Dynamics of Entangled cis-1,4-Polyisoprene Confined to Nanoporous

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Dynamics of Entangled cis-1,4-Polyisoprene Confined to Nanoporous Alumina Christos Politidis,† Stelios Alexandris,† Georgios Sakellariou,‡ Martin Steinhart,§ and George Floudas*,† †

Department of Physics, University of Ioannina, 45110 Ioannina, Greece Department of Chemistry, National and Kapodistrian University of Athens, 15771 Athens, Greece § Institut für Chemie neuer Materialien, Universität Osnabrück, D-49069 Osnabrück, Germany ‡

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S Supporting Information *

ABSTRACT: The dynamics of a series of entangled cis-1,4-polyisoprenes located within self-ordered nanoporous alumina templates are studied as a function of the degree of confinement, 2Rg/d (Rg is the radius of gyration and d is the pore diameter) with dielectric spectroscopy and temperature-modulated differential scanning calorimetry. For the higher molecular weights, the segmental dynamics obtained on cooling speed-up under confinement resulting in a lower glass temperature, Tg, with respect to the bulk, scaling as ΔTg = −62 × (2Rg/ d). This effect is discussed in terms of the proposed relation of the glass temperature to the interfacial energy. Under confinement, a new process appears with an Arrhenius temperature dependence and with a dielectric strength that increases linearly with the increasing degree of confinement. This mode is discussed in terms of the adsorption/desorption kinetics of segments in the vicinity of the pore walls. The particular geometry employed here with the electric field being parallel to the polymer/surface interface maximizes the contribution of adsorbed segments. Moreover, with temperature-modulated differential scanning calorimetry and dielectric spectroscopy, we address the origin of the dual glass temperature, Tg, found on the heating traces. By employing several temperature/annealing protocols, we show that the higher Tg is conditional; it appears only when the lower Tg is crossed on the previous cooling run. These findings could suggest that the lower Tg is the one closer to equilibrium.

I. INTRODUCTION A challenge in several emerging technologies is the requirement for smaller, more efficient, and smarter devices. However, the properties of polymeric materials close to interfaces are significantly different from the bulk.1 Much of this behavior stems from the fact that at interfaces the local structure, or “packing” of monomers, differs from the bulk, due to polymer−substrate interactions.2−6 Understanding the role of packing and of interfacial interactions will enable the design of polymer interfaces with controlled physical properties (wettability, adhesion, aging, viscosity, glass temperature, and associated dynamics) required for a number of applications (coatings, membranes, and organic electronic devices). Earlier works studied the effect of confinement on the dynamics of type-A polymers including cis-1,4-polyisoprene (PI) and poly(propylene glycol) (PPG).7−18 Type-A polymers are advantageous, especially for dielectric studies, because of the non-zero components of the dipole moment perpendicular and parallel to the chain contour giving rise to the respective segmental and global chain modes (the latter being a sum of several normal modes). In these studies, the confining medium varied from three-dimensional (3D) (in controlled porous glasses)7,13,18 to one-dimensional (1D) (in thin polymer films).8−11,14 Because of the different polymer/substrate © XXXX American Chemical Society

interactions, several contradictory results emerged from these studies. Nevertheless, there is a consensus that for PIs bearing molecular weights below the entanglement molecular weight (Me ∼ 5000 g/mol) there is a broadening of the segmental and chain mode dynamics under confinement.7,15 For higher molecular weights a new mode was reported at frequencies intermediate to the bulk segmental and normal mode processes. The latter mode was attributed to the dynamic adsorption/desorption process of chain segments that resulted in a faster sub-chain relaxation of suppressed intensity.7,9,14 Self-ordered nanoporous aluminum oxide (AAO) contains arrays of parallel, cylindrical nanopores that can be employed as a model system in studying the effect of two-dimensional (2D) confinement on polymer conformation and dynamics. 19−22 Recent progress in this field has been the demonstration for successful imbibition of different polymers within AAO and the elucidation of the imbibition mechanisms. It was shown that the effective viscosity the chains are experiencing during imbibition can differ by orders of magnitude from its bulk value.23−26 Polymer imbibition has Received: March 14, 2019 Revised: April 19, 2019

A

DOI: 10.1021/acs.macromol.9b00523 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules been discussed by two competing mechanisms. The first is the standard hydrodynamic flow resulting in a parabolic flow profile.24 According to this mechanism, a strongly attractive surface to the polymer creates a layer of immobile chains, resulting in an increase of the effective viscosity and slower imbibition. The other mechanism is based on the reptation model, leading to a plug flow profile and to the reduction in the effective viscosity (faster imbibition).23,24 Other studies of amorphous polymers within AAO explored the chain conformation and chain mobility issues.27−38 It was shown that interfacial energy39,17 plays a significant role in controlling the segmental dynamics of polymers under confinement within AAO. A general trend for a decreasing glass temperature relative to the bulk with increasing interfacial energy was demonstrated. Here, we explore the effect of 2D confinement on the segmental and chain dynamics of a series of entangled PIs. All earlier investigations on type-A polymers (PPG, PI) located inside AAO were made in low molecular weight unentangled or lightly entangled polymers.15−17 In the case of 1,4-PI, the main effect of confinement was the broadening of both segmental and chain modes.15 In the case of PPG, confinement resulted in the speed-up of segmental dynamics.16 Furthermore, annealing effects in the latter system were found to systematically affect the segmental dynamics. Entangled chains, on the other hand, can mitigate polymer/surface interactions further away from the interface. For the higher molecular weights employed here, the segmental dynamics of PI obtained on cooling consistently speed-up under confinement resulting in a lower glass temperature, Tg. This effect is discussed in view of the proposed relation of the glass temperature to the interfacial energy. Under confinement, a new process is evidenced with an Arrhenius temperature dependence. This mode is attributed to the adsorption/desorption kinetics of segments in the vicinity of the pore walls. Moreover, by employing several thermal protocols in temperature-modulated differential scanning calorimetry and dielectric spectroscopy (DS) we address the origin of the dual glass temperature, Tg, found on the heating traces. The results suggest that the lower Tg is closer to equilibrium under confinement.

Table 1. Molecular Characteristics, Gyration Radii, and Glass Temperatures from DSC (Rate 10 K/min) and DS (at τ ∼ 100 s) sample PI PI PI PI PI

Mn (kg/mol)

Mw (kg/mol)

PDI

Rg (nm)

TgDSC (K)

TgDS (K)

8.5 13.5 20.0 50.0 100.0

8.8 14.3 20.8 52.5 106.0

1.04 1.06 1.04 1.05 1.06

3.0 3.8 4.6 7.2 10.2

208 208 210 208 211

206 207 206 206 209

8.5 13.5 20 50 100

was obtained (i) following the infiltration kinetics as a function of time (according to the modified Lucas−Washburn relation)23−26 and (ii) by weighing the templates before and after each infiltration to constant mass. II.III. Scanning Electron Microscopy (SEM). Scanning electron microscopy (SEM) measurements were made using an LEO Gemini 1530 SEM, operated at acceleration voltages from 0.75 to 6 kV. SEM images of the empty and infiltrated AAO templates revealed a homogenous surface containing pores organized in a hexagonal lattice with a narrow distribution of pore diameters (Figure S2, Supporting Information). II.IV. Temperature-Modulated Differential Scanning Calorimetry (TM-DSC). Temperature-modulated differential scanning calorimetry (TM-DSC) measurements were made with a Q2000 (TA Instruments) using cooling/heating rates in the range of 10−1 K/min and oscillation periods from 20 to 200 s. A specific rate/period pair was employed for each measurement according to β=

ΔTg nP

60 s/min

(1)

Here, β is the cooling/heating rate, ΔTg is the full width at half height of Tg, n is the number of cycles across the Tg width, and P is the oscillation period. For PI, ΔTg = 20 °C and the number of cycles used was n = 6 for efficient deconvolution of the modulated signal. The rate/period pairs used in this study were: 20 s, 10 °C/min; 40 s, 5 °C/ min; 60 s, 3.3 °C/min; 80 s, 2.4 °C/min; 100 s, 2 °C/min; 150 s, 1.3 °C/min, and 200 s, 1 °C/min. In addition, standard differential scanning calorimetry (DSC) measurements were made using different cooling/heating rates in the range of 20−1 K/min. The instrument was calibrated for best performance in the specific temperature range and heating/cooling rate. The calibration sequence included a baseline calibration for the determination of the time constants and capacitances of the sample and reference sensor using a sapphire standard, an enthalpy and temperature calibration for the correction of thermal resistance using indium as a standard (ΔH = 28.71 J/g, Tm = 428.8 K), and a heat capacity calibration with sapphire as a standard. Samples used in the DSC were prepared by etching of the infiltrated AAO templates, so as to remove the Al bottom, followed by smooth grinding. Five different thermal protocols were employed: (i) TM-DSC measurements on heating and cooling in the temperature range from −120 to 40 °C with different oscillation periods and heating/cooling rates, (ii) TM-DSC measurements on heating with a rate of 10 °C/min and an oscillation period of 20 s following annealing at −120 °C for different annealing times in the range of 5− 120 min after cooling with a rate of 10 °C/min from 40 to −120 °C, (iii) standard DSC measurements on heating, all with a rate of 10 °C/ min, following cooling with different rates in the range of 10−1 °C/ min, (iv) standard DSC measurements on heating with a rate of 20 °C/min following cooling from 40 °C to a temperature located between the two Tgs (T ≈ −65 °C) and (v) TM-DSC measurements on heating with different rates and oscillation periods following quenching in a liquid nitrogen bath. Quenching experiments were made by placing the samples in a liquid nitrogen bath (−170 °C) after annealing at 40 °C for 1 h. This procedure was repeated before every TM-DSC heating measurement for different heating rates and oscillation periods.

II. EXPERIMENTAL SECTION II.I. AAO Templates. Self-ordered AAO (pore diameters of 25, 35, 65, and 400 nm; pore depth of 100 μm) was prepared following previously reported procedures.19−22 In addition, the templates were characterized for conicity using a focused ion beam. A small deviation from parallelism was found. Al with a thickness of about 1 mm at the bottom of templates served as the lower electrode. Prior to infiltration, all AAO templates were placed in an oven under vacuum at a temperature of 170 °C for 8−10 h. This procedure removes the majority of OH groups from the AAO surface. II.II. Samples and Method of Infiltration. cis-1,4-Polyisoprene (PI) (the microstructure was 93% 1,4 and 7% 3,4 units) was synthesized via anionic polymerization following standard procedures.40 Their molecular characteristics and glass temperatures are shown in Table 1. Infiltration of PIs inside AAO was performed under vacuum ( 0.2. The strength of the intermediate process has an approximately linear dependence with the

Figure 4. (a) Dielectric loss curves as a function of frequency for PI 50 kg/mol located inside AAO with a pore diameter of 25, 35, 65, and 400 nm at 248 K. Arrows indicate the approximate position of the intermediate process. (b) Dependence of the dielectric strength ratio of the intermediate to the segmental process on the degree of confinement (2Rg/d). The line is the result of a linear fit.

increasing degree of confinement, as Δεint/Δεα = 2.4 × (2Rg/ d) as shown in Figure 4b.

Table 2. VFT Parameters for the Segmental and Global Chain Relaxation, and DS Glass Temperatures of cis-1,4-Polyisoprenes in the Bulk Employed in This Study α-process sample (kg/mol) PI PI PI PI PI

8.5 13.5 20 50 100

τ0 (s)a

Mn (g/mol) 8.5 1.35 2.0 5.0 1.0

× × × × ×

103 104 104 104 105

1 1 1 1 1

× × × × ×

10−12 10−12 10−12 10−12 10−12

B (K) 1270 1252 1312 1259 1269

± ± ± ± ±

10 8 8 6 3

longest chain mode T0 (K) 168 169 166 167 170

± ± ± ± ±

2 2 2 2 2

τ0 (s) 8 2.9 1.4 7.6 5.4

× × × × ×

10−9 10−8 10−7 10−6 10−5

B (K) 1521 1512 1486 1285 1322

± ± ± ± ±

14 10 11 69 96

T0 (K) 158 160 161 170 172

± ± ± ± ±

1 1 1 3 4

Tg (K) (DS)b 206 208 206 206 209

± ± ± ± ±

1 1 1 1 1

Held fixed to the value τ = 10−12 s. bAt τ = 100 s.

a

D


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Macromolecules The relaxation times, τmax, (i.e., the relaxation times at maximum dielectric loss) for all processes corresponding to temperatures above the glass temperature are depicted in Figure 5.

desorption process of segments in the vicinity of the pore walls (see below). This energy can be compared with the energy of adhesion, Eadh, defined as Eadh = (NA/N*) × Wadh × A, where the work of adhesion is, Wadh = γSP(1 + cos θο), γSP is the interfacial energy (γSP = 9.5 × 10−3 N/m)39 and θο is the Young’s contact angle (cos θο = 0.88),39 A is the pore surface area and N* is the number of segments in contact with the pore walls (scaling as N1/2 for a single Gaussian chain, N is the number of repeat units on the polymer backbone). The estimated energy of adhesion (∼200 kJ/mol) is higher than the activation energy of the intermediate process (7 kJ/mol) being closer to the activation energy of the segmental process (∼50 kJ/mol) at 290 K. This may reflect the fact that other forces are present that greatly increase the energy of adhesion. A mode intermediate to the segmental and chain modes in cis-1,4-polyisoprenes has already been reported when confinement is in 1D (in thin films)9,14 and in 3D (in controlled porous glasses).7 In all cases, it was attributed to the adsorption/desorption process of polymer segments giving rise to a faster sub-chain relaxation of reduced relaxation strength. The intermediate mode here bears several similarities and one major difference to 1D and 3D confinement. When confinement is in 2D, its dielectric strength is a strong function of the degree of confinement. The prediction is that under conditions of stronger confinement, i.e., when 2Rg/d ∼ 1, this will become the dominant process for 1,4-PI. Evidently, cylindrical confinement is preferential for this mode and there is a simple (geometrical) reason for this. The direction of the applied electric field within the nanopores is parallel to the pore axis and hence to the alumina/polymer interface. This geometry maximizes the dipole contribution of adsorbed PI segments since their dipole moment is parallel to the electric field. Contrast this with polymer films where the polymer/ substrate interface is perpendicular to the applied electric field, in this case, the contribution from adsorbed PI segments is minimal. These results on the intermediate process can be discussed in view of recent molecular dynamics (MD) simulations for 1,4-polybutadiene confined between two graphite walls (i.e., 1D confinement).57 MD results have shown that weakly attractive forces between the wall and individual segments can bind the polymer near the wall. By analyzing the intermediate incoherent scattering function, it was shown that the adsorption/desorption process of individual segments has an Arrhenius temperature dependence over a broad range of temperatures with an activation energy of ∼37 kJ/mol. At lower temperatures, this process merged with the segmental (α-) process, the latter with the usual VFT temperature dependence. The Arrhenius process found experimentally has time scales that at higher temperatures (T ∼ Tg + 50 K) are ∼5 decades slower than the segmental process. On lowering the

Figure 5. Arrhenius relaxation map for the segmental (open symbols) and the most intense chain mode (filled symbols) processes of bulk PI 20 and 100 kg/mol (black square symbols) as well as for PI 20 and 100 kg/mol located inside self-ordered AAO with pore diameters of 400 nm (red circles), 65 nm (up triangles), 35 nm (down triangles), and 25 nm (rhombi). Data were obtained on cooling from higher temperatures. In the case of confined PI, confinement-induced processes (crossed symbols) are also shown. The uncertainty in the relaxation times is smaller than the symbol size for 20 kg/mol and approximately the symbol size for 100 kg/mol. Gray-filled symbols are from TM-DSC (obtained on cooling). The lines represent VFT fits.

The shown DS relaxation times were obtained during cooling from the higher temperatures. The importance of the particular thermal protocol will become apparent later. The figure shows a speed-up of the segmental process upon confinement independent of molecular weight (for M > Me). This finding is further confirmed by temperature-modulated DSC experiments obtained on cooling, that will be discussed in detail below (TM-DCS data are shown for some selected pore sizes for the two molecular weights in Figure 5). For PI 20 kg/ mol located inside AAO templates with diameters of 400−25 nm, the most intense chain mode is still visible and its relaxation times are included in the figure (filled symbols). A slower process with an Arrhenius temperature dependence is also evident and is attributed to a Maxwell−Wagner−Sillars polarization of heterogeneous dielectrics.41 For PI 100 kg/mol located inside AAO templates with a diameter of 400 nm, the most intense chain mode is still evident with similar relaxation times to the bulk polymer (filled squares and spheres). However, in the smaller pores, the dynamics are dominated by the intermediate process. This process has an Arrhenius temperature dependence with a small activation energy (typically ∼ 7 kJ/mol). It is attributed to the adsorption/

Table 3. VFT Parameters for the Segmental Modes and DS Glass Temperatures of PI with Mn = 20 kg/mol Located Inside AAO with Different Pore Diameters PI 20 kg/mol VFT parameters

bulk

400 nm

65 nm

35 nm

25 nm

τ0 (s)a B (K) T0 (K) Tg (K) (DS)

1 × 10−12 1312 ± 8 166 206

1 × 10−12 1488 ± 47 158 ± 2 204

1 × 10−12 1640 ± 37 147 ± 2 198

1 × 10−12 1782 ± 17 138 ± 1 194

1 × 10−12 1852 ± 31 130 ± 1 188

Held fixed at τ = 10−12 s.

a

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advancing contact angle θadv > θ0 (when the contact line moves to the side of the free solid surface), and the receding contact angle θrec < θ0 (when the contact line moves to the side of the liquid). As a next step the surface energy of alumina, γSV, is needed. To this end we measured advancing and receding contact angles of several reference liquids on a flat alumina surface that was prepared in the same way as the AAO membranes resulting in γSV = 36.3 ± 0.5 mN/m.39 We found that interfacial tension plays a significant role in the segmental dynamics of polymers under confinement within AAO. There is a trend for a decreasing glass temperature relative to the bulk with increasing interfacial energy. PDMS exhibits the highest interfacial energy and the highest reduction in glass temperature within AAO. However, unentangled PIs did not follow the proposed scaling.15 In Figure 7, we present a summary of

temperature, the two processes approach and coincide at a temperature approximately near the bulk Tg (Tx = 208 K). Following the arguments provided by the MD simulations,57 the adsorption/desorption process of the whole chain will be much slower given the high number of segments in contact with the wall (scaling as N1/2 for a Gaussian chain). This time scale can be much slower than the one experienced by an individual segment. For a chain with N segments (the PI with 100 kg/mol has N = 1470), the relaxation time for the whole coil should scale as τoN3, where το is the relaxation time of a single segment (here taken as that of the α-process) and the corresponding relaxation time for the coil is ∼9 decades slower, a range much beyond our experimental window. Apart from this intermediate process, the segmental dynamics consistently speed-up with the increasing degree of confinement when examined by cooling. The corresponding VFT parameters are included in Table 3 and the changes in Tg relative to the bulk are discussed as a function of the degree of confinement with the aid of Figure 6. In agreement with earlier

Figure 7. Corrected dependence of ΔTg = TgAAO − Tgbulk on interfacial energy obtained at 290 K based on ref 39. Note that the data do not refer to exactly the same pore diameter nor to identical 2Rg/d conditions. Uncertainties (both on the horizontal and vertical axes) are included.

Figure 6. Dependence of ΔTg = TgAAO − Tgbulk on (a) the inverse pore diameter and (b) on the degree of confinement (2Rg/d) for PI located inside AAO. Lines correspond to linear fits of the data. Error bars correspond approximately to the symbol size.

the results for the different polymers including entangled PIs. Interfacial energies in the figure were calculated at 290 K, whereas the change in Tg is defined as: ΔTg = TgAAO − Tgbulk. Although the data do not refer all to the same pore diameter, there is a clear correlation between the two quantities and PI follows the same scaling. Evidently, this effect is stronger for entangled chains as concluded by comparing different PI’s. This correlation does not exclude that other effects (packing, surface roughness) play some role. III.III. One Versus Two Tgs. There exist several reports in the literature suggesting the existence of two glass temperatures when different polymers (PS, PMMA, and PPG) are investigated under 2D confinement and within the same AAO templates.58−62 This effect has been discussed in terms of a two-layer model proposed by Park and McKenna.63 According to the model, molecules at the interface and at the center of pores (core) have distinctly different mobilities and vitrify at different temperatures. The higher and lower Tg’s were assigned to strongly adsorbed layer and to the core layer, respectively, the latter having a bulk-like Tg. Furthermore, the higher Tg increased with decreasing pore size, whereas the lower Tg was unaffected in the case of PMMA, whereas it decreased in PS. Another approach suggested even a third layer between the interface and the core. To explore this point, we investigated the current PIs with TM-DSC and DS on cooling and subsequent heating using different thermal protocols. We discuss the TM-DSC results first for two molecular weights and two pore diameters with respect to Figure 8. In both cases, reversing heat capacity exhibits a single, albeit broad, step on cooling and a dual step on heating. Baseline traces are also shown for comparison. The

data of unentangled PIs confined within the same AAO templates, e.g., for PI with Mw = 8.5 kg/mol, there is only a minor decrease in the glass temperature relative to the bulk. However, for the higher molecular weights, ΔTg exhibits a stronger dependence on the inverse pore diameter. In Figure 6b, the same glass temperatures are plotted as a function of the degree of confinement. The distinctly different behavior for the lower and higher molecular weights is evident. Furthermore, in this representation, the data for the higher molecular weights can collapse onto a single curve as ΔTg = −(62 ± 2) × (2Rg/ d). The results on the change of the segmental dynamics of entangled PIs under 2D confinement can be discussed in view of the recently reported relation to the interfacial energy.39 Results from several amorphous polymers with various glass temperatures and polymer/substrate interactions confined within self-ordered nanoporous alumina indicated a correlation to the interfacial energy, γSP. The interfacial energy, γSP or γSL (γSL and γSP refer to the same quantity, and denote “liquids” and “polymers”, respectively) is a measure of the difference in the strength of attractive interactions between surface molecules and the solid from the interactions between the surface molecules and bulk molecules. The interfacial tension/energy was calculated with the Young’s equation that connects the three interfacial tensions, the solid−air γSV, the liquid−air γLV, and the solid− liquid γSL as γLV cos θ0 = γSV − γSL. The angle θ0 is the Young’s contact angle that is expected at equilibrium, defined as cos θ0 = (cos θadv + cos θrec)/2, and involves measurements of the F


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all show an increasing signal for the lower temperature peak and a concomitantly decreased signal for the higher temperature peak. This result indicates that the higher temperature feature is kinetically controlled. To explore a possible correlation of the second step obtained on heating with enthalpy relaxation, we studied the heat capacity as a function of annealing time. Samples were annealed at −120 °C for different time intervals (from 5 to 120 min) and the heating traces were recorded with the same rate (10 °C/min). The heating traces did not show appreciable differences for the different annealing times (Figure S5, Supporting Information) excluding the possibility that this feature associates with enthalpy relaxation. Next, we investigate the effect of crossing the low Tg on cooling. To this end, two samples with PI 100 kg/mol located inside AAO with a pore diameter of 400 nm (the corresponding degree of confinement 2Rg/d ∼ 0.05) and a PI with 50 kg/mol located inside AAO with a pore diameter of 65 nm (2Rg/d ∼ 0.22) were first cooled (with a rate of 20 °C/ min) to −120 °C and subsequently heated with the same rate. The DSC traces are shown with the gray curves and exhibit two steps with the one at higher temperatures being the prominent one. In a second experiment, both samples were cooled with the same rate but to a temperature located between the two steps (i.e., at −65 °C). In this experiment, the specimen did not cross over to the lower Tg. Subsequent heating from this temperature (with the same rate) shows the absence of any step in the heating trace. That is, without crossing the low Tg the higher Tg does not appear. This finding is remarkable as it demonstrates that the higher Tg appears only if the lower Tg is crossed on the cooling curve (Figure 10).

Figure 8. Heat capacity, cP, (top) and dcP/dT (bottom) as a function of temperature obtained from TM-DSC heating and cooling traces with a rate of 3.3 °C/min and an oscillation period of 60 s for (a) PI 100 kg/mol located inside AAO pores with a diameter of 400 nm and (b) PI 50 kg/mol in 65 nm AAO pores. Baseline traces obtained with identical conditions are also shown for comparison (dashed lines). The Tgs obtained on cooling (heating) are shown with the blue (red) arrows. The heat capacity traces have been shifted vertically for clarity.

single Tg obtained on cooling and the low Tg obtained on heating agrees with the DS results on the segmental process that speeds-up on confinement, whereas the location of the high Tg obtained on heating coincides with the bulk polymer Tg. We stress here that previously published results on a number of polymers by DSC referred to heating curves.58−62 As a next step and in an effort to understand the origin of the higher Tg in the heating curves, we investigated the rate dependence of the DSC traces. For this purpose, different cooling rates were used (in the range from 10 to 1 °C/min) followed by heating with a constant heating rate (10 °C/min). The DSC heating traces for the two confined polymers are shown in Figure 9. The DSC traces (in the derivative of specific heat with respect to temperature) obtained on heating

Figure 10. DSC heating traces (rate 20 °C/min) of the heat capacity (cP) (top) and derivative of heat capacity with temperature (bottom) for (a) PI 100 kg/mol located inside 400 nm and (b) PI 50 kg/mol located inside 65 nm AAO pores following cooling with 20 °C/min. (Gray line) Heating from −120 °C and (red line) heating from −65 °C. Baseline traces obtained with identical conditions are also shown for comparison.

Figure 9. (a) DSC heating traces of heat capacity (cP) (top) and the temperature derivative of cP curves (bottom) plotted as a function of temperature for PI 100 kg/mol confined in 400 nm following cooling with different rates (10−1 °C/min). (b) DSC heating traces of heat capacity (cP) (top) and the temperature derivative of cP curves (bottom) plotted as a function of temperature for PI 50 kg/mol confined in 65 nm following cooling with different rates (10−1 °C/ min). All measurements were employed with a heating rate of 10 °C/ min. Black arrows in dcP/dT indicate the direction of peak evolution. The heat capacity traces have been shifted vertically for clarity.

Lastly, we explored the effect of very fast cooling (quenching) on the TM-DSC traces obtained on subsequent heating. This is shown in Figure 11 for two samples, one PI with 100 kg/mol located inside AAO with a pore diameter of 400 nm and one with 50 kg/mol located inside AAO with a pore diameter of 65 nm. In both cases, heating traces are compared to the corresponding slowly cooled samples. Fast G


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Figure 11. Derivative of heat capacity with T, dcP/dT as a function of temperature obtained from TM-DSC heating traces following hyperquenching at −170 °C (from 40 °C) for (a) PI 100 kg/mol in 400 nm with a rate of 3.3 °C/min and an oscillation period of 60 s and (b) PI 50 kg/mol in 65 nm with a rate of 1 °C/min and an oscillation period of 200 s (blue lines), in comparison to the slowly cooled samples (black lines).

cooling was applied by transferring the DSC pan into liquid nitrogen. Quenched samples exhibit a single and very intense peak in the derivative of heat capacity with temperature, located in the vicinity of the bulk Tg, in contrast to the slowly cooled samples that exhibit the dual steps discussed earlier. These results are in agreement with the literature.61 It has been suggested that when the infiltrated polymer is exposed to fast cooling, thermal stresses develop along the radial direction due to a mismatch in thermal expansion coefficients between the polymer (α = 6.6 × 10−4 K−1)64 and the AAO membrane (α = 7.7 × 10−6 K−1).65 In principle, the thermal mismatch can be strong that can remove adsorbed chains from the pore walls and lead to a single bulk-like Tg. To further explore the origin of the two Tg’s, DS measurements were performed by following two different protocols in analogy to DSC. In the first protocol, data were recorded on cooling from 333 to 193 K and subsequent heating to 333 K. The corresponding curves and relaxation times are shown in Figure 12. The main feature of the relaxation times is that they display hysteresis below about 250 K. On cooling, the relaxation times are faster than the bulk, whereas, on heating, they approach the bulk behavior. Furthermore, on cooling below 217 K, the dielectric loss curves tend to become asymmetric from the lower frequency side. At 205 K, the loss curve is very broad at its maximum suggesting a bimodal distribution. This is in agreement with the broad and asymmetric DSC curves obtained on cooling (Figure 8). On subsequent heating (from the lowest temperature, 193 K) the dielectric loss curves are faster and bimodal, in accordance with the dual Tg’s found in DSC (additional comparison in Figure S7, Supporting Information). In addition, the intermediate process approach and merge with the slower DS process (i.e., the high Tg in TM-DSC) at a temperature located in the vicinity of the bulk Tg. This was also the case in the MD simulations of 1,4-polybutadiene.57 In the second protocol, the specimen was cooled only to 212 K, i.e., without crossing the lower Tg, and heated immediately after. In this case, the relaxation times did not show any hysteresis, they remained faster than the bulk in agreement with the TM-DSC results (Figure 10). The presence of bimodal loss curves on cooling and subsequent heating below some “critical” temperatures could also be interpreted as the system crossing a spinodal temperature.66 However, in this picture, the origin of

Figure 12. (Left) Dielectric loss curves for PI 100 kg/mol located inside the AAO template with 400 nm pore diameter obtained on cooling to 193 K (top) and subsequent heating (bottom). Curves exhibit a 2 K increase. (Right) Arrhenius relaxation map showing segmental (circles) and chain (squares) relaxation times obtained on cooling (filled blue) to 191 K and subsequent heating (filled red); in a second protocol, data were obtained on cooling (open blue) to 211 K and subsequent heating (open red). The black dashed line gives the segmental times in the bulk. The uncertainty in the relaxation times is smaller than the symbol size. The lines represent VFT fits. The low and high Tg’s from TM-DSC are depicted at isochronal conditions (τ ∼ 10 s) with yellow squares (obtained on heating with P = 60 s and a rate of 3.3 °C/min). The intermediate process (Figure 5) is omitted for clarity.

the two liquid phases undergoing demixing is not clear at present. All results taken together suggest that cooling from higher temperatures gives rise to the lower Tg. This feature relates mainly, but not solely, to the interfacial energy. The higher the interfacial energy, the lower the glass temperature and entangled PIs follow the same dependence as for other polymers investigated earlier. On the other hand, the high Tg appears solely on heating, e.g., when starting from the nonequilibrium glassy state. Furthermore, it is totally absent when the lower Tg is not crossed during the previous cooling. Although it is inappropriate and even dangerous to seek the “equilibrium” glass temperature in a system with adsorbed/ desorbed segments and with configurations (loops, trains, etc.) not shared with the bulk, we will, nevertheless, undertake such H


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a pursuit. Our findings suggest that the low Tg (faster segmental process) is closer to equilibrium. In this picture, the higher Tg (slower segmental process) associates with a bulklike behavior, which is restored by the desorption of segments from the pore walls due to the different thermal expansion coefficients of the polymer and alumina. These conditions are met when the lower Tg is crossed. This could further suggest that the lower Tg plays the role of a spinodal temperature.66

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*E-mail: gfl[email protected]. ORCID

Georgios Sakellariou: 0000-0003-2329-8084 Martin Steinhart: 0000-0002-5241-8498 George Floudas: 0000-0003-4629-3817 Notes

The authors declare no competing financial interest.

IV. CONCLUSIONS The dynamics investigation of entangled PI’s located within self-ordered alumina templates as a function of the degree of confinement provided some features not common with unentangled PI’s studied earlier within the same nanopores. The segmental dynamics of entangled polyisoprenes speed-up on confinement and the degree of change depends on the degree of confinement, 2Rg/d, as ΔTg = −(62 ± 2) × (2Rg/d). For unentangled PIs, this effect is very weak. The decrease in the glass temperature is discussed in terms of the postulated relation to interfacial energy. A new process is reported for entangled PIs and for the higher degrees of confinement. The strength of this process increased linearly with the increasing degree of confinement as Δεint/Δεα = 2.4 × (2Rg/d). This intermediate process has an Arrhenius temperature dependence and small activation energy. The origin of the new mode, identified only in entangled PIs, is discussed in terms of the adsorption/desorption kinetics of segments in the vicinity of the pore walls. This mode bears similarities with the mode found earlier in polymer films (where confinement is 1D) and in controlled porous glasses (3D confinement) and one major difference. The contribution from adsorbed 1,4-PI segments, with dipole moment parallel to the pore wall, is maximized when confinement is in 2D since the electric field is applied in the same direction. This explains its relatively weak dielectric strength under 1D confinement where the electric field is perpendicular to the polymer/substrate interface. Lastly, we address the origin of the dual Tg, reported by DSC during heating of some polymers confined within the same alumina templates. By following several different temperature/ annealing protocols, temperature-modulated DSC identified two Tg’s on heating, but a single Tg on cooling, the latter coinciding with the single Tg obtained in DS during cooling. We have shown that the higher Tg is conditional; it appears only when the lower Tg is crossed on the previous cooling run; it is absent when cooling is stopped in between the two Tg’s. These findings suggest that the low Tg (faster segmental process) is closer to equilibrium. In this picture, the higher Tg (slower segmental process) associates with a bulk-like behavior which is restored by the desorption of segments from the pore walls due to the different thermal expansion coefficients of the polymer and alumina.

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ACKNOWLEDGMENTS

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REFERENCES

The current work was supported by the Research unit on Dynamics and Thermodynamics of the UoI co-financed by the European Union and the Greek state under the NSRF 2007− 2013 (Region of Epirus, call 18). We are thankful to ChienHua Tu (MPI-P) for the SEM measurements.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00523. Method of infiltration, SEM images of empty and infiltrated AAO, analysis of DS spectra and the TM-DSC thermal protocol (PDF) I


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Dynamics of Entangled cis-1,4-Polyisoprene Confined to Nanoporous

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