Physical Ageing of Polystyrene: Does Tacticity Play a Role?

The ageing kinetics of amorphous atactic (a-PS), isotactic (i-PS), and syndiotactic (s-PS) polystyrene were studied by means of flash-differential scanning calorimetry. The specimens were aged for up to 2 h at six different ageing temperatures: the optimum ageing temperature, that is, the temperature at which the enthalpy overshoot at the glass transition is maximal for the given elapsed time, and five ageing temperatures ranging from 20 to 80 K below the optimum ageing temperature. A logarithmic increase of the enthalpy overshoot with ageing time is observed for specimens at their optimum ageing temperatures. For temperatures significantly lower than the optimum, there is a range where the enthalpy overshoot is constant, but for higher temperatures (still below the optimum), a logarithmic increase is also observed. Moreover, the ageing kinetics appear to depend on tacticity, with s-PS and i-PS exhibiting the slowest and fastest ageing kinetics, respectively, and a-PS exhibiting ageing kinetics between these two extremes.

Introduction

Glasses are known to be far from their thermodynamic equilibrium, and their structural relaxation toward equilibrium, via a sequence of molecular rearrangements, is known as physical ageing.[1] Physical ageing of polymeric glasses is known to affect the material properties, like the mechanical[2,3] or gas-transport properties,[4] posing limitations on their applications. A lot of studies have been conducted on the influence of physical ageing of glassy polymers on yielding,[1−3,5,6] creep,[7−9] volume relaxation,[8,10−14] enthalpy changes,[9,11,15−17] molecular-scale dynamics,[18−21] and structural changes.[22−24] However, the connection between the molecular structure and the ageing kinetics has not yet been established.

Despite the fact that numerous techniques are employed to study the large number of properties affected by physical ageing in glassy polymers, only one of them can cool and heat the material rapidly enough to allow probing of the ageing kinetics by starting from a “true” rejuvenated amorphous state. This technique is flash-differential scanning calorimetry (flash-DSC) in which ultra-high heating and cooling rates (>100 000 K/min) can be applied.[25] The majority of the ageing studies with flash-DSC involve measurements concerning a single material such as atactic polystyrene (a-PS),[26−30] polycarbonate (PC),[29] poly lactic-acid,[31,32] and others.[33,34] Until now, there are only very few studies investigating the effect of tacticity on the ageing kinetics[35] of glassy amorphous polymers. The main reason for the lack of studies is that syndiotactic and isotactic polymers crystallize under normal cooling rates, resulting in a semicrystalline material. For polystyrenes, there is another limiting factor next to the high crystallization rate[36] of s-PS, namely, its melting temperature is very close to its degradation temperature, which makes the preparation of an amorphous sample in oxygen atmosphere impossible because the material starts to degrade before the crystallinity is erased. The high crystallization rate can be tackled by the high cooling rate that flash-DSC offers, and the complete melting of crystals before the material degrades has been taken care of by using a nitrogen atmosphere during the measurement.

In this work, we study the effect of tacticity on the ageing kinetics at high and low ageing temperatures for atactic, isotactic, and syndiotactic polystyrene using flash-DSC in their glassy state.

Methodology

Materials

Atactic and syndiotactic PS (Figure ) with syndio contents ≥90% were bought in powder and pellet forms, respectively, from Polymer Source.[37] Isotactic PS (Figure ) with 90% isotactic content was bought in the powder form from Scientific Polymer Products.[38] The corresponding molecular weights and polydispersity indices (PDIs) are listed in Table .

Figure 1

Stereochemistry of (a) atactic, (b) syndiotactic, and (c) isotactic polystyrene.

Table 1

Number-Average Molecular Weight Mn and PDI of the Polystyrene Samples

sample	Mn (kg/mol)	PDI (-)
a-PS	412	1.05
s-PS	250	3.5
i-PS	400	2

Differential Scanning Calorimetry

Flash-Differential Scanning Calorimetry

Experiments were carried out in Mettler Toledo Flash-DSC 1 equipped with a Huber TC100 intracooler under a constant flow of dry nitrogen using UFS1 sensors.

Differential Scanning Calorimetry

Experiments were carried out in a Mettler-Toledo 823e/700 module with a Cryostat intracooler using a 50 μL aluminum pan under a constant flow of dry nitrogen.

Sample Preparation

For the flash-DSC measurements, very small specimens of material of approximately 30–170 ng were cut and put onto the sensor with the use of an eyelash. For the conventional DSC, the powder-form samples were put in an aluminum pan with a mass between 5 and 10 mg.

Estimation of Sample Mass

In the case of the flash-DSC measurements, the sample mass cannot be measured with a conventional scale because the weight is too small (nanogram). For semicrystalline materials, the mass can be estimated as follows. A sample of known mass is cooled and heated in conventional DSC at 20 K/min, and the specific melting enthalpy (Δhm) is calculated by peak integration of the heating curve. Afterward, a sample of unknown mass is cooled at 20 K/min and heated at 1000 K/s in the flash-DSC equipment. The melting enthalpy (ΔHm) is calculated from the heating curve, and the mass of the flash-DSC sample can be determined by

In the case of amorphous polymers, the sample mass can be estimated by using the method of Cebe et al.,[39] employing the liquid heat capacity from flash-DSC (cooling rate 1000 K/s) and the specific heat-capacity from the ATHAS bank.[40] The sample mass mam is determined bywhere C is the heat capacity obtained from the flash-DSC experiments far above the glass transition temperature and c is the specific liquid heat capacity taken from the ATHAS bank. The validity of the method is confirmed by applying both eqs and 2 to a semicrystalline sample. The error between the two mass-estimation methods is found to be about 5%.

Methods

In order to study the ageing kinetics of the selected materials, the temperature protocol shown in Figure was used. The following steps can be identified: Step i: the sample was heated well above Tg (a-PS) or Tm (s-PS and i-PS) at a rejuvenation temperature Trej (Table and Figure ) in order to erase its thermomechanical history (i.e., thermal rejuvenation). Step ii: The sample was rapidly quenched at a cooling rate of 1000 K/s to an end-quenching temperature Tq well below Tg, and subsequently heated rapidly (heating rate: 1000 K/s) above Tg to obtain the heating curve which serves as a reference state. Step iii: The sample is rapidly quenched (1000 K/s) and then heated (1000 K/s) to the chosen ageing temperature, Ta, and held at that temperature for a specific ageing time ta. Step iv: The sample was quenched rapidly (1000 K/s) at 25 °C for ageing temperatures higher than 25 and 0 °C for ageing temperatures below 25 °C to capture the aged state and heated rapidly (1000 K/s) above Tg (or Tm) to obtain the endothermic peak caused by ageing, and to thermally rejuvenate the sample for the next measurement. Step v: One more cycle of quenching and heating was performed to validate the rejuvenated state of the polymer (heating curve).

Figure 2

Schematic representation of the flash-DSC heating protocol: (i) Heating above Tg or Tm, (ii) reference-state heating curve, (iii) isothermal ageing for ageing time ta and at temperature Ta, (iv) aged-state heating curve, and (v) reference-state heating curve. The values of rejuvenation, Trej, and end-quenching temperature, Tq, are provided in Table .

Table 2

Glass-Transition Temperature, Tg, and Melting Temperature, Tm, for a-PS, s-PS, and i-PS, Measured during Heating with a Heating Rate of 1000 K/s, and Rejuvenation, Trej, and End-Quenching Temperatures, Tqa

sample	Tg (°C)	Tm (°C)	Trej (°C)	Tq (°C)
a-PS	128		190	25 and 0
s-PS	124	270	310	25 and 0
i-PS	126	240	270	25 and 0

The end-quenching temperature is 25 °C for ageing temperatures higher than 25 and 0 °C for ageing temperatures below 25 °C.

Analysis

The analysis of experimental data concerning the cooling-rate dependence of Tg and physical ageing can be analyzed in terms of enthalpy loss (ΔHa) or the fictive temperature (Tf).[29] Tool[41] defined Tf as a measure of the glass structure. The intersection of the extrapolated glass line and the extrapolated liquid line determines Tf. The Tf of an aged glass is related to the change in enthalpy with ageing[29]where ΔHa is the enthalpy loss upon ageing, Tf is the fictive temperature of the aged glass, Tf0 is the fictive temperature of the unaged glass, and ΔC is the step change in heat capacity. During physical ageing, Tf0 decreases to an equilibrium value, while ΔHa increases from a zero value to the equilibrium enthalpy value.[29] We chose to analyze our data using the ΔHa changes. Both types of analysis will yield identical conclusions/observations. The analysis procedure is described below.

Fitting a Straight Line to the Liquid Regime[29]

The calculation of the enthalpy overshoot of the aged specimen (i.e., the integral under the C(T)-curve) relies on drawing an unbiased liquid line, especially when a large overshoot is present. Thus, each heating scan was superposed with the subsequent scan of a freshly quenched specimen. The liquid line was determined as the best linear fit of the C(T)-curve at high temperatures, away from the enthalpy overshoot and the transition region. A consistent liquid line is crucial for calculating the integral under the C(T)-curve. As shown in Figure , the enthalpy overshoot of the aged specimen is calculated in between the point where the C(T)-curve departs from the linear liquid line till the point where it intersects again. This integral is considered positive. Then, we apply the same procedure to the rejuvenated sample and subtract its integral from that of the aged one.

Figure 3

Representative curve for the calculation of the enthalpy loss ΔHa upon ageing, according to the Petrie method.[42]

Determination of Excess Enthalpy

The excess enthalpy was determined using the method of Petrie[42] in which the enthalpy loss ΔHa upon ageing is calculated by the difference of the integrated C(T)-curves of the aged and reference (rejuvenated) material (Figure )

Two measurements per sample are conducted for each ageing time and temperature.

Sensor Corrections

Conditioning and correction were performed on the flash-DSC chip sensors before the sample is positioned on the sensor according to the manufacturers recommended protocol. No additional temperature corrections were applied because the calibration by the manufacturer was found to have an error of about 0.6–0.7 K.[43]

Results

In Figure , the flash-DSC heating curves for atactic, syndiotactic, and isotactic amorphous PS annealed at various ageing temperatures and ageing times are shown. It can be seen that the area of the endothermic peak as well as the temperature where the endothermic peak appears are increasing with the ageing time. Also, the absence of a melting peak, as a result of the high cooling rate (1000 K/s) in the case of semicrystalline polymers, validates the fact that the samples are in an amorphous state (Figure ).

Figure 4

Heat flow Q versus temperature T for (a) a-PS, (b) s-PS, and (c) i-PS, for various ageing times.

We study the effect of ageing temperature Ta on the excess enthalpy ΔHtot – ΔHrej for an annealing time of 10 min for atactic, syndiotactic, and isotactic amorphous PS (Figure ). Figure a shows that for a-PS, the excess enthalpy increases linearly with temperature where it reaches a maximum at around 102 °C (≈26 K below the glass-transition temperature). After this temperature, the enthalpy overshoot decreases linearly. Similarly, the s-PS (Figure b) excess enthalpy follows a linear increase with an optimum at ≈96 °C, (≈28 K below Tg) and a decrease after this optimum as well. i-PS (Figure c) has a similar behavior with an optimum enthalpy overshoot at ≈94 °C (32 K below Tg). Based on these results, we choose the temperature in which each polymer shows the largest overshoot as the optimum ageing temperature (Topt), determined by fitting a polynomial of the fifth order to the ΔHtot – ΔHrej versus Ta data (Figure ). We perform measurements also at 20 K (Topt-20K), 30 K (Topt-30K), 40 K (Topt-40K), 60 K (Topt-60K), and 80 K (Topt-80K) below Topt for all specimens. It is also noted that the behavior displayed in Figure on the left and right sides of the maximum, Topt, is asymmetric; similar observations have been made earlier.[44] The fact that the left side changes only smoothly with temperature is indicative of non-α-processes being relevant in this regime.

Figure 5

Excess enthalpy, ΔHtot – ΔHrej, vs annealing temperature, Ta, for (a) a-PS, (b) s-PS, and (c) i-PS. The ageing time is ta = 10 min. Lines represent the polynomial fits (see main text).

In Figure , the excess enthalpy (ΔHtot – ΔHrej) as a function of the ageing time for the various ageing temperatures for atactic, syndiotactic, and isotactic PS is shown. It can be seen that ΔHtot – ΔHrej follows a logarithmic increase with time for the optimum ageing temperatures. For very short ageing times (≤0.1 s), the ΔHtot – ΔHrej for the three PS specimens is close to zero. For longer ageing times (≥10 s), the excess enthalpy shows a logarithmic increase for all specimens. At ageing temperatures below the optimum (Figure ), it can be observed that the increase of ΔHtot – ΔHrej does not follow a logarithmic increase and is reduced compared to that for long ageing times. Similar to the observations for maximum ageing temperature for short ageing times, the enthalpy overshoot observed for the three PS specimens is close to zero.

Figure 6

Excess enthalpy, ΔHtot – ΔHrej, vs ageing time, ta, for (a) a-PS, (b) s-PS, and (c) i-PS.

Using time–temperature superposition, an activation energy can be determined. In Figure , the ΔHtot – ΔHrej curves are shifted horizontally along the logarithmic ageing-time axis, taking Topt as a reference. The good superposition of lines allows calculating the activation energy by plotting the logarithmic shift-factor (a) as a function of temperature and obtaining an Arrhenius plot for temperatures from Topt-40K to Topt-20K. The activation energies Ea for a-PS, s-PS, and i-PS calculated from the slope (Ea/R, where R is the gas constant) in Figure are found to be (166.6 ± 4.0) kJ/mol for a-PS, (163.8 ± 6.0) kJ/mol for s-PS and (144.4 ± 9.7) kJ/mol for i-PS. Even if we take the lowest values for Ea/R for a-PS and s-PS, we cannot reach the highest value for i-PS. This indicates that despite the differences being subtle, they are by no means negligible.

Figure 7

Excess enthalpy obtained from time–temperature superposition using the optimum ageing temperature as the reference, Tref = Topt, for (a) a-PS, (b) s-PS, and (c) i-PS.

Figure 8

Arrhenius plot of the shift factor, aT, for i-PS (half-filled circles), s-PS (filled circles), and a-PS (empty circles). The activation energy is represented by the slope of the lines.

The slope in the Arrhenius plot (Figure ) for a-PS calculated in this work has a value of around 20 kK, while the slope calculated in the work of Koh and Simon[43] has a value of 13 kK. Considering that in this work, we used a limited temperature range for the construction of the Arrhenius plot in Figure compared to the work of Koh and Simon,[43] errors may have been introduced because of the errors in the shift factors. Despite these differences, the activation energies measured by flash-DSC are significantly smaller than the ones typically reported in the literature for the α-process,[45] a fact that was also noted earlier.[46] The relatively small activation energies are, again, supporting the idea that non-α-processes are relevant for the low-temperature behavior of the glass.

Furthermore, we quantify the ageing rate from the slope of ΔHtot – ΔHrej in the range where it exhibits a linear increase with respect to the logarithm of time

In Figure , the ageing rate, Rag, is plotted as a function of the ageing temperature Ta. At Topt-80K, Rag is close to zero, increases slightly with ageing temperature at Topt-60K, and has a large increase at Topt-40K. The ageing rates for i-PS, a-PS, and s-PS are comparable for temperatures from Topt-80K to Topt-40K. In addition, a-PS exhibits higher ageing rates than s-PS for temperatures above Topt-40K, where i-PS has the highest ageing rate of all specimens at the optimum Ta.

Figure 9

Ageing rate (Rag) as a function of ageing temperature for i-PS (half-filled circles), s-PS (filled circles), and a-PS (empty circles).

Discussion

PS[15,47] as well as other glassy polymers such as PC[48,49] and PVC[50] have been reported to have logarithmic enthalpy overshoot increase at high-temperature ageing. For ageing at the optimum ageing temperature, the enthalpy overshoot increases logarithmically with time. For ageing temperatures below the optimum ageing temperatures, ageing shows a non-logarithmic dependence on time. The farther the ageing temperature of the material is from its optimum ageing temperature, the longer the material stays in an arrested state until it shows a logarithmic increase in excess enthalpy with time (Figure ), similar to the enthalpy increase which has been reported for PC.[48]

While all materials exhibit the same ageing mechanisms for all temperatures (logarithmic increase of excess enthalpy with Topt and delayed increase of the excess enthalpy with ageing at temperatures far below optimum), it is worth noting the effect of tacticity on the ageing rate (Figure ). Specifically, a-PS and i-PS show a similar ageing rate for temperatures from Topt-40K to Topt-20K, while at the optimum ageing temperature, the fastest ageing kinetics are observed for i-PS. s-PS shows the slowest ageing kinetics between the three polymers, specifically for temperatures from Topt-40K to Topt.

We believe that the reason behind the difference of the rate at which a-PS, s-PS, and i-PS age is related to the difference in chain flexibility of those polymers. Nakaoki and Kobayashi[51] studied, by solid-state high-resolution 13C NMR, the gauche content of amorphous atactic, syndiotactic, and isotactic PS, finding 27.9, 25.0, and 34.3%, respectively. Based on their results, they concluded that i-PS is more likely to have fewer trans sequences, which leads to a shorter random coil and to a smaller characteristic ratio (C∞). This has been confirmed by small-angle neutron scattering studies which have revealed that the characteristic ratio is C∞s-PS > C∞a-PS > C∞i-PS, that points out that the stiffest chain is the one of s-PS.[52] Specifically, the C∞s-PS value is 7.9 to 13 for increasing Mw from 214 000 to 380 000 g/mol.[53] The C∞a-PS value is 6.7 to 9.6 for increasing Mw from 325 000 to 500 000 g/mol, and the C∞i-PS values are 4.9 and 5 for Mw = 254 000 and 500 000 g/mol, respectively.[53] Syndiotactic sequences make the polymer chain rigid[54] and slow down the reorganization of the chains, which consequently leads to slower ageing kinetics, as it has been shown in our measurements (Figure ). Tensile creep measurements on polyimide Kapton-H and cellulose acetate butyrate ester have also suggested that the ageing kinetics are slower for the more rigid polymers.[55]

As shown above, the rate of ageing decreases with increasing chain stiffness, s-PS ageing significantly slower than i-PS. This is in stark contrast to the behavior of these two materials in crystallization; s-PS crystallizes about hundred times faster than i-PS because of differences in the conformation of the C–C backbone and the work of chain folding.[56] This contrast shows that ageing and crystallization are clearly distinct phenomena.

Conclusions

The effect of tacticity on the ageing kinetics of glassy amorphous PS was investigated by flash-DSC. Our results show that the tacticity does have an effect on the physical ageing kinetics, with syndiotactic and isotactic PS showing the two extremes, slow and fast ageing kinetics, respectively, and atactic PS showing ageing kinetics between these two extremes.

The enthalpy overshoot of all PS specimens follows a logarithmic increase with ageing time at their optimum ageing temperature. For temperatures far below its optimum, there is a range, different for each specimen, where the enthalpy overshoot is constant, whereas at higher temperatures (but still below the optimum temperature), it also shows a logarithmic increase. In addition, the activation energy for i-PS is found to be the lowest, while the activation energies of a-PS and s-PS have the same values within experimental error. The results reported in this paper indicate that non-α-processes are relevant for the low-temperature behavior of the glass.