Comparative Study on the Molecular Dynamics of a Series of

Article pubs.acs.org/Macromolecules

Comparative Study on the Molecular Dynamics of a Series of Polypropylene Glycols K. Kaminski,*,†,‡ W. K. Kipnusu,‡ K. Adrjanowicz,§ E. U. Mapesa,‡ C. Iacob,‡ M. Jasiurkowska,‡ P. Wlodarczyk,⊥ K. Grzybowska,† M. Paluch,† and F. Kremer‡ †

Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland Institute of Experimental Physics, University of Leipzig, Linnestrasse 5, 04103 Leipzig, Germany § NanoBioMedical Centre, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan, Poland ⊥ Institute of Non-Ferrous Metals, ul. Sowinskiego 5, 44-100 Gliwice, Poland ‡

ABSTRACT: Broadband dielectric spectroscopy (BDS) is employed to study the molecular dynamics of hydroxyl- (OH-) and amino- (NH2-) terminated polypropylene glycols (PPGs) of varying molecular weight. Besides the dynamic glass transition (α relaxation), a normal mode process and a secondary γ-relaxation is observed, the latter being assigned to librational fluctuations of the polar COC moiety. Additionally a further process is found and proven in two independent experiments (annealing PPGs at high temperatures and physical aging) to originate from residual H2O impurities in the sample and is therefore not related to the dynamics of PPG. It is occasionally, albeit incorrectly, discussed in the literature as Johari−Goldsten (JG) relaxation. Furthermore, aging in the systems under study is analyzed and found to follow the Nagel−Leheny equation.

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shown by Engberg et al.4 Such a direct comparison between polypropylene glycols terminated by OH and CH3 exhibited a pronounced effect of the strong H-bonds on the dynamics of polymers. It should be stressed that change of the character of intermolecular interaction (removal of H-bonds) also has great impact on the dynamics of the glassy state of glycols. Grzybowska et al30 investigated dipropylene glycol (DPG) that exhibits two secondary relaxation processes and a modified sample having no hydroxyl groups. From high pressure measurements of DPG, they found that the slower process (β) seen as an excess wing is sensitive to pressure while the faster one observed as a well separated relaxation peak is insensitive. This finding, supported by the predictions of the coupling model by Ngai, enabled the identification of the β process in polypropylene glycols as a genuine JG process.31 On the other hand, insensitivity of the γ process to the compression was a clear indication of its intramolecular origin. In fact Grzybowska et al.30 pointed out that in the modified sample (having no ability to form H-bonds) the γ- relaxation process was completely suppressed. Consequently, it was concluded that this mode in DPG and in the whole family of glycols is connected to the hydrogen bonds Finally, the behavior of molecular dynamics of PPGs under high pressure provides useful information about H-bonds.32−34 It was demonstrated in DPG that the fragility index increases with compression as usually observed for the H-bonded systems. However, after passing some threshold value of pressure (p≈800 MPa), the steepness index starts to drop, achieving at p = 1.7 GPa the same value as that determined

INTRODUCTION Polypropylene glycols (PPGs) are glass forming polymer model systems. Numerous studies devoted to the molecular dynamics of PPGs by different techniques such as dielectric spectroscopy,1−10 calorimetry,11 various light scattering methods12−14 mechanical experiments,15 neutron scattering,16 and nuclear magnetic resonance (NMR)17 have been performed. Dielectric studies revealed that PPGs having higher molecular weight (2000 and 4000) exhibit a normal mode relaxation process similar to what has been reported for polyisoprene,18−21 poly(oxyethylene)22 or polylactide.23 The normal mode, which is slower than the structural relaxation, is observed only in macromolecules having a net dipole moment parallel to the main chain (type A polymer).24 The net dipole moment is given by summation of dipole moments of monomeric units aligned along the main backbone. The dielectric strength of the normal mode depends on the square of the dipole moment, molecular weight and fluctuation of the end-to-end vector of the chain. Very recently, Gainaru et al25 showed that the normal mode of PPGs having intermediate molecular weight is described very well by the Rouse model.26 However, it is worth noting that previous works27,28 have reported a breakdown of this model near Tg. Moreover the breakdown of themorheological complexity found in PPG 400 and 4000 by Schlosser and Schoenhals is well demonstrated and explained in ref 29. It was also observed that the glass transition temperature (Tg) does not strongly depend on the molecular weight for the studied PPGs. Significant change in Tg was observed only in the case of monomers and dimers of propylene glycol. Thus, it was concluded that structural relaxation dynamics is rather insensitive to the chain length variation. On the other hand, completely different behavior was found in the case of propylene glycols terminated by the CH3 moiety; in these systems, the dynamics was strongly dependent on the Mw as © 2013 American Chemical Society

Received: December 21, 2012 Revised: January 31, 2013 Published: February 20, 2013 1973

dx.doi.org/10.1021/ma302611x | Macromolecules 2013, 46, 1973−1980

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from ambient pressure data.35 Moreover, high pressure measurements confirmed very unusual behavior of the γrelaxation around the glass transition temperature in tripropylene glycol. At ambient pressure, the temperature dependence of the γ-relaxation in this compound showed a minimum closer to Tg. However, many authors questioned this finding and considered it as an artifact originating from the strong overlapping of the structural and fast secondary relaxation process around the glass transition temperature. Under high pressure measurements, both modes were clearly separated and hence, it was demonstrated that the peculiar behavior of the secondary relaxation process around Tg has a real physical origin.36 In this context one can also refer to the paper by Ngai et al37 who provided the physical picture for this experimental finding. Finally, high pressure data enabled to quantify the relative contribution of density and temperature to the structural relaxation process. It turns out that temperature is a dominant factor governing molecular dynamics of propylene glycols just as expected for the H-bonded glass formers, although volume contributions cannot be neglected.38 In this paper we present dielectric data for two series of polypropylene glycols terminated by hydroxyl and amino moieties. It is well-known that the strongest and the most effective hydrogen bonds are formed by the hydroxyl groups as opposed to the much weaker H-bonds obtained between amino units. We therefore probe the effect of the strength of H-bonds (formed by terminal amino/hydroxyl groups) on the molecular dynamics of polypropylene glycols. In the current study, we found several differences between the dynamics of OH- and NH2-terminated polypropylene glycol. These include the following: dependence of the glass transition temperature on molecular weight, change in relative ratio between dielectric strength of structural and normal mode, shape of the structural relaxation process and fragilities. Moreover, we also analyzed and discussed aging data collected for both types of polypropylene glycols. We observed that isostructural relaxation times in the glassy state follow the same temperature dependence irrespective of the molecular weight of the investigated PPGs. Finally, we have demonstrated that isostructural relaxation times can be evaluated from the analysis of the fast relaxation process, just as in the case of saccharides,39 using the approach recently proposed by Casalini and Roland.40

employing a nitrogen gas cryostat, and temperature stability of the sample achieved was better than 0.1 K. Calculations of dimer structures were performed by means of density functional theory (DFT) with use of X3LYP hybrid functional which is dedicated for the hydrogen bond description. The geometry was optimized on the X3LYP/631G** level of theory. Interaction energies were calculated at X3LYP/6-31++G** level of theory. All calculations were performed using Orca quantum package ver. 2.9.0.51

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RESULTS AND DISCUSSION Computations. In order to get information about strength of H-bonds in the samples studied herein, we carried out DFT calculations. One should expect that substitution of the terminal OH group by NH2 significantly affects the molecular dynamics as a result of the change in the H-bonding network. In order to check this expectation, hydrogen bond energies, distances and angles in the molecular dimers consisting of two tripropylene glycols (TPG) with OH and NH2 (PPG 200) terminal groups, have been calculated. Interaction energies are determined as a difference between the energy of a dimer and that of two single isolated molecules (EI = Ed − Es1 − Es2). The interaction energy is a sum of van der Waals and hydrogen bond energy. The van der Waals energy in case of attraction of two small molecules is approximately equal to 5 kJ/mol, therefore it should be comparable in both TPG dimers. The major part of interaction energy is hydrogen bond energy. Thus, ability to form hydrogen bonds can be estimated by direct comparison of interaction energies EI of both dimers. In Scheme 2, two optimized dimers as well as all hydrogen bond parameters are presented. As one can see in case of TPG Scheme 2. Structures of TPG Dimers with OH and NH2 Terminal Substituentsa

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EXPERIMENT AND COMPUTATION Polypropylene glycols (terminated by OH and NH2 groups) with purity higher than 98% were supplied by Sigma-Aldrich. The chemical structures are presented in Scheme 1. For clarity, PPGs of molecular weight 200, 400, 1025, 2000, and 4000 have degrees of polymerization (n) equal to 2, 5, 16, 33, and 68, respectively. Isobaric measurements of the dielectric permittivity ε*(ω) = ε′(ω) − iε″(ω) were carried out using the Novo-Control Alpha dielectric spectrometer over the frequency range from 10−2 to 107 Hz. The temperature was controlled by the Quatro system,

a

Introduction of NH2 group in place of OH causes significant drop in the ability of forming hydrogen bonds.

with NH2 terminal groups, NH---O hydrogen bond practically does not exist, while OH---O is a fairly strong H- bond in the OH-ended TPG. Interaction energy between two OH-ended TPG molecules is 2.5 times higher than the energy between NH2-ended TPGs (15.7 vs 6.4 kJ/mol). Moreover, the distance between donor hydrogen and acceptor oxygen in OH-ended TPGs is 2A, which is typical for strong hydrogen bonds. This simple analysis leads to the conclusion that in the regular PPG sample, hydrogen bonds formed between terminal hydroxyl

Scheme 1. Chemical Structures of Investigated Polypropylene Glycols with n = 2, 5, 16, 33, and 68

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molecular weight in standard polypropylene glycols is related to the formation of strong effective H-bonds between different chains. This is corroborated by the work reported by EckertKastner et al13,14 who carried out dynamic as well as static light scattering measurements on PPG and PEG blends. They observed cluster formation which significantly affected molar mass and its distribution in examined samples. On the other hand, the shape of the structural relaxation in amino terminated PPGs is independent of the Mw. Similar finding was reported for polystyrene,41 poly(dimethylsiloxane),42 and polyisobutylene,43 all being polymers without H-bonds. One can suppose that in case of amino-ended PPGs, the strength of these peculiar interactions has been significantly reduced, limiting abilities to form clusters. Thus, the molar mass as well as polydispersity of the sample was not significantly affected . As a result, the α-loss peak is invariant to the change in molecular weight. It is also worth noting that the shape of the structural relaxation process in amino- and hydroxyl-terminated PPG 4000 is the same. It means then that at this molecular weight, the role of H-bonds is almost negligible. Thus, the α-loss peaks of both materials are the same. In Figure 2, panels e and f, we also depict dielectric loss spectra measured at almost the same temperatures for aminoand hydroxyl-terminated PPG 4000 and PPG 2000. The loss spectra were normalized with respect to the maxima of the structural relaxation process of PPGOH 4000. At the isochronal conditions, it is clear that (i) the separation between the normal mode and the structural relaxation process becomes greater with increasing molecular weight, (ii) the dielectric strength of the normal mode decreases slightly with the increase in molecular weight, and (iii) the separation between primary relaxation and normal mode is slightly greater in amino- than in hydroxyl-terminated PPGs. In Figure 3a, the dielectric strengths of the normal mode and structural relaxation process in the amino- and hydroxylterminated PPG 4000 are plotted versus inverse temperature. The Δε were obtained from the analysis of the loss peaks of the normal mode and structural relaxation using the HavriliakNegami function. In Table 1 representative Havriliak−Negami parameters obtained for the hydroxyl- and amino-terminated PPG 2000 and 4000 at three different temperatures are collected. It can be seen that the dielectric strength of the normal mode in amino glycols is almost the same as in nonmodified samples. Moreover, in Figure 3b, the temperature dependence of the relative ratio (R) between the normal mode and structural relaxation in both types of PPG 4000 are depicted. We observe that R is larger in amino-terminated polypropylene glycols. In order to account for these observations, we calculated the dipole moments that are parallel and perpendicular to the skeleton of examined PPGs. As a first step, eq 1, which is commonly used to determine the dielectric strength of the normal mode, was applied

OH groups and oxygen atoms form bridges in the PPG chain that cause the entire structure to be more rigid than the PPG molecules with amino (NH2) groups at the ends of the chains. As a consequence of these structural modifications, the molecular dynamics of both series of PPG differ. However, it is worth adding that influence of H-bonds on the dynamics of PPGs is expected to be significant only in the case of very small systems such as PPG200 or 400. On the other hand, the role of H-bonds should be less important with increasing length of the chain. Dielectric Data. The dielectric data shows that besides the structural relaxation, the normal mode process is observed for samples having molecular weight greater than 400. The normal mode becomes more separated from the α- relaxation with increasing degree of polymerization. Consequently, the normal mode is well separated in PPGs having molecular weight higher than 1000 g/mol. In Figure 1, dielectric loss spectra measured for the hydroxyland amino-terminated PPG 4000 are presented. It is clear that

Figure 1. Dielectric loss spectra measured for (a) PPG OH 4000 and (b) PPG NH2 4000 above and below the glass transition temperature..

in both cases there are two relaxation processes i.e normal mode and structural process above the Tg. Hence, substituting OH units by amino moiety did not affect orientation of the dipole moments which still seems to be aligned along the contour of the skeleton of the polymer. Consequently, in amino glycols, one can follow dynamics of the normal mode by means of dielectric spectroscopy. From the loss spectra presented in Figure 1, it can also be deduced that both relaxation processes are sensitive to the temperature change although the α process seems to be more sensitive to the temperature drop than the normal mode. After passing the glass transition, secondary relaxation processes become detectable in the available frequency window. We can observe one well separated secondary relaxation process in both hydroxyl- and amino- terminated PPG 4000. The origin of these modes and the additional one which is usually reported in literature (not seen in our loss spectra) will be discussed later in this article. In Figure 2, panels a−d, dielectric loss spectra measured close to the glass transition temperature for the series of hydroxyl- and amino-terminated PPGs having different molecular weights are presented. It can be seen that in case of standard (that is, OH-terminated) polypropylene glycols, the α-loss peak becomes broader with increasing molecular weight. The change in shape of the α-loss peak with decreasing

Δε =

4 ∏ NAμII 2 FOnsager 3kTM w

⟨r 2⟩

(1)

where μII2, is the square of the dipole moment parallel to the polymer chain per monomer unit, Mw is the molar mass of the chain, NA is the Avogadro number, Fonsager ≈ 1 is the internal field factor and ⟨r2⟩ is the time correlation function that is proportional to the fluctuation of the end-to-end-vector. Equation 2 shows that slight differences in Δε of normal modes in amino- and hydroxyl-terminated polypropylene 1975


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Figure 2. (a and b) Superimposed structural loss spectra measured for PPGOH having different molecular weights. (c and d) superimposed loss spectra of the PPGNH2 measured at indicated temperatures. (e and f) Superimposed loss spectra measured for (e) PPG 4000 terminated by hydroxyl and amino moieties; and (f) PPG 2000 terminated by hydroxyl and amino moieties, as indicated.

Figure 3. Dielectric strength of the normal mode (NM) and structural relaxation (α) process plotted versus inverse temperature for the hydroxyland amino-terminated PPG 4000 (a); relative ratio, R, between the dielectric strength of the normal mode and structural relaxation process of the same samples is shown in part b.

glycols can be mainly associated with the μII2. The ⟨r2⟩ can be assumed to be identical for the PPGs in the current study since they have almost the same backbone structure. Hence, by comparing the dielectric strength of the PPGs having the same Mw, the following expression is obtained: μIINH

2 2

= μIIOH

2

is the dipole moment aligned along the contour of PPGNH2. In order to determine the dipole moment perpendicular to the backbone of the PPGNH2, we applied the following equation:25 μII 2 ΔεNM = C∞ 2 Δεα μ⊥

ΔεNH2 ΔεOH

(3)

Here C∞ (≈ 5.05) denotes stiffness of the chains as discussed in ref 25, which should be identical to the stiffness of PPGNH2 because of the similarity in backbone structure. With this assumption, we obtained μ⊥ ≈ 0.75 D for PPGNH2. As can be seen, the values of dipole moments that are parallel and perpendicular to the backbone are slightly smaller in case of PPGs terminated by the NH2 units.

(2)

Using the dielectric strengths of the normal mode in aminoand hydroxyl-terminated PPGs estimated from dielectric measurements, and the value of μIIOH = 0.16 D obtained from the work by Gainaru et al.,25 we get μNH2 ≈ 0.155 D which 1976


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Table 1. Havriliak−Negami Parameters Havriliak−Negami α process

Havriliak−Negami Normal Mode temp, K 232 218 208 232 218 208 244 228 216 244 228 216

sample PPGOH 2000 PPGOH 2000 PPGOH 2000 PPGNH2 2000 PPGNH2 2000 PPGNH2 2000 PPGOH 4000 PPGOH 4000 PPGOH 4000 PPGNH2 4000 PPGNH2 4000 PPGNH2 4000

Δε 0.71 0.89 0.77 0.45 0.66 0.52 0.56 0.67 0.68 0.55 0.66 0.71

τ [s]

α −4

3.32 × 10 0.024 1.63 1.25 × 10−4 0.005 69 0.38 1.47 × 10−4 0.0055 0.303 1.13 × 10−4 0.0036 0.1846

0.92 0.93 1 0.91 0.92 0.93 0.95 0.97 0.91 0.93 0.94 0.93

β 0.74 0.56 0.41 0.75 0.47 0.55 0.58 0.49 0.64 0.53 0.46 0.48

Δε 4.98 5.29 5.55 2.80 2.93 3.11 2.87 3.40 3.61 2.32 2.90 3.06

τ [s] 2.95 × 3.51 × 0.17 9.14 × 6.84 × 0.019 1.63 × 6.90 × 5.97 × 1.24 × 4.32 × 7.49 ×

−6

10 10−4 10−7 10−5 10−7 10−6 10−4 10−7 10−6 10−4

α

β

0.88 0.91 0.85 0.84 0.91 0.84 0.84 0.89 0.86 0.81 0.85 0.84

0.45 0.42 0.48 0.47 0.37 0.44 0.62 0.42 0.45 0.74 0.44 0.43

values of Tg obtained for the samples under study are plotted against Mw in Figure 5a. Tg increases only slightly with increase

The characteristic relaxation rates of the structural, normal mode and secondary relaxation processes were determined from the respective loss peaks using Havriliak−Negami functions and their temperature-dependences are plotted in Figure 4. Additionally, in the relaxation map, we also included β-relaxation times for hydroxyl-terminated PPG that were taken from literature.25

Figure 5. (a) Dependence of the glass transition temperature on molecular weight for the amino- and hydroxyl-terminated PPGs. The solid lines are fits to eq 7. The molecular weight dependence of the fragility of the studied materials is presented in part b.

of the molecular weight in nonmodified PPGs in accordance with what was previously reported in literature. On the other hand, the Tg of amino-terminated glycols depends on Mw in agreement with the Fox−Flory equation:

Figure 4. Relaxation times versus inverse temperature for the PPG samples studied in the current work. Some data from the literature (L)25 is also included in this relaxation map. Inset: Dielectric loss spectra of PPG NH2 showing water relaxation which is removed after annealing.

Tg = Tg ∞ −

(4)

while the secondary relaxation processes are described by the Arrhenius equation written as:

⎛ E ⎞ τβ = τ0exp⎜ a ⎟ ⎝ kBT ⎠

(6)

where C is an empirical constant connected to the free volume present in the polymer sample. By fitting the data in Figure 6a by eq 6, we obtained Tg∞ = 200.5 K and 199 K for the polypropylene glycols terminated by the OH and NH2 groups, respectively. It can be seen that the variation of Tg with Mw decreases with the increase in degree of polymerization for both groups of polymers. Slightly higher Tg∞ in standard PPGs is related to the stronger H-bonding interaction between chains. Thus, weakening of the strength of H-bonds has significant effect on variation of Tg with Mw at least below the entanglement molecular weights. We recall that the entanglement molecular weight of the hydroxyl-terminated PPG was estimated to be equal to Mw = 5500 g/mol.44 In this context, one must be reminded of the fact that it has been reported that the glass transition temperature for polystyrene (Mw = 2000 g/

The structural and normal mode follow the Vogel-FulcherTammann (VFT) equation given by: ⎛ D T ⎞ τα = τ0 exp⎜ T 0 ⎟ ⎝ T − T0 ⎠

C Mw

(5)

Dynamics of the Structural Relaxation Process. The glass transition temperature Tg is usually estimated from dielectric data as the temperature at which τα = 100 s. The 1977


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expected that for a very high degree of polymerization, the role of H-bonds is marginal. Dynamics of Secondary Relaxation Processes. As stated earlier, there are two secondary relaxation processes reported in literature in the glassy state of hydroxyl-terminated PPGs while only one can be detected in amino-terminated ones. It was shown that the slow (β) process (not seen in our measurements) in hydroxyl-terminated PPGs is sensitive to pressure and satisfies the criteria of the coupling model by Ngai.31 Hence, it was classified as a genuine JG relaxation process. On the other hand, Grzybowska et al have proven that fast relaxation (γ) (observed in our loss spectra) in OHterminated PPG is surely connected to the hydrogen bonds.30 Since activation energies of the γ mode in amino- and hydroxylterminated PPGs are the same, we can expect that fluctuation of the terminal groups is the source of the observed secondary relaxation process in both series of polypropylene glycols. Very recently, another point of view on the origin of the β-process in polypropylene glycols was presented by Gainaru et al.25 who showed that by simple annealing at temperatures higher than 423 K, one can suppress this relaxation. Hence, it was concluded that this mode is not a JG relaxation, but is rather connected to the residual moisture present in the investigated samples. Suffice to say that we have also made the same observation in the current work(see inset to Figure 4); samples exposed to ambient atmosphere, exhibited a “slow β-process” which disappeared after the sample was annealed at 423 K in nitrogen atmosphere for 6 h. It follows therefore, indeed, that the so-called β-relaxation in polypropylene glycols is related to the residual water. This is further corroborated by the fact that, contrary to what was shown in literature, it does not satisfy the predictions of the coupling model (CM) as shown later in this discussion. The γ-process observed in all samples was not affected by annealing and has identical activation energy Ea ∼ 30 kJ/mol. This process is connected to H-bonds as shown by Grzybowska et al.30 In Scheme 3, we schematically provide a simple visualization of all modes observed in our studied samples. Aging Experiment. In order to obtain the isostructural relaxation times deep in the glassy state, physical aging experiments were performed for OH- and NH2-terminated PPGs. Basing on this approach, the permittivity is measured as a function of time at fixed frequency and temperature (below Tg). We analyzed the dielectric loss spectra in the vicinity of the maximum of the γ process which also gives reliable results in case of H-bonded systems.39 In Figure 6c, representative dielectric loss spectra measured much below the glass transition

Figure 6. (a and b) Time dependence of the permittivity measured at indicated frequencies in amino- and hydroxyl-terminated PPG 4000. The solid lines are the best fits to the eq 8. Dielectric loss spectra measured during physical aging of amino-terminated PPG 4000 at T = 173 K are shown in part c.

mol) is unaffected by variation of the terminal moiety from H to CN.45 However, in the current work, a change in Tg is expected since an alteration of the terminal group affects the overall strengths of the intermolecular interactions. We also calculated fragility index from eq 7 and plotted it versus Mw as shown in Figure 5b. m = d(log10 τα)/d(Tg /T )|(Tg / T ) = 1

(7)

This parameter changes with molecular weight in standard PPGs while in case of amino-teminated PPGs, it is almost invariant. The fragility of polymers is affected by symmetry of the monomer, presence of bulky pendant groups, tacticity, and stereogeometry as well as packing.45−48 Since modified and nonmodified PPGs have almost the same skeleton, their fragilities should be mainly determined by intermolecular interactions as demonstrated in the section devoted to the DFT calculations. As can also be seen from Figure 5, there’s a significant difference between the glass transition temperature as well as fragility observed in the amino- and hydroxyl-PPGs of low molecular weight. However, as the main skeleton becomes longer these discrepancies become smaller and seem to vanish for polypropylene glycols of very high molecular weight. This is related to the weakening of the role of H-bonds in governing the molecular dynamics of samples studied herein. It is

Scheme 3. PPG Hydroxyl-Terminated PPG with Degree of Polymerization n = 6 with the Assignments of the Normal Mode, α-, β-, and γ-Relaxations

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τ0 = (tc)n (τα)1 − n

temperature for the PPGNH2 4000 are shown. The amplitude of γ-process decreases due to decrease of the local density fluctuations which govern the amplitude of these motions (i.e., the average angle of orientation and number of fluctuating dipoles). The time dependence of the dielectric loss measured at fixed frequencies at three different temperatures in amino- and hydroxyl-terminated PPGs are shown in Figure 6, parts a and b. The data was fitted by the following equation derived by Nagel and Leheny.49 ⎫ ⎧ ⎡ t ⎤ βag ⎨Δε″(f ̃ , tag ) exp⎢ ag ⎥ + εeq″(f ̃ )⎬ ⎣ τag ⎦ ε″(f ̃ , tag ) ⎭ ⎩ = ̃ ̃ ε″(f , tag = 0) ε″(f , tag )

(9)

where (1 − n) is the stretch exponent (βKWW = 0.5), τα is the isostructural relaxation time and tc = 2 ps. In Figure 4, the results of these calculations show that primitive relaxation times estimated from eq 9 do not match experimental data for the βprocess seen in PPGOH. This further supports the fact that βrelaxation observed in polypropylene glycols is not a JG process as suggested in literature, but originates from the residual moisture.

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CONCLUSIONS In this paper, two series of very similar polypropylene glycols of different molecular weights terminated with OH and NH2 units have been investigated. We found that change in interactions (weakening of the strength of the H-bonds) has a real impact on the dynamics of the structural relaxation process while in case of the normal mode this effect is much less pronounced. It was shown that the shape of the structural relaxation process gets broader with increasing molecular weight in PPGOH while it is constant for amino-terminated PPGs. This peculiar behavior can be explained in view of the cluster formation in PPGOH. This process probably influences effective molecular weight of the sample. Moreover, we demonstrated that Tg and fragility have different dependences on molecular weight of the polypropylene glycols. Evolution of fragility in polymers was described in view of the change in strength of H bonds in PPHOH and PPGNH2. We also calculated the dipole moments that are parallel and perpendicular to the backbone of the PPG 4000 terminated by the OH and NH2 units. In addition we demonstrated that the apparent β-process in PPGs originates from residual moisture. Finally, to complete the relaxation map of glycols, physical aging was carried out. Basing on this experiment, we were able to estimate isostructural relaxation times deep in the glassy state of investigated materials. Interestingly, below Tg, isostructural relaxation times follow the same temperature dependence irrespective of the sample. Moreover, independent analysis of aging data enabled us to certify that in fact βag is very close to the βKWW that is evaluated from analysis of the α-loss peak in the vicinity of the glass transition temperature.

(8)

where ε”eq(f) ≡ ε” ( f, tag → ∞) is an equilibrium value, Δ ε” ( f, tag) = ε″ ( f, tag = 0) − ε″eq is the change of ε″ during aging, τag is the aging time (which is identified with the structural relaxation time τα), βag is the stretch exponent (βag(T < Tg) = βKWW(Tg), which can be obtained from fitting the KWW function to the structural loss peak measured above or in the vicinity of the Tg. It was found that βag does not vary with temperature and is equal to βKWW.40,50 During the fitting procedure, we used βag fixed to 0.61 (PPG 400), 0,55 (PPG 2000) and 0.5 (PPG 4000 and amino glycols). The isostructural relaxation times were obtained from the simultaneous fitting of all curves with fixed stretch exponent. To confirm that βag is approximately equal to βKWW, (in the vicinity of the glass transition temperature) we fitted the data with βag as a free parameter and found that these two parameters (βag βKWW) are identical within the range of uncertainties. The temperature dependence of the isostructural relaxation times obtained from this approach is included in Figure 4. The absolute values are much shorter than the equilibrium structural relaxation times and hence they are referred to as isostructural values.40 It should be stressed that it is commonly discussed that after passing the fictive temperature (Tf), the structure of a glass is nearly fixed and evolves very slowly with time. This implies that configurational entropy Sc remains frozen. One can add that eq 8 should not be used to evaluate structural relaxation times in the vicinity or just below the Tg, because, at such conditions, the structure of glass strongly depends on time of aging and evolves very quickly with time. For this reason we performed aging experiments well below the Tg to be sure that the structure of PPGs was fixed and the evolution of τag was negligible. The isostructural relaxation times in the glassy state (Figure 4) follow an Arrhenius type of thermal activation and are almost the same irrespective of the molecular weight of the sample. However, one should notice that if we jump 2 K below Tg and wait long enough to equilibrate the sample and repeat this procedure upon lowering temperature, then structural relaxation times should follow the VFT dependence. Furthermore, structural relaxation times obtained in such a way are the equilibrium ones. We further used the temperature dependence of the isostructural relaxation times to test the coupling model (CM) predictions for β process in PPGOH 4000 just as it was shown in ref.40 CM is very often used to identify a genuine JG relaxation. On the basis of this approach, the primitive relaxation time τ0, which is often referred as the JG relaxation time, is given by

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS K.K gratefully acknowledges financial support from the Polish National Science Centre within the program Sonata 2 entitled ”High pressure polymerization. The kinetic studies” and the SFB-TRR 102 (Germany). W.K.K. is thankful for funding from the DFG (Germany) and NOW (The Netherlands) within the IRTG focus project: “Diffusion in porous materials”. E.U.M. is grateful for financial support from DFG SPP1369 Priority Program (Polymer-Solid Contacts: Interfaces and Interphases). K.A. acknowledges financial assistance from National Centre for Research and Development (Nanomaterials and their potential application in nanobiomedicine).

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REFERENCES

(1) Pawlus, S. S.; Hensel-Bielowka, S.; Grzybowska, K.; Zioło J. Paluch, M. Phys. Rev. B. 2005, 71, 174107. 1979


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