spectra deconvolution there would be a pronounce increase of the proportion of chains
against that of rings from the sodium to the calcium metaphosphates; however, both
zinc and magnesium metaphosphates show a change of tendency with a decrease of the
chains/rings ratio. In principle, it could be supposed that a high amount of rings (glasses
16
with lowest and highest cationic potentials) can be related to lower activation energies
and, on the other hand, with higher molar volume glasses.
At high temperatures, it seems that the ration between bond strength and molar volume
as well as the medium range order structure do not influence the activation energy in the
same degree. The more or less linear increase of activation energy, except with a small
decrease for zinc and magnesium glasses, seems to be dominated through the cationic
potential of the modifier.
In an attempt of going forward into the relationship between medium range order
structure and the viscosity of the glasses, we have plotted the Doremus ratio against the
chemical shift anisotropy values calculated for the metaphosphate glasses studied, as
shown in Fig. 15. Even though the number of data points studied in this first case is still
small, the plot shows that the Doremus ratio decreases with the increase of the
proportion of chains in the glass in an approximately linear tendency. Among all
glasses, lithium metaphosphate is the one showing a more different behaviour through a
higher deviation. It can be derived that the gap between both activation energies will be
lower if the proportion of chains in the glass network is higher.
5. Conclusions
The analysis of viscosity through the different models has shown that kinetic fragility
may take different values depending on which model is employed; meanwhile Tg values
are quite similar between each other, independently of the model, and to those
determined by dilatometry. The glass composition determines the short and medium
range order structure in the glass network through the cationic potential and the
averaged kinetic fragility increases with the modifier’s cationic potential within the
alkali and alkaline-earth series, being higher in alkali than in alkaline-earth glasses.
17
However the calculated value for the zinc metaphosphate shows the lowest among all
glasses. The activation energy of viscous flow above Tg seems to be influenced by bond
strength and molar volume while that of the melt increases with M-O covalency,
following a different mechanism. The results of the local structure in the glasses,
through the chemical shift anisotropy values, showed a relatively close relationship with
the Doremus ratio between activation energies in different temperature ranges,
suggesting that the a representation of the viscous flow in terms of the atomic structure
of the glasses could be done.
Acknowledgements
Funding from project MAT2010-20459 from Ministerio de Economía y Competitividad
(MINECO) of Spain is acknowledged. L. Muñoz also thanks the MINECO for her PhD
scholarship (BES-2011-044130) as well as the Inorganic Chemistry Department of the
Faculty of Science of the Universidad Autónoma de Madrid (UAM) for the Scholarship
for Postgraduate Studies.
18
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21
Figure captions:
Figure 1. Viscosity data points of 50MO.50P2O5 (M=Mg,Ca,Sr,Ba,Zn) and
50M’2O.50P2O5 (M’=Li,Na) glasses and best fits of the experimental values to VFT
equation.
Figure 2. Viscosity data points and best fits to MYEGA equation as a function of Tg/T.
Figure 3. Tg of 50MO.50P2O5 (M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na)
glasses obtained by dilatometry and by models vs. cationic potential (a). Relationship
between Tg obtained by dilatometry and the product of cationic potential and
coordination number (CNM-O) (b). The lines are drawn as a guide for the eyes.
Figure 4. Kinetic fragility of alkali (M’=Li,Na), alkaline-earth (M=Mg,Ca,Sr,Ba) and
zinc metaphosphate glasses as a function of cationic potential. The lines are drawn as a
guide for the eyes.
Figure 5. Activation energy of viscous flow at low and high temperatures of
50MO.50P2O5 (M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na) glasses versus the
cationic potential. The lines are drawn as a guide for the eyes.
Figure 6. Molar volume and average single bond strength in the glass network of
50MO.50P2O5 (M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na) glasses versus the
cationic potential. The lines are drawn as a guide for the eyes.
Figure 7. Doremus ratio of 50MO.50 P2O5 (M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5
(M’=Li,Na) glasses vs. cationic potential. The line is drawn as a guide for the eyes.
Figure 8.
31
P MAS NMR spectra of 50MO.50 P2O5 (M=Mg,Ca,Sr,Ba,Zn) and
50M’2O.50P2O5 (M’=Li,Na) glasses. The inset represents the
31
P NMR chemical shifts
of the glasses as a function of cationic potential (Z/a). The line represents the linear fit
of chemical shift data with a regression coefficient (R2) of 0.97.
22
Figure 9. Static
31
P NMR spectra of NaPO3 as an example of the metaphospahte glass
series.
Figure
10.
Variation
of
δCSA
and
δ33
components
of
50MO.50
P2O5
(M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na) glasses with cationic potential.
The lines are drawn as a guide for the eyes.
Figure 11. Raman spectra of 50MO.50 P2O5 (M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5
(M’=Li,Na) glasses. Discontinuous lines show the bands attributed to bending (δ) and
stretching (νS) vibration modes of P-O bonds.
Figure
12.
Relative
intensity
of
50MO.50P2O5
(M=Mg,Ca,Sr,Ba,Zn)
and
50M’2O.50P2O5 (M’=Li,Na) glasses as a function of cationic potential. The inset shows
the deconvolution of νS Q2 (O-P-O) band into two Gaussians attribute each of it to the
presence of chains and rings arrangements in the glass network. The lines is drawn as a
guide for the eyes.
Figure 13. Raman shifts of the Q2 units symmetric bands of 50MO.50P2O5
(M=Mg,Ca,Sr,Ba,Zn) and 50M’2O.50P2O5 (M’=Li,Na) glasses against the cationic
potential. The lines are drawn as a guide for the eyes.
Figure 14. Variations of the ratio between the single bond strength and the molar
volume, and activation energy for viscous flow at low temperature. The lines are drawn
as a guide for the eyes.
Figure 15. Doremus ratio versus the chemical shift anisotry of the metaphosphate
glasses. The line is drawn as a guide for the eyes.
23
14
Na
Li
Ba
Sr
Ca
Zn
Mg
VFT Fit
log  ( in dPa.s)
12
10
8
6
4
2
0
200
400
600
800
1000
1200
T (ºC)
Figure 1
24
14
log  ( in dPa.s)
12
10
8
6
Na
Li
Ba
Sr
Ca
Zn
Mg
MYEGA Fit
4
2
0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Tg/T
Figure 2
25
600
Dilatometry
Viscosity Models
600
Dilatometry
Mg
Mg
Zn
Ca
Ca
Sr
Ba
400
Ba
Zn
Li
Na
1.2
300
b)
a)
1.6
400
Li
Na
300
0.8
500
Sr
2.0
-1
Z/a (A )
2.4
2.8 4
Tg (ºC)
Tg (ºC)
500
6
8
10
12
14
-1
Z/a (A ) x CNM-O
Figure 3
26
100
80
Li
Na
m
60
40
Ba
Sr
Ca
Mg
Zn
20
0.8
1.2
1.6
2.0
2.4
2.8
-1
Z/a (A )
Figure 4
27
1500
Low T
High T
Li
Ea (kJ/mol)
1200
900
Na
Ba
Ca
Sr
Mg
600
Zn
300
0
0.8
1.2
1.6
2.0
2.4
2.8
-1
Z/a (A )
Figure 5
28
320
Na
Li
Ba
Zn
42
Sr
Ca
300
40
3
B (kJ/mol)
Mg
Vm (cm /mol)
310
44
290
38
280
270
0.8
B
Vm
1.2
1.6
2.0
2.4
36
2.8
-1
Z/a (A )
Figure 6
29
18
Li
16
14
Na
RD
12
10
Ba
8
Sr
Zn
6
Ca
4
Mg
2
0.8
1.2
1.6
2.0
-1
Z/a (A )
2.4
2.8
Figure 7
30
Na
-22.5
Li
-25.0
Ba
Sr
-27.5
Ca
-30.0
Zn
-32.5
31
P- Chemical Shift (ppm)
-20.0
Mg
1.0
1.5
2.0
2.5
-1
Z/a (A )
Mg
Intensity (a.u.)
Zn
Ca
Sr
Ba
Li
Na
10
0
-10
-20
-30
-40
-50
31
P Chemical shift (ppm)
Figure 8
31
Intensity (a.u.)
22
NaPO3
11
33
150
100
50
0
-50 -100 -150 -200 -250
P Chemical Shift (ppm)
31
Figure 9
32
-120
33
Ca
CSA
Sr
-130
Zn
Mg
Ba
 (ppm)
Li
-140
-150
Na
-160
-170
0.8
1.2
1.6
2.0
2.4
2.8
-1
Z/a (A )
Figure 10
33
2
S Q (O-P-O)
(P-O)
S (P-O-P)
1
S (Q )
2
as Q
Mg
Intensity (a.u)
Zn
Ca
Sr
Ba
LiP
NaP
0
200
400
600
800
1000 1200 1400 1600
-1
Raman Shift (cm )
Figure 11
34
1.00
Sr(PO3)2
Intensity (a.u)
0.95
0.90
Na
Irelative
0.85
0.80
2
S Q (O-P-O)rings
2
S Q (O-P-O)chains
Li
1000
1100
1200
1300
-1
0.75
Raman Shift (cm )
Ba
Zn
0.70
Mg
Sr
0.65
0.8
1400
Ca
1.2
1.6
2.0
2.4
2.8
-1
Z/a (A )
Figure 12
35
1250
Zn
Li
1200
Na
Mg
Ca
Ba Sr
-1
Raman Shift (cm )
2
S Q (O-P-O)chains
1150
2
S Q (O-P-O)rings
Ba
2
S Q (P-O-P)
Ca
Sr
775
Zn
750
Na
Mg
Li
725
700
0.8
1.2
1.6
2.0
2.4
2.8
-1
Z/a (A )
Figure 13
36
9.0
1600
Li
Mg
3
8.0
1400
Ca
Na
1200
Sr
Zn
1000
Ba
7.5
800
Ea (kJ/mol)
B/ Vm (kJ/cm )
8.5
7.0
6.5
0.9
600
BM-O/ Vm
Ea
1.2
1.5
1.8
2.1
2.4
400
2.7
-1
Z/a (A )
Figure 14
37
18
Li
16
14
Na
RD
12
10
Sr
8
Ba
6
4
2
-150
Ca
Mg
Zn
-145
-140
-135
-130
-125
-120
-115
CSA (ppm)
Figure 15
38