Signatures of the fast dynamics in glassy polystyrene by multi-frequency, high-field electron paramagnetic resonance of molecular guests

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Abstract

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field Electron Paramagnetic Resonance spectroscopy at three different Larmor frequencies (95 190 and 285 GHz). Two different regimes separated by a crossover region are evidenced. Below 180 K the rotational times are nearly temperature-independent with no apparent distribution. In the temperature range 180–220 K a large increase of the rotational mobility is observed with widening of the distribution of correlation times which exhibits two components: (i) a delta-like, temperature-independent component representing the fraction of spin probes w which persist in the low-temperature dynamics; (ii) a strongly temperature-dependent component, to be described by a power-distribution, representing the fraction of spin probes 1  w undergoing activated motion over an exponential distribution of barrier heights g(E). Above 180 K a steep decrease of w is evidenced. The shape and the width of g(E) do not differ from the reported ones for PS within the errors. The large increase of the rotational mobility of the spin probe at 180 K is ascribed to the onset of the fast dynamics detected by neutron scattering at Tf = 175 ± 25 K.

Introduction

Particular interest and a current subject of strong controversy is the so called fast dynamics of glasses, occurring in the time window 1  102 ps with several studies carried out mainly by neutron [1], [2], [3], [4], [5], Raman scattering [6], [7], [8], [9] and high-field Electron Paramagnetic Resonance (HF-EPR) [10], [11]. It is observed that on heating in a temperature range below the glass transition temperature Tg the dynamics of glass-forming systems deviates from the harmonic behavior and quasielastic scattering starts to accumulate in the low frequency range of the scattering function S(Q,ω). Accordingly, the temperature dependence of the atomic mean-squared displacement also starts to deviate from the linear dependence. We will denote by Tf the onset temperature above which the deviation from the harmonic behavior becomes apparent.

The microscopic origin of the fast dynamics is still a question open to a strong controversy. The role of carbon–carbon torsional barriers to drive the fast dynamics of glass-forming polymers was also pointed out [1]. In the particular case of polystyrene (PS) of interest here, Tf was found to be 175 ± 25 K [3] and 200 K [4]. For PS the onset of the fast motion has been ascribed to the change of the librational dynamics of the side-chain phenyl ring [3], [4] with expected involvement of the main-chain through the connecting bonds [12], [13]. According to Nuclear Magnetic Resonance (NMR) the flip motion becomes frozen at about 190 K [14].

In glasses the dynamics is thermally activated in the substructures of the minima of the energy landscape [15]. Important information is conveyed by the energy barrier distribution g(E) which is only weakly temperature-dependent in the glassy state [16]. For glassy PS this was tested by scaling light scattering data [17]. Buchenau confirmed that conclusion by comparing results from several techniques covering a wide time window from 1 Hz up to about 100 GHz [18]. The same result has been reached by HF-EPR [10], [11], [19].

The shape of the energy-barriers distribution g(E) in glasses has been extensively investigated via experiments [8], [10], [11], [16], [17], [19], [20], [21], [22], [23], [24], theories [25], [26], [27], [28], [29] and simulations [30]. Basically, two different distributions are usually recovered, the gaussian distribution [8], [16], [20], [21], [24], [25], [30], [31] and the exponential distribution [8], [10], [11], [17], [19], [22], [26], [27], [28], [29].

It is interesting to relate g(E) with the density of states, i.e. the distribution of the minima of the energy landscape. On the upper part of the landscape, being explored at high temperatures, the Central Limit theorem suggests that the density is gaussian [30]. At lower temperatures the state point is trapped in the deepest low-energy states which are expected to be exponentially distributed following general arguments [27]. Different models [28] and numerical simulations [29] support the conclusion. In particular, trap models suggest that g(E) has the same shape of the exponential density of states [28] .

If the average trapping time τ before to overcome the barrier of height E at temperature T is governed by the Arrhenius law,τ=τ0exp(E/kT),k being Boltzmann’s constant, the distribution of barrier heights induces a distribution of trapping times ρ(τ). The explicit form of ρ(τ) for an exponential distribution of barrier heights with width E¯ isg(E)=0ifE<Emin,1E¯exp-E-EminE¯ifEEmin,and ρ(τ) is expressed by the power-law distribution (PD)ρPD(τ)=0ifτ<τPD,xτPDxτ-(x+1)ifττPD,with x=kT/E¯ and τPD = τ0exp(Emin/kT). Note that the absence of energy barriers below Emin does not change the shape of ρPD and allows for the temperature dependence of τPD.

If the width of the energy-barriers distribution is vanishingly small, a single trapping time, i.e. a single correlation time (SCT), is found withρSCT(τ)=δ(τ-τSCT).The use of suitable probes to investigate the relaxation in glasses by NMR [14], [20], [21], [23], [32], EPR [31], [33], [34], [35] and Phosphorescence [36] studies is well documented. In particular, during the last few years continuous-wave (CW) and pulsed HF-EPR techniques were developed involving large polarizing magnetic fields, e.g. B0  3T corresponding to Larmor frequencies about 95 GHz (W band), [37], [38] or even larger frequencies [19], [39], [40]. HF-EPR is widely used in polymer science [10], [11], [19], [41], [42], [43], [44]. One major feature is the remarkable orientation resolution [44] due to increased magnitude of the anisotropic Zeeman interaction leading to a wider distribution of resonance frequencies [45]. Recently, HF-EPR studies evidenced the exponential distribution of the energy barriers of the deep structure of the energy landscape [19] as well as clear signatures of the onset of fast motion in glassy PS [43], [44] in full agreement with neutron [1], [2], [3], [4], [5] and Raman scattering [6], [7], [8], [9]. These studies were carried out at 190 and 285 GHz. Here, novel results from HF-EPR at 95 GHz are presented and compared to the previous ones.

Section snippets

Lineshape

The EPR signal is detected in paramagnetic systems. Since most polymers are diamagnetic, paramagnetic probe molecules (spin probes) are usually dissolved in them. The main broadening mechanism of the EPR line shape of the spin probe is determined by the coupling between the reorientation of the latter and the relaxation of the electron magnetization M via the anisotropy of the Zeeman and the hyperfine magnetic interactions. When the molecule rotates, the coupling gives rise to fluctuating

Experimental details

Atactic PS was obtained from Aldrich and used as received. The weight-average molecular weight is Mw = 230 kg mol−1, polydispersity Mw/Mn = 1.64 and Tg = 367 K. The free radical used as spin probe was 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) from Aldrich. TEMPO has one unpaired electron spin S = 1/2 subject to hyperfine interaction with the nitrogen nucleus with spin I = 1. The chemical structures of PS and TEMPO are shown in Fig. 2.

Notice that TEMPO and the phenyl group of PS have similar shape. TEMPO

Results

Fig. 3 shows the lineshape at 95 GHz of TEMPO in PS at 50 K. It is seen that the lineshape is well fitted by a single correlation time (SCT model, Eq. (4), two adjustable parameters, τSCT, ϕ). The small discrepancy between the simulation and the peak at low magnetic field was already noted [38]. At such very slow reorientation rates the lineshape is weakly sensitive to the jump size. In fact, the quality of the fit does not change if the jump angle ϕ spans the range 20°–60°.

Fig. 4 shows the

Discussion

It is interesting to compare the exponential energy-barrier distribution which is experienced by TEMPO, g(E), and gPS(E), i.e. the exponential distribution of barrier-heights of PS which was evidenced by internal friction [22], Raman [8] and light scattering [17]. The measured widths were E¯IF/k=760±40K, E¯Raman/k=530±60K and E¯LS/k=530±40K, respectively. Fig. 6 shows that the distribution of energy barriers g(E) probed by TEMPO has not only the same exponential shape of the PS one, but it

Conclusions

The reorientation of the spin probe TEMPO in PS has been studied by high-field Electron Paramagnetic Resonance spectroscopy at three different Larmor frequencies (95,190 and 285 GHz). Two different regimes separated by a crossover region are evidenced. Below 180 K the rotational times are nearly temperature-independent with no apparent distribution. In the temperature range 180–220 K a large increase of the rotational mobility is observed with widening of the distribution of correlation times

Acknowledgements

J. Colmenero and A.P. Sokolov are gratefully acknowledged for helpful discussions.

References (47)

  • R. Böhmer et al.

    Prog. Nucl. Mag. Reson.

    (2001)
  • E. Rössler et al.

    Polymer

    (1985)
  • H. Blok et al.

    J. Mag. Reson.

    (2004)
  • D. Leporini et al.

    J. Non-Cryst. Solids

    (2002)
  • J. Colmenero et al.

    Phys. Rev. B

    (1998)
  • T. Kanaya et al.

    Adv. Polym. Sci.

    (2001)
  • B. Frick et al.

    Colloid Polym. Sci.

    (1995)
  • T. Kanaya et al.

    J. Chem. Phys.

    (1996)
  • B. Frick et al.

    Phys. Rev. B

    (1993)
  • Y. Ding et al.

    Macromolecules

    (2004)
  • V.N. Novikov et al.

    J. Chem. Phys.

    (1997)
  • A.P. Sokolov et al.

    Europhys. Lett.

    (1997)
  • A.P. Sokolov et al.

    Phys. Rev. B

    (1995)
  • V. Bercu et al.

    Europhys. Lett.

    (2005)
  • V. Bercu et al.

    J. Chem. Phys.

    (2005)
  • J. Schaefer et al.

    Macromolecules

    (1984)
  • R. Khare et al.

    Macromolecules

    (1995)
  • H. Sillescu

    Makromol. Chem., Macromol. Symp.

    (1986)
  • C.A. Angell

    Nature

    (1998)
  • L. Wu et al.

    Phys. Rev. B

    (1992)
  • N.V. Surovtsev et al.

    Phys. Rev. B

    (1998)
  • U. Buchenau

    Phys. Rev. B

    (2001)
  • V. Bercu et al.

    J. Phys.: Condens. Matter

    (2004)
  • View full text