Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Double Mechanism for Structural Recovery of Polystyrene Nanospheres Natalia G. Perez-De-Eulate† and Daniele Cangialosi*,†,‡ †
Centro de Física de Materiales CFM (CSIC-UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain ‡ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain ABSTRACT: Geometrical confinement can profoundly affect the dynamics of glass-forming polymers. In this context intense research has been mostly devoted to the understanding of how polymers subjected to 1-D confinement, that is, thin films, vitrify when cooled from the supercooled melt or recover equilibrium while in the glassy state. With the aim of extending our knowledge to other kinds of confinement, here we consider polystyrene (PS) nanospheres, that is, systems subjected to 3-D confinement. We investigate the physical aging following the enthalpy recovery in the glassy state employing fast scanning calorimetry, allowing heating/cooling rates as large as ∼1000 K/s. These systems have been previously shown to exhibit suppressed glass transition temperature in comparison to bulk PS. We find accelerated recovery toward equilibrium, in line with previous findings on other confined polymer glasses exhibiting weak interactions with the substrate. Furthermore, the time evolution of the enthalpy exhibits two mechanisms of equilibration. Apart from a slow one, normally observed in proximity of the glass transition, a fast, mildly activated mechanism of equilibration is observed. We emphasize the analogy with bulk glasses, also exhibiting this behavior though on considerably larger time scales.
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INTRODUCTION The study of vitrification resulting from cooling a metastable liquid previously supercooled below its melting temperature is an area of active research.1,2 Vitrification is generally viewed as taking place in a temperature range, addressed as the glass transition, at which molecular motion becomes so slow that the system cannot maintain equilibrium and transforms into a nonequilibrium glass. The connection with the molecular mobility highlights the kinetic nature of the glass transition. However, it has to be pointed out that the kinetics of vitrification and the molecular mobility are two conceptually different aspects of glass dynamics.3 In particular, the former aspect involves the irreversible transformation of a system in equilibrium into a nonequilibrium glass. In contrast, measuring the molecular mobility entails the determination of an intrinsic property of the equilibrium supercooled liquid. As such, the characterization of the vitrification kinetics requires the application of a nonlinear perturbatione.g., a cooling ramp, where changing continuously the temperature implies irreversible, from a thermodynamic viewpoint, entropy loss on glass formation1,3whereas to determine the molecular mobility, a perturbation in the linear regime, fulfilling the fluctuation− dissipation theorem,4,5 is needed. Having pointed out this conceptual difference, efforts to correlate the glass transition to the molecular mobility have been pursued in the past. In most cases, with some notable exceptions,6 bulk glass-formers show a one-to-one correlation between glass transition and molecular mobility.7,8 © XXXX American Chemical Society
The main consequence of the kinetic nature of the glass transition is that glasses, owing to their nonequilibrium nature, slowly evolve toward equilibrium, a phenomenon known as structural recovery9 or physical aging.10−13 The study of this phenomenon is of great fundamental interest because of the information that can be provided on the fate of the dynamics and thermodynamics below Tg.13−15 Recently, studies on both polymeric16−18 and other kind of glasses19−25 have shown that for glasses aged during very long times and considerably below Tg equilibrium recovery proceeds via two or, in some cases, several mechanisms, each drawing the glass to a relative free energy minimum, until the thermodynamic state of the extrapolated liquid line is achieved. The slow mechanism of equilibrium recovery exhibits the standard super-Arrhenius behavior typical of glass dynamics.17 In contrast, a much milder temperature dependence is encountered for the fast mechanism.17,22,26 This finding raises the question on the molecular origin of fast mechanisms of equilibrium recovery. Unfortunately, in bulk polymers the time scales required to observe multiple steps toward equilibrium are usually larger than days.16,17,27 This calls up for the search of kinetic pathways able to accelerate equilibrium recovery. Recently, numerous experimental efforts have shown that the time scale to approach equilibrium can be considerably reduced Received: March 8, 2018 Revised: April 11, 2018
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DOI: 10.1021/acs.macromol.8b00502 Macromolecules XXXX, XXX, XXX−XXX
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Figure 1. Upper panels: AFM images of PS nanospheres by the flash nanoprecipitation method55 after heating at 473 K for several minutes in a vacuum oven. Lower panels: histograms represent the size distribution plots. Black solid lines are log-normal fits, and the reported values of the diameter correspond to the maximum of the distribution.
in polymers confined at the nanoscale.13,28,29 Such characteristic is especially evident in the well-documented observation of Tg suppression in variously confined polymers, including thin films,30−32 nanocomposites,13,33,34 and nanospheres.35−38 In general, Tg suppression in confinement is associated with weak interactions of the polymer with the surrounding medium.39 In other words, Tg suppression in confinement can be viewed as the ability to keep equilibrium at temperatures lower than the bulk. Hence, it is anticipated that confined glasses, exhibiting Tg suppression, are expected to age faster than the bulk. This has been actually observed in several confined glasses. When the time scale to reach equilibrium is considered as the metric to define the kinetics of physical aging, stacked polystyrene (PS) films annealed at a given temperature in the glassy state have been shown to evolve faster than the bulk homologue.40,41 This is reflected in the achievement of films with density higher than the bulk, as demonstrated by X-ray reflectivity measurements42 and ellipsometry.43 Such acceleration of equilibrium recovery in thin films exhibiting Tg suppression often results in an apparent drop of the rate of variation of a given property.44−47 This is due to the reduced thermodynamic driving force, as highlighted by Priestley et al.48,49 using depth-resolved fluorescence. Altogether, these results indicate that confined polymer glasses exhibiting Tg suppression are potentially ideal systems to provide insights into the different mechanisms of equilibrium recovery. Studies on thin PS films actually show that when aged considerably below Tg, thin PS films recover equilibrium via two mechanisms,50,51 a fact that was exploited to obtain glasses with low fictive temperature (Tf), that is, the temperature at which a glass with a given state would be at equilibrium. In such a way, decreases of Tf as large as 70 K below Tg were achieved. In this work, we investigate the effect of 3-D confinement on the physical aging behavior following the enthalpy recovery of glassy PS nanospheres deposited on a silicon oil by fast scanning calorimetry (FSC).52 This system have been recently
shown to exhibit significant Tg suppression53 in ways analogous to PS nanospheres suspended in water35 or surrounded by atmospheric gas.36 Furthermore, when aged in proximity of Tg, PS nanospheres suspended in water were found to recover equilibrium faster than the bulk.54 Our study, by extending the aging time and temperature range at which enthalpy recovery is investigated, show acceleration of physical aging and the presence of two mechanisms of equilibration. These findings are analogous to those obtained for 1-D confinement, that is, polymer thin films.50,51 Hence, they point toward the universality of the behavior exhibited by polymers subjected to different dimensionalities of confinement.
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EXPERIMENTAL SECTION
Materials and Sample Preparation. PS nanospheres were prepared from high molecular weight linear polystyrene (Mw = 1408 kg/mol and Mw/Mn = 1.17) from Polymer Source Inc. The nanospheres were obtained following the flash nanoprecipitation method.55 First, PS was dissolved in tetrahydrofuran (THF; GPC grade; Sigma-Aldrich). Thereafter, PS solution was mixed with a nonsolvent, that is, ultrapure water (Milli-Q grade). The resulting dispersion PS/THF/water was left for 2 days in a fume hood to allow for THF evaporation, and the remaining dispersion PS/water was freeze-dried to obtain the nanospheres powder. The achieved diameters were quantified using atomic force microscopy (AFM) by depositing a drop of PS/water suspension onto silicon oxide wafer (SiOx) and subsequently by drying for 12 h at room temperature. Three different diameters were obtained by tuning the initial concentration of PS in THF, resulting in a maximum of particle diameter distribution at 230, 320, and 500 nm. This is shown in Figure 1, where the AFM images of all investigated systems are presented. These correspond to sample heated for several minutes at 473 K in a vacuum oven. This time is by far larger than that spent at such temperature in FSC experiments, that is, 0.1 s. This demonstrates the morphological thermal stability of the obtained nanospheres. In the lower panels of the same figure, the discrete particle diameter distribution, together with the log-normal fits, is presented. B
DOI: 10.1021/acs.macromol.8b00502 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Fast Scanning Calorimetry Measurements. Fast scanning calorimetry (FSC) was carried out by means of the Mettler Toledo Flash DSC1 based on chip calorimetry technology, equipped with an intracooler, allowing for temperature control between −90 and 450 °C, and nitrogen purged and calibrated with melting indium. In order to guarantee good thermal contact between the nanopsheres and the chip, a layer of poly(dimethylsiloxane) (PDMS) with Mw = 1000 g/ mol and Mw/Mn = 1.25 with thickness of several tens nanometers was deposited on top of the chip. This polymer is completely incompatible with PS.56 Subsequently, PS nanospheres were placed on top of the PDMS layer. Immediately after, all the prepared samples were placed inside a vacuum oven at 343 K for 12 h in order to remove any trace of solvent and to ensure the good deposition of the nanospheres. The calorimeter directly delivers the heat flow rate (HF) exchanged by the sample with the external world with no need of calibration. HF depends on the sample specific heat and on the heat required to maintain the temperature of the sample above that of the cold block (∼−100 °C). The mass of PS deposited on the chips was between 100 and 500 ng. This was obtained from the magnitude of the heat flow rate jump (ΔHF) in the range of temperature of the glass transition. This is related to the total specific heat jump (ΔCp) through ΔHF = mΔCpq
where Cpm and Cpg are the specific heat of the melt and the glass, respectively. A heating rate of 1000 K/s for the sample masses employed in the present study results in an error in the determination of Tf as large as ±2 K. This uncertainty is essentially caused by the lag at heating/cooling rates of the order of 1000 K/s, as shown in a recent work.60
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RESULTS Information regarding the way vitrification kinetics on cooling from the supercooled melt is modified in PS nanospheres employed in the present study are crucial to understand the way equilibrium is recovered in the glass.13 Our recent cooling rate dependent characterization of the glass transition showed that Tf decreases with decreasing the nanospheres diameter.53 Such decreases are marked at low cooling rate, whereas cooling at ∼1000 K/s, that is, in the conditions of the present work, results in Tf suppression smaller than ∼8 K. Table 1 reports an Table 1. Tf (in K) for all Investigated Polymers bulk PS 392 K
(1)
In an experiment carried out at a given cooling rate q, the mass of the sample can be evaluated from such equation. This can be done if ΔCp at the glass transition is known from independent measurements, for instance, those performed by standard DSC. In the case of PS, the specific heat both in the melt and glassy state has been widely characterized in the past.57 Once the samples mass is known, the total specific heat can be evaluated by eq 1 in any condition and at any temperature. FSC experiments aiming to determine the amount of recovered enthalpy were conducted in both isochronal and isothermal conditions. In both cases, FSC experiments began erasing the previous thermal history by holding samples at 473 K for 0.1 s and subsequently quenching to 183 K at 1000 K/s. Afterward, samples were heated up to the selected aging temperature at 1000 K/s and kept at such temperature for the selected aging time. Finally, samples were cooled down to 183 K and immediately heated up at 1000 K/s for data collection. The employed thermal protocol is outlined in Figure 2.
For isochronal experiments an aging time of 60 min and a temperature ranging from Tg of the nanospheres until 248 K were considered. Isothermal aging experiments were conducted for aging times varying between 0.1 and 105 s at temperatures ranging from Tg to Tg − ∼80 K. The thermodynamic state achieved after aging at given conditions was characterized using the fictive temperature, Tf.58 This was obtained using the Moynihan method:59
f
T ≫ Tg
(Cpm − Cpg ) dT =
T ≪ Tg
∫T ≫T
g
(Cp − Cpg ) dT
320 nm 384.5 K
230 nm 384 K
overview of the Tf at 1000 K/s taken from ref 53. Given the fact that the equilibrium thermodynamics is affected only at conditions of confinement much more extreme than those of the present study,61,62 this implies that the thermodynamic starting point of glasses obtained from PS nanospheres consists of an enthalpy lower than that of the corresponding bulk. The physical aging of PS nanospheres is monitored following the enthalpy recovery after a given annealing time and temperature. This can be done from two different viewpoints: (i) isochronal enthalpy recovery experiments, where the aging time is fixed and the temperature is varied; (ii) isothermal enthalpy recovery experiments, where the aging temperature is kept fixed and the time is varied. We start our discussion showing specific heat scans of all investigated systems aged in isochronal conditions. The values in excess to the reference unaged samples are shown in Figure 3. Data refer to 60 min annealings over a wide range of aging temperatures. Irrespective of the investigated systems, when aging at temperatures close to Tg, all excess specific heat scans exhibit a pronounced endothermic overshoot at temperatures above ∼400 K. This is the typical signature of physical aging investigated by calorimetry.63 When aging is carried out at temperatures progressively farther from Tg in the glassy state, the endothermic overshoot decreases in height, becomes broader, and shifts to lower temperatures. However, while such overshoot tends to disappear for bulk PS, its presence is clearly visible even at the lowest aging temperatures for PS nanospheres. Data shown in Figure 3 allow determining the aging temperature dependence of the Tf achieved after 60 min annealing. This is shown in Figure 4, where Tf as a function of aging temperature is displayed for all investigated systems. Bulk PS and nanospheres with 500 nm diameter follow the behavior generally observed in this kind of experiments, consisting of a minimum in Tf. In nanospheres with diameter 500 nm, such a miminum is found at a temperature lower than bulk PS. This behavior results from the role of two competing effects: the temperature variation of the driving force for physical aging and that of the molecular mobility. The driving force for physical aging, that is, the distance from equilibrium, increases with decreasing temperature. This effect induces the initial decrease
Figure 2. Thermal protocol employed to determine the amount of recovered enthalpy after aging for a given time, ta, at a given temperature, Ta.
∫T
500 nm 385 K
(2) C
DOI: 10.1021/acs.macromol.8b00502 Macromolecules XXXX, XXX, XXX−XXX
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Figure 3. Heat flow in excess to the unaged reference of samples aged for 60 min at the indicated temperatures obtained at a heating rate of 1000 K/ s for bulk PS (upper left panel) and PS nanospheres with diameter 500 nm (upper right panel), 320 nm (lower left panel), and 230 nm (lower right panel). The inset in the lower right panel is a magnification of the low-temperature part of the main panel.
more detail in the next section, this result points toward the existence of two mechanisms of equilibrium recovery. Further insights into the physical aging behavior of PS nanospheres are provided by isothermal enthalpy recovery experiments. In Figure 5, as a showcase, excess specific heat scans for nanospheres with diameter 230 nm after aging 343 K for different times are presented. As a general feature, aging in such conditions results in the progressive development of an endothermic overshoot. The resulting aging time dependence
Figure 4. Aging temperature dependence of the fictive temperature Tf achieved after aging for 60 min for all investigated systems.
of Tf with decreasing aging temperature. In contrast, reducing the temperature involves a slowdown of the molecular mobility, which in turn results in an increase of the Tf reached after 60 min aging. Given the general picture of physical aging, we note that PS nanospheres with diameter 320 and 230 nm exhibit important deviations from the standard behavior. These are based on a nonmonotonous dependence of the Tf on the aging temperature. In particular, these systems, apart from the minimum in Tf at temperatures close to Tg, reveal the presence of an additional minimum at lower temperatures. As discussed in
Figure 5. Specific heat in excess to the unaged reference obtained at a heating rate of 1000 K/s for nanospheres with diameter 230 nm aged at the indicated aging times and at 343 K. D
DOI: 10.1021/acs.macromol.8b00502 Macromolecules XXXX, XXX, XXX−XXX
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Figure 6. Aging time evolution of the fictive temperature Tf, shown as its difference with Ta, for bulk PS (upper left panel) and PS nanospheres with diameter 500 nm (upper right panel), 320 nm (lower left panel), and 230 nm (lower right panel). The dashed lines in (a) are the logarithmic fits to time-dependent Tf data in the time interval of maximum variation and at the plateau.
decay until a plateau with Tf > Ta. In some cases, the onset of a second decay is detected. This is the case of nanospheres with 320 and 230 nm aged between 343 and 358 K. At the lowest investigated aging temperature the first plateau in Tf may differ from the final ultimate thermodynamic state, with Tf = Ta, by as much as 60 K. This is the case of nanospheres with 230 nm diameter aged at 303 K.
of Tf, in terms of the distance from the equilibrium Tf, that is, the aging temperature Ta, is displayed Figure 6 (bottom right panel). As can be observed, the aging time evolution of Tf exhibits an initial decay to a plateau during the first 100 s. This corresponds to a Tf considerably larger than Ta, a result indicating that the thermodynamic state of the glass at such plateau corresponds to a much higher enthalpy than that of the extrapolated supercooled liquid line. However, on further aging the onset of a further decay toward the final thermodynamic state is observed after an aging time between 104 and 105 s. An important observation is that in the time interval of the plateau in Tf, that is, at isoenthalpic conditions, specific heat temperature scans exhibit pronounced evolution. The initially broad low-temperature endothermic peak shifts to higher temperatures and becomes increasingly narrower. An overview of the aging time dependence of Tf is presented in Figure 6, where data for all investigated systems are presented over a wide temperature range. In the explored aging time scale, bulk PS exhibits the standard behavior with one decay toward equilibrium. This result is consistent, even quantitatively, with recent reports on the enthalpy recovery of bulk PS by FSC.64,65 As mentioned in the Introduction, in bulk glasses much larger aging time scales are required to observe nonmonotonous decay of the thermodynamic state toward equilibrium.16,17 In contrast, as anticipated showing the result on nanospheres with 230 nm diameter aged at 343 K, the time evolution of Tf in PS nanospheres exhibits more complex behavior. While in proximity of Tg a single decay to Tf ∼ Ta is observed, aging at lower temperatures results in a relatively fast
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DISCUSSION
Altogether, both physical aging data in isochronal and isothermal conditions reveal the presence of two mechanisms of equilibrium recovery. This result is consistent with those obtained in thin PS films.50,51 Furthermore, the existence of two temperatures of vitrification was shown by Pye et al.66 investigating the temperature dependence of the film thickness by ellipsometry in free-standing PS films. Experiments at low cooling rates (
