Tensile Fracture of Molecular Glasses Studied by Differential

Dec 21, 2016 - Molecular glasses indomethacin and ortho-terphenyl were formed and fractured by cooling a liquid on a less thermally expansive substrat...
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Tensile Fracture of Molecular Glasses Studied by Differential Scanning Calorimetry: Reduction of Heat Capacity by Lateral Constraint Yinshan Chen,† C. Travis Powell,‡ and Lian Yu*,†,‡ †

School of Pharmacy, ‡Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53705, United States ABSTRACT: Molecular glasses indomethacin and ortho-terphenyl were formed and fractured by cooling a liquid on a less thermally expansive substrate. In-plane tension was created by the mismatch of thermal expansion coefficients and accumulated to cause catastrophic network fracture. Differential scanning calorimetry was used to characterize the process. The heat of fracture exceeds by 10 times the strain energy released, and matches the excess enthalpy stored by an elastic film that is cooled under lateral constraint. The constrained film has a smaller heat capacity than a free-standing film, by approximately 0.01 J/g/K or 1%. This allows the constrained film to reach higher enthalpy on cooling and the excess enthalpy is released at fracture.

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INTRODUCTION

times lower. This property is important because fracture affects many applications of molecular glasses. For example, the fracture of organo-silicate insulation films causes shorting in electronics;12 the fracture of biopreservation matrices leads to loss of activity;13,14 the fracture of amorphous drugs creates free surfaces and speeds up crystallization.15 Differential scanning calorimetry (DSC) is a commonly used technique for characterizing glasses and the glass transition. In a typical experiment, a glass-forming liquid is placed in a metal pan and cooled; its transition to a glass is signaled by a decrease of heat capacity. We report here that in such an experiment, a molecular glass is easily fractured, releasing heat and showing an increase of heat capacity. This occurs because the molecular glass adheres to a less thermally expansive substrate and tension builds upon cooling to a high enough level to cause fracture. Under spatial constraint, the glass sample has smaller heat capacity and stores excess enthalpy during cooling relative to a free-standing film; this excess enthalpy is released as heat at fracture. For the systems studied, indomethacin (IMC) and ortho-terphenyl (OTP), lateral constraint reduces the heat capacity by approximately 0.01 J/g/K or 1% relative to a freestanding film, in excellent agreement with theoretical prediction.

Organic glasses of relatively low molecular weights (“molecular glasses”) are important in pharmaceutics for improving solubility and bioavailability,1,2 in food science,3,4 and in organic electronics.5−8 Despite progress in developing these materials, a still poorly understood property is their low resistance to fracture. As Figure 1 shows, molecular glasses and crystals have much lower fracture toughness than polymers and metals,9−11 with the critical stress intensity factors Kc at least 10

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THEORETICAL SECTION To perform a well-controlled fracture experiment, a glassforming liquid of uniform thickness h is cooled on a substrate that has a smaller thermal expansion coefficient (a silicate Figure 1. Comparison of fracture toughness of various materials. Data source: ref 10 for ice, silica/silicate, engineering polymers, and alloys; ref 9 for small-molecule organic glasses (solid circles); ref 11 for smallmolecule organic crystals (open diamonds). © XXXX American Chemical Society

Received: November 10, 2016 Revised: December 17, 2016 Published: December 21, 2016 A

DOI: 10.1021/acs.jpcb.6b11347 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B coverslip) (Figure 2a).9 The whole assembly is placed in a DSC pan for characterization (see later). Because of the different

Figure 3. Enthalpy H of a glass film formed under different spatial constraints. Below a set temperature (≈ Tg), H decreases with cooling at the rate Cp for a free-standing film, at the rate Cv for a constantvolume sample, and at the rate CF for a laterally supported film. At fracture, the enthalpy of a supported film is conjectured to decrease to that of a free-standing film with release of heat Qfrac. Figure 2. (a) Experimental set up. In-plane tension is created by cooling an organic glass film adhering to a thermally less expansive substrate and builds to rupture the film. (b) Fracture occurs all-at-once at a well-defined temperature for a given film thickness (42 μm in this case), producing a network structure in which the cell size is roughly the film thickness.9

the specific volume, and M is the bulk modulus. For a glassforming film under lateral constraint as in our experiment, Lion et al. obtained20 Cp − C F = 2α(α − αs)TsetVE /(1 − ν)

where CF is the heat capacity of the 2D-constrained film at the reference temperature Tset. If the network fracture releases tension throughout the film, its enthalpy should decrease to the level of the free-standing film. The heat released by this mechanism is given by

thermal expansion coefficients, in-plane tension develops in the organic layer during cooling. This tension can be relaxed in the liquid state, but builds up in the glassy state according to σ// = (α − αs)(Tset − T )E /(1 − ν)

(1)

Q frac = (Cp − C F)(Tset − Tfrac)

where E is Young’s modules, ν is Poisson’s ratio, α and αs are the thermal expansion coefficients of the sample and the substrate, and Tset is the temperature at which viscous relaxation is slow enough for stress to build up. Tset is approximately the end point temperature of the glass transition on cooling detected by DSC. At low enough temperature (high enough tension), the organic film fractures, all at once, forming a network structure (Figure 2b).9 According to fracture mechanics, a crack tip can advance if the local stress is high enough so that the strain energy release rate, G, exceeds some critical value Gc.16,17 Powell et al. have reported the Gc values for IMC and OTP.9 This work is concerned with the heat released at fracture Qfrac. Here we review two known sources for Qfrac. For tough materials (e.g., polymers and steel), a significant part of the strain energy released at fracture becomes heat.18,19 For our situation of all-at-once fracture, the heat released by this mechanism is given by Q frac ≈ GcSA

(3)

= 2α(α − αs)Tset(Tset − Tfrac)VE /(1 − ν)

(4)

where Tfrac is the temperature of fracture, taken to be slightly below Tset. Later we will show that eq 4 well describes the heat of fracture observed. Eq 4 can also be derived from the theory of thermoelasticity.21,22 At fracture, our glass film contracts suddenly. This process can be treated as adiabatic and is expected to cause a temperature rise within the sample. For a glass film under lateral constraint, ΔT is given by ΔT = 2αTσ///(ρCp)

(5)

where σ// is the change of in-plane tension relative to a stressfree state. In a DSC cell, this sudden change of sample temperature is equilibrated with a heat flow of the amount CpΔT. Expressing the in-plane tension by eq 1, we obtain eq 4.

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MATERIALS AND METHODS IMC (99% pure) and OTP (99% pure) were obtained from Aldrich and used as received. Table 1 collects the relevant properties of these materials. To prepare an IMC sandwiched sample, a known amount of IMC (1−4 mg) was melted between two 5 mm-diameter silicate coverslips and then quenched to room temperature. The thickness of the samples was 30−160 μm. To prepare an IMC sample with a free surface, one of the silicate coverslips was replaced with a Kapton film, which was peeled off at room temperature. The thickness of the sample was 100−260 μm. For the preparation of an OTP sandwiched sample, a known amount of liquid OTP

(2)

where SA is the specific surface area created by fracture (in m2/ g). A second source of heat is the excess enthalpy stored in a laterally constrained film that is cooled. With cooling, the enthalpy of a glass film decreases at a rate equal to its heat capacity (Figure 3). For a free-standing film, the rate is the constant-pressure heat capacity Cp. Under spatial constraint, the heat capacity is lower. Constrained to a constant volume, the reduction of heat capacity is the well-known result Cp − Cv = 9α2TVM, where Cv is the constant-volume heat capacity, V is B

DOI: 10.1021/acs.jpcb.6b11347 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Table 1. Physical Properties of IMC,a OTP,b and the Silicate Coverslipc material IMC OTP silicate coverslip

Tg, K

E, GPa

M, GPa

α, ppm/K

ν

ρ, g/cm3

V, cm3/g

315 246 830

4.1 4.3 73

6.9 6.4 82

65 87 7.2

0.36 0.33 0.21

1.34 1.13 2.6

0.75 0.88 0.38

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RESULTS Figure 4 shows the typical SEM images of tensile fracture in an organic glass observed in this work. Note that the cracks are perpendicular tunnels running through the film. Figure 5 shows

IMC: ρ from ref 23, measured at room temperature; E and ν from ref 24; α is calculated from the ellipsometry TEC αobs25 using a

α=

( 11 −+ νν )αobs + ( 1 2+νν )αs, where α

(silicon). M=

26

s

is the TEC of the substrate

V is calculated from ρ. M is calculated from E using

E(1 − ν) . bOTP: (1 + ν)(1 − 2ν)

ρ and α are from ref 27 and given at 246 K.

α is taken to be 1/3 of the volumetric value. E is calculated from isothermal compressibility27 and assumed ν (0.33). V is calculated from ρ. M is calculated from E using M =

E(1 − ν) . cSilicate (1 + ν)(1 − 2ν)

Coverslips: All data from the manufacturer.28 M is calculated from E using M =

E(1 − ν) . (1 + ν)(1 − 2ν)

Figure 5. Detection of the heat of fracture by DSC. This sample is 90 μm-thick IMC between two silicate coverslips and placed in an aluminum pan (picture). Note the repeatability of the fracture temperature and heat in repeated temperature cycles.

(2−11 mg) was introduced with a pipet between two 5 mmdiameter coverslips and allowed to spread at 283 K. The thickness of OTP sandwiched sample was controlled to be 120−500 μm. DSC was performed with a TA Instruments Q2000 unit. To measure the energy release at fracture, a sample was placed in an aluminum DSC pan. An IMC sample was heated at 10 K/ min to 343 K (323 K for an open sample), held for 3 min, and cooled at 10 K/min to ca. 10 K below the fracture temperature. The fractured sample was heated back to 343 K at 10 K/min and cooled to fracture again, up to three times. An OTP sample (always sandwiched) was cooled at 10 K/min from 268 to 228 K and then at 3 K/min to about 10 K below the fracture temperature. The sample could be heated and refractured, up to three times. To determine the area of fracture surface, the fracture pattern of each sample was observed and recorded through a light microscope (Olympus BX3-URA). Scanning electron microscopy (SEM) analysis was performed on side view on a field-emission LEO 1530 low voltage and highresolution operated at 5 kV and 5 mm working distance using an in lens secondary electron detector.

typical DSC data of a fracture process. Cooled at 10 K/min, the sample first undergoes a glass transition (Tg) and shows an abrupt release of heat (Tfrac). The temperature Tfrac matches that obtained previously by observation through a microscope.9 The process of glass formation and fracture can be repeated by heating the sample above Tg to heal the cracks and cooling again (cycles 2 and 3). The three cycles detected consistent Tfrac (259 K) and heat release Qfrac (0.7 mJ or 0.3 J/g). The heat release by fracture is fast and relatively small and it is necessary to confirm that DSC can measure this heat reliably. Figure 6a shows the validation data. Here, the measured heat of crystallization for a small indium sample is compared with the expected value for its mass. The indium mass was chosen so the calibration range covers the observed heat of fracture (0.3−2.8 mJ). The agreement is excellent between the measured and expected heats. In Figure 6a the red symbols correspond to

Figure 4. SEM images of fracture in a sucrose benzoate film 120 μm thick. C

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sandwich to the open geometry increases Tfrac.9 Note the increase of Qfrac with decreasing Tfrac. For IMC, open and sandwich samples form a single trend, as expected for mechanically thin films in lateral constraint.20 The temperature slope of Qfrac on Tfrac is 0.0095 J/g/K for IMC and 0.015 J/g/K for OTP. These results indicate that a fractured film has a higher heat capacity than the film before fracture. This latter conclusion was confirmed by direct measurements, shown below. Figure 8 shows a DSC cooling trace across a fracture event. Note the step-up of the baseline after the fracture event. This

Figure 6. Validation of the DSC’s ability to measure heat of fracture. (a) Measured and expected heat of indium crystallization. (b) Normalized heat release kinetics for pure indium, indium between two Kapton films, and a fractured IMC. The raised baseline after fracture is caused by an increase in heat capacity.

Figure 8. DSC cooling trace for an IMC sample (6.00 mg). Note the step-up of the baseline from before to after fracture, indicating an increase of heat capacity.

baseline change indicates an increase of heat capacity. For IMC, we obtain the heat capacity change of the film at fracture ΔCfrac = 0.011 ± 0.003 J/g/K (n = 33). This result is independent of the cooling rates used (5, 10, and 15 K/min). The same increase of heat capacity upon fracture was observed for OTP, with ΔCfrac = 0.016 ± 0.004 J/g/K (n = 10). These values agree within experimental error with the slopes of Qfrac against Tfrac and later will be attributed to the reduction of heat capacity by lateral constraint. To close this Results Section, we comment on the possibility that the thermal event observed at fracture is in fact an instrumental noise. Our results do not support this view. Figure 5 shows that the thermal event is always exothermic and repeatable for each sample. Were it a random noise, the event should be either exothermic or endothermic and not repeatable. Figure 7 shows that Qfrac increases systematically with decreasing Tfrac. This behavior also would not be expected for an instrumental noise. In the next section, we provide an explanation for the observed thermal event at fracture.

indium samples directly placed in an Al pan and the blue symbols to samples sandwiched between Kapton films and then placed in an Al pan. The Kapton films slowed the heat transfer out of the indium sample so that the heat release rate roughly matched that of a fractured molecular glass (Figure 6b). No difference is seen between the two types of samples, indicating that DSC can measure the heat of fracture of organic glasses. Figure 7 shows the heat of fracture Qfrac for IMC and OTP glass films as a function of fracture temperature Tfrac. The range of Tfrac was obtained by varying the sample thickness as thinner films fractured at lower temperatures.9 In the case of IMC, Tfrac was also varied through sample geometry: changing the

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DISCUSSION This study has demonstrated that it is possible to use DSC to measure the fracture of organic glasses. In this section, we interpret the heat of fracture observed. We show that the measured heat greatly exceeds the strain energy released at fracture, and is well explained by the excess enthalpy stored by an elastic film that is cooled under lateral constraint. For tough materials, the heat release rate at fracture can be a large part of the strain energy release rate,18,19 and we first consider whether the same holds for the molecular glasses of this study. In this case, the heat released is given by eq 2: Qfrac ≈ GcSA. According to Powell et al., Gc = 1.08 J/m2 for IMC and 0.9 J/m2 for OTP.9 They also found that the glass film fractures

Figure 7. Heat released at fracture Qfrac vs fracture temperature Tfrac. D

DOI: 10.1021/acs.jpcb.6b11347 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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7: 0.0095 J/g/K for IMC and 0.015 J/g/K for OTP. Second, they should match the directly measured heat-capacity change upon fracture (Figure 8): 0.011 ± 0.003 for IMC and 0.016 ± 0.004 for OTP. In both comparisons, we find good agreement between theory and experiment. This agreement supports the notion that lateral constraint reduces the heat capacity of a glass film, allowing it to store excess enthalpy on cooling, which is then released as heat at fracture.

all-at-once to a cellular pattern whose average cell size is roughly the film thickness h (Figure 2a).9 SA is approximately given by 4/(ρh), where ρ is the density (Table 1). Figure 9

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CONCLUSION The heat release at fracture has been successfully measured by DSC for molecular glasses formed on a thermally less expansive substrate and placed under tension by cooling. The measured heat is much larger than the strain energy released and agrees with the excess enthalpy stored by cooling an elastic film under lateral constraint. The phenomenon is also understood on the basis of a temperature rise on adiabatic contraction. DSC is an important and common technique for characterizing glasses and the glass transition. In this context, the heat capacity measured is usually regarded as Cp (constant-pressure heat capacity) for experiments performed at ambient pressure.29−31 This work has shown that in a standard DSC measurement, an organic glass can develop a large stress because of its adherence to a substrate or container that has a different thermal expansion coefficient. The resulting stress can be so high as to cause fracture. DSC can detect the heat released at fracture and a change in the apparent heat capacity. For the systems of this study (IMC and OTP), heat capacity increases by 1% at fracture, corresponding to the difference between a free-standing film and a laterally constrained film. This effect, though small, means that the apparent heat capacity cannot be rigorously interpreted as Cp. This effect also plays an important role in the measurement of frequency-dependent heat capacity of liquids near Tg.32 For tough materials, the heat release rate at fracture can approach the strain-energy release rate.18,19 This is not the case, however, for the easy-to-fracture molecular glasses. The heat release observed by our experiment is dominated by the thermoelastic effect, not the release of strain energy. It is conceivable that the experiment can be reconfigured to measure fracture toughness if stress is introduced by isothermal loading and if tougher materials are tested. The method could be applied to study the fracture of crystalline materials and their difference from glasses in fracture. Fracture could be induced by compression as opposed to tension by heating a constrained film from a strain-free state.

Figure 9. Comparison of heat of fracture observed and expected for the strain-energy release rates of IMC and OTP.

shows the calculated output GcSA for this mechanism of heat release. It is evident that the GcSA value is much smaller than the Qfrac measured (symbols), by roughly a factor of 10 on average. This result indicates that the heat measured must be from another source. Stated differently, if Qfrac is used to calculate Gc, the result would be 10 times larger than the known value. We now show that the observed heat of fracture can be explained on the basis of reduced heat capacity by spatial constraint. As illustrated in Figure 3, the heat capacity of a laterally constrained film is smaller than that of a free-standing film. Upon cooling from a strain-free state (at Tset), a laterally constrained film has higher enthalpy than a free-standing film. We assume that at the point of fracture, tension is released and the sample goes from a constrained state to a free-standing state, releasing an amount of heat Qfrac that corresponds to the enthalpy difference between the two states (down arrow in Figure 3). For a small temperature change from Tset, Qfrac is given by eq 4. In Figure 7, the predicted Qfrac (lines) is compared with experimental data. A good agreement is found between experiment and theory. In this prediction, all the parameters are from the literature (Table 1); only Tset is allowed to vary. For IMC, the best-fit Tset, 294 K, lies between the previously reported values (291 K for sandwich films; 298 K for open films);9 for OTP, the best-fit Tset, 231 K, is slightly above the previously reported 225 K. The different Tset values are within experimental error. A further test of our model is to assess the agreement between the predicted (Cp − CF) by eq 3 and the observed heat capacity change upon fracture ΔCfrac. According to eq 3, (Cp − CF) = 0.011 J/g/K for IMC and 0.018 J/g/K for OTP. These predictions can be tested against two sets of experimental values. First, they should match the Qfrac vs Tfrac slopes in Figure

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +1 608 263 2263. ORCID

Yinshan Chen: 0000-0001-8833-0255 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the NSF (DMR-1234320) for supporting this work. REFERENCES

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