Letter pubs.acs.org/macroletters
Glass Transition and Molecular Dynamics in Polystyrene Nanospheres by Fast Scanning Calorimetry Natalia G. Perez-de-Eulate,† Valerio Di Lisio,‡ 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 ‡ Department of Chemistry, Università degli Studi di Roma “la Sapienza”, Piazzale Aldo Moro 5, 00185 Rome, Italy S Supporting Information *
ABSTRACT: We employ fast scanning calorimetry (FSC) to characterize the glass transition of polystyrene (PS) nanospheres. We observe suppression of the glass transition temperature (Tg) in comparison to bulk PS, both in terms of limiting fictive temperature (Tf) and temperature range of vitrification. At the same time, the polymer molecular mobility is found to be independent of the nanospheres diameter and bulk-like. Importantly, apart from the fact that this result has been obtained on the same samples and experiments and at comparable time scales, in all cases, a perturbation of the entropy is induced. Hence, to understand these results, the conceptual difference between vitrification kinetics and molecular mobility is highlighted. The main consequence of the outcome of the present study is that arguments beyond those based on the modification of the molecular mobility must be accounted for to explain Tg suppression in polymer glasses subjected to nanoscale confinement. for thickenesses of ∼100 nm for freestanding polystyrene (PS) films.13,14 Beside this observation, a number of studies, where τ is measured by techniques probing the linear response, show the presence of a dominant component with bulk-like dynamics.15−18 To explain these results, two main hypotheses have been formulated. On one side, it has been argued that in nanoscale confinement Tg and molecular dynamics are decoupled.8,9,19−21 Beside, the role of free surface to speed dynamics, which has been shown in several studies,22−25 has been invoked to explain Tg suppression in confinement.7 By investigating vitrification kinetics on cooling and molecular mobility of PS nanospheres, this Letter aims to address the origin of Tg suppression in polymer glasses subjected to nanoscale confinement. PS nanospheres, when subjected to soft confinement, for instance, suspended in water26 or exposed to air,27,28 have been shown to exhibit Tg suppression in ways analogous to freestanding PS films. To this end, we have employed fast scanning calorimetry (FSC), covering a cooling/heating range of 0.1−1000 K/s, on PS nanospheres obtained by flash precipitation29 with diameter of 230, 320, and 500 nm. This allowed the determination of the Tg, assigned using the concept of limiting fictive temperature (Tf),30 and the vitrification kinetics, in terms of total specific heat (Ctot p ) step. Furthermore, through the step response analysis,31,32 via the temperature dependence of the complex
C
ooling down a supercooled liquid, provided that crystallization is avoided, entails the formation of a glass, a process known as vitrification or glass transition.1 The origin of such phenomenon still needs to be clarified, though the connection to the slowing down of the molecular mobility with decreasing temperature is generally emphasized. In particular, the glass transition temperature (Tg), that is, the temperature at which vitrification takes place on cooling, is found at the point the time scale for molecular mobility, characterized by a relaxation time τ, becomes so long that the system falls out of equilibrium with respect to the supercooled liquid state. Though with some exceptions,2 in bulk glass formers the way vitrification occurs has been one-to-one related to τ.3,4 Notwithstanding this connection, it has to be pointed out that vitrification and molecular mobility are conceptually different aspects of the glass transition.5 The former is determined applying a large perturbation to the system, that is, a cooling ramp. Conversely, measuring the time scale of molecular mobility entails the application of perturbations smaller than the amplitude of the spontaneous fluctuations. This kind of determination fulfills the fluctuation dissipation theorem (FDT) and is addressed as the linear response of the system.6 The connection between vitrification and molecular mobility has been recently challenged investigating glass dynamics under nanoscale confinement.7−9 Nanostructured glasses with free interface,10 unslaved by an underlying adsorbing layer,11 exhibit significantly modified vitrification kinetics, resulting in substantial Tg depression.12 This can be as large as 70 K and visible © XXXX American Chemical Society
Received: July 3, 2017 Accepted: July 21, 2017
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DOI: 10.1021/acsmacrolett.7b00484 ACS Macro Lett. 2017, 6, 859−863
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Figure 1. Specific heat vs temperature plots on heating at 1000 K/s after cooling at the indicated rates.
specific heat, we determined the relaxation time corresponding to a frequency range 1−150 Hz. Our results indicate that Tg decreases with the nanospheres diameter. Contrariwise, τ was found to be independent of the nanospheres diameter. Hence, our results provide compelling evidence, beyond what it was previously found,17,27 of the decoupling between Tg and molecular dynamics in glasses under nanoscale confinement. Figure 1 shows specific heat scans obtained at 1000 K/s of PS nanospheres with varying diameter and bulk PS after cooling at the indicated rates. A common feature of all curves is the presence of a main endothermic overshoot increasing in magnitude with decreasing the cooling rate. (Specific heat scans of nanospheres with 320 nm diameter exhibit additional secondary overshoot at higher temperatures. Such profile has been observed by others and its origin is at present unknown.33 However, as noticed in ref 33, the effect on Tf of considering these peaks is of the order 1 K.) However, the following qualitative differences can be observed: (i) The onset of devitrification progressively shifts toward lower temperatures with decreasing diameter; (ii) Such shift is especially evident for nanospheres with 230 nm diameter, which exhibit excess specific heat at about 340 K, that is, considerably below the location of the main overshoot. This suggests that devitrification in the smallest nanospheres begins via a fast mechanism of equilibration, before the standard mechanism responsible for the main endothermic overshoot, takes over. This result is consistent with the finding of a two-step recovery of equilibrium in both bulk polymers,34 thin PS films,35,36 and other glasses.37,38 The cooling rate dependence of Tf is presented in Figure 2. This was determined from data of Figure 1 using the Moynihan
Figure 2. Cooling rate dependence of Tf for all investigated systems. Error bars in the Tf are smaller than ±1 K. g g method:39 ∫ T≫T (Cpm − Cpg)dT = ∫ T≫T Tf T≪Tg (Cp − Cpg)dT; where Cpm and Cpg are the specific heat of the melt (dashed lines in Figure 1) and the glass (dashed dotted lines in Figure 1), respectively. Inspection of Figure 2 indicates that Tf deviates from bulk behavior and decreases with the nanospheres diameter. Furthermore, the differences among systems are enhanced at lower cooling rates. This result is consistent with those obtained in thin PS films by FSC.33,40 It also qualitatively agrees with standard calorimetric determination of the Tf of silica capped PS nanospheres.41 Furthermore, Tf values obtained on cooling at 0.1 K/s match with those obtained on PS nanospheres at a similar cooling rate by standard calorimetry in water26 and by capacitive dilatometry in
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DOI: 10.1021/acsmacrolett.7b00484 ACS Macro Lett. 2017, 6, 859−863
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and higher harmonics: ω = k2π/tp, where k in an integer. Employing basics period of tp = 0.05, 0.1, and 1 s, a frequency range between 1 and 150 Hz could be accessed. The lower panel of Figure 3 shows the normalized real part of the complex specific heat: C′p_norm = (C′p − C′pg)/(C′pm − C′pg), where C′pg and C′pm are the real part of the specific heat in the glass and melt state, respectively−as a function of temperature at 20 Hz. This frequency corresponds to a time scale comparable to the cooling rate employed to determine the total specific heat of the upper panel of Figure 3. Given the linearity of the response, Cp′ (T) contains only reversible contributions.42 Within the experimental error, all Cp′ (T) curves basically collapse on each other, indicating that the linear responses of PS nanospheres and bulk PS are identical. The linear response for all investigated systems and frequencies is shown in Figure 4, where plots of the reciprocal
nanospheres exposed to air.27 This means that Tg suppression is independent of whether PS nanospheres are surrounded by air, water, or PDMS. Figure 3 (upper panel) shows the temperature dependence tot tot of the normalized total specific heat: Ctot p norm= (Cp − Cpg )/
Figure 3. Upper panel: total specific heat, obtained as the ratio of the average heat flow rate and an underlying cooling rate of 20 K/s, as a function of temperature. Lower panel: real part of the complex specific heat at 20 Hz, obtained as the ratio of the Fourier transformation of heat flow and cooling rate signals, as a function of temperature. Both results are obtained in the same experiment based on a step-response protocol. tot (Ctot pm − Cpg ); obtained on cooling at 20 K/s from the stepmethods, as the ratio of the baseline corrected average heat flow rate and the underlying cooling rate: Ctot p = HWavg/q (see Supporting Information for details).42 This consists of both reversible and irreversible contributions and, thereby, provides information on how vitrification takes place. As can be observed, decreasing the nanospheres diameter results in a progressive lowering of the temperature range at which vitrification occurs, that is, a decrease of Tg. Furthermore, nanospheres exhibit broadening of the vitrification range, increasing with decreasing the diameter, in comparison to bulk PS. In the most extreme case, PS nanospheres with 230 nm diameter vitrify in a temperature range of ∼40−45 K. Altogether, our results, showing negative deviations from bulk behavior of both Tf and the temperature range of vitrification, indicate that PS nanospheres are able to maintain equilibrium at temperatures lower than bulk PS. Step response analysis provided the complex specific heat by Fourier transformation of the heat flow and cooling rate after a temperature jump of 2 K. Such jump ensures linearity of the response, as temperature fluctuations of supercooled liquids in the glass transition region are always larger than 2 K.43,44 This guarantees that the intrinsic molecular motion is determined in this way. The frequency dependent complex specific heat (Cp*(ω)) was determined as the ratio of the Fourier transformation of the heat flow rate (HF(t)) and the instantaneous cooling rate (q (t)):31,32
Figure 4. Reciprocal of the relaxation time as a function of the inverse temperature, obtained considering the midpoint of the step of the real part of the specific heat.
of τ as a function of the inverse of the temperature are shown. Such plot was built considering the midpoint of the step of the real part of the specific heat. The figure indicates that the invariance of molecular dynamics is verified in the whole investigated temperature range. Furthermore, Figure 4 shows that our data generally agree with those previosuly reported by dielectric relaxation and specific heat spectroscopy on both bulk PS and thin films in different configurations.15−17 Altogether our results show that delayed vitrification on cooling from the melt state in PS nanospheres is unrelated to a modification of the molecular mobility. This conclusion is straightforwardly evidenced by comparing the upper and lower panel of Figure 3, and Figures 1 and 4. Importantly this finding was achieved on samples prepared in identical conditions and, in the case of data of Figure 3, in the same experiment. In this case, the step-response protocols allow accessing simultaneously the reversible specific heat, resulting from the applied linear perturbation, and the total specific heat, originating from a nonlinear perturbation, that is, the underlying cooling ramp. The latter contains contributions to the specific heat related to the irreversibility of the vitrification process.1,42 Apart from clarifying the nonrelaxational origin of Tg suppression in confinement, our results imply that vitrification in PS nanospheres exhibit pronounced irreversibility. This is tot evident from the difference between C p_norm (T) and C′p_norm(T). In bulk PS, such a difference is tiny, implying that vitrification occurs in a sharp range and at temperatures close to those relevant for linear dynamics. At the opposite, for
t
Cp*(ω) =
∫0 p HF(t )e−iωt dt t
∫0 p q(t )e−iωt dt
(1)
Here ω is the frequency and tp the basic period of the stepresponse protocol (see Supporting Information). Equation 1 allows determining the linear response at the basic frequency 861
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nanospheres with 230 nm diameter the transformation from supercooled liquid to glass covers a broad temperature range, extending well below the temperature at which Cp_norm ′ = 0. Finally, it is worth pointing out that Cp_norm ′ plots shown in the lower panel of Figure 3 provide no indication for the presence of a layer with enhanced mobility in proximity of the interface. However, the thickness of such layer was estimated to be of the order of a few nanometers.18,45 This means that for nanospheres with the lowest investigated diameter, such a layer would correspond to a portion of material too small to be detectable by our step-response analysis. For instance, specific heat spectroscopy provided evidence for a fast component of molecular mobility for PS films with thickness smaller than 20− 30 nm,24 that is, at conditions of nanoscale confinement considerably more extreme than those of the present study. Hence, while our results do not supply any indication against the presence of a layer with enhanced dynamics at the interface, they certainly provide compelling evidence that arguments beyond the role of such interfacial layer must be accounted for to explain Tg suppression in nanoscale confinement. In summary, the present work aimed to carry out a stringent test on whether Tg suppression in polymer glasses under nanoscale confinement should be attributed to the presence of accelerated molecular mobility at the free interface or rather is a phenomenon that can be observed even in the presence of bulk-like linear dynamics. To do so, we exploited the ability of FSC to characterize all aspects of glass dynamics. Investigating PS nanospheres, we show cogent arguments in favor of the latter explanation. The main consequence of the presence of suppressed Tg in the presence of bulk-like molecular dynamics is that suitable theoretical frameworks must include purely geometric arguments to describe such suppression.
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MATERIALS AND METHODS
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ASSOCIATED CONTENT
Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +34 943018806. Fax: +34 9430158004. ORCID
Daniele Cangialosi: 0000-0002-5782-7725 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS D.C. and N.G.D. acknowledges the University of the Basque Country and Basque Country Government (Ref. No. IT-65413 (GV)), Depto. Educación, Universidades e Investigación; and Spanish Government (Grant No. MAT2015-63704-P, (MINECO/FEDER, UE)) for their financial support.
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REFERENCES
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S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00484. Atomic force microscopy (AFM) of PS nanospheres are provided. The thermal protocols to determine Tf and to carry out step-response analysis (PDF). 862
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