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Final Year Physics Project Final Report

I. Introduction
The aim of this project is to study how the glass forming liquid glycerol behaves when confined to nanometre-sized pores in a glass substrate. Calorimetric measurements of the thermal properties of glycerol soaked glass are taken, looking for the characteristic glass transition.
The behaviour of liquids confined to nanometre pores is not yet fully understood – it has been seen throughout published literature to differ from that seen in a macroscopic system (to be explained further in the theory section of this report). This is theorised to be due to the interplay of several effects, but no overall consensus has been reached.
Therefore, a comparison between different pore sizes and bulk measurements is made, to try and explain in context of the current literature what changes there are, if any.
There are several prominent practical applications in industry, in addition to the drive to fully understand the theoretical underpinnings of the glass transition phenomena. Glasses are found in both nature and technology [1], some examples being window glass [2], and their use in food processing [3] (plasticization affects foods that contain sugar/starch – absorption of water lowers the glass transition temperature below room temperature, causing a loss of crispness in food items like biscuits [4]).
There is a practical importance to knowing the glass transition of a material: it sets the temperature T > Tg a material has to be worked above, or the temperature T < Tg the final set glass has to be used below [4].
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When looking specifically at confinement, finite size effects (caused by the
nanometre confinement scale, explained
further in the theory) are relevant to fluid
flow in carbon nanotubes [5, 6] and controlled drug release [7]; interfacial effects
can be applied when creating amorphous
polymer surfaces (a lowered glass transition
at a surface could have effects on adhesion
and wear) [8].
A. What is a glass?
The nature of a glass as given by Rao [9] is
that of an amorphous solid produced from
the supercooling of a liquid. Debenedetti
and Stillinger [1] describe glasses as disordered, lacking the periodicity of crystal
matrix, but still exhibiting the mechanical
properties of a solid.
A glass, when heated, will always exhibit
a glass transition at temperature Tg corresponding to a sudden change in heat capacity, a second order thermodynamic property. This separates glasses from other
amorphous materials which do not show a
glass transition; glasses are only the amorphous solids obtained by the supercooling
of melts [9].
There are a number of different definitions of the glass transition throughout literature reflecting observations of the
changes that occur in the properties of the
material undergoing the transition (other
than heat capacity), two of which are [10]:
1. The temperature at which observation
times are no longer shorter than relaxation times [11], which can be described in terms of a ratio between the
observation and relaxation time, or the
Deborah ratio.” This is unity at the
glass transition temperature Tg. The
term was coined after the Prophetess
Deborah, who said what may appear
stationary to a mortal, would not be
so to a deity.
2. Where the supercooled liquid has a
viscosity of 1013 Poise.
The glass transition phenomenon is also
described by two theories: kinetics and
thermodynamics [11]. These are explained
in the subsequent sections.
A..1 Phase transitions and the thermodynamic description of the
glass transition
In order to understand the glass transition,
it’s important to understand the theory behind phase transitions as a whole. Phase
transitions occur in thermodynamic equilibrium, i.e. they are constant temperature
and pressure processes. In an equilibrium
state, Gibbs free energy:
G = H – TS (1)
2
Figure 1: A classic phase transition diagram,
constructed from the lines of intersection of
the g surfaces and projected onto the pressuretemperature plane.
is at a minimum for a fixed temperature
T and pressure P, where S is the entropy
[12, 13]. H is the enthalpy (H = U – PV
where U is internal energy, and V is volume), equivalent to the heat evolved in
a constant pressure process. The specific
Gibbs function g (The Gibbs function G,
equ. (1), per unit mass m) must be a
continuous function of P and T for a single phase (i.e. solid, liquid or gas). Two
phases are in equilibrium where their specific Gibbs functions g are equal, and the
classic phase transition diagram (Fig. 1)
is a projection of the lines of intersection
of the g functions for the solid, liquid, and
gas phases onto the pressure-temperature
plane [14].
Phase transitions (sublimation, vaporisation, and fusion) occur when crossing
these lines of intersection, and are known
Figure 2: A first order transition (a) showing
a discontinuity in volume V, entropy S or enthalpy H, in comparison to the glass transition
(b) which does not show a true discontinuity
and instead has a glass transition range over
which the transition takes place.
as first order phase transitions as the first
order derivatives of the Gibbs function G
(Equ. (1)): S = –@G @T
P
and V = @G
@P
T
are
discontinuous at the transition point (see
Fig. 2) [15].
At the glass transition, the first derivative quantities of Gibbs free energy (V, S)
remain continuous, unlike in the previously
discussed ormal” phase transitions. The
second derivative quantities (heat capacity Cp, thermal expansivity α, and volume
compressibility β) have a sharp (but continuous) change at Tg [16]. However, these
are not true discontinuities as the change
occurs over a range of values (known as the
glass transition range, see Fig. 2), and as
such the glass transition is not a true phase
transition [1], so instead it is often called
a pseudo second order transition in literature [9].
An abrupt change in the heat capacity
is apparent in a change of gradient in en-
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thalpy H or heat flow q as T is varied:

@2G
@T2 P (2)
Figure 3: A constant pressure diagram showing the temperature dependence of the volume or enthalpy of a liquid. The lines a (slow
cooling rate) and b (faster cooling rate) are
those followed by a liquid forming a glass,
with glass transitions at Tg(a) and Tg(b) respectively. Line c is followed by the liquid
forming a crystal, when the cooling rate is not
fast enough to produce a glass.
This allows calculation of T
g (as shown
in Fig. 3) by extrapolation of the lines
of constant gradient – where they cross is
defined as T
g. This constitutes a thermodynamic description of the glass transition.
Stable states of the system other than
the systems state of least energy, called
metastable states,” exist to complicate
this picture. The persistence of a
metastable state depends on the absence of
nuclei which can start the phase transition
process. Examples include supersaturated
vapours (when there are no nuclei present
to initiate condensation); superheated liquids (very pure liquids heated above boiling point without boiling taking place) [14];
and most importantly to this project, supercooled liquids (remaining liquids in the
phase diagram solid region) [12], which are
required for glass formation.

The most common way to make a glass is
to cool a viscous liquid fast enough to avoid
crystallisation, known as the supercooling
route to the vitreous state [1]. Crystallisation is governed by two factors: nucleation
and growth [9]. The required cooling rate
to bypass crystallisation is determined by
the velocity of crystallisation ν of the particular material:
ν =
L(Tm – T)
3πa2ηTm (3)
where L is the latent heat of fusion; a is
the distance particles move during the occurrence of crystallisation (of the order of
the lattice spacing); and η is the coefficient
of viscosity (of the melt) [9]. Viscosity increases exponentially during cooling, causing ν to decrease rapidly. Crystallisation
is therefore circumvented by rapid cooling.
When cooled, a liquid samples possible configurations to find the lowest energy state.
Rearrangement of molecules ultimately becomes so slow that they cannot adequately
sample all configurations in the available
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time as the cooling rate is too fast [17].
At this point, they are frozen on the lab
timescale (i.e. minutes) [1]. The slower the
rate of cooling, the longer the time available for configuration sampling and therefore the colder it can become before falling
out of liquid-state equilibrium [1]. Consequently, Tg should increase with cooling
rate; in practise, however, the dependence
is weak, and therefore Tg is an important
material characteristic [1].
As a glass forming liquid is cooled from
above Tm to Tg, it will typically undergo a change in viscosity of several orders
of magnitude. At these high viscosities,
the supercooled liquid is now essentially a
solid. Consequent relaxation (structural rearrangements) cannot occur as relaxation
times become long [9], and the liquid structure is unable to adjust as temperature
changes when T < Tg. The timescale for relaxation within the supercooling liquid increases continuously as the temperature is
decreased [18]. If crystallisation does not
occur, the timescale is of the order of hundreds of seconds when T
g is reached [18],
and a rough calculation is performed by
Rao [9] giving the characteristic relaxation
time τ as:

η G1
1012:6 Pa s
where G1 is the infinite frequency shear
modulus with the typical value of 1010
Pa at T
g. When the glass transition is
observed by DSC, enthalpy relaxation
times are appropriate – ≈100 s at Tgwith
a heating/cooling rate of 10 K/min [9].
The behaviour of τ as T
g is approached is commonly plotted using the
Vogel-Fulcher equation [19{21]:
τ = τ0 expT –AT0 (5)
including fitting parameters τ0, A and T0.
This simplifies to the Arrhenius equation
when T0 = 0.
Figure 4: A modified Arrhenius plot reproduced from Angell [18]. Liquids at the upper edge (SiO2, GeO2) are strong; liquids at
the lower edge (o-terphenyl, chlorobenzene)
are fragile. Glycerol is found near the middle
of the plot, showing deviation from Arrhenius
behaviour.
Most relaxation processes studied in supercooled liquids involve the response to either a thermal or mechanical stress; however, relaxation phenomena depend not
just on the type of stress imposed but
5
also on the molecular nature of the observed system [18, 22]. Relaxation time increases with Arrhenius form in some liquids, but shows very non-Arrhenius behaviour in others – Angell [18] normalises
the temperature of a number of studies
on different glass forming materials by the
Tg
for each system to produce a modified
Arrhenius plot (Fig. 4). Angell classifies
the behaviour into two categories based on
this plot: at the upper edge, there is a relatively weak departure from Arrhenius behaviour, and these materials are labelled
strong (this includes classical network oxide
glasses); at the lower edge, the behaviours
are highly non-Arrhenius, instead following
the form of the V-F equation and are fragile (including molecular and simple ionic
glasses). Strong and fragile refers to the
stability of short and intermediate range
order in the liquid against temperature increase [13, 18].
II. Theory
A. Identifying phase transitions
Abiad [23] gives a comprehensive overview
of the methods and theories used to describe the glass transition phenomena; a
summary of the techniques relevant to this
project is given here. The exact value of
the glass transition can vary depending on
the technique and material used (closely
associated to how sensitive the measured
property is to changes in temperature), and
the particular determination of what exactly constitutes the glass transition (for
example, it can be reported as the onset
temperature where the first changes are observed in the measured properties, or as
the inflection point, the midpoint of the
slope connecting the onset and offset horizontals) [23].
A..1 DSC
In the DSC the temperature of the sample
unit (the sample plus reference material) is
varied at a constant rate, and the heat flow
(energy required to maintain ∼zero temperature difference between the 2 samples)
is measured [23]. Tg can be found from the
heat flow profile – for details on this, please
see Methodology. The particular definition
of T
g used must be kept consistent, but
any trends identified should be comparable
regardless of method.
B. Effect of cooling and heating
rate on the glass transition
Tg
is expected to increase with both cooling rate [1, 21], and heating rate [24{26].
Some results give a linear relationship
between T
g and the logarithm of heating
rate ’ [24, 25, 27]. Conversely, Br¨uning et
al [21] found the linear fit inappropriate,
and instead fits log(’) to a variation of the
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V-F equation (5):
’ = B expTg0 A– Tg  ≡ Tg = Tg0 + lnAB’
(6)
where A, B and Tg0 are fit parameters, Tg0
being the theoretical value of Tg in the infinitely slow cooling/heating limit. This fit
was found to work well for cooling/heating
rates over three orders of magnitude [21].
An alternative fit is also suggested [21]:
Tg
= T0
g + A ln ’’02 (7)
Vollmayr et al [28] also find a V-F dependence for cooling rate γ:
Tg
(γ) = T0 – B
ln(Aγ) (8)
derived from (5) by assuming τ / γ–1 i.e.
relaxation time is of the order of inverse
cooling rate. Using a form for τ predicted
by mode coupling theory, it was further derived that:
Tg
(γ) = Tc + (Aγ)1=δ (9)
where Tc is another fitting parameter (see
[28] for the full derivation).
C. Effect of confinement on the
glass transition
A review of the work done to quantify the
effect of confinement on the melting transition is given by Christenson [29], and the
Gibbs-Thomson model for the change in
melting temperature Tm in confinement
compared to bulk is widely used; unfortunately, there is no such model for the effect
of confinement on the glass transition [30].
Jackson and McKenna [31] were the first
to publish DSC data showing a depression
in T
g for organic liquids confined to small
nanometre pores; while not the first to observe a change in Tg on confinement, it
was the first paper to highlight that conventional theories (entropy models and free
volume concepts of the glass transition [31])
do not explain this result [30]. Since then,
studies have been performed using a variety
of techniques on a large range of materials.
Jackson and McKenna [31] originally studied the T
g of o-terphenyl and benzyl alcohol
in controlled pore glasses (CPG) as a function of pore size, and found the reduction
in T
g increased as pore size was decreased.
Alcoutlabi and McKenna [30] summarise
a large sample size of the observed effects on the glass transition: that Tg increases [7, 32]; decreases [7, 19, 31, 33, 34];
stays the same [7, 35]; or disappears entirely [36] under confinement. The variation in T
g seems to depend upon the measurement technique, the type of substrate
used, the preparation of the substrate [36],
and the type of glass former used. While it
has been shown in a large body of work that
there is a surface or interfacial effect on the
change in Tg, it is unclear as to whether
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there is a domination of intrinsic size effect at the nanometre scale, or whether the
confinement effects are primarily due to the
surface interactions. Dosseh et al [37] observed that interfacial effects may cause an
increase in T
g, whereas intrinsic size effects
tend to decrease T
g; Zheng [36] notes that
this may also depend on how full the pores
are.
C..1 Pore Geometry
Troflymuk [7] points out that in the reviews by Alcoutlabi and McKenna [30] and
McKenna [38], there is a dearth of data
from a wide range of pore sizes using representative glass formers, or that this data
is only for CPG matrices. In CPGs such as
Vycor and Gelsil glasses, pore size and geometry are not perfectly controlled: while
assumed to have cylindrical pores (as in
[34], for example), the glasses are rather
characterised by their pore connectivity
(pores form continuous pathways through
the glass, as a result of the formation process [9, 39]). This structure is not an ideal
periodic arrangement of pores with simple
geometry in isolation from each other; taking this into consideration, Trofymluk instead used ordered mesoporous silica, with
a porosity composed of a narrow pore size
distribution of hexagonal, periodic arrays
of cylindrical pores [7]. Regardless of the
specific pore geometry, there is expected to
be a finite size effect due to the nanometre
dimensions of the pores.
C..2 Finite Size Effects
In the Adam and Gibbs configurational entropy model, molecules rearrange cooperatively in regions of a characteristic size,
known as the cooperativity length ξ of the
glass transition [19, 40]. ξ increases as T
decreases towards T
g, becoming comparable to the dimensions of the pores [33]. If
the size of the filled confinement space is
less than ξ, there should be a deviation
from bulk behaviour (relaxation, seen by
dielectric measurements, will occur faster),
and the deviation should lessen as sample
size is increased until it disappears at scales
greater than ξ [19]. However, this is complicated in real experiments by chemical interfacial effects that potentially mask or dominate over the finite size effects.
Pissis et al [33] performed the first dielectric experiments on confined glass formers (using 4 nm Vycor glass), investigating
the α relaxation associated with T
g. The
results were a broadening of the dielectric
loss in confinement compared to bulk, due
to the change in relaxation behaviour that
is linked to the change in ξ [30].
Further to this, trends have been seen between T
g and the size of the pores. Zhang
et al [34] deduced a linear relationship between T
g and the inverse of the confin-
8
ing pore radius for all glass formers studied. Trofymluk [7] saw a difference in relationship with different glass formers: for
o-terphenyl, Tg decreases as pore size does;
for glycerol, there was a gradual increase in
Tg
with pore size; and for salol, a reduction in T
g was observed compared to bulk,
followed by an increase until Tg was identical to the bulk in the smallest pore sizes. It
was concluded in the study that Tg is dependent on the combination of glass former
and matrix used.
C..3 Interfacial Effects
The molecules of a liquid can interact with
the surface of the matrix they are confined
to depending on which materials are used,
and this interaction is an important factor
that affects the dynamics of glass formers in
nanometre pores. Silica (e.g. in glass matrices such as Vycor) has hydroxyl groups
(silanols) on its surface, which can potentially create hydrogen bonds with the liquid. Hydrogen-bonded liquids have been
shown to form strong bonds with these surface silanols, creating an interfacial layer
adjacent to the pore surface – Melnichenko
et al [32] found this by dielectric spectroscopy: confinement of propylene glycol
and poly(propylene glycol) in pore sizes of
10 nm showed two separate liquid phases,
one associated with an interfacial layer, the
other with an inner pore volume (shown in
Fig. 5). This study showed sluggish dynamics that is associated to the hydrogen
bonding with the silanols, producing a significant increase in T
g for the interfacial
phase. Pissis et al [19] also came to this
conclusion: a slow relaxation was found in
a comparatively immobile interfacial layer,
due to interactions between the liquid and
the wall, resulting in a higher Tg compared
to the bulk. An increase in T
g is in agreement with the entropy model and free volume concept mentioned previously.
Figure 5: The interior of pores within a confining matrix, showing the interfacial layer and
inner bulk volume. Left shows a larger pore
than on the right. The interfacial layer stays
the same thickness regardless of pore size; instead, it is the inner bulk volume that scales
with the pore size.
However, an observed increase in Tg is
contradictory to the studies done (on
glycerol and other hydrogen bonding
substances) by Jackson and McKenna [31]
by DSC (mentioned previously), Pissis
et al [33] by dielectric spectroscopy, and
Zhang et al [34] by DSC, all of which
observed a decrease in T
g on confinement
(it is worth noting that there is no clear
9
disparity overall between DSC and dielectric measurements in this collection of
studies).
Arndt et al [35] showed that the thickness of the interfacial layer increases with
the number of hydroxyl groups of the glass
former (i.e. with an increasing molecular interaction between glass former and
matrix) – glycerol, having three hydroxyl
groups, was shown to have a thicker interfacial layer than salol, with one hydroxyl group. Glycerol was also shown in
Fourier-Transform-Infrared (FTIR) spectroscopy [7] to form strong bonds with surface silanols.
For molecules with one hydroxyl group,
the interfacial layer shows as a separate
relaxation peak in dielectric measurements [35, 41]. From interpretation of
relaxation spectra, Gorbatschow et al [42]
created a three-layer model for low molecular weight H bonded liquids (as shown in
Fig. 6), composed of regions of solid-like,
interfacial and bulk-like molecular dynamics. The interfacial and solid-like regions
remain approximately unchanged as pore
size is varied, while the bulk-like scales
with the pore size (see Fig. 5). There is
the additional implication of cooperatively
rearranging clusters being unable to exist
below the nanometre scale.
Observation of a second glass transition,
Figure 6: The three layer model as proposed
by Gorbatschow et al [42] for a H-bonded liquid. The solid line traces the relaxation rate
through the layers. A solid-like layer is present
next to the confinement material, which can
only be detected in a lessening of dielectric
signal strength. In the interfacial layer, the
relaxation increases to that of the bulk rate
from slow at the solid-like layer. Gorbatschow
et al [42] found no dependence of the layer
structure on temperature.
seen in DSC curves [36] for propylene
glycol at a higher temperature than the
bulk T
g, is additional evidence in support
of the theory of interfacial layers. Trofymluk et al [7] monitored excess loading of
pores (the study focussed on wetting of
the pores to observe interface interaction)
by a second Tg equal to that of the bulk
material.
Silanization reduces the wettability (the
intermolecular interaction of a liquid with
a neighbouring solid surface, in order for
contact to be maintained [43]) of glass surfaces [44]; as such, it has been studied as a
way of decreasing the interaction between
glass formers with hydrogen bonds and the
wall by Zheng and Simon [36]. In unsilanized pores, surface wetting was prefer-
10
ential and the fullness of the pore decided
whether T
g was unchanged (in low fillings
where size effects were balanced by interfacial effects) or decreased (dominant size
effects). It was found that the liquids did
not wet the surface of silanized pores and
formed plugs.It was found that the liquids
did not wet the surface of silanized pores
(instead forming plugs), and Tg decreased
regardless of how full the pores were, indicating interfacial effects no longer competed with size effects. However, silanization may also change roughness, curvature,
and dimensions of the pore, and this needs
to be taken into consideration [45].
III. Methodology
A. Materials
Glycerol (glycerine) is the glass forming liquid studied in this report [46]. It is confined
to two substrates: the first, nanoporous
Corning Vycor 7930 glass (having an average pore size of 4 nm, and a 28% porosity) [47]; the second, believed to have an average pore size of 7 nm. Unfortunately, the
origin and technical details of the second
substrate are unknown. Small angle x-ray
scattering (SAXS) analysis confirmed the
porous nature of the glass but did not elucidate a pore size. Future measurements using mercury intrusion porosimetry should
be performed to properly characterise this
glass.
Direct comparison can be made to
results found by studies using the same 4
nm Vycor glass confinement with glycerol
as the glass former.
The Vycor R process forms porous
glasses by leaching of phase separated
glasses, the result of which is a very
porous, silica-rich skeleton (earning the
trade name hirsty glass”) through which
the pores form continuous pathways [39].
This allowed the substrate to be filled
simply by soaking a piece of glass in a
sealed beaker of glycerol for a minimum
of 72 hours, over which the majority of
the pores are filled. The glycerol remains
in the pores indefinitely due to its high
viscosity. Due to the high surface volume
of the interior pore matrix (250 m2/g) [47],
surface signal is negligible in comparison,
and additionally the surface of the filled
glass was wiped to remove excess glycerol.
Sichina [4] recommends using a sample
mass of 10-20 mg, and, in order to minimise thermal gradients, keep the sample
as thin and flat as possible. Disks of ≈
1 mm thickness were cut from a long
rod of the 7 nm glass with a diamond
saw, these were then broken into smaller
pieces to fit the geometry of the 40 µL
aluminium DSC pans. Unfortunately no
intact rod of the 4 nm glass was available,
11
so more irregularly shaped samples of this
glass had to be used, keeping in mind the
recommendations.
The 4 nm Vycor was previously cleaned,
though unfortunately left open to air for
a prolonged period of time afterwards so
contamination cannot be ruled out. The
7 nm glass did not receive any cleaning or
treatment prior to use, so contaminants
are present within the glass, obvious
from its yellow discolouration and surface
stickiness.
It became important to prepare fresh
samples of bulk glycerol and run them as
soon as possible after preparation, completing all the heating or cooling rates back to
back, for reasons discussed fully in the results.
B. Measurements with DSC
Differential scanning calorimetry measurements were taken with a Mettler Toledo
DSC1-STAR using liquid nitrogen coolant.
The effect of changing the heating and cooling rate on the glass transition in the two
types of glycerol soaked glass, as well as
bulk glycerol, is investigated. A large selection of integer heating rates between 3
and 20 K/min are explored, following consistent automatic cooling down to 123 K
by the DSC, the subsequent heating taking
the DSC back up to 298 K. Cooling rates
were varied in subsequent study, from 3 15
K/min (again down to 123 K) followed by
a constant heating rate of 9 K/min (back
up to 298 K). It is important to note that
preliminary measurements on dry samples
of both glasses showed no features in the
DSC heat flow profiles, so any contamination present in the glass does not exhibit
phenomena related to melting, freezing or
glass transition.
C. Identification of the glass
transition
Figure 7: The onset and midpoint glass transitions as analysed by the Stare software. The
onset is taken as the point of intersection of
the gradient of the line before the step and the
gradient of the step. The midpoint is found
by taking the bisector (blue dashed line) “of
the angle between the tangents (black dashed
lines) above and below the glass transition.”
The midpoint is the intersection between this
bisector and the heat flow curve [48]. The
temperature at which the enthalpy relaxation
peak occurs can be analysed as the extrapolated peak.
Tg
is found from the resultant heat flow
12
profile (see Fig. 7). The analysis is performed using the Stare analysis method [48]
on software provided with the DSC. For
this study, the midpoint value is used, as
it is generally accepted to be the most reproducible and reliable measure of Tg [49].
In some cases, an enthalpy relaxation
peak (see Fig. 7) can be seen. This
is thought to occur if the heating rate is
greater than the cooling rate through the
glass transition, and as such is effected
by the thermal history of the sample [48].
Storage of the sample below Tg (known as
physical aging), as well as internal stresses
in the sample are important in that they
will effect the enthalpy relaxation peak
shown [50]. Unfortunately, the complete
thermal history (including prior processing
and storage) of the glycerol used in this experiment is unknown.
D. Calculation of errors
The provided software did not calculate an
error on T
g, so instead this was calculated
by two methods and both errors taken into
consideration. First, the same glass transition was analysed in the software several
times from scratch, and the standard deviation on an average result was noted. Then,
to check consistency of the DSC itself, the
same sample of 4 nm glass was subjected
to 6 repeated runs, for a faster 8 K/min
and a slower 4 K/min heating rate. Again,
standard deviation on an average result was
noted.
This second test also afforded a look at
any trend present in the Tg that may result
from cycling the same sample continuously;
none was found.
IV. Results
Figure 8: A comparison of the shape of heat
flow curves at a heating rate of 9 K/min for
(i) bulk glycerol, (ii) 4 nm pores and (iii) 7 nm
pores. Bulk glycerol shows one Tg; however,
both 4 and 7 nm pores show a main glass transition (Tg(1)) and a secondary glass transition
(Tg(2)). The inset shows a zoomed in view of
the 4 nm pore curve, as Tg(2) is shallow – it
also shows a slight enthalpy relaxation peak.
Examples of typical DSC heat flow
curves on heating the samples at 9 K/min
(after prior cooling) is given in Fig. 8,
showing all three types of sample.
There are some notable features present:
bulk glycerol shows a pronounced enthalpy
13
Figure 9: A comparison of curves for varying heating rates. From left to right: 4 nm pores, 7 nm
pores and bulk glycerol. Heating rates from top to bottom: 3 K/min (pink); 4 K/min (red); 5
K/min (orange); 6 K/min (yellow); 7 K/min (green); 8 K/min (turquoise); 9 K/min (blue); 10
K/min (purple).
relaxation peak (which may also be present
to a lesser degree in the 4 nm), and both the
4 nm and 7 nm glycerol-soaked glass show
a suspected second glass transition event
(subsequently labeled Tg(2)) which is shallow in the 4 nm but very pronounced in
the 7 nm. These are assumed to be glass
transitions and analysed as such alongside
the main glass transition in the subsequent
sections.
A. Effect of heating on the glass
transition
Heating rate is varied in integer increments
between 3 and 10 K/min (some data extends beyond this to 20 K/min), with a
prior cooling rate that is constant for all
heating rates. This cooling rate is set by
the DSC itself.
Fig. 9 shows the change in the curves
when varying the heating rate for each type
of sample. As heating rate increases, so
does the heat flow supplied to the sample.
This increases the step height in the y axis
of the glass transition, in comparison to a
lower heating rates.
As heating rate increases, so does Tg for
all of the samples, as well as Tg(2) for the
4 and 7 nm, and the temperature of the
enthalpy relaxation peak in glycerol.
Fig. 10 presents Tg against log(’), as
proposed by Lasocka [27] to be a linear fit.
As evidenced by the curved trend of the
majority of the data points and the definite shape to their residuals (not pictured),
a linear fit is not appropriate. On initial inspection, it appears that a linear fit can be
made to the main T
g of the 7 nm glass;
however, when this fit is made, the shape
to the residuals (inset) appear to indicate
14
that this fit is, again, not appropriate. An
alternate fit needs to be applied.
Figure 10: Black filled squares: Tg(1) 4 nm;
black square outlines: Tg(2) 4 nm; purple filled
circles: T
g(1) 7 nm; purple circle outlines:
Tg
(2) 7 nm; green filled triangles: Tg bulk.
A linear fit is applied to Tg(1) 7 nm, with fitting parameters: gradient = ; y-intercept = .
The residuals for this fit are inset. Errors are
too small to be seen.
A..1 Bulk Glycerol
It is important to collect bulk glycerol data
so a comparison can be made with the confined glycerol, to elucidate any behavioural
change.
As seen in Fig. 9, the large enthalpy relaxation peak of glycerol does not disappear at any of the heating rates. It remains of the same magnitude in relation to
the height of the glass transition, however
stretches out a little in temperature range
(i.e. in the x axis) as the heating rate increases.
Bulk glycerol was found to exhibit
Figure 11: A demonstration on the step change
caused by leaving the glycerol sample before
resuming DSC analysis – the first set of heating rates, up to 9 K/min, were performed immediately after the sample was prepared and
fit to Equ (9). The sample was left in the pan
for 2 days before analysis resumed.
different behaviour in T
g as time passed
after the initial preparation of the sample
– Fig. 11 is an example of this. After the
heating run at 9 K/min, a gap of two days
passed, resulting in a step in Tg that is
clearly visible. Before the step, Tg can be
fit with Equ. (8), with the random spread
of residuals supporting this fit. After
the step, the fit no longer converges. It
appears that the sample has hardened, or
cured, in the intervening time, or perhaps
absorbed water from the atmosphere as
the pans are not hermetically sealed.
Zheng et al [36] also studied glycerol, and
discarded any pans that changed in weight
from the initial weight, as it indicated
improper sealing of the pans – this was
not done here, but if the experiment
was continued, this should be taken into
15
account. Consequently, data after the
step was determined invalid. Particular
care had to be taken to run the glycerol
immediately after preparing the sample,
not allowing any time to elapse between
runs.
Figure 12: all valid heating runs for bulk glycerol. Inset are the two runs that are fit by
Equ. (9); the black line fits this equation for
the concatenated data.
Figure 13: Mean Tg midpoint values from the
Fig. 12 data with standard deviation error;
values are given in Tab. 1.
Fig. 12 comprises all the valid data for
bulk glycerol samples. Some of the data
(inset) could be fit with Equ. (9), and
it was found that the concatenated data
(black line fit) could also be fit with this
function. This led to averages of Tg at
each heating rate being taken, as in Fig. 13,
showing a realistic error from the standard
deviation. The average values are taken as
the value for bulk glycerol when comparing
between bulk and the porous glasses.
Heating Rate (K/min) Tg (oC)

Table 1: Mean T
g midpoint values from the Fig.
12 data with standard deviation error, plotted as
Fig. 13.
A..2 4 nm Pores
The 4 nm sample was analysed at heating
rates from 3 – 20 K/min in integer intervals. From Fig. 9, it appears that the 4
nm shows a what appears to be a slight enthalpy relaxation peak at the higher (7 – 10
K/min) heating rates.
Fig. 14 fits the two glass transitions
present in the 4 nm glycerol-soaked glass at
each heating rate to Equ. (9), from Vollmayr et al [28]. The equations (Equ. (6)
and (7)) given by Br¨uning et al [21] did not
converge when a fit was attempted, simi-
16
larly to the bulk glycerol.
The fit works well for T
g(1); however,
the size of the residuals indicate that the
fit is poor for Tg(2) – this is likely due to
the shallowness of the transition making
the analysis more difficult. The need for
a larger error on the values of Tg(2) is likely.
Figure 14: Black filled squares: Tg(1) 4 nm;
black square outlines: Tg(2) 4 nm. Both sets
of data are fit with Equ. (??), fitting parameters are given in the text.
A..3 7 nm Pores
For the 7 nm glycerol-soaked glass (Fig.
15), it is found that neither the Equ’s []
given by Vollmayr et al [28] nor those given
by Br¨uning et al [21] converge upon fitting.
This may indicate that the linear fit proposed by Lasocka [27] (fitted to Tg(1) of
the 7 nm in Fig. 10) is actually appropriate, or that another fit needs to be found;
regardless, this confirms that the behaviour
of T
g on varied heating rates in the 7 nm
pores is not the same as that of the 4 nm.
Figure 15: Purple filled circles: Tg(1) 7 nm;
purple circle outlines: Tg(2) 7 nm. No fits
given in the theory section converge for this
data.
B. Effect of cooling on the glass
transition
Figure 16: DSC heat flow curves for cooling at
3 K/min from 25 to -150 oC then heating at 9
K/min back up to 25 oC. The black line is the
4 nm pores; purple is the 7 nm pores.
Cooling while keeping the heat constant
at 9 K/min was investigated for odd inte-
17
gers from 3 – 15 K/min (both above and
below the heating rate). From Fig. 16 it
can be seen that there is now a glass transition on cooling, as well as those on heating. It is important to note that no second transition appears on cooling. Unfortunately, Tg(2) for the 4 nm pores is now so
shallow that it cannot be reliably analysed.
The transition on cooling is much less pronounced than that on heating so the error
on the T
g value became higher, and there
became an additional difficulty when cooling at the higher rates (≥ 9 K/min). The
range of the glass transition is so large that
the software deemed the analysis invalid,
though still quoted values for the transition (these are therefore used, though the
reader should keep in mind the questionable validity of the data). Bulk glycerol
was not tested here – this could be done in
future experiments.
Fig. 17 compares the glass transitions at
each value of cooling rate. The first feature
to note is that the glass transitions on heating do not change for both sample types,
as evidenced from the gradients: at a gradient of ≈ 0.5, the gradient is not significantly different from zero, and additionally
the error puts the gradients in the range of
zero. So changing the cooling rate, above
or below heating rate, has no effect on the
glass transition on heating.
Looking at the glass transition on cooling, there becomes a dependence when the
Figure 17: Investigating the effect of varying
the cooling rate with a fixed heating rate of
9 K/min. Both glass transition upon cooling
and glass transition(s) upon heating are
plotted here. Black filled squares: Tg(1) 4
nm; gradient: (–0:01 ± 0:02) min-1; intercept:
(–85:2 ± 0:2) oC.
Purple filled circles: Tg(1) 7 nm; gradient:
(–0:01 ± 0:02) min-1; intercept: (–83:7 ± 0:2)
oC.
Purple circle outlines: Tg(2) 7 nm; gradient: (–0:058 ± 0:045) min-1; intercept:
(–57:8 ± 0:4) oC.
Black/purple half-filled squares/circles:
Tg
(cooling) 4 and 7 nm respectively.
cooling rate becomes greater than the heating rate at 9 K/min. As cooling rate increases, the glass transition shifts to lower
temperatures. The fit of this slope did
not converge for any of the equations given
in the theory, as there were not enough
degrees of freedom to perform the fitting.
More cooling rates would have to be investigated to properly elucidate any trends.
C. Effect of confinement on the
glass transition
In order to analyse the effect that confinement has on glycerol, comparison has to be
18
Figure 18: ∆Tg = Tg(4nmor7nm) – Tg(bulk).
The dotted line at y = 0 indicates the bulk
glycerol baseline, with an associated error in
green. Black filled squares: Tg(1) 4 nm; black
square outlines: Tg(2) 4 nm; purple filled circles: T
g(1) 7 nm; purple circle outlines: Tg(2)
7 nm.
made between bulk glycerol and the 4 and 7
nm confined glycerol samples at the various
heating rates. Unfortunately, comparison
of the results for 4 and 7 nm at the various
cooling rates (with fixed heating rate) cannot be made to bulk glycerol as it was not
investigated.
Fig. 18 shows the change in Tg compared
to that of bulk glycerol. Values for the
maximum and minimum shifts in T
g can
be found in Tab. 2. It can be seen that
Tg
(1) for both 4 nm and 7nm has a negative shift in T
g – 4 nm is very similar in
value to bulk, with some points within the
error of the bulk value, and a maximum
shift of only (–1:1 ± 0:9) K.
7 nm has a larger shift in Tg compared to
4 nm, with a maximum shift of (–6:1±0:7)
K. This definitely shows a deviation from
bulk. 7 nm also appears to be converging
on the bulk value as heating rate increases
– to confirm this trend, further measurements would have to be taken at higher
heating rates.
However, Tg(2) for both 4 and 7 nm has a
large (in comparison to the small shifts for
Tg
(1); this is an order of magnitude larger)
positive shift in Tg, with maximum values
of (+29:0 ± 0:6) K and (+20:3 ± 0:6) K
respectively. The positive shift in the 4 nm
is larger than that of the 7 nm.
Sample min ∆Tg max ∆Tg
4 nm T
g(1) -0.8 ± 0.9 -1.1 ± 0.9
4 nm T
g(2) +26.4 ± 0.8 +29.0 ± 0.6
7 nm T
g(1) -3.3 ± 0.6 -6.1 ± 0.7
7 nm T
g(2) +16.8 ± 0.8 +20.3 ± 0.6
Table 2: Maximum and minimum ∆ T
g for each
different sample type, corresponding to Fig. 18.
To explore the second glass transition,
runs were done down to -80 oC – theoretically low enough for the second transition
to manifest, but not low enough for the
first. This was in order to test whether the
second transition relied on the existence of
the first. Fig. 19 shows this run in comparison to regular runs performed down to -150
oC – the second transition appears, regardless of the existence of the first. However,
it is shifted in value by [] and [] for the 7
and 9 K/min heating rates respectively.
19
Figure 19: Green: 7 K/min heating rate; blue:
9 K/min heating rate. Dashed lines are from
previous regular runs cooling down to -150 oC;
solid lines are cooling down to -80 oC. Inset
is a comparison of Tg between -150 oC runs
(triangles) and -80 oC runs (squares).
V. Discussion
To improve the overall quality of the data,
a number of improvements could have been
made to the method – properly cleaning the
glass to rid it of any contaminants, drying
it out to remove water before use, and then
storing the samples under desiccant to ensure that no water is absorbed by the hydroscopic glycerol would be an unquestionable improvement.
A. Effect of heating and cooling
rate on the glass transition
As expected from theory [], as heating rate
increases, so does Tg for all the sample
types (bulk glycerol, 4 nm pores and 7 nm
pores). The dependence is shown to be described by Equ. (9) in many cases. It is also
found that cooling rate increase has no effect on the transition upon heating, and for
the transition on cooling, causes a decrease
in T
g, in contradiction to theory []. This
data is likely not valid, however – the slight
step change is over a very large range, and
is deemed invalid by the software. Furthermore, a fit could not be made to this data.
Further investigation into a wider range of
cooling rates would need to be investigated
to properly analyse any trend.
B. Effect of confinement on the
glass transition
The results for both confinements show a
second glass transition, higher in temperature than that of the first transition; this
second transition has been seen previously
by [] and has been linked to a potential interfacial layer within the pore volume [].
A two layer model is potentially supported
here by the appearance of the second transition.
The initial glass transition is a lower temperature than that of bulk for both 4 and
7 nm pores (in the case of the 4 nm pores,
very close to the bulk transition), whereas
the second glass transition is much higher
than bulk. This also potentially supports
the two-layer theory: the layer with a lower
Tg
is likely the inner bulk volume, shifted in
Tg
predominantly by finite size effects; the
layer with higher Tg is then the interfacial
layer, as suggested by [?]. Mel’nichenko
20
et al [32] also saw a significant increase in
Tg
for the interfacial layer by a maximum
of 47 K – while these previous results were
not found using glycerol, for comparison,
the results presented here saw a maximum
shift of (+29.0 ± 0.6) K.
However, the similarity between the 4 nm
first transition and the bulk value complicates this picture. This would suggest a
picture where finite size effects do not come
into play at all. In a pore as small as 4 nm,
finite size effects would be expected on any
bulk volume within the pore. Interestingly,
Trofymluk et al [7] found that salol had an
identical T
g to bulk in the smallest pore
sizes ().
From comparison of the sizes of the step
in heat flow at the glass transitions (see
Fig. 8), the inner bulk volume has a much
larger step and therefore can be inferred to
fill more of the total pore volume than the
interfacial layer. The 4 nm pore Tg(2) is
much shallower than that of the 7 nm –
a weaker signal which could potentially be
due to a less-present interfacial layer. If the
interfacial layer thickness does not change
with pore size, this could be due to less
surface area per pore and therefore less interfacial layer volume per pore. However,
it would be expected that there are more
pores present in the 4 nm glass than the 7
nm for the glasses to be of the same porosity (by measuring mass uptake of water
by samples of both, they were determined
to be of approximately the same porosity,
within error), so this effect would be balanced out.
This analysis is predominantly complicated by the actual pore diameter of the 7
nm” glass being unknown. Valid comparison between the 4 and 7 nm glass cannot be
made until the 7 nm is properly classified,
VI. Conclusions
You should be drawing conclusions as you
discuss your results but this section acts as
a summary. Many people will read the conclusion first to get a feel for the quality of
the results, etc. So this can be an important section.
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