Glass Physics and Chemistry, Vol. 28, No. 4, 2002, pp. 232–238. Original Russian Text Copyright 2002 by Fizika i Khimiya Stekla, Startsev, Golubeva.Specific Features of Changes in the Properties of One- and Two-Alkali Borate Glasses Containing Water: III. Thermal Expansion and the Structural and Mechanical Relaxation Parameters of Two-Alkali Borate Glasses Yu. K. Startsev and O. Yu. Golubeva Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, ul. Odoevskogo 24/2, St. Petersburg, 199155 RussiaAbstract—The thermal expansion and stress relaxation in mixed alkali borate glasses containing lithium, sodium, and potassium oxides with a total alkali oxide content of 15 mol % are measured on an inclined quartz dilatometer and a relaxometer. The experimental data obtained are used to determine the thermal expansion coefficients and the structural and mechanical relaxation parameters. No deviations from the additivity are found in the concentration dependences of the thermal expansion coefficient and the calculated parameters determining the width of the spectra of the structural and stress relaxation times. The IR absorption spectra of the studied glasses are recorded in the range of stretching vibrations of hydroxyl groups. Analysis of the IR spectra makes it possible to assume that the content of residual water in the structure of borate glasses affects the manifestation of the mixed alkali effect in the properties of these glasses.
pairs of alkali oxides: Li2O–Na2O, Na2O–K2O, and
The relaxation dependences of the properties in the
Li2O–K2O. The total alkali oxide content was equal to
glass transition range can be quantitatively described in
15 mol %. The as-batched and as-analyzed composi-
the case when the kinetic parameters of the structural
tions of the studied glasses and their designations were
and mechanical relaxation are determined for the
given in our previous work [2]. The glass designations
glasses under investigation. However, no data on sys-
indicate the type of alkali cations and their as-batched
tematic investigations into the influence of composition
content (in mol %) in the glass composition. For exam-
on these parameters are available in the literature. It
ple, the designation L3N12 corresponds to lithium
was of interest to elucidate how the replacement of one
sodium borate glass with the as-batched composition
alkali oxide by another oxide in series of mixed alkali
involving 3 mol % Li2O and 12 mol % Na2O.
borate glasses affects the parameters of their structural
Boric acid and carbonates of the corresponding
alkali metals (chemically pure) were used as the initial
In our earlier work [1], we determined the tem-
components for the preparation of the batch. The
perature dependences of the viscosity in the range
glasses were synthesized in a platinum crucible with a
1010–1013 dPa s for three series of one- and two-alkali
volume of 200 ml in a Globar-heater electric furnace at
borate glasses. When one alkali oxide was replaced by
temperatures of 1150–1200°C for 1.5–2 h.
another oxide, we observed negative deviations from an
The water content in the glasses under investigation
additive behavior, i.e., the mixed alkali effect, in the
was estimated by IR absorption spectroscopy. The tech-
concentration dependences of the viscosity isotherms
nique was described in detail in [1]. The IR spectra
for the studied series of mixed alkali glasses.
were recorded on an SF-2-LSS spectrophotometer
The aim of the present work was to investigate the
designed at the Laboratory of Glass Properties
manifestation of the mixed alkali effect in the concen-
(Grebenshchikov Institute of Silicate Chemistry, Rus-
tration dependences of the thermal expansion coeffi-
sian Academy of Sciences) and a commercial Shi-
cient, the structural relaxation parameters determined
madzu IR-470 (Japan) spectrophotometer.1
from dilatometric curves, and the mechanical relax-
All the glasses studied were synthesized under iden-
ation parameters for two-alkali borate glasses.
tical conditions and likely involved approximatelyequal amounts of residual water. This assumption is
confirmed by the estimates of water content in certain
Glass synthesis. In this work, we studied three
1 We are grateful to V.Kh. Khalilov for performing the measure-
series of mixed alkali borate glasses with the following
ments on the IR-470 spectrophotometer.
1087-6596/02/2804-0232$27.00 2002 MAIK “Nauka /Interperiodica”
SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES
Designations and some properties of the studied glasses: thermal expansion coefficients below (α
g) and above ( l) the glass
transition range, glass transition temperatures Tg, and parameters of structural (bs and logKs) and mechanical (bσ and logKσ)
glasses from the IR spectroscopic data. Since the
vided a way of calculating the relaxation parameters [1]
method of determining the water content in mixed
of the Tool–Narayanaswamy model according to the
alkali borate glasses has not been developed, the calcu-
ISC algorithm [4]. The constant bs and the modulus Ks
lations were carried out using the technique proposed
characterizing the structural relaxation process were
for one-alkali borate glasses [1]. The results of calcula-
determined with a special optimizing program that
tions showed that the water content in the glasses stud-
minimizes the square of the difference between the
computed and experimental values of the thermal
Measurements of thermal expansion. The thermal
expansion in the dilatometric loops obtained upon cool-
expansion of the glasses was investigated on an
ing and subsequent heating at the same rate. The calcu-
inclined quartz dilatometer with a small measuring load
lated parameters bs and Ks are presented in the table.
[3] under thermocycling conditions. The rate of changein the temperature was equal to 3 K/min. The obtained
Mechanical relaxation. The mechanical relaxation
dilatometric curves were used for determining the ther-
was investigated on a relaxometer [5] whose operation
mal expansion coefficients in ten-degree temperature
is based on measuring the time dependence of the force
ranges above the upper boundary of the glass transition
under a constant deformation produced by a modified
McLoughlin dynamometer [6]. Samples were prepared
l ) and twenty-degree ranges below the lower
boundary of the glass transition range (α
in the form of cylindrical springs coiled from fibers
drawn from melts of the studied glasses directly in the
are listed in the table. The technique of measurements
course of glass making. The prepared glass springs [7]
and data processing was described in more detail in [1].
were not subjected to any additional treatment, whichruled out the possibility of reacting the samples with
Structural relaxation. The dilatometer design
water vapors contained, for example, in the flame of a
made it possible to perform measurements over a wide
range of temperatures, including the glass transitionrange. By using this dilatometer, we measured the
Numerous experiments (see, for example, [7–9])
dilatometric hysteresis loops whose processing pro-
demonstrated that mechanical relaxation processes in
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
glasses can be successfully described by the fractional
Analogous signals from the reference thermocouple
and the small-displacement transducer arrive at thevoltmeter and are digitized. The converter samples the
corresponding channel through a multiplexer, converts
the analogous signal into a binary decimal code, andtransmits it to computer memory for primary process-
where σ(t) and σ0 are the stresses in the sample at the
instants of time t and t = 0, respectively; τσ is the most
The thermocouple thermopower and the signal from
probable stress relaxation (Kohlrausch) time; and the
the displacement transducer are the recorded quantities.
constant bσ (0 < bσ ≤ 1) determines the width of the
The temperature with due regard for the applied correc-
spectrum of the stress relaxation times τσ. The smaller
tions and the displacement in terms of length are the
the constant bσ, the longer the time it takes for the
relaxation process to be completed. At bσ = 1, Eq. (1)
The data obtained are corrected for systematic
transforms into a simple exponential equation. At
errors in measurements by a primary processing pro-
present, in the literature on relaxation phenomena,
gram. When operating with the relaxometer, one of
Eq. (1) proposed by Kohlrausch [10] for representing
these errors is the error of the thermopower measure-
the stress relaxation in quartz fibers of electrometers is
ment for a particular thermocouple. In order to allow
referred to as the Kohlrausch–Williams–Watts equation
for this error, the thermocouple in the operating posi-
(see, for example, [11]). This equation is very conve-
tion directly in the relaxometer furnace was preliminar-
nient from the viewpoint of experimenters (because it
ily calibrated against the melting temperatures of pure
includes only two parameters!), even though it has
metals followed by applying the corresponding correc-
defied theoretical treatment by virtue of an infinite dis-
tion to all the temperatures measured. As a conse-
continuity at the time t = 0. However, this equation is
quence, the error of the temperature measurement was
used to advantage not only for the description of the
reduced to ±0.5 K, variations in the temperature during
mechanical relaxation and not only in inorganic
isothermal treatments for one day did not exceed ±0.5 K,
and the error of the stress measurement at a small-dis-
De Bast and Gilard [12] showed that the ratio
placement transducer sensitivity of 0.02 µm was as
between the relaxation time τσ entering into Eq. (1) and
small as ±0.5%. As a result of these errors, the errors of
the viscosity of the studied glass is constant and inde-
pendent of temperature (because the temperature
dependences of the relaxation time and the viscosityare very similar to each other), that is,
The investigation of the stress relaxation can be
essentially simplified using a preliminary stabilization
of the samples, i.e., such heat treatment which results in
almost completion of the structural relaxation. Indeed,
the study of the mechanical relaxation against the back-
where Kσ is the constant numerically equal to such a
ground of the structural relaxation involves additional
viscosity of the glass at which the time τσ is equal to 1 s.
problems [13]. With the aim of overcoming these prob-
The smaller the constant Kσ at a certain fixed viscosity,
lems, experimenters should preliminarily determine the
the lower the relaxation process rate. This circumstance
parameters characterizing the kinetics of the structural
permits one to represent the data obtained on the stress
relaxation at different temperatures in the same plot in
The mechanical relaxation in the stabilized samples
can be studied by performing the following three addi-
0– log t , which is termed the mus-
ter curve in the English-language literature [9].
tional operations: (1) the preliminary measurement of
Therefore, the investigation into the kinetics of
the temperature dependence of the viscosity, (2) the
stress relaxation amounts to determining the parame-
determination of the structural stabilization time at a
chosen experimental temperature (for example, accord-
ing to the procedure recommended in [14]), and (3) the
In our relaxometer, the system of experimental data
stabilization of the sample at the chosen temperature.
collection consists of the following components: an
In a number of works (see, for example, [5, 13]),
IBM PC AT 286 computer, a CAMAC or unibus data
analysis of the experimental data with the use of Eq. (1)
converter, a small-displacement transducer on the basis
was reduced to the linearization of this equation by tak-
of a mechanotron (a vacuum-tube twin diode with an
ing the double logarithm and the determination of the
elastic diaphragm) or an inductive transducer, a mea-
suring instrument [a V7-28 digital voltmeter (for
σ and bσ by the least-squares tech-
CAMAC) or a V7-34 digital voltmeter (for unibus)],
thermoelectric transducers (reference and controlling
It follows from Eq. (1) and the results obtained by
thermocouples), a temperature controller of the PTR-
Kurkjian [8] that, when processing the experimental
105 type (AO Thermex), and a resistance furnace.
data on stress relaxation, the stress σ0 should be deter-
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES
included the possibility of choosing the initial instant of
time and the stress at this instant by a researcher.2
The concentration dependences of the glass transi-
tion temperature calculated from the dilatometric
curves obtained upon cooling of the glasses studied are
plotted in Fig. 1. This figure also shows the concentra-
tion dependences of the structural thermal expansion
coefficient αs, which is equal to the difference between
the thermal expansion coefficients determined at tem-
peratures above and below the glass transition range(α
s = αl – αg ). The lines in Fig. 1 are represented by the
polynomials of best approximation to the experimental
The glass transition temperatures of glasses in all
three series are characterized by the negative deviation
from the additivity. This agrees with the behavior
observed for the concentration dependences of the vis-
The replacement of smaller sized cations by larger
sized cations leads to an increase in the structural ther-
mal expansion coefficient. Note that this increase is
largest for lithium potassium series and reflects the ten-
dency to a change in the amount of fourfold-coordi-
nated boron in the glass structure [15]. No deviations
from the additivity are found in the concentration
dependences of the structural thermal expansion coeffi-
Figure 2 displays the concentration dependences of
the kinetic parameters of the structural (bs) and
mechanical (bσ) relaxations and the dependences of the
Kohlrausch relaxation times τs and τσ. These times
were calculated by the relationship Kj = η/ τj, where Kj
are the moduli derived by processing the data on the
structural (j ≡ s) and mechanical (j ≡ σ) relaxations.
The relaxation times for lithium sodium, sodium potas-
sium, and lithium potassium glasses are given at 420,
400, and 410°C, respectively. The solid lines in Fig. 2are represented by the polynomials of best approxima-
Fig. 1. Concentration dependences of (1) the glass transi-
tion to the experimental data on the parameters τj
tion temperature Tg and (2) the structural thermal expansion
coefficient αs for (a) lithium sodium, (b) sodium potassium,and (c) lithium potassium glasses.
As can be seen from Fig. 2, the behavior of the con-
centration dependences of the relaxation times forglasses in all series reflects the behavior of the concen-
mined as precisely as possible; i.e., it is necessary to
tration dependences of the viscosity. It should be noted
account for the noninstantaneous character of deforma-
that the structural relaxation times are somewhat longer
tion. The influence of this factor resides in the fact that
than the mechanical relaxation times. This is in agree-
the first reliable measurement of relaxing stresses can
ment with a similar difference previously found for
be carried out only beginning with a certain instant of
commercial multicomponent silicate glasses [5, 7, 9,
time when the relaxation can proceed in part, and,
hence, processes described by shorter relaxation times
As one alkali oxide is replaced by another alkali
will be completed. For this reason, the zeroth instant of
time should be chosen between the last measurement
s and bσ have a certain tendency
to increase; however, this increase is within the limits of
before the starting of deformation and the first mea-surement after its completion. The algorithm used in
2 The computer code for this algorithm was developed by
our work for determining the parameters τσ and bσ
A.I. Priven (AO Thermex, St. Petersburg).
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
Fig. 2. Concentration dependences of the kinetic parameters of the structural (bs and τs) and mechanical (bσ and τσ) relaxations for (a) lithium sodium, (b) sodium potassium, and (c) lithium potassium glasses: (1) bs, (2) τs, (3) bσ, and (4) τσ.
their computational error. The dependences of the
to their number calculated from the additivity principle
parameters bs and bσ do not deviate from the additive
Our investigation of the thermal expansion and the
structural and mechanical relaxations in alkali borate
glasses with a total alkali oxide content of 15 mol %revealed that the mixed alkali effect manifesting itself
Zhong and Bray [16] studied mixed alkali borate
in the deviation from the additivity is not observed in
glasses at a total alkali oxide content of 40 mol % anddrew the inference that the manifestation of the
the concentration dependences of these properties. The
mixed alkali effect in the properties of these glasses
found linear dependences of the properties allow us to
is associated with a decrease in the number of boron
assume that the content of fourfold-coordinated boron
atoms in the fourfold-coordinated state as compared
obeys the additivity principle upon replacement of one
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
SPECIFIC FEATURES OF CHANGES IN THE PROPERTIES
glasses, the intensities of the absorption bands with a
groups are close to each other, whereas the absorption
bands with a maximum at 3.5 µm have different inten-sities. According to the data obtained in different works
[17, 18], the latter absorption band is assigned to the so-called bound hydroxyl groups linked by hydrogen
bonds to the nonbridging oxygen atoms that are formed
upon introduction of alkali oxides into the glass struc-ture. As can be seen from Fig. 3, the intensity of the
absorption band associated with the bound hydroxyl
groups for mixed alkali glasses of all the series studiedis lower than that for the corresponding binary glasses.
This can indicate that a smaller number of hydrogen
bonds are formed in the structure of alkali borate
glasses containing two alkali oxides.
The replacement of smaller sized alkali cations by
larger sized cations results in a decrease in the number
of hydrogen bonds and a linear decrease in the numberof fourfold-coordinated boron atoms in mixed alkali
glasses. This favors the viscous flow and leads to a neg-
ative deviation from the additivity in the concentrationdependences of the viscosity without deviations from
the additivity in the concentration dependences of thethermal expansion coefficient and the relaxation
Moreover, in our previous work [2], we noted that
no mixed alkali effect is observed for anhydrous
glasses. This fact can also be explained by the possibleinfluence of two alkali oxides in the glass composition
The results of the above investigation into the con-
centration dependences of the thermal expansion coef-ficient and the structural and mechanical relaxationparameters for mixed alkali borate glasses with a total
Fig. 3. Comparison of the IR absorption spectra of (a) lith- ium sodium, (b) sodium potassium, and (c) lithium potas-
alkali oxide content of 15 mol % can be summarized as
sium glasses: (1) L15B, (2) LN7.5, (3) N15B, (4) NK7.5,
(5) K15B, and (6) LK7.5 (see table).
(1) No deviation from the additivity is found for the
structural thermal expansion coefficient and the struc-
alkali oxide by another alkali oxide in the glasses of the
tural and mechanical relaxation parameters upon
replacement of one alkali oxide by another alkali oxidein the glass composition.
On the other hand, in our earlier work [2], we
showed that the concentration dependences of the vis-
(2) The mixed alkali effect in the concentration
cosity for the same glasses are characterized by the
dependences of the glass transition temperature and the
mixed alkali affect manifesting itself in negative devia-
structural and mechanical relaxation times manifests
itself in negative deviations from the additivity. Thisagrees with the behavior observed for the concentration
The IR absorption spectra K(λ) (where K is the
absorption coefficient in terms of cm–1 and λ is thewavelength in terms of µm) of mixed alkali borate
(3) The replacement of one alkali oxide by another
glasses with the same contents of alkali oxides for three
oxide leads to a change in the parameter bs characteriz-
studied series and the spectra of the corresponding
ing the structural relaxation and does not noticeably
binary alkali borate glasses are compared in Fig. 3. It is
affect the parameter bσ characterizing the stress relax-
seen from this figure that, for binary and mixed alkali
GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
(4) The content of residual structural water in mixed
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alkali borate glasses likely affects the manifestation of
of a Commercial Glass, J. Am. Ceram. Soc., 1973,
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der Torsion, Ann. Phys. Chem., 1863, vol. 119, pp. 337–
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of Changes in the Properties of One- and Two-Alkali
(DNLR) Approach and Relaxation Phenomena: Part I.
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13. Mazurin, O.V., Damdinov, D.G., and Startsev, Yu.K.,
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GLASS PHYSICS AND CHEMISTRY Vol. 28 No. 4 2002
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Introduction This week, we will treat bacteria to make them competent to take up plasmid DNA. The process of DNA uptake is transformation , since it alters the genetic compliment of the bacteria (they now have a new plasmid). LEARNING GOALS: 1. Learn how to treat bacteria to take up plasmid DNA. 2. Understand the process of transformation. 3. Know how we select for bacteria that hav