Glass Forming Glycerol Behaviour in Varying Glass Substrate Pores

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].

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.

A1 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- 3 thalpy H or heat flow q as T is varied:

Cp = @T = @T =
@H	@q
P	P

@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.

A2 Supercooling transition and the glass

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 4 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:

τ = ≈ 1010 Pa = 400 secs

(4)

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].

A1 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 6 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 7 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.

C1 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.

C2 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.

C3 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.

A1 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)

10 9 8 7 6 5 4 3 1

-84.8 ± 0.4 -85.1 ± 0.8 -85.6 ± 0.7 -86.4 ± 0.5 -86.9 ± 0.7 -87.8 ± 0.5 -88.4 ± 0.7 -89.1 ± 0.6 -91.6 ± 0.4

Table 1: Mean T g midpoint values from the Fig. 12 data with standard deviation error, plotted as Fig. 13.

A2 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.

A3 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.

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