Polyisoprene dielectric relaxation

FIGURE 24.10 Dielectric relaxation times from Figures 24.7 through 24.9 plotted versus 7V, with mode independent -y = 3.0 (1,4-polyisoprene), = 2.5 (polypropylene glycol), and = 2.65 (polyoxyhutylene). 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

The best proof of invalidity of the confinement scenario is provided by the DSC and dielectric relaxation data from Arrese-Igor et al. (2010) on the highly asymmetric blends of polyisoprene (PI) of molecular weight Af = 2700 with poly(tert-butylstyrene) (PtBS) of two different molecular weights M = 1300 and Mn = 2300. Their DSC measurements confirm the presence of two separate glass transition temperatures of the PI and the PtBS components for blends with less than 50% of PI. The components Tgf and Tgs of PI and PtBS in 35% and 20% PI blends from DSC are indicated by arrows in Figures 5.28 and 5.29, where the dielectric relaxation times data are presented in an Arrhenius plot. Like that discussed before in the PEO/PMMA blends, the detection of Tgf of the fast component by DSC, PI in the present case has basically ruled out the confinement scenario. This is because the relaxation time of order of 100 s obtained by DSC has to be that of the a-relaxation of the PI component. 

Both cis-polyisoprene (PI) and poly(vinyl ethylene) (PVE) have the type-B dipoles perpendicular to the chain backbone, and PI also has the type-A dipoles parallel along the backbone (cf. Figure 3.2). The dielectric relaxation detects the fluctuation of these dipoles, as explained in Section 3.2.2. The fluctuation of the type-B dipoles is activated by the fast, local motion of the monomeric segments, which enables the dielectric investigation of this motion. In contrast, the slow dielectric relaxation of PI due to the type-A dipoles exclusively detects the fluctuation of the end-to-end-vector R (see Equation 3.23). These dielectric features of PI and PVE are clearly noted in Figure 3.11, where the e" data are shown for a PI/PVE blend with the component molecular weights Mp, = 1.2 x 1(P and Mpyp = 6 x 1(P and the PI content rvpi = 75 wt% (Hirose et al., 2003). The data measured at different temperatures are converted to the master curve after the time-temperature superposition with the reference temperature of T, = -20°C, as explained later in more detail. The three distinct dispersions seen at high, middle, and low... 

Watanabe, H., Y. Matsumiya, E. van Ruymbeke, D. Vlassopoulos, and N. Hadjichristidis. 2008. Viscoelastic and dielectric relaxation of a Cayley-tree type polyisoprene Test of molecular picture of tube dilation. Macromolecules 41 6110-6124. 

FIGURE 21.11. Dependence of the mean dielectric relaxation time, T = (2 irr max) on molecular weight, M, for the normal mode process of c/s-1,4-polyisoprene (A) at 320 K data are reported by Adachi and Kotaka ( ) in [5a]. Taken from [5b] with permission. 

The DRIS formalism has been recently used [84] for the theoretical interpretation of dielectric relaxation measurements of bulk cis-polyisoprene (cis-PIP)... 

P. G. Santangelo and C. M. Roland, Temperature Dependence of Mechanical and Dielectric-Relaxation in Cis-l,4-Polyisoprene Macromolecules 31, 3715-3719 (1998). 

Watanabe, H., Yamada, H. Urakawa, O. (1995). Dielectric relaxation of dipole-inverted cis-polyisoprene solutions, Macromolecules 28(19) 6443-6453. doi 10.1021/maOO 123a009. 

We now turn from binary polymer solvent systems to ternary polymer matrix solvent systems. Dielectric relaxation studies using polyisoprenes as probe chains in polybutadiene -heptane solutions were examined by Urakawa,... 

Dielectric relaxation spectra of cfs-polyisoprene in benzene, at concentrations from the dilute up almost to the melt, were obtained by Adachi, et a/. (4). The polymer s and were 86 and 102 kDa, respectively. Relaxation spectra are shown in Eigure 7.9 lower-frequency stretched exponentials and higher-frequency power laws describe each spectrum well, though both frequency regimes were not reached with every solution. The exponentials are clearly stretched, with 5 < 1 the power-law exponents x e (1.2,1.38) are seen to be close to those of other polyisoprene systems. For the most concentrated solutions at very high frequency, an additive constant reflects the first visibility of the higher-frequency segmental diffusive modes, as explored by Adachi, era/. (31). 

Figure 7.16 Dielectric relaxation spectrum of a 47.7 kDa Mw di-polyisoprene having nonparallel dipoles due to one inversion at the molecular center, dissolved in 700 Da polybutadiene at a concentration of 27 g/1, using original measurements by Watanabe, etal.Cil), with simple-exponential and power-law fits.

Figure 7.17 Dielectric relaxation spectrum of a 21 kDa triblock copolymer (58 g/1 in hexadecane) in which the central 3 kDa is the type-A c -polyisoprene and the two terminal ends are 8 kDa dielectrically inert polybutadienes, using original measurements by Adachi, et al.(2). The high- and low-frequency features are here interpreted as segmental motion and whole-chain reorientation, respectively.

H. Watanabe, O. Urakawa, and T. Kotaka. Slow dielectric relaxation of entangled linear cw-polyisoprenes with asymmetrically inverted dipoles. 1. Bulk systems. Macromolecules, 26 (1993), 5073-5083. 

O. Urakawa and H. Watanabe. Dielectric relaxation of dipole-inverted cis-polyisoprenes in solutions Concentration dependence of the second-mode relaxation time. Macromolecules, 30 (1997), 652-654. 

Dielectric properties reflect different averages of chain configuration and motion than viscoelastic properties and can thus be used to track features of chain dynamics that are different from those to which the stresses respond [27]. For example, the longest dielectric relaxation time is twice the longest Rouse stress relaxation time. Thus, this technique is useful for evaluating molecular models for relaxation processes, particularly constraint release mechanisms in the tube model as shown in Section 9.5.3.1. Cis-polyisoprene is particularly well suited for dielectric relaxation studies [28]. 

Bahar, I., Erman, B., Kremer, F., Fischer, E. Segmental motions of cis-polyisoprene in the bulk state—interpretation of dielectric-relaxation data. Macromolecules 25(2), 816-825... 

Fig. 1.3 Relaxation map of polyisoprene results from dielectric spectroscopy (inverse of maximum loss frequency/w// symbols), rheological shift factors (solid line) [7], and neutron scattering pair correlation ((r(Q=1.44 A )) empty square) [8] and self correlation ((t(Q=0.88 A" )) empty circle) [9],methyl group rotation (empty triangle) [10]. The shadowed area indicates the time scales corresponding to the so-called fast dynamics [11]...

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Comparison of the dielectric and viscoelastic relaxation times, which, according to the above speculations, obey a simple relation rn = 3r, has attracted special attention of scholars (Watanabe et al. 1996 Ren et al. 2003). According to Watanabe et al. (1996), the ratio of the two longest relaxation times from alternative measurements is 2-3 for dilute solutions of polyisobu-tilene, while it is close to unity for undiluted (M 10Me) solutions. For undiluted polyisoprene and poly(d,/-lactic acid), it was found (Ren et al. 2003) that the relaxation time for the dielectric normal mode coincides approximately with the terminal viscoelastic relaxation time. This evidence is consistent with the above speculations and confirms that both dielectric and stress relaxation are closely related to motion of separate Kuhn s segments. However, there is a need in a more detailed theory experiment shows the existence of many relaxation times for both dielectric and viscoelastic relaxation, while the relaxation spectrum for the latter is much broader that for the former. 

For rubbers such as NR (or synthetic 1,4-polyisoprene) (Santangelo and Roland, 1998) and polybutadiene (both 1,2- and 1,4-isomers) (CareUa et al., 1986), LCB increases the temperature sensitivity of the viscosity and terminal relaxation time. Thus, by comparing apparent activation energies, or, in the more usual case where the behavior is non-Arrhenius, the temperature dependence of the ratio of relaxation times for an unknown and a linear sample of the same polymer, inferences can be drawn concerning LCB (Figure 3.9). For polymers such as 1,4-polyisoprene, which have a dipole moment parallel to the chain, dielectric measurements of the normal mode can be used to measure the temperature dependence and thus assess the presence of LCB. 

Interesting entanglement relaxation behavior is observed in zones III and IV. As an example of this behavior. Figure 3.5 shows the G and G" data for binary blends of monodisperse linear ds-polyisoprene (PI) samples with Ml = 2.1 X 1(P (PI21) and M2 = 3.1 x 1(P (PI308) reported by Watanabe et al. (2004a). The data for the dielectric loss e" are also shown (bottom panel). Those M, are well above Me,buik (= 5.0 x 10 for bulk PI), and the components are mutually entangled in the blends. 

Test of time-temperature superposability for dielectric loss data of a miscible blend of cis-polyisoprene (PI12 Mp, = 1.2 x 1(H) and poly(vinyl ethylene) (PVE60 Mpyp = 6 x 1(H) with the PI content rup, = 75 wt%. (Data taken, with permission, from Hirose, Y, O. Urakawa, and K. Adachl. 2003. Dielectric study on the heterogeneous dynamics of miscible polyisoprene/ poly(vinyl ethylene) blends Estimation of the relevant length scales for the segmental relaxation dynamics. Macromolecules 36 3699-3708.)... 

Hirose, Y., O. Urakawa, and K. Adachi. 2003. Dielectric study on the heterogeneous dynamics of miscible polyisoprene/poly(vinyl ethylene) blends Estimation of the relevant length scales for the segmental relaxation dynamics. Macromolecules 36 3699-3708. 

Watanabe, H., Y. Matsumiya, and T. Inoue. 2002. Dielectric and viscoelastic relaxation of highly entangled star polyisoprene Quantitative test of tube dilation model. Macromolecules 35 2339-2357. 

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