Study of Increasing Pressure and Nanopore Confinement Effect on the

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Study of Increasing Pressure and Nanopore Confinement Effect on the Segmental, Chain, and Secondary Dynamics of Poly(methylphenylsiloxane) K. Adrjanowicz,*,†,‡ R. Winkler,†,‡ K. Chat,†,‡ D. M. Duarte,†,‡ W. Tu,†,‡ A. B. Unni,†,‡ M. Paluch,†,‡ and K. L. Ngai§ †

Institute of Physics, University of Silesia, 75 Pulku Piechoty 1, 41-500 Chorzow, Poland Silesian Center for Education and Interdisciplinary Research (SMCEBI), 75 Pulku Piechoty 1a, 41-500 Chorzow, Poland § CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy Macromolecules Downloaded from pubs.acs.org by WESTERN UNIV on 05/08/19. For personal use only.

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ABSTRACT: The effect of increasing pressure and two-dimensional (2D) confinement on the dynamics of glass-forming polymer poly(methylphenylsiloxane) (PMPS) was investigated with the use of dielectric spectroscopy. We demonstrate that the glass-forming polymer confined to nanoporous alumina might obey the density scaling relation similar to that in the bulk and that the same value of the scaling exponent is used to superimpose the α-relaxation time measured under different thermodynamic conditions. Our comprehensive analysis of the relaxation processes detected in the dielectric loss spectra of PMPS allows us to identify the Johari−Goldstein β-relaxation which for a bulk polymer shows up as a well-resolved peak while under 2D nanoconfinement only as an excess wing. In contrast to previous studies, we provide dielectric evidence of an additional α′-relaxation, slower than the segmental (α-) dynamics, which is related to the chain dynamics of PMPS.

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interpretation from that of the common finding. At high temperature, the structural α-relaxation times τα(T) of the confined liquid are no different from the bulk according to the Vogel−Fulcher−Tammann (VFT) dependence. However, on lowering the temperature, the dynamics of the confined liquid becomes abruptly faster than in the bulk, as evidenced by a characteristic departure of τα(T) from the VFT law. Moreover, as the pore size decreases, such a departure from bulk-like behavior shifts toward higher temperature. With the help of differential scanning calorimetry (DSC), it has been demonstrated that the onset temperature associated with the deviation from bulk τα(T) signifies the glass-transition temperature of the interfacial layer, that is, the fraction of molecules which are attached and interact directly with the surface of the pore (Tg,interface).22 Then, decoupled from the interfacial layer, the molecules in the core relax faster compared to those in the bulk and vitrify at a much lower temperature (Tg,core). Moreover, it was found that below Tg,interface, the relaxation dynamics of the core molecules enters the isochoric condition, that is, when the specific volume V, as well as the density of the confined liquid becomes fixed. Cooling the core liquid under isochoric condition indicates the development of reduced or negative pressure. Therefore, the

INTRODUCTION Studies of the dynamics and transport properties of molecular liquids and polymers at the nanometer length scale have been carried out in various ways and in different configurations. The changes in the properties from that observed in the bulk are instructive. For polymers, the studies are mostly carried out on nanometer thin films either freestanding1,2 or supported on a substrate,3,4 confined in nanoporous glasses either native or silanized to avoid absorption at the surface of the nanopores,5−8 and also on polymer films confined between layered silicate inorganic hosts.9 Nanoconfinement of various polymers was studied in nanoporous alumina [anodized aluminum oxide (AAO)],10−12 which is composed of cylindrical non-crosslinking channels that are uniform in length and diameter. In the case of molecular liquids, the studies on confinement effects were reported mostly for mesoporous silica (MCM-41 and SBA-15) or nanoporous glasses (CPG or Vycor) used as the host material.13−17 When the size is reduced to nanometers, it is commonly observed that the structural relaxation becomes faster and the glass-transition temperature is reduced. The observed changes are usually explained by the finite size effect, leading to a decrease in the cooperativity of the structural relaxation.18,19 However, recent studies of van der Waals liquids including salol,20 tetramethyltetraphenyl-trisiloxane (DC704), and polyphenyl ether (5PPE), confined in AAO21 with dimension ranging from 150 to 18 nm, show a slightly different © XXXX American Chemical Society

Received: March 15, 2019 Revised: April 23, 2019

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DOI: 10.1021/acs.macromol.9b00473 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules temperature dependence of τα(T) for confined liquid can be described very well by extrapolating the corresponding isochoric dependences from the high (positive) range of pressure to a negative pressure domain. This implies that the τα(T) measured in confined geometry may obey the density scaling relation, or in other words, τα(T) is a function of ργ/T, similar to that for the bulk liquids. This expectation was verified for molecular glass-forming liquids such as salol, DC704, 5PPE, and fenofibrate constrained in nanopores. Remarkably, in all these cases, the value of the scaling exponent γ turned out to be exactly the same as that determined from the high-pressure studies of the bulk samples.20−23 This interesting finding reported for the van der Waals molecular liquids confined in AAO leads naturally to the question whether the same applies to polymeric/macromolecular systems. Or in other words, can we relate the glassy dynamics of a polymer conf ined to a nanometer scale with its macroscopic behavior? To answer this question, we have chosen poly(methyphenylsiloxane) (PMPS) and performed the same measurements and analyses of the data in bulk and when embedded within AAO nanopores. The advantage of choosing PMPS is the availability of bulk viscoelastic,24 dynamic lightscattering measurements,25,26 and dielectric measurements carried out at ambient and elevated pressures that also include testing the density scaling relation, ργ/T.27−31 The relaxation dynamics of PMPS has also been investigated in the presence of geometrical nanoconfinement via dielectric measurements of ultrathin films9,32 and nanoporous glass with size decreasing to 2.5 nm.6 The results presented in the following sections demonstrate the validity of the ργ/T scaling for nanoporeconfined PMPS with exactly the same scaling exponent γ as in the bulk. However, before studying nanoconfinement, we have also characterized the temperature T and pressure P dependence of τα(T) for bulk PMPS. It was found that a secondary relaxation with relaxation time τβ shifts with P in concert with τα, which implies that it belongs to the class of secondary relaxations bearing connection with the primary α-relaxation. Moreover, we found that the frequency dispersion of αrelaxation as well as the separation between the two relaxations given by the difference, log τα(T,P) − log τβ(T,P), is invariant to variations of T and P at constant τα(T). These interesting results noted for bulk PMPS is worth reporting in this paper as well and will be reported at the end of the Results and Discussion section.

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Mn = 23 360 and PDI of 1.16, Paluch et al. reported Tg = 245.7 K (τα = 1 s), while for PMPS of Mn = 27 300 and PDI = 1.04, Boese et al. determined Tg = 247 K (DSC).33 The fragility parameter determined for PMPS 21.7k is m = 84 (lit. 86),31 while the stretching exponent quantifying the width of the α-relaxation was found to be βKWW = 0.50 (lit. 0.51).31 From that, one can see that at 0.1 MPa (for a bulk sample), we found a very good match between our data and that reported in the literature. As confining templates, we have used commercially available AAO membranes (InRedox, USA) composed of uniform arrays of unidirectional and non-cross-linking nanopores. Isotropic AAO membranes used in this study were characterized by the following properties: (i) size: 10 ± 0.1 mm, thickness 50 ± 2 μm, pore size 20 ± 3 nm, pore density: 5.8 × 1010 cm−2, and porosity 12 ± 2%; (ii) size: 10 ± 0.1 mm, thickness 100 ± 5 μm, pore size 120 ± 14 nm, pore density: 1.5 × 109 cm−2, and porosity 16 ± 2%. Before filling, the AAO membranes were dried at 473 K in a vacuum oven for 24 h to remove any volatile impurities from the nanochannels. Then, they were used for confining of the viscous polymer. For that, a thin film of PMPS was placed on top of each AAO membrane. Infiltration was carried out at 353 K under vacuum (48 h) and then without vacuum for up to 2 weeks to ensure that the material flows into the nanopores by the capillary forces. After infiltration, the surface of the membrane was carefully cleaned using delicate dust-free wipes. Membranes were weighed before and after infiltration. The end of the filling procedure is when the mass of the confined polymer does not change with infiltration time. The estimated filling degree of PMPS in AAO nanopores achieved in this studycalculated by taking into account porosity of the membrane, density of bulk PMPS, and mass of the template before and after infiltration is expected to vary within 90− 95%. Methods. Dielectric relaxation studies were carried out by using a Novocontrol alpha analyzer. For bulk PMPS, we use standard plate− plate electrodes of 20 mm diameter separated by a Teflon spacer of 70 μm thickness. Nanoporous AAO templates (50 μm thickness and 10 mm diameter) filled with the investigated polymer were placed between two circular electrodes (diameter: 10 mm). Bulk and confined materials were measured as a function of temperature in the frequency range from 10−2 to 106 Hz. The temperature was controlled with stability better than 0.1 K by Quattro system. The dielectric spectra for nanopore-confined PMPS were collected on slow cooling with the rate of 0.2 K/min, as well as on slow heating followed by a rapid quench (∼10 K/min), as the values of the glass-transition temperatures Tg_core and Tg_interface depend on the thermal history. Therefore, it is very important to report the exact experimental protocol used for nanopore-confined samples. The glass-transition temperatures Tg_core and Tg_interface determined from dielectric and calorimetric techniques are consistent if in both cases we follow approximately the same thermal protocol. This has been already validated for different glass-forming polymers in the literature.22,34,35 The raw dielectric data of PMPS confined to AAO nanopores actually represent a combined response of alumina matrix plus polymer embedded in the pores. This would mean that in order to obtain their individual contributions, a deconvolution of both responses from the total dielectric signal of the composite is required. However, in such a nanopore-composite scenario, the only variable which will be affected is the intensity of the dielectric signal of the confined polymer, while not the position of the maximum of the loss peak, see, for example, SM in ref 11. As in this study we concentrate on the evolution of the α-relaxation time in nanopore confinement, while not on the absolute values of the dielectric strength, we have omitted doing such correction. For dielectric studies at elevated pressure, we have utilized the high-pressure system with an MP5 micropump and a control unit (Unipres, Institute of High-Pressure Physics, Warsaw, Poland). The pressure was exerted by using a silicon oil transmitted to the pressure chamber (MV1-30 vessel) by a system of capillary tubes (Nova Swiss). The real and imaginary parts of the complex permittivity were measured within the same frequency range as the atmospheric pressure data using impedance Alpha-A Analyzer (Novocontrol

EXPERIMENTAL SECTION

Materials. The polymer under study is poly(methylphenylsiloxane), labeled in the text as PMPS, with Mn·103 = 21.7 and polydispersity index (PDI) = 1.28 purchased from Polymer Source Inc. The molecular structure of PMPS is shown in Scheme 1. The sample was used as received, without further purification. The glass-transition temperature of bulk PMPS 21.7k determined from DSC measurements is Tg = 245.5 K. From the dielectric relaxation studies, we get Tg = 245.8 K. To be consistent with the literature data, we define Tg as a temperature at which τα = 1 seconds. For PMPS of

Scheme 1. Structure of PMPS 21.7k

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Figure 1. Dielectric loss spectra plotted vs frequency for (bulk) PMPS as measured under ambient pressure conditions (a) above and (b) below the glass-transition temperature. The dashed line is the fit to eq 1 with βKWW = 0.5. The dotted line in panel (a) is the slope of the low-frequency side of the α-relaxation which turned out to be almost temperature independent below 278 K. The inset shows the enlarged view of dielectric loss spectra recorded at higher temperatures. GmbH, Montabaur, Germany). The temperature was controlled by the highly dynamic temperature control system (Presto W85, Julabo). The sample was maintained between 20 mm in diameter plate−plate capacitor with a Teflon spacer and separated from the pressuretransmitting silicon oil by tightly wrapping it with a Teflon tape. Calorimetric measurements of PMPS in 20 nm AAO nanopores were carried out by using a Mettler Toledo DSC apparatus equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor (heat flux sensor with 120 thermocouples). Temperature and enthalpy calibrations were performed by using indium and zinc standards. Crucibles with prepared samples (crushed membranes containing confined PMPS or either bulk polymer) were sealed and cooled down to 173 K at the rate of 50 K/min. DSC thermograms were recorded on heating with the rate of 10 K/min over a temperature range from 153 to 323 K. Tg values were determined as the point corresponding to the midpoint inflection of the extrapolated onset and end of the transition curve. To generate isochores, a combination of pressure−volume− temperature and high-pressure dielectric relaxation measurements is required. From the first one, we get changes in specific volume (Vsp) in supercooled liquid/liquid state as a function of temperature and pressure, while from the second onethe behavior of the α-relaxation time at different combinations of T and P. For bulk PMPS, the results of dielectric relaxation studies on increased pressure as well as pressure−volume−temperature (PVT) data can be found in the literature.28−31 Using Tait’s parametrization of the PVT data,36 we switch from experimentally measured τα(T,P) to τα(T,V) dependences (see Figures 1 and 4 in ref 30). Evolution of τα as a function of T and Vsp is commonly described by using the modified temperature− volume version of the Avramov model.37 Values of the fitting parameters that we have obtained for PMPS are as follows: log10(τ0/s) = −9.87, A = 178.78 cm3γ g−γ K, D = 5.05, and γ = 5.53. Parametrized in the entire T−V plane, τα dependences were used to generate the isochoric dependences and use them to describe α-relaxation times in either positive (bulk high-pressure) or negative pressure regime (nanopores).

response of PMPS. Its temperature evolution turned out to be consistent with the dielectric α-relaxation time. Dielectric relaxation measurements of bulk PMPS at ambient pressure are shown in Figure 1a,b at temperatures above and below Tg,bulk, respectively. The frequency dependence of the α-loss peaks are well fitted by the Fourier transform of the Kohlrausch−Williams−Watts fractional exponential correlation function38,39 φ(t ) = exp[−(t /τα)βKWW ]

(1)

with βKWW = 0.50 for all temperatures above Tg. For the sake of clarity, only the fit at 245.5 K is presented in Figure 1. The temperature dependence of τα(T) at ambient pressure is thus determined. The loss spectra ε″(f) show the presence of not only the prominent α-relaxation but also a slower α′-relaxation at higher temperatures and a well-resolved β-relaxation at lower temperatures in the supercooled liquid (Figure 1a) and glassy state (Figure 1b). The α′-relaxation appears as a broad excess contribution on the low-frequency flank of the α-loss peak. We remark that the intensity of the dielectric α′-relaxation is very weak (even lower than the secondary relaxation, see Figure 1a) and becomes almost completely overlapped by the dominant α-relaxation in the vicinity of the glass transition. Therefore, the analysis of τα′(T) dependence was possible only at higher temperature regime, far above Tg. Below 278 K, the slope of the low-frequency side of the α-relaxation is s = 0.75, and it was found to be almost temperature independent. The subsequent increase of ε″(f) at lower frequencies is the conductivity contribution of no interest. The signatures of an additional relaxation process of much longer length scale than the segmental motions were also reported for PMPS based on the dynamic light-scattering studies27,33 and rheology11 while until now not in the dielectric data. As we suppose, α′-relaxation must be somehow related to the chain dynamics. However, it is rather uncertain if it can be interpreted as the normal mode, similar to that found in the dielectric loss spectra of polypropylene glycol (PPG) or cispolyisoprene (PI). According to the standard terminology, polymers can be divided into three categoriestype A, B, and Cdepending on the orientation of the dipole moment with respect to the polymer backbone. Macromolecules with a fixed

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RESULTS AND DISCUSSION Before the study of the changes caused by nanoconfinement, we characterized the relaxation dynamics of bulk PMPS, by calorimetry and dielectric relaxation. In the calorimetric response of PMPS, only a single glass-transition event is detected at Tg = 245.5 K. The temperature-modulated DSC technique has also revealed α-relaxation process associated with the glass-transition event in complex heat capacity C

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ature-independent slope of less than 1. The puzzling nature of α′-relaxation can also be discussed in terms of the dynamics of hydroxyl-terminated siloxane chains that might produce supramolecular association and hence result in the emergence of an additional relaxation process in the dielectric loss spectra, as reported for polydimethylsiloxane.44 In addition to that, based on molecular dynamics simulations and light-scattering studies, it has been suggested that the presence of α′-relaxation in PMPS might be attributed to substantial orientation correlations between the phenyl rings in the chains.45 The previous dielectric studies of bulk PMPS at various molecular weights were also not able to resolve the βrelaxation, which may belong to the special class of secondary relaxations called the Johari−Goldstein (JG) β-relaxations having properties strongly connected to that of the αrelaxation.46 There is indeed such connection of the pressure and temperature dependences of their relaxation times τβ(T,P) and τα(T,P) of bulk PMPS, but discussion of the results will be deferred. This is because the focus of this paper is on the changes in the relaxation dynamics of PMPS caused by confinement within AAO nanopores. Notwithstanding, the dielectric loss data of the bulk liquid at elevated pressures are reported in Figure 2a,b at temperatures 292 and 372 K. Although the results of the dielectric studies on increased pressure for PMPS can be found in the literature, we have decided to repeat it, to ensure that we compare the nanopore and bulk glassy dynamics for exactly the same material. The dcconductivity contribution was subtracted from the total dielectric loss by assuming that the shape of the α-relaxation process remains (T,P) invariant (see the inset in Figure 2a). Because of huge dc-conductivity which shows up in dielectric loss spectra of PMPS, we could not observe well-separated α′relaxation under elevated pressure. Nevertheless, the inset in Figure 2a demonstrates that there are some signatures of an additional chain relaxation mode also in the high-pressure dielectric data. The excess contribution on the low-frequency side of the loss peak measured at 50 MPa and 293 K has the slope of s = 0.6, indicating for the presence of chain connectivity on time scale only slightly longer than the segmental relaxation.

dipole moment along the chain are called type A polymers. For type B polymers, the dipole moment is attached perpendicular to the chain skeleton, while for type C polymers, the dipoles are in a more or less flexible side chain. There are no solely Atype polymers. However, some macromolecules might have the dipole moment component parallel (such as 1,4 cis-PI) or perpendicular (PVC) to the chain.40 Normal mode shows up in the dielectric spectra because of the accumulation of the dipole moment along to the polymer chain backbone (type A polymer). According to the theoretical calculations, the mean-square dipole moment for PMPS chains of Mw ≈ 20k is 0.6−0.7 D (see Figure 6 in ref 41). For PPG, the value of the dipole moment is quite similar, 0.57−0.64 D.42 The dipole moment of skeletal bonds in PPG is μ0(C−O) = 1 D, whereas for PMPS, μ0(Si−O) = 0.6 D. Comparison of both polymer backbones is given in Scheme 2. Scheme 2. Comparison of PPG (Left) and PMPS (Right) Backbones

As these values are quite similar, the presence of the dipole moment along the siloxane backbone and therefore normal mode contribution cannot be immediately excluded. On the other hand, except the normal mode, in the dielectric relaxation spectra of some polymers, an additional chain mode appears with a length- and time-scale intermediate between normal and segmental processes. It is due to nonzero resultant dipole moment that comes from the concerted motion of several repeat units along the chain.43 This process termed as sub-Rouse mode shares some similar characteristics with the α-relaxation. It can be detected on the low-frequency flank of the loss peak that cannot be approximated using linear frequency dependence. For PMPS 21k, we also found that the low-frequency tail of the segmental relaxation has a temper-

Figure 2. Isothermal dielectric loss spectra collected upon isothermal compression of PMPS at (a) 292 and (b) 372 K. Because of huge dcconductivity, the spectra obtained close to the glass-transition region were corrected by subtracting the conductivity contribution, while assuming the superposition for the α-relaxation [see the inset in panel (b)]. The inset in panel (a) shows a comparison of the dielectric loss spectra taken at different combinations of temperature but with approximately the same peak maximum. D

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Macromolecules The dielectric relaxation data as that presented in Figures 1 and 2 together with the PVT results enable the determination of the temperature dependence of the bulk isochoric relaxation times. Some of these curves will be extrapolated from the positive range of pressure down to negative pressures to compare with experimentally measured τα(T) of PMPS liquid confined in the AAO nanopores. Studies on nanopore confinement were performed by varying with a diameter of the AAO pores from 20 to 120 nm. Although the measurements were also carried out in 40, 60, and 100 nm pores, for clarity of the data presentation, we demonstrate here only the results for the two extreme pore sizes. Shown in Figure 3 are the representative dielectric loss

Figure 4. Dielectric loss spectra for PMPS confined within 20 nm size AAO alumina as measured below Tg_interface at few temperatures, namely, 238, 235.5, 233, and 228 K. The appearance of excess wing seems to indicate the unresolved JG relaxation in 20 nm confinement. The arrow indicates the frequency of the end of the excess wing as the JG frequency. The inset demonstrates the dielectric response of the empty alumina membrane recorded at 223 and 183 K, as well as confined PMPS as measured at 183 K (filled red symbols).

be associated with the mobility of the polymer segments which are slowed down by the interactions with the pore walls. As will be demonstrated in the further part of this paper, this mode has exactly the same temperature dependence as α′relaxation seen in the bulk where attractive interactions with the bound interface are neglected. Interestingly, the α′relaxation is much more prominent for a 20 nm confined material than in the bulk, where it is at most 10−20% of the main peak. One of the explanations of this finding is that the two-dimensional (2D) geometrical confinement induces some kind of ordering/orientation within the polymer chains which will increase the correlation between the dipole moments. The much larger width of the α-loss peak than that of the bulk liquidas quantified with the use of the β KWW parameteris shown by the example at 263 K in Figure 5a. It is due to the spatial heterogeneous dynamics of the “core” liquid in contact with the interfacial layer consisting of molecules interacting directly with the confining wall, as also observed by the others (e.g., ref 8 11,). With lowering the temperature, the segmental relaxation broadens, even more, indicating for further increase of the heterogeneous motion of segments in the pores, see Figure 5b. We can associate this effect with the kinetic freezing of the interfacial layer, at Tg_interface, which introduces an additional degree of the heterogeneity to the system. Determined from the loss peak frequencies, the relaxation times τα(T) of PMPS confined in 120 and 20 nm pores are presented as a function of the reciprocal temperature in Figure 6 and compared with τα(T) of bulk PMPS. The temperature dependence of the latter is well described by the VFT law, as shown by the dashed line in Figure 6. At high temperatures, there is no difference in τα(T) between the confined and the bulk liquid. However, on lowering the temperature, the αrelaxation of the confined sample abruptly becomes faster than that of the bulk. This effect is manifested by the departure of the τα(T) dependence from the VFT law. The departure occurs at a much shorter time scale or a higher temperature for the liquid confined in 20 nm pores than the 120 nm pores.

Figure 3. Dielectric loss spectra of PMPS confined to 20 nm in diameter alumina nanopores as recorded on slow heating with ∼0.2 K/min from 293 K down to 223 K with the step of 5 K. The inset shows the dielectric loss spectrum recorded for the confined material at 273 K with α′- and α-relaxations clearly visible together in the experimentally accessible frequency window.

spectra of PMPS liquid embedded within 20 nm size AAO nanopores collected over a wide temperature range from 203 to 293 K. At and near 293 K, only the loss from the chain modes with broad frequency dispersion appears accompanied by the conductivity contribution at lower frequencies. Starting at 273 K, the α-loss peak emerges on the high-frequency end of the chain mode as shown in the inset of Figure 3, and both processes shift to lower frequencies on a further decrease of temperature. By contrast to the spectra of bulk PMPS in Figures 1 and 2, the β-relaxation is no longer resolved as a pronounced loss peak. However, its presence is suggested by an excess wing appearing on the high-frequency flank of the αloss peak, as also shown in Figure 4. The collected results indicate that even at a very low temperature (T = 183 K), we were not able to detect any additional secondary relaxation process in the loss spectra of confined PMPS (see the inset in Figure 4). In this case, the dielectric response of nanoporeconfined material is almost the same as that of the empty membrane. Therefore, a noticeable increase of ε″ toward higher frequency is most probably related to the dielectric response of the empty membrane rather than any additional local mode whose maximum is at frequencies above the range of the instrument. Herein, it is also worth to mention that an additional slow mode seen in the dielectric response of confined PMPS cannot E

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Figure 5. (a) Comparison of the normalized dielectric loss spectra for PMPS in the bulk and when confined to 20 nm AAO nanopores at T = 263 K. The dashed lines represent the KWW fit with βKWW = 0.5 and 0.19 for bulk and nanopore-confined material, respectively. (b) Superposition of the dielectric loss spectra recorded at a few different temperatures located above (273 and 265.5 K) and below (245.5, 250.5 K) the vitrification temperature of the interfacial layer. The spectra were normalized with respect to the peaks maxima.

temperature at which we observe a characteristic kink in τα(T) dependence occurs at 253 and 261 K, respectively, in 120 and 20 nm pores. We can indeed ascribe it to the vitrification temperature of the interfacial layer as also proven by DSC, Tg_interface(DSC) = 262 K in 20 nm and Tg_interface (DSC) = 255 K in 120 nm size AAO templates. Therefore, it is rather convincing that these two effects are connected. On the other hand, for confined PMPS, the DSC thermograms are much different from that commonly recorded for molecular liquids embedded within alumina templates. Figure 7 demonstrates the occurrence of three glass-transition events in 20 nm pores, just as it was also observed for poly(methyl methacrylate) in alumina nanopores.48 This can be interpreted in terms of a three-layer model, which predicts the occurrence of not only “core” and “interfacial” layers of much different mobility but

Figure 6. Temperature evolution of the segmental (α-)relaxation time for PMPS. Filled symbols refer to the bulk sample, while the open ones refer to PMPS inside the AAO membranes with the average pore diameter of 20 and 120 nm. Temperature evolution of the αrelaxation time for the bulk material was fitted with the use of VFT equation. Below the temperature at which τα(T) for nanoporeconfined polymer starts to deviate from the bulk, we describe the data using isochoric dependences (dashed lines). The glass-transition temperature of the core molecules was defined as T at which τα = 1 s.

Previously, we have demonstrated for the three molecular liquids, salol, DC704, and 5PPE, that the departure of τα(T) from the bulk VFT dependence is due to glass transition of the interfacial layer at Tg,interface.20−22 Below that temperature, the relaxation time τα(T) of the liquid in the core assumes a much weaker temperature dependence, and vitrification will transpire at a glass-transition temperature, Tg,core, significantly lower than the bulk Tg. Faster than in the bulk glassy dynamics of PMPS was interpreted in the literature in terms of an inherent length scale of the underlying molecular motions.6 Nevertheless, more recent experimental data attribute it with density frustration and reduction in the packing density.47 For PMPS, the

Figure 7. DSC curve recorded for PMPS confined within 20 nm diameter AAO nanopores on heating with 10 K/min. Prior the sample was quenched to lower temperatures with 50 K/min. The thickness of each layer was calculated using the formula proposed by Li and coworkers.48 The inset shows derivative of heat flow upon heating. F

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Figure 8. (a) Log−log plot of glass-transition temperature Tg_core vs the glass-transition volume Vg_core (for isochores, Vg_core = V) for PMPS confined to AAO nanopores. From the slope, we get the scaling exponent γ = 5.6. The value of Tg and Vg for the bulk sample was determined assuming that the glass-transition event occurs once τα = 1 s. (b) Dependences of dielectric α-relaxation times vs the scaling quantity 1/TVγ for PMPS. The scaling plot includes confinement data, measured in the temperature range between Tg_core and Tg_interface, as well as high-pressure results of the bulk material.

also an “interlayer” composed of polymer chains constrained in between the two other fractions. However, it is not yet clear if the intermediate mobility should produce any signatures in the dielectric response of the nanopore-confined polymer. Demonstrated before in salol, DC704, and 5PPE is that below Tg,interface, the relaxation dynamics of the core molecules is governed by the isochoric condition of constant V, and the density ρ of the confined liquid is independent of temperature.20,21 This property is based on the criterion that isochoric τα(T) dependences should always collapse when plotted versus Tg/T.49 This important finding in nanoconfined molecular liquids is confirmed by the two-steps procedure. First, the isochoric τα(T) dependence of bulk liquid from the measured τα(T,P) data are generated by parametrizing τα(T,V) dependences with the use of the modified temperature−volume version of the Avramov model.37 Second, the bulk isochoric dependence τα(T) plotted against Tg,bulk/T together with τα(T) of the confined core liquid plotted against Tg,core/T should fall onto a master curve. The same procedure was successfully tested to verify that the τα(T) values measured in nanopore confinement are indeed isochoric also for PMPS. The specific volume frozen in nanopores below Tg,interface is estimated by that of the isochoric bulk τα(T,V) dependence describing well the τα(T) of the former. The latter is shown by the two dashed lines in Figure 6 with V = 0.8748 and 0.8782 cm3/g for pore sizes of 120 and 20 nm, respectively. The results show that the temperature dependence of the αrelaxation time in confined geometry can be described well by extrapolating the corresponding isochoric curves from the high (positive) range of pressure to a negative pressure domain. The other dotted line with V = 0.8708 cm3/g is the isochoric bulk τα(T,V) dependence used to determine the volume Vg of bulk PMPS at Tg,bulk = 245.8 K. Having determined the constant volume V of PMPS confined in 120 and 20 nm pores for all temperatures below Tg,interface including Tg,core, and Vg of bulk PMPS, the density scaling exponent γ of the TVγ dependence of τα(T,V) for the

confined and bulk PMPS can be obtained from a simple and well-established relation between the glass-transition temperature Tg and volume Vg, log10 Tg = A − γ log10 Vg.50,51 Because the isochoric condition is fulfilled for the confined PMPS, Vg in the relation is replaced by the constant V. By plotting log Tg,core against log V together with log Tg,bulk versus log Vg of bulk PMPS in Figure 8a, the scaling exponent γ determined from the slope of the linear dependence has the value of 5.6. Remarkably, this value of γ for confined PMPS is the same as that of bulk PMPS determined previously from the P and T dependences of τα(T,P) and the equation of state (P,V,T).30 Moreover, this value is not far from the value of 5.1 for DC704 and 5.5 for 5PPE, but much larger than other polymers such as 2.6 for polyvinylacetate, 1.9 for polyvinylethylene, and 3.0 for PI, which can be rationalized by the flexibility of the PMPS chains.52−54 The scaling parameter 5.6 is used to test the density scaling law for the nanoconfined PMPS. In Figure 8b, we have plotted isochoric α-relaxation times as a function of 1000/TVγ. Included are α-relaxation times of bulk PMPS measured along the two different isotherms (292 and 372 K) and along the atmospheric pressure isobar. The confinement data measured at fast and slow cooling rates (10 and 0.2 K/min, respectively) and bulk data at ambient and elevated pressures fall closely on a single curve when described in terms of the same scaling variable T−1V−γ, with γ = 5.6. Thus, PMPS confined in pores of different sizes and of the different thermal protocols still obeys the density scaling relation with the same exponent γ as the bulk material. Explanation of this significant experimental finding comes from the fact that density scaling is related to the intermolecular potential and the value of the scaling exponent γ is related to the slope of the repulsive part of the potential determined at a distance much smaller than that of the first peak of g(r).54−59 This feature of the intermolecular potential is not changed when going from the bulk material at ambient or elevated pressures to the confined core liquid at constant volume or under negative pressure. A G

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Figure 9. (a) Comparison of the dielectric loss spectra for bulk PMPS collected at two different combinations of (T,P) while having approximately the same α-loss peak frequency. The arrows show the location of the primitive relaxation frequency calculated from the coupling model. The analysis is based on the assumption that the α-relaxation obeys time−temperature superposition. The inset shows pressure dependence of the secondary relaxation time estimated based on the dielectric data collected at 293 K. (b) Dielectric loss spectra for bulk PMPS at four temperatures located above and below Tg at 0.1 MPa (243, 241, 238, and 236 K). Arrows indicate the location of the primitive relaxation frequency of CM. As the shape of the α-relaxation peak does not change above Tg, we artificially shift its maximum to match into the actual loss spectra collected at a lower temperature (below Tg). This procedure allows us to extend the frequency range (above that available in the experiment) and see on one spectrum the separation of the time scales between segmental and secondary processes.

to the literature value. Therefore, the results of the dielectric studies collected in nanopore confinement together with some principle relation connecting the density scaling exponent to various dynamics and thermodynamic quantities can be used, for example, to determine the pressure coefficient of the glasstransition, dTg/dP, isothermal compressibility or isobaric thermal expansion coefficient for the bulk material. Hence, it provides ready access to information that usually requires performing high-pressure experiments. The other way round, from the density scaling relation, successfully tested at various (T,P) conditions and the calorimetric analysis of nanoporeconfined material (to detect Tg_interface), it is possible to predict the behavior of α-relaxation dynamics in 2D confinement, with no need of the direct measurements. As mentioned in the Introduction section, we found a wellresolved secondary relaxation of bulk PMPS not noted before by others. This finding offers an opportunity to investigate the pressure and temperature dependences of its relaxation time τβ(T,P) to ascertain whether it is the JG β-relaxation connected with the α-relaxation in dynamic and thermodynamic properties. Also found is a process slower than the α-relaxation in both bulk and nanoconfined PMPS, and its origin needs clarification. The results from these investigations are reported just below. Secondary relaxation having dynamic and thermodynamic properties mimicking those of the primary α-relaxation is potentially of fundamental importance.61−63 One property is the pressure dependence of its τβ(T,P). The best evidence of the pressure dependence is the loss data measured at 293 K at different pressures (Figure 2). The β-relaxation is resolved as broad loss peaks at 170 and 210 MPa, and the shift of the maximum loss with increasing pressure verifies that τβ is pressure dependent. It would be optimal if the α-relaxation is observed at the same pressure and temperature conditions. Unfortunately, the presence of the conductivity at lower frequencies, which is insensitive to pressure, preempts direct observation of the α-loss peak at 210 MPa. Notwithstanding, the α-loss peaks at lower pressures than 210 MPa were recovered by subtracting the conductivity relaxation in the manner as shown by the isothermal spectra at 373 K in Figure 2b, and the τβ(T,P) determined and fitted by the pressure

number of corroborative evidence has been given to show that the density scaling of τα(T,P) actually originates from that of τβ(T,P).59,60 From the more local nature of the JG β-relaxation, we expect that the density scaling of τβ(T,P) will be unchanged by nanoconfinement and consequently also for τα(T,P). On the other hand, it is puzzling why other properties of the αrelaxation including glass-transition temperature and isobaric fragility are drastically changed when nanoconfined, but γ is unchanged? So far, the density scaling idea was tested for low-molecularweight glass-forming liquids confined to AAO nanopores. This is the first example of the confined polymer which also shows such behavior, meaning that the finding that the density scaling idea can be satisfied under 2D confinement is a more universal observation, not essentially limited to a particular system. It is also worth noting that the principle idea of the density scaling is that the mean relaxation time (not the dielectric strength or its distribution) measured under different thermodynamic conditions scales as 1/TVγ. This is the reason why we have focused only on the (mean) time scale of the segmental dynamics. So far, there is no scaling approach which will account for the dielectric strength or shape of the relaxation process in glass-forming systems (neither in the bulk nor under nanoscale confinement). The validity of the density scaling idea in nanoporeconfinement opens an exciting possibility to connect or even predict the macroscopic and nanoscale behavior of glassforming liquids and polymers. As an example, we give here EV/ EP quantity, that is, the ratio of the first derivatives of the τα(T) dependences measured at constant volume and constant pressure, which quantifies the importance of density fluctuations (=0) and thermal energy (=1) on the glassy dynamics. For bulk PMPS, the EV/EP ratio determined at Tg (τα = 1 s) is 0.526 ± 0.06, which indicates that a change in temperature as to the change in thermal energy produces a similar effect on its glassy dynamics as the volume change induced by compression.30 However, EV/EP can also be determined from the results obtained in nanoconfinement. The ratio of the activation energies calculated at Tg_interface for PMPS confined within 120 nm AAO nanopores (EV) together with ambient pressure isobar (EP) gives 0.57, which stays close H

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Macromolecules analog of the VFT law as shown in the inset of Figure 9b. Extrapolating the dependence to 210 MPa enables us to obtain an estimate of τα(T,P) at P = 210 MPa and T = 292 K, which is approximately the same as τα(T,P) of the spectrum at P = 0.1 MPa and T = 241 K shown in Figure 1. By inspection of Figure 9a, it is clear that the β-loss peaks at the two different combinations of P and T are located in the same spectral range, and the frequency of the loss peaks are approximately the same. Thus, our dielectric loss data of bulk PMPS provide another example of the invariance of the separation between the two relaxations or the ratio τα(T,P)/τβ(T,P) to large variations P and T and corresponding thermodynamic conditions. This property found before in many molecular systems55,64−72 and a few polymers60,73−75 indicates the fundamental importance of the JG β-relaxation in its strong connection to the α-relaxation. Another general property of the JG β-relaxation is the approximate correspondence between the τβ(T,P) and the primitive relaxation time τ0(T,P) calculated from the Coupling Model equation τα(T , P) = [tc−nτ0(T , P)]1/ [1 − n]

Figure 10. Complete relaxation map which includes segmental (α-), normal mode (α′-), and secondary relaxation of PMPS, both in the bulk and under 2D nanoconfinement. Filled symbols refer to the bulk sample, while the open ones refer to PMPS inside AAO membranes with the average pore diameter of 20 and 120 nm. Temperature evolution of the α-relaxation time for bulk material was fitted with the use of VFT equation, while the secondary relaxation with the use of Arrhenius equation. Below the temperature at which τα(T) for nanopore-confined polymer starts to deviate from the bulk, we use isochoric dependences (dashed lines). Dependences of τα and τα′ for PMPS 10k obtained with the use of PCS and rheology (PMPS 29.5k) were taken from the literature.11,27

(2)

where (1 − n) is the Kohlrausch exponent βKWW in eq 1, and for PMPS, its value is 0.50 at a temperature near Tg. Basically, the primitive relaxation is the precursor of the distribution of processes composing the JG β-relaxation, and therefore, only approximate agreement of τβ(T,P) and τ0(T,P) in their orders of magnitude can be expected and it is emphasized by writing the relation as τβ(P , T ) ≈ τ0(P , T )

workers on PMPS with Mw = 29.5 kg/mol.11 As τη(T) is many orders of magnitude longer than τα′(T) but Mw of the two PMPS differ by less than 10%, we can distinguish the α′relaxation from the terminal relaxation. Previously, the study of PMPS of lower Mw = 5 kg/mol24 has found the α′-relaxation, and because the molecular weight is so low, it was interpreted as the sub-Rouse modes. In that case, the separation between α′ and α modes do not exceed more than 2−3 decades, as revealed from photon correlation spectroscopy study. Included in Figure 10 are the τα′(T) data of PMPS with Mw = 10 kg/mol obtained from PCS measurements by Patkowski and coworkers.27 The separation of the α′-relaxation from the αrelaxation measured by [log τα′(T) − log τα(T)] does not change much with increasing Mw from 5, 10, and up to 27.7 kg/mol (the present sample), which is in accord with the interpretation of the α′-relaxation as the sub-Rouse modes of PMPS. Although the data are limited, τα′(T) of PMPS does not seem to change as much as τα(T) by nanoconfinement. Our finding is consistent with the sub-Rouse relaxation times having weaker temperature dependence at constant pressure, pressure dependence at constant temperature, and thickness dependence of polymer thin films than segmental α-relaxation time τα(T).77 The experimental evidence from studies of various polymers of these thermal-rheological, piezo-rheological, TVγ-rheological, and thickness-rheological complexities can be found in ref 78. PMPS has all of these complexities except thickness-rheological, but it is replaced by nanosizerheological complexity. The α′-relaxation seen in the dielectric loss spectra of nanopore-confined PMPS cannot be interpreted in terms of the surface-induced mode (interfacial relaxation). The polymer segments immobilized at the pore walls and therefore revealing much slower dynamics vitrify at Tg_interface which we know to depend on the pore diameter. Because of the very small intensity, the interfacial dynamics could not be directly

(3)

The best situation in an experiment to verify this approximate relation is where the β-relaxation is resolved, and β-loss peak frequency, f max(T,P), provides directly a characteristic frequency to compare with f 0(T,P) = 1/ [2πτ0(T,P)] and to verify relation 3. The location of the calculated f 0(T,P) for the two spectra in Figure 9a is indicated by the two arrows. As can be seen, there is an approximate agreement between f max(T,P) and f 0(T,P), and thus relation 3 is verified. The results imply density scaling of τβ(T,P) and τα(T,P) with the one and the same scaling exponent γ as found in other systems.59,76 The same procedure to calculate f 0(T) was applied to ambient pressure data at four temperatures of 243, 241, 238, and 236 K. The vertical lines of the same color as the data shown in Figure 9b indicate that the calculated f 0(T,P) is in approximate agreement with f max(T). As already noted, the dielectric loss spectra collected for PMPS confined in 20 nm alumina nanopores show a clear excess wing seen in the temperature range Tg_interface. This indicates for the unresolved JG relaxation also present under nanoconfinement. Interestingly, by taking the frequency of the end of the excess wing as the JG frequency, we found that the corresponding relaxation times are nearly the same as the JG relaxation times for the bulk sample (see open stars added to the relaxation map presented in Figure 10). Finally, we come back again to α′-relaxation observed in the dielectric loss spectra of bulk as well as nanopore-confined PMPS. The α′-relaxation times, τα′(T), are presented versus the reciprocal of temperature in Figure 10 together with τα(T), τβ(T) of bulk, and nanconfined PMPS with Mw = 27.7 kg/mol. Added in the figure are the terminal chain relaxation times τη(T) from rheological measurements by Floudas and coI

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followed in the dielectric loss spectra of nanoconfined PMPS. Nevertheless, the presence of such an interfacial layer still affects the segmental mobility of the confined polymer, which we see as a kink in τα(T) dependence at the temperature where the interfacial mobility becomes frozen.

REFERENCES

(1) Forrest, J. A.; Dalnoki-Veress, K. The Glass Transition in Thin Polymer Films. Adv. Colloid Interface Sci. 2001, 94, 167−195. (2) Alcoutlabi, M.; McKenna, G. B. Effects of Confinement on Material Behaviour at the Nanometre Size Scale. J. Phys.: Condens. Matter 2005, 17, R461−R524. (3) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Size-Dependent Depression of the Glass Transition Temperature in Polymer Films. Europhys. Lett. 1994, 27, 59−64. (4) Forrest, J. A.; Dalnoki-Veress, K.; Stevens, J. R.; Dutcher, J. R. Effect of Free Surfaces on the Glass Transition Temperature of Thin Polymer Films. Phys. Rev. Lett. 1996, 77, 2002−2005. (5) Schönhals, A.; Goering, H.; Schick, C.; Frick, B.; Zorn, R. Glassy Dynamics of Polymers Confined to Nanoporous Glasses Revealed by Relaxational and Scattering Experiments. Eur. Phys. J. E 2003, 12, 173−178. (6) Schönhals, A.; Goering, H.; Schick, C.; Frick, B.; Zorn, R. Glass Transition of Polymers Confined to Nanoporous Glasses. Colloid Polym. Sci. 2004, 282, 882−891. (7) Jackson, C. L.; McKenna, G. B. The Glass Transition of Organic Liquids Confined to Small Pores. J. Non-Cryst. Solids 1991, 131-133, 221−224. (8) Wübbenhorst, M.; Napolitano, S. Dynamics in Geometrical Confinement. In Advances in Dielectrics; Kremer, F., Ed.; Springer International Publishing: Cham, 2014. (9) Anastasiadis, S. H.; Karatasos, K.; Vlachos, G.; Manias, E.; Giannelis, E. P. Nanoscopic-Confinement Effects on Local Dynamics. Phys. Rev. Lett. 2000, 84, 915−918. (10) Alexandris, S.; Sakellariou, G.; Steinhart, M.; Floudas, G. Dynamics of Unentangled cis-1,4-Polyisoprene Confined to Nanoporous Alumina. Macromolecules 2014, 47, 3895−3900. (11) Alexandris, S.; Papadopoulos, P.; Sakellariou, G.; Steinhart, M.; Butt, H.-J.; Floudas, G. Interfacial Energy and Glass Temperature of Polymers Confined to Nanoporous Alumina. Macromolecules 2016, 49, 7400−7414. (12) Li, L.; Zhou, D.; Huang, D.; Xue, G. Double Glass Transition Temperatures of Poly(Methyl Methacrylate) Confined in Alumina Nanotube Templates. Macromolecules 2014, 47, 297−303. (13) He, F.; Wang, L. M.; Richert, R. Dynamics of Supercooled Liquids in the Vicinity of Soft and Hard Interfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 144205. (14) Trofymluk, O.; Levchenko, A. A.; Navrotsky, A. Interfacial Effects on Vitrification of Confined Glass-Forming Liquids. J. Chem. Phys. 2005, 123, 194509. (15) Zhang, J.; Liu, G.; Jonas, J. Effects of Confinement on the Glass Transition Temperature of Molecular Liquids. J. Phys. Chem. 1992, 96, 3478−3480. (16) Brás, A. R.; Frunza, S.; Guerreiro, L.; Fonseca, I. M.; Corma, A.; Frunza, L.; Dionísio, M.; Schönhals, A. Molecular Mobility of Nematic E7 Confined to Molecular Sieves with a Low Filling Degree. J. Chem. Phys. 2010, 132, 224508. (17) Morineau, D.; Xia, Y.; Alba-Simionesco, C. Finite-Size and Surface Effects on the Glass Transition of Liquid Toluene Confined in Cylindrical Mesopores. J. Chem. Phys. 2002, 117, 8966−8972. (18) Arndt, M.; Stannarius, R.; Groothues, H.; Hempel, E.; Kremer, F. Length Scale of Cooperativity in the Dynamic Glass Transition. Phys. Rev. Lett. 1997, 79, 2077−2080. (19) Kremer, F.; Huwe, A.; Arndt, M.; Behrens, P.; Schwieger, W. How Many Molecules Form a Liquid? J. Phys.: Condens. Matter 1999, 11, A175−A188. (20) Adrjanowicz, K.; Kaminski, K.; Koperwas, K.; Paluch, M. Negative Pressure Vitrification of the Isochorically Confined Liquid in Nanopores. Phys. Rev. Lett. 2015, 115, 265702. (21) Adrjanowicz, K.; Kaminski, K.; Tarnacka, M.; Szklarz, G.; Paluch, M. Predicting Nanoscale Dynamics of a Glass-Forming Liquid from Its Macroscopic Bulk Behavior and Vice Versa. J. Phys. Chem. Lett. 2017, 8, 696−702. (22) Adrjanowicz, K.; Kolodziejczyk, K.; Kipnusu, W. K.; Tarnacka, M.; Mapesa, E. U.; Kaminska, E.; Pawlus, S.; Kaminski, K.; Paluch, M.

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CONCLUSIONS We studied the effect of increasing pressure and 2D confinement on the glass-transition dynamics of PMPS using dielectric relaxation spectroscopy. We showed that the glassforming polymer confined within nanoporous alumina templates might obey the density scaling relation as in the bulk. The same value of the scaling exponent used to superimpose the α-relaxation time in the bulk and under nanoscale confinement opens an exciting possibility to connect or even predict the macroscopic and nanoscale behavior of glass-forming polymers, the same as it applies to molecular liquids. However, for polymer materials, which in general show a pronounced influence of the pressure/volume effects on the dynamics, deviation from the bulk-like behavior in 2Drestricted geometry is manifested more clearly. In the dielectric loss spectra, the confinement effect results in a characteristic kink of the τα(T) dependence and a significant broadening distribution of the relaxation times, while in the calorimetric data, we detect the presence of three glass-transition events associated with the dynamics of core, interfacial, and interlayer fractions of the molecules. This study also provides a comprehensive analysis of the relaxation modes detected in the dielectric response of PMPS. We use high-pressure data to demonstrate that the secondary relaxation detected in the glassy state of PMPS is a JG βrelaxation that for a bulk polymer shows up as a well-resolved peak, while under 2D nanoconfinement by an excess wing appearing on the high-frequency flank of the α-loss peak. In contrast to the previous study, we report the presence of the additional α′-relaxation associated with the chain mobility in dielectric response of PMPS. Its intensity is much weaker than the dominant segmental (α-)relaxation but still clearly visible at higher temperatures for the bulk sample as well as in nanopores. The separation of the α′-relaxation from the αrelaxation was found not to change much in nanoconfinement. The behavior of such α′-mode in the dielectric response of siloxane-chain-based polymers, observed both on increased pressure and in the nanopores, is of great interest to investigate further.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

K. Adrjanowicz: 0000-0003-0212-5010 K. Chat: 0000-0002-6972-2859 W. Tu: 0000-0001-8895-4666 K. L. Ngai: 0000-0003-0599-4094 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Centre (Poland) within the project OPUS 14 nr. UMO-2017/27/B/ ST3/00402. M.P. acknowledges the financial supported from the National Science grant no. DEC 2014/15/B/ST3/00364. J

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DOI: 10.1021/acs.macromol.9b00473 Macromolecules XXXX, XXX, XXX−XXX