Counterbalance between Surface and Confinement Effects As Studied

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

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Counterbalance between Surface and Confinement Effects As Studied for Amino-Terminated Poly(propylene glycol) Constraint in Silica Nanopores Wycliffe K. Kipnusu,*,† Mahdy M. Elmahdy,‡ Mohamed Elsayed,§,∥ Reinhard Krause-Rehberg,§ and Friedrich Kremer*,⊥ †

GROC.UJI, Institute of New Imaging Technologies, Universitat Jaume I, Avda. Sos Baynat s/n, 12071 Castellón, Spain Department of Physics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt § Department of Physics, Martin Luther University Halle, 06099 Halle, Germany ∥ Department of Physics, Faculty of Science, Minia University, 61519 Minia, Egypt ⊥ Peter-Debye-Institute, University of Leipzig, Linnéstraße 5, 04103 Leipzig, Germany

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‡

ABSTRACT: Broadband dielectric spectroscopy (BDS) and orthopositronium annihilation lifetime spectroscopy (PALS) are combined to study the molecular dynamics and the free volume of poly(propylene glycol) terminated with amino end groups (PPG-NH2) in the bulk state and when confined in native and silanized unidirectional silica nanopores with average diameters of 4, 6, and 8 nm. In the bulk state, three dielectric relaxation processes are observed: (i) the fast β-relaxation assigned to the librational fluctuations of the −O−NH2 moiety, (ii) the α-process corresponding to the dynamic glass transition, and (iii) the (slower) chain dynamics or normal mode (NM) relaxation. Under confinement in native nanopores, the β-process becomes slower, while the α and the normal mode relaxation processes become faster and broader and demonstrate a lower dielectric strength with decreasing pore diameter. In silanized nanopores the normal and β-processes are nearly bulklike, but the α-process still remains faster than bulk closer to the Tg. All these findings can be comprehended as controlled by the counterbalance between surface and confinement effects. The former are caused by attractive interactions with the solid walls of the nanopores (resulting in an additional slower process which is removed after silanization), and the latter are caused by an increase of the f ree volume of the polymer segments due to a less efficient packing as proven by orthopositronium annihilation lifetime spectroscopy. These results conform to the cooperative free volume model (CFV).

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INTRODUCTION Soft materials confined in nanopores exhibit significant differences in their structural and dynamic properties compared to the bulk state.1,2 This phenomenon is important for industrial and biological applications as well as the need for basic understanding of the effects of nanoconfinement.3,4 In this study, we show how the local and global (chain) dynamics of a polymer are influenced under 2D geometrical constraints in hydrophobic and hydrophilic silica nanopores. In this context, molecular dynamics is affected by the changes in the packing density and the interaction of the polymer chains with the confining matrix. Factors such as finite size effects, free volume, and interface effects are discussed as key parameters responsible for the enhancement of molecular dynamics and the shift in the phase transition temperatures.5−14 Recent studies have highlighted the importance of the material’s interaction at the interface on the overall dynamics of molecules at the nanoscale.12,14−18 A pertinent study of thin polymer films annealed for a long time revealed that the glassy dynamics and the glass transition temperature are bulklike and independent of the layer thickness.11,19−23 These results are discussed in terms of the © XXXX American Chemical Society

perturbation of polymer density at the interface and the increase in the number of irreversibly adsorbed chains during the equilibration at time scale much longer than the reptation time (often identified as segmental relaxation times).14,15 Earlier controversies regarding the dynamic glass transition Tg of polymer systems confined in thin films (i.e., 1D confinement) are also rationalized by the free volume hole diffusion (VFHD) model proposed by Boucher et al.24,25 Within this framework, diffusion of free volume holes to the available interfaces of the system establishes the equilibrium during cooling. The state of the equilibrium therefore depends on the molecular mobility and the proximity to the interfaces. This implies that the surface of a thin film can easily maintain liquidlike equilibrium at lower temperatures, and hence the film thickness dependence of the Tg depression is expected if measured by surface-sensitive techniques within the T < Tg regime. This is corroborated by the finding that the polymer film thickness invariant segmental dynamics is sometimes Received: December 18, 2018 Revised: January 29, 2019

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DOI: 10.1021/acs.macromol.8b02687 Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

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decoupled from the Tg determined from the differential scanning calorimetry (DSC),26,27 especially if the latter is measured in a heating run from the glassy state. Moreover, the finding that the surface layer equilibration time for a vapordeposited glass within T < Tg is faster than the extrapolated structural relaxation by about 5 orders of magnitude28 is in accord with the VFHD model. Most recently, Lipson and coworkers have also extended their cooperative free volume model29,30 to explain dynamics of polymer thin films.31 A similar rigorous study of systems confined in nanopores is lacking. In this type of system, molecules are restricted within two-dimensional (2D) geometries, which means that the density perturbation due to the interfacial energies is higher. Furthermore, as a result of higher surface area to volume ratio in nanopores, the surface effect becomes much higher compared to thin films. Recently, we performed a direct comparison of the molecular dynamics of a polymer when confined both in thin films (1D) and in nanopores (2D) and found that the segmental dynamics remained bulklike for the case of thin films, but the polymer experienced depressed Tg in nanopores.11 Therefore, 2D confined molecules are inevitably affected by the counterbalance between confinement and surface effects.8,32−34 The confined molecules at the center of the pores often exhibit faster structural relaxation compared to to those in the bulk state34−36 while the mobility of molecules at the interface is decreased. Recently, Talik et al.13 examined the behavior of modified PPG derivatives, where the OH terminal groups are replaced with −NH2 and −OCH3. The H-bond formation between the polymers and the pore walls results in the increase of the glass transition temperature of the polymers attached to the pore walls in the following order: PEG-OH, PEG-NH2, PEG-OCH3. Moreover, they noted that the reduction in Tg correlates with an increase in the interfacial energy as similarly reported by Alexandris et al.9 By suitable chemical modification, the surface chemistry of porous materials can be altered from hydrophilic to hydrophobic, and vice versa.37 Hexamethyldisilazane (HMDS) is among the most popular surface-modifying agents whose molecules react strongly with the free surface hydroxyl groups of alumina, eliminating the solid−liquid interaction. High silanization power of HMDS on various hydroxyl-bearing surfaces, including alumina, has been demonstrated in a number of studies.8,11,38−41 In this study, we investigate the effects of nanoconfinement by studying the molecular dynamics and free volume of a glassforming poly(propylene glycol) (PEG) terminated with amino end functional group (PEG-NH2) in the bulk state and when incorporated into native and silanized silica nanopores having pore diameters in the range of 4, 6, and 8 nm. PEG-NH2 is a special type of polymer because it exhibits three relaxation processes at different lengths and time scales. It is therefore a suitable model system for testing the effects of 2D confinement. Broadband dielectric spectroscopy (BDS) and positron annihilation lifetime spectroscopy (PALS) are employed to investigate the molecular dynamics and free volume, respectively. The results show that the glassy dynamics of PPG-NH2 in native and silanized nanopores become faster as the average pore diameters decrease. This is ascribed to the reduced packing density of the molecules at the center of the pores which is corroborated by PALS.

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EXPERIMENTAL SECTION

Amino-terminated polypropylene glycol (PPG-NH2) chemically named as poly(propylene glycol) bis(2-aminopropyl ether) having number-average molecular weight of Mn = 4000 g/mol and purity higher than 98% was supplied by Sigma-Aldrich and used as received. The chemical structure of the investigated molecule is presented in Scheme 1.

Scheme 1. Chemical Structure of the PPG-NH2 Sample

Preparation of Nanoporous Silica (pSiO2) Membrane. The electrochemical etching technique was employed to prepare the nanoporoes silica (pSiO2) membranes from highly doped (0.005 Ω cm) p-type ⟨100⟩ oriented monocrystalline silicon wafers in a homebuilt anodization cell. Details of this procedure is found in ref 11. In brief, direct current densities (j) in the range 20−120 mA cm−2 are applied through an electrolyte consisting of hydrofluoric acid (HF, 48%) and ethanol (C2H5OH, 99%) purchased from Sigma-Aldrich and mixed in the ratio of 1:1. The exfoliated nanoporous silicon membranes are then thermally oxidized to silica. Pore diameters between 4 and 10 nm with porosity varying from 15% to 24% were obtained. The scanning electron micrograph (SEM) image and the nuclear magnetic resonance (NMR) cryoporometry of pSiO2 reveal the nonintersecting pores and the pore size distribution, respectively, as given in refs 11 and 42. Silanization is the covering of a surface with a coating that contains silane-like molecules making the surface chemically inert. To do so, another set of the prepared pSiO2 was silanized by reacting with the hexamethyldisilane (HMDS) (purity 99.9%, purchased from SigmaAldrich) in the vacuum chamber at 350 K for 6 h and later evacuated to remove the unreacted HMDS. Infiltration of PPG-NH2 into Silica Nanoporoes. Details concerning the procedure of infiltration of the polymers into nanoporoes membranes can be found in refs 34 and 42. Briefly, the empty membranes were annealed in a high vacuum chamber (10−6 mbar) at 573 K for 24 h to remove water and other volatile impurities. As a second step, the annealing temperature was then decreased to 300 K before the PPG-NH2 sample was injected into the closed vacuum where the pores were filled by capillary wetting. After 24 h, the sample setup was annealed at 373 K in a vacuum (10−3 mbar) for 1 h before the second injection of the sample was done. This was repeated three times to improve the filling fraction. Excess material on the surface of the membrane was removed by wiping with a tissue paper. Samples were finally annealed at 423 K in a vacuum (10−6 mbar) for 24 h and weighed thereafter. In the experiment, we used membranes with different pore diameters: 4, 6, and 8 nm. The filling ratio of the pores was determined from weighing the empty and filled membranes. We calculated the filling fraction by taking into account the porosity of the nanoporous membranes and the density of the material with the assuming bulk density of PPG-NH2. A similar procedure was used during silanization with the exception that the vacuum chamber was evacuated to get rid of the ungrafted HDMS before injecting the probe sample. With this approach, we achieved complete filling of the nanopores with the investigated sample as confirmed by gravimetric and PALS measurements. Broadband Dielectric Spectroscopy (BDS). Dielectric measurements in the frequency (10−2−107Hz) and temperature (130−350 K) ranges were performed using a Novocontrol high-resolution alpha analyzer under a pure nitrogen atmosphere. The sample temperature was controlled in a nitrogen jet using a Quatro controller with stability better than 0.1 K. For measurement of PPG-NH2 contained in pSiO2 membranes, the sample was sandwiched between platinum electrodes after a thin aluminum foil (∼800 nm) was placed on both sides of the membranes to improve the contacts. The complex dielectric B


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Macromolecules permittivity ϵ* = ϵ′ − iϵ″, where ϵ′ is the real part and ϵ″ is the imaginary part, is a function of frequency ω and temperature (T). In all cases, superposition of the empirical Havriliak−Negami (HN) function including a conductivity term (eq 1) was used to fit the isothermal dielectric loss data2 ÄÅ ÉÑ n Δϵj ÅÅÅ ÑÑÑ σ0 Å ÑÑ ϵ″(ω) = − ∑ ImÅÅÅ Ñ αj γj Ñ Å ÑÑ ω ϵ0 [ + ωτ ] 1 ( i ) Å j HN j=1 (1) ÅÇ ÑÖ where σ0 is the dc conductivity, ϵ0 is the permittivity in free space, ω is the angular frequency (ω = 2πf) of the external applied electric field, Δϵ is the dielectric relaxation strength, τHN is the characteristic relaxation time, and α and γ are the shape parameters (with the limit 0 < α, αγ ≤ 1) describing the symmetrical and asymmetrical broadening of the distribution of relaxation times. From τHN, the relaxation time at maximum loss τmax can be obtained analytically as follows: ÅÄÅ ÑÉ−1/ α ÅÅ sin πα ÑÑÑ Ñ ÅÅÅ 2 + 2γ Ñ ÑÑ τmax = τHNÅÅÅ ÑÑ παγ ÅÅ Ñ ÅÅ sin 2 + 2γ ÑÑÑ (2) ÅÇÅ ÑÖÑ

( ) ( )

The non-Arrhenius temperature dependence of τmax is approximated by the Vogel−Fulcher−Tammann (VFT) equation

ij B yz zz τmax = τ0 expjjj j T − T0 zz k {

Figure 1. Temperature dependence of the dielectric loss (ϵ″) measured at 11.97 Hz for bulk PPG-NH2 and when confined in native (a) and silanized porous silica membranes (b) having unidirectional nanoporoes with average diameters in the range 4−8 nm. Arrows indicate the locations of the secondary (β) and interfacial relaxation processes while the positions of the segmental and normal modes relaxations are indicated by the short-dashed and short-dotted lines, respectively. The chemical structure of the investigated molecule is included in (b). The experimental accuracy corresponds to the size of the symbols if not indicated otherwise by error bars.

(3)

while the Arrhenius temperature dependence is described by ij E yz zz τmax = τ0 expjjj j kBT zz k {

(4)

where τ0 is the high temperature limit of the relaxation time, B = DT0 with D being the fragility parameter (a measure of the extent of deviation from the Arrhenius T-dependence), T0 is the Vogel temperature, E is the activation energy, and kB is the Boltzmann constant. Positron Annihilation Lifetime Spectroscopy (PALS). To perform positron annihilation lifetime measurements, we employed a fast−fast coincidence system with a time resolution of 215 ps.43−45 The positron source (20 μCi 22Na), wrapped in a Kapton foil, was sandwiched between nanoporous silica layers (500 μm thick) when empty or filled with PPG-NH2. The assembled samples were sealed and placed in a vacuum chamber (10−6 mbar) consisting of a temperature controller. The samples were measured in the temperature range 130−320 K in steps of 5 K while accumulating (4−5) × 106 counts per each positron lifetime spectrum. The source contribution of 13.8% was determined by measuring a silicon reference sample (218 ps). After source and background corrections, the positron lifetime spectra were analyzed by the lifetime LT 9 program46 to three components which arise from the annihilation of parapositronium (Ps) (τ1 = 125−150 ps), free positrons (τ2 = 350− 450 ps), and ortho-Ps pickoff (τ3 = 1.3−3.9 ns).

chains. The fourth process observed at high temperature is assigned to the interfacial interaction of PPG-NH2 with the surface of native pore walls. The same relaxation processes discussed above also appear in the isothermal dielectric loss spectra but in a reversed order where the faster β-process occurs at higher frequencies while slower relaxations like those due to the surface effects and the normal mode are detected at lower frequencies. In Figure 2, we selected the temperatures at which the normal and segmental modes are clearly seen within the experimental frequency window. The intensity of the normal mode of the samples confined in nanopores decreases with the reduction of the confining pore sizes. It also broadens compared to the bulk sample (Figure 2b−d). In 4 nm, this process is nearly smeared out. Notably, for the sample confined in native silica nanopores, dynamics of the normal mode is more affected than that of the segmental mode which results to the changes in the ratio of their dielectric strengths and a reduction of the separation between the time scales of the two processes. This is attributed to the surface effects which are more pronounced for the NM process because this mode involves the fluctuation of the entire polymer chain; hence, it becomes more sensitive to the interfacial interactions. The global chain dynamics, in the bulk PPG-NH2, exhibits a true end-to-end dipole vector fluctuation where the α shape parameter is close to 1, but the confined PPG-NH2 in native and silanized silica pores show a broader distribution of relaxation times on reducing the degree of confinement. Because of a larger surface area in silica nanopores, the chain−substrate interaction increases, causing adsorption of some chains on the pore walls and hence leading to faster dynamics and increased broadening of ϵ″(ω). To eliminate the surface effects, we silanized the silica nanopores by reacting with HDMS. The normalized dielectric loss of the

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RESULTS AND DISCUSSION The isochronal dielectric loss spectra of PPG-NH2 in the bulk state and when confined in native nanoporoes with diameters in the range 4−8 nm (Figure 1) show four dielectric active processes at low, intermediate, and high temperatures. The fast secondary relaxation termed the β-process is located at lower temperatures and is attributed to the librational fluctuations of the −O−NH2 moiety in the sample. The second process named the α-process, also known as structural or segmental fluctuation (SM) of the polymer, is related to the dynamic glass transition and occurs in the temperature range between 200 and 250 K. The third process is the normal mode (NM), which is slower than the segmental process and involves the fluctuation of the end-to-end dipole vector along the polymer C


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Figure 4. Comparison of the dielectric loss data (ϵ″) of bulk PPGNH2 (filled black squares) and PPG-NH2 confined in native (open symbols) and silanized (filled symbols) silica pores with average diameter in the range 4−8 nm normalized with respect to the maximum loss value of the segmental mode (SM) at temperatures of 236 K. The experimental accuracy corresponds to the size of the symbols if not indicated otherwise by error bars.

native PPG,10 modified PPG derivatives,13 and poly(cis-1,4isoprene) incorporated in self-ordered AAO membranes.47 Surface interactions also cause changes in the dielectric strength (Δϵ) of the relaxation processes. A comparison of the Δϵ of the SM and NM relaxation processes in bulk, native, and silanized pores (Figure 5a,b) shows a reduction of the dielectric strength with decreasing the pore sizes. The change in the temperature dependence of Δϵ for the bulk sample can be attributed to the effect of temperature on the H-bond network formation. Under confinement, the surface interactions are more dominant such that this temperature change is no longer noticeable. Furthermore, the silanized nanopores demonstrate higher dielectric strength compared to the corresponding native ones. The reduction of Δϵ in native pores is due to the adsorption of a significant number of molecules to the pore walls. To estimate the thickness of the adsorbed molecules ξ(T), we employed the equation ÄÅ ÉÑ ÅÅÅ ÑÑÑ Δϵ − ϕ Δϵ m a ÑÑ ξ(T ) = R pÅÅÅ1 − ÅÅ ϕ(Δϵb − Δϵa) ÑÑÑÑÖ (5) ÅÇ where Δϵm is the measured total dielectric strength of the sample, ϕ is the porosity of silica laysers, Δϵb is the dielectric strength of bulklike molecules in the pores, and Δϵa is the dielectric strength of adsorbed molecules. Rp = rb + ξ is the average radius of the pores where rb is taken as the radius of a region at the center of the pore occupied by the bulklike molecules. It is important to note that Δϵm includes the contributions from Δϵb and Δϵa. For instance, if the interfacial process is observed, the data are usually fitted by the sum of the HN functions (eq 1). The dielectric strength of the main process and that of the adsorbed molecules are added together to get Δϵm. The volume-corrected dielectric strength data of the segmental relaxation processes in the bulk and that of the interfacial process in nanopores were used for Δϵb and Δϵa, respectively. Further information about the derivation of eq 5 can be found in ref 8. Using eq 5, the ξ(T) is obtained as displayed in the inset of Figure 5a. The resulting ξ(T) is within the limits of experimental uncertainty confinement and temperature independent with relatively constant values of 0.25 and 0.4 nm for pore diameters of 6 and 4 nm, respectively. It is noteworthy that the estimated values of ξ(T) are in good accord with previously reported data for low molecular weight glass-

Figure 2. Dielectric loss spectra (ϵ″) for bulk PPG-NH2 (a) and infiltrated PPG-NH2 into native silica pores with average diameter in the range 4−8 nm (b−d) for identical selected temperatures as indicated. The solid lines are the summation of two HN functions with the conductivity contribution. The experimental accuracy corresponds to the size of the symbols if not indicated otherwise by error bars.

segmental and normal modes for the bulk PPG-NH2 and when confined in native and silanized silica pores with average diameter in the range 4−8 nm are depicted in Figures 3 and 4. Indeed, the spectral broadening is decreased and the NM become more resolved in silanized pores than in native pores.

Figure 3. Comparison of the dielectric loss data (ϵ″) of bulk PPGNH2 (filled black squares) and PPG-NH2 confined in native (open symbols) and silanized (filled symbols) silica pores with average diameter in the range 4−8 nm normalized with respect to the maximum loss value of the segmental mode (SM) at selected temperatures of 212 K. The experimental accuracy corresponds to the size of the symbols if not indicated otherwise by error bars.

The HN-broadening parameters (α and αγ) for bulk, native, and silanized nanopores are given in Tables 1 and 2 at the selected temperatures. At lower temperatures, the shape parameters for confined samples (native and silanized) are systematically less than that of bulk PPG-NH2. Similar broadening of the distribution of the segmental and chain relaxation times with decreasing pore size was observed for D


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Table 1. Havriliak−Negami Broadening Parameters for the SM Relaxation (α-Process) of the Bulk Sample and When Confined in Native Silica Nanopores bulk α

T (K) 218 224 230 236 242

8 nm

0.83 0.85 0.84 0.84 0.84

± ± ± ± ±

αγ 0.04 0.04 0.04 0.04 0.04

0.40 0.37 0.39 0.39 0.52

± ± ± ± ±

6 nm

α 0.02 0.02 0.02 0.02 0.02

0.60 0.68 0.74 0.73 0.71

± ± ± ± ±

αγ 0.12 0.12 0.12 0.12 0.12

0.48 0.43 0.40 0.42 0.51

± ± ± ± ±

α 0.1 0.1 0.1 0.1 0.1

0.52 0.68 0.74 0.72 0.71

± ± ± ± ±

4 nm αγ

0.1 0.14 0.1 0.1 0.1

0.44 0.38 0.42 0.43 0.49

± ± ± ± ±

α 0.1 0.1 0.1 0.1 0.1

0.45 0.49 0.52 0.53 0.57

± ± ± ± ±

αγ 0.1 0.1 0.1 0.1 0.1

0.48 0.43 0.52 0.53 0.57

± ± ± ± ±

0.1 0.1 0.1 0.1 0.1

Table 2. Havriliak−Negami Broadening Parameters for the SM Relaxation (α-Process) of the Sample Confined in Silanized Silica Nanopores 8 nm sil α

T (K) 218 224 230 236 242

0.74 0.70 0.70 0.69 0.76

± ± ± ± ±

6 nm sil αγ

0.15 0.14 0.14 0.14 0.15

0.36 0.34 0.49 0.47 0.45

± ± ± ± ±

4 nm sil

α 0.1 0.1 0.1 0.1 0.1

0.65 0.73 0.70 0.65 0.68

± ± ± ± ±

αγ 0.13 0.15 0.14 0.13 0.14

0.40 0.35 0.38 0.48 0.75

± ± ± ± ±

α 0.1 0.1 0.1 0.1 0.15

0.50 0.55 0.65 0.61 0.63

± ± ± ± ±

αγ 0.1 0.11 0.13 0.12 0.13

0.33 0.52 0.46 0.66 0.64

± ± ± ± ±

0.1 0.1 0.1 0.13 0.13

characteristic of a local process. On the other hand, the activation energies of confined samples in native and silanized nanopores are in the ranges of 18−27 and 24−30 kJ/mol, respectively. The activation energies E and the pre-exponential factors τ0 for the fast secondary relaxation (β-process) of bulk and confined material are compiled in Table 3. The changes of the activation energies of the confined system with respect to the bulk sample is attributed to surface interactions of −O− NH2 and the silanol groups in silica nanopores. Such interactions induce changes in the conformation and interfacial density, hence causing the observed reduction in the activation energies.54 Figure 6a,b shows that at high temperatures the relaxation rates of SM for all pore sizes collapse to that of the bulk material. But by decreasing the temperature, the relaxation rates deviate from each other in such a way that the separation takes place at lower temperatures with decreasing pore size. This becomes clearer by fitting the segmental relaxation rates (Figure 6b) with the VFT equation (eq 3). With the estimated parameters, given in Table 3, a dynamic glass transition temperature Tg is obtained by extrapolating to the temperature where the relaxation rate is 0.01 s−1. As shown in Table 3, Tg decreases with decreasing pore size. This means that the molecular dynamics within the nanopores is faster than in the bulk state as Tg of the confined system is approached. This speeding up of the dynamics of the α-relaxation within the nanopores compared to the bulk can be discussed in the framework of density change and surface melt interaction. It is known that the density change below 1% can lead to an increase of free volume and correspondingly to a decrease of Tg. Although the degree of filling of the pores with the polymer melt was very carefully controlled, however, it is very difficult to detect density changes smaller than 1% for such systems experimentally, and therefore the density change hypothesis is most probably responsible for the reduction of Tg. This assumption is confirmed by PALS measurements as discussed below. Furthermore, the decrease of Tg can also be discussed considering surface−melt interactions. Because of the surface tension, the density in the center of nanopores can be smaller than close to the walls. To study these effects, additional investigations were performed on silica

Figure 5. Dielectric relaxation strength (Δϵ) of the segmental mode (SM) (filled symbols) and normal mode (NM) (open symbols) for bulk PPG-NH2 and PPG-NH2 infiltrated into 4 and 6 nm native (a) and silanized (b) silica pores. Insets: (c) temperature dependence of the approximate thickness of the interfacial layer ξ of PPG-NH2 in pores with average diameters of 4 nm (filled black pentagons) and 6 nm (filled up triangles). The error bars are smaller than the size of the symbols if not shown.

forming liquids confined in nanoporous materials.8,48,49 Considering the ratio between the pore diameter and the interfacial layer, our results are also comparable to those determined for PPG infiltrated into AAO temples with 73 nm (ξ ∼ 12 nm)50 and for PMMA,51 salol52 confined within AAO membranes, and poly(vinyl alcohol) (PVA)/silica nanocomposites.53 From the fitting analysis of the obtained spectra (Figures 2 and 3) by three superposed Havriliak−Negami (HN) functions with an additional term related to the dc conductivity (eq 1), one can determine the mean relaxation times of the local (β), segmental mode (SM), normal mode (NM), and the interfacial processes. The β-process is depicted at high frequency/low temperature in Figure 6. For the bulk material, this process is described by the Arrhenius equation (eq 4) with a single activation energy E = 31 kJ/mol and a τ0β × 10−15 s, E


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Figure 6. Activation plot of the relaxation rates corresponding to the normal mode (NM) (filled symbols), segmental mode (SM) (open symbols) and the secondary relaxation processes (β) (half-filled symbols) for bulk PPG-NH2 and PPG-NH2 infiltrated into 4, 6, and 8 nm native (a, b) and silanized (c, d) silica nanopores. The interfacial relaxation processes is represented as dot center symbols in (a). The bulk glass transition temperature Tg value determined by DSC at a scanning rate of 10 K/min is also shown as green square in (b) and (d). The solid lines in (b) and (d) are VFT fits to the SM-process (eq 3) and Arrhenius fits to the β-process (eq 4). The fitting parameters of the two relaxation processes (α and β) of the native and silanized pores are compiled in Table 3. The experimental accuracy corresponds to the size of the symbols if not indicated otherwise by error bars.

Table 3. Vogel−Fulcher−Tammann (VFT) Fit Parameters (Eq 3) and the Glass Transition Temperatures (Tg) for the Segmental Mode (α-Relaxation) of Bulk PPG-NH2 and PPG-NH2 Confined in Native and Silanized Porous Silica Membranes having Nanopores with Average Diameter in the Range 4−8 nm as Well as Activation Energy E and Pre-exponential Factor τ0 for the Fast Secondary Relaxation (β-Process) α-process sample

−log [τ0 (s)]

bulk 8 nm 6 nm 4 nm 8 nm sil 6 nm sil 4 nm sil

12.5 14.0 14.0 14.0 13.2 15.0 17.0

β-process

B (K) 959 1825 1826 2025 1356 2116 2662

± ± ± ± ± ± ±

30 40 20 40 80 180 80

T0 (K) 169.5 133 131 121 152 132 125

± ± ± ± ± ± ±

0.7 0.9 0.5 0.9 2 2 2

BDS

Tg (K) 198 183 181 176 190.2 186 185.5

± ± ± ± ± ± ±

1 1 1 1 1 1 1

−log[τ0 (s)] 14.6 12.8 9.9 9.5 14.0 13.6 11.6

E (kJ/mol) 31 27 20 18 30 28 24

± ± ± ± ± ± ±

0.3 0.4 0.4 0.4 0.9 0.7 1

Overall, the results discussed above are attributed to the interplay between the surface and confinement effects where the latter is more sensitive to the changes in the packing density of the constrained molecules. This is corroborated by the PALS measurements of the bulk PPG-NH2 and when confined in native and silanized nanopores with average pore diameters of 4 and 8 nm. The orthopositronium (o-Ps) lifetime (τ3) component of the PALS results is related to the size of the voids or more generally the free volume in which the positronium is trapped. We obtained effective τ3 for the sample confined in silica nanopores by subtracting the τ3 component of the silica matrix for each corresponding measured temperature. The temperature dependencies of the lifetime τ3 of the o-Ps of the bulk and confined samples are depicted in Figures 7a. τ3 decreases until it becomes nearly temperature invariant as the system approaches the isochoric state deep in the glassy regime. This is related to the development of negative pressure for systems confined in nanopores as discussed in refs 55 and

nanopores having passivated internal surfaces, which was done by silanization of the material by HMDS (Figure 6b). As for the untreated material (Figure 6b) also for the silanized material, a decrease of the glass transition is observed with decreasing pore size. In Table 3, the Tg values are compared for the untreated as well as for the silanized pores. The Tg values of silanized nanopores are slightly higher than in the corresponding native ones but still lower than in the bulk. The chain dynamics of PPG-NH2 under confinement in native nanopores show faster relaxation rate than the bulk. This fast dynamics is due to the chain adsorption which can effectively reduce the end-to-end distance of the free terminal subchains, resulting in a faster relaxation. Also, the changes in the packing density of the constrained molecules in smaller pores would also allow for more free volume leading to faster chain dynamics compared to the bulk. In silanized pores (Figure 6c,d), the chain dynamics is slower compared to the pristine silica pores but is still faster than the bulk. F


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cooperative mechanistic structure involving both temperature and free volume. We tested the typical implementation of this model for our samples by plotting log τ versus (Vhc/Vf)(T*/ T)b for PPG-HN2 in the bulk state and when confined in nanopores. In this framework, we fixed Vhc to the volume of single polymer chain (6.84 Å3) calculated from bulk density of the investigated PPG-NH2 and T* to room temperature (300 K). By optimizing or rather manually adjusting only the parameter b, all the respective data for segmental and normal mode processes collapsed into separate single straight lines as shown in Figure 8. The b values listed in Table 4 are smaller

Figure 7. (a) Temperature-dependent orthopositronium lifetime (τ3) measured in the bulk of PPG-NH2 and when confined in the native (open symbols) and silanized (filled symbols) nanopores having mean pore diameters of 4 and 8 nm. (b) Temperature dependencies of the free volume (Vf) obtained from orthopositronium annihilation lifetime (τ3) via the Tao−Eldrup model are displayed for the PPGNH2 in the bulk state (filled squares) and when confined in native and silanized nanopores with mean pore diameters of 4 and 8 nm, respectively. The error bars are smaller than the size of the symbols if not shown.

Figure 8. Plot of log τmax for the segmental (SM) and normal (NM) modes relaxations against the rescaled free volume and temperature according to the cooperative free volume (CFV) model. The plot includes data for PPG-NH2 in the bulk state and when confined in native and silanized silica nanopores having pores diameters of 4 and 8 nm as shown in the legend. The b-parameter values are listed in Table 4. The inset shows the change of the dynamic glass transition temperature with respect to the bulk values (ΔTg = Tg(pore) − Tg(bulk)) versus pore size for native (open symbols) and silanized (filled symbols) nanopores. The Tg’s are the extrapolated values from the dielectric measurements given in Figure 6. The error bars are smaller than the size of the symbols if not shown.

56. The slight change of slope at higher temperatures is simply due to the fact that τ3 coincides with τα within this temperature range. Most importantly, 2D constrained samples show higher τ3 values as the finite size of confinement decreases (i.e., decreasing pore sizes). This means that free volume increases with confinement. We converted τ3 data into free volume (Figure 7b) according to the Tao−Eldrup model57 which assumes that positrons annihilate in spherical regions of low electron densities. Silanized nanopores show similar T dependence of free volume as the corresponding native pores, but with slightly lower values. Higher free volume in liquid samples denotes reduced packing density of the molecules which supports our interpretation of the molecular dynamics shown in Figure 6 and discussed above. Notably, the confinement effect, or rather the influence of reduced packing density, is more evident for the SM than the NM, which is mostly affected by the surface effects. More recently, the effect of the chemical modification of PPG end groups on the molecular dynamics under 2D confinement and the polymer/matrix interactions have been investigated by means of DSC, BDS, surface tension, and contact angle. Results reveal that Tg of the polymers attached to the pore walls increases with the ability of H-bond formation. Moreover, the reduction in Tg of the investigated PPG’s correlates well with an increase in the solid−liquid interfacial tension.12 The interfacial interaction also affects molecular packing and hence the free volume which is detected by PALS measurement (Figure 7). This supports the dynamics data in Figure 6. Recently, Lipson and co-workers have developed the cooperative free volume (CFV) model to explain the importance of free volume in the discussion of glassy dynamics.29−31 Within this approach the relaxation time 1 (τ) is proportional to V × f (T ). The CFV model has a

for the confined samples compared to the bulk state, and it is even lower for native than in silanized pores. Notably, the b parameter (b = −(∂ ln Vf/∂ ln T)τ) in the CFV model is considered as a measure of the relative importance of changing free volume to that of temperature.31 In this respect, lower b values imply greater sensitivity to the volume changes than temperature. This interpretation conforms to our combined structural relaxations and free volume data. A general scheme of the density profile in nanopores with respect to bulk and the corresponding molecular dynamics response is represented in Figure 9. In this respect, the combined molecular dynamics and free volume data in this study underpin the importance of free volume for understanding molecular dynamics under constrained geometries.

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CONCLUSIONS The molecular dynamics of PPG-NH2 under 2D geometrical constraints have been investigated by means of BDS and PALS. 2D confinement was achieved by infiltrating the polymer into unidirectional silica nanopores with average diameters of 4−8 nm. The BDS measurements of the bulk material revealed three relaxation processes named as β, segmental mode (SM), and normal mode (NM) relaxations. The β-process occurred at lower temperatures and involves librational fluctuations of the −O−NH2 moiety in the sample while the α (SM) and NM relaxations are connected to the dynamic glass transition and

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Table 4. b-Parameter Values of the Cooperative Free Volume Model Applied to PPG-NH2 Data in the Bulk State and When Confined in Native and Silanized Silica Nanopores As Shown in Figure 8 segmental mode (SM) normal mode (NM)

bulk

8 nm sil

4 nm sil

8 nm native

4 nm native

4.0 ± 0.2 3.90 ± 0.2

3.91 ± 0.2 3.86 ± 0.2

3.90 ± 0.2 3.86 ± 0.2

3.65 ± 0.2 3.20 ± 0.2

3.63 ± 0.2 2.90 ± 0.2

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Figure 9. Schematic representation of the molecular packing density profile inside the hydrophilic (native) and hydrophobic (silanized) nanopores. The dynamic responses of the molecules at different locations inside the nanopores are compared.

the fluctuation of the end-to-end dipole vector along the polymer chains, respectively. The confinement in native nanopores leads to speed-up of the dynamics of the α and normal mode relaxation processes in addition to the appearance of additional process related to the polymer/ surface interaction. Silanization of the inner pore walls results in faster dynamics of the α and normal mode relaxation processes with decreasing the pore diameter, but the mean relaxation rate is slightly slower than in native nanopores. Furthermore, the interfacial relaxation process observed in native nanopores is fully removed. All these findings are discussed in the framework of reduced packing density in nanopores, which in turn results in a higher free volume and subsequently speed-up of the dynamics, as proven by orthopositronium annihilation lifetime spectroscopy.

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AUTHOR INFORMATION

Corresponding Authors

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

Wycliffe K. Kipnusu: 0000-0003-0643-7716 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by SFB/TRR 102 within the project “Polymers under multiple constraints: restricted and controlled molecular order and mobility” is gratefully acknowledged. H


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Counterbalance between Surface and Confinement Effects As Studied

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