The segmental dynamics of a miscible polymer blend A. Alegría, I. Cendoya, J. Colmenero, J.M. Alberdi (Univ. Pais Vasco San Sebastián), B. Frick (ILL).

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The segmental dynamics of poly(vinyl methyl ether) (PVME) in a blend containing 65 wt% PVME and 35 wt% D-polystyrene was investigated on the backscattering spectrometer IN10. A quasielastic broadening of the spectra is apparent at T > 350 K and shows a strong dependence on the momentum transfer. We show that an approach which is normally used to describe the blend dynamics on a macroscopic time scale also describes well the neutron results. We also find a good agreement with nuclear magnetic resonance and dielectric spectroscopy.

The segmental dynamics of a miscible polymer blend are different from those corresponding to each of its components. This fact is usually ascribed to fluctuations of concentration (FC) present in such systems.

In this framework the blend can be regarded as a superposition of regions with different relaxation behaviour and which depends on the local concentration of the components j_A and j_B in these regions. Usually, the relaxation function of a pure polymer is found to follow a stretched exponential function. Thus in the blend one might try to superimpose the relaxation functions of the components by taking the concentration fluctuations into account. This approach is in agreement with observations from macroscopic relaxation techniques. From macroscopic measurements it is found that the effect of FC is less noticeable for high temperatures where the characteristic times approach the mesoscopic range (T > T_g + 50 K). However, there is not much direct experimental information available on the mesoscopic and microscopic time or spatial scales. This range can be explored by quasielastic neutron scattering.

Using partial deuteration the dynamics of a single component of a blend can be investigated by neutron scattering. Similarly, in dielectric experiments mainly the relaxation of the component with the higher dipole moment can be observed. Thus, both techniques explore the relaxation function F (t) of one blend component. Within the FC picture F(t) can be regarded as a superposition of distributed relaxation processes, each of these accounting for the pure polymer relaxation F_pure (t).

At temperatures far above T_g, the distribution of relaxation times is well approximated by a log-normal one, so the relaxation of one component in the blend can be written as:

(1)

were t_m is the most probable relaxation time, depending on the average concentration of the investigated component, and s accounts for the distribution width.

The system poly(vinyl methyl ether)/polystyrene (PVME/PS) is one of the most extensively studied miscible polymer blends.

The contribution of PVME to the segmental dynamics of this blend has been studied by means of dielectric relaxation (DR) and nuclear magnetic resonance (NMR) techniques, among others.

We performed QENS on the IN10 backscattering spectrometer investigating a blend (T_g = 260 K) with protonated PVME (65 wt%) and deuterated PS (dPS) (T-range 350-430 K; energy window ± 10 meV and momentum transfer 0.2 Å^-1 < Q < 2 Å^-1 ). Therefore, after data correction, we were looking mainly at the protonated PVME.

Figure 1 (left): QENS spectra of PVME 65%wt/dPS 35%wt blend obtained at 400 K. The solid lines correspond to the simultaneous fitting according to the model proposed in this work.

Figure 2 (right): Temperature dependence of both s, obtained from macroscopic measurements, and the characteristic relaxation times as obtained from macroscopic and microscopic measurements. The solid line was used for the evaluation of the values of s for the fitting of the QENS spectra.

The QENS spectra of this blend show a clear Q-dependent broadening (see Fig. 1). For pure PVME we had found previously that the relaxation function, i.e. the intermediate scattering function I(Q,t), follows a stretched exponential function for 350 K < T < 400 K:

I(Q,t)° exp(2)

and the relaxation time shows a power law dependence on the momentum transfer Q:

As a consequence of this power law one can rewrite eq. 1 as follows:

(4)

Thus the Q-dependence drops out from the distribution function and only the intermediate scattering function I_pure depends on Q. Eq. 4 was used to analyse the blend data. Thereby I_pure (Q,t) was taken from the pure PVME and the distribution width s was fixed from DR and NMR measurements (see Fig. 2). Therefore, in addition to a flat background which accounts for the fast rotation of the PVME methyl group, C_m remains the only relevant fitting parameter. A simultaneous fitting of all Q spectra was performed at each temperature.

The fitting curves to the QENS spectra (see Fig. 1 for 400 K) show that the model can perfectly well describe the segmental dynamics of PVME in the blend. Converting results for C_m from the fits into relaxation times t_m according to eq. 3, we can compare the QENS, dielectric and NMR results.

We find that not only the relaxation times obtained from QENS follow the T-dependence of the macroscopic relaxation times, but they also coincide around the same Q value which has previously been determined for pure PVME (Q = 0.86 Å^-1), see Fig. 2.

Thus a consistent description for the microscopic and macroscopic relaxation behaviour of miscible blends is found.