Poly frequency dependence

H.C.F. Martens and H.B. Brom, Frequency-dependent electrical response of holes in poly(/j-phcnylcnc vinylene), Phys. Rev. B, 60 R8489-R8492, 1999. 

The term S represents the strength of the network. The power law exponent m was found to depend on the stochiometric ratio r of crosslinker to sites. When they were in balance, i.e. r = 1, then m - 1/2. From Equations (5.140) and (5.141) this is the only condition where G (co) = G (cd) over all frequencies where the power law equation applies. If the stochiometry was varied the gel point was frequency dependent. This was also found to be the case for poly(urethane) networks. A microstructural origin has been suggested by both Cates and Muthumkumar38 in terms of a fractal cluster with dimension D (Section 6.3.5). The complex viscosity was found to depend as ... 

Fig. 4.13 (a) Semilogarithmic plot of conductivity versus the nanotube content (wt%) in poly(phenylene vinylene-co-2,5-dioctoxy-m-phenylene vinylene) (PMPV) [2]. (b) Frequency dependent conductivity of carbon nanotubes at different wt% in PmPV (filled symbols) and polyvinyl alcohol (PVA) (unfilled symbols) based composites [250]. 

The temperature and frequency dependence of the complex dielectric permittivity a for both 2-chlorocydohexyi isobutyrate (CCHI) and poly(2-chlorocyclohexyl acrylate) (PCCHA) is reported. The analysis of the dielectric results in terms of the electric modulus suggests that whereas the conductive processes in CCHI are produced only by free charges, the conductivity observed in PCCHA involves both free charges and interfacial phenomena. The 4x4 RIS scheme presented which accounts for two rotational states about the CH-CO bonds of the side group reproduces the intramolecular correlation coefficient of the polymer. 

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... 

Figure 4. Frequency Dependence of Loss Factor Peak Temperature for Poly(vinyl acetate) + Filler.

As already indicated, (p. 170) the dispersion of the Kerr effect in the range of radio frequencies is a characteristic property of rigid-chain polymer solutions. This can be seen in Figs. 59-61 which show frequency dependences of EB for solutions of polj chlorohexyl isocyanate)s, cellulose earbanilate and ladder polychlorophenylsiloxane. Similar dependences have been obtained for poly(butyl isocyanate) various cellulose ethers and esters and ladder polysiloxanes ... 

Figure 5.7 Frequency dependences of the storage (Q) and loss (-h) moduli for poly(dimethylsilox-ane) (PDMS) samples whose reactions were quenched at the times indicated (see Fig. 5-6). The data are time-temperature-shifted to the reference temperature T gf of 34°C, and they are shifted additionally by an amount A on the logarithmic axis to keep the curves from overlapping. The vertical shift factors bf are given by p T sf)T d/ p T)T), where p is the density. (From Winter and Chambon 1986, with permission from the Journal of Rheology.)...

Poncet et al. (1999) monitored frequency-dependent dielectric measurements to examine the phase-separation process in poly(2,6-dimethyl-1,4-phenylene ether) (PPE) in a DGEBA-MCDEA resin. Dielectric measurements measured the build up in Tg both in the PPE-rich continuous phase and in the epoxy-rich occluded phases for 30-60-wt.% PPE mixtures. In the 30% PPE mixmre, the rate of reaction of the thermoset phase is equivalent to that of the neat system due to two opposing effects, namely a slower reaction rate due to dilution and a low level of conversion at vitrification due to the presence of high-Tg PPE. In the 60-wt.% mixture the dilution effect of the PPE has a large effect of decreasing the reaction rate. The continuous thermoplastic-rich phase vitrifies first, followed by the thermoset occluded phase. The final morphology (size of occluded particles and composition of continuous phase) is affected by kinetics, diffusion and viscosity during phase separation. 

Figures 3.7 and 3.8 shows the frequency dependencies of Ti and NOE measured for the CH2 (rrr) carbon of poly(methyl methacrylate) (PMMA) in a deuterated chloroform solution at 55°C [10]. Different curves indicate the simulated results obtained by using the box-type distribution, log- distribution, 2r and 3t models described above. As is clearly seen in Fig.

Dielectric measurements on poly(vinyl acetate) were obtained utilizing a Fourier transform dielectric spectrometer developed in our laboratory (6). A voltage step pulse was applied to the sample and the time dependent Integrated current response, Q(t), was collected by computer. The frequency dependent dielectric properties, e and e" were then obtained from the Fourier trans-... 

The dielectric loss behavior of PVAc was similar to that of the other polymers. An Increase in dielectric Intensity of the polymer s S mechanism was directly proportional to the amount of unclustered water. In addition when clustered water was present two separate low temperature peaks occurred as shown In the frequency dependent data of Figure 8. The higher frequency peaks were the result of clustered water. This is confirmed by the similarity between poly(vinyl acetate) and the clustered water peaks of other polymers as plotted in Figure 7. 

Kazama et ai reported that H NMR Tjj] as a function of frequency in poly(paraphenylene sulphide) (PPS) doped heavily with SO,", showed the inverse square law of frequency [371]. The diffusion coefficient estimated using (6.14) from such a frequency dependence was much smaller than that of the neutral soliton in trans-PA. 

The frequency and temperature dependent dielectric losses in lightly doped poly-3 methylthiophene have been studied by Pameix [44b]. The frequency dependence (S) of ac conductivity (UacCxw ) was found to decrease linearly with temperature in agreement with a hopping model. 

The principle can also be applied to dielectric data, which can be shifted either along the temperature or the frequency axis. An example of the latter type of shift is shown in Figure 13.26, where instead of time-dependence measurements the frequency dependence of the 3-relaxation in poly(vinyl acetate) has been studied at fixed temperature in the range 212 to 266 K. A master curve can be constructed for this relaxation region by plotting (e Vemax) against logio ( / max) where the max subscript refers to the peak maximum at each experimental temperature. 

FIGURE 13.26 (a) Frequency dependence of e" for the P-relaxation in poly(vinyl acetate) measured at different temperatures, (b) Master dielectric loss curve for the data in (a) (O) compared with similar data for the P-relaxation of poly(vinyl benzoate) ( ). (From Ishida, Y. et al., Roll. Z. 180, 108, 1962. With permission from Dr. Dietrich Steinkopff Verlag, Darmstadt.)... 

Temperature-Modulated Calorimetry of the Frequency Dependence of the Glass Transition of Poly(ethylene terephthalate) and Polystyrene... 

Figure 9.15. X -(GVGIP)32o frequency dependence of loss shear modulus, G" (0.02 to 200 Hz), and of loss permittivity (20 Hz to 10 Hz) as a function of temperature. When the frequency of the loss maximum is sufficiently low, for example, near 1 kHz, loss shear modulus and loss permittivity can both be determined and have been demonstrated to superimpose for the case of the loss maximum for poly(propylene diol). In the case of X -(GVGIP)32o, the maximum occurs at a frequency that is too high to be reached by shear modulus measurements. Nonetheless, the two measurements are... 

When a polymer exhibits a maximum in the imaginary part of the dielectric permittivity (the loss permittivity, e") at frequencies less than 200 Hz, it becomes possible to make comparisons with the frequency dependence of shear moduli and most specifically with the loss shear modulus, G". This has been done for polypropylene diol, also called poly(oxypropy-lene), where there is reported a near perfect superposition of the frequency dependence of the normalized loss shear modulus with that of the normalized loss permittivity as reproduced in Figure 3. The acoustic absorption frequency range of interest here is 100 Hz to 10 kHz, yet present macroscopic loss shear modulus data can be determined at most up to a few hundred Hz. Nonetheless, for X -(GVGIP)32o there is a maximum in loss permittivity, e", near 3 kHz that develops on raising the temperature through the temperature range of the inverse temperature transition. With the width of the loss permittivity curve a distinct set of curves as a function of temperature become... 

Fig. 26 Viscoelastic properties of electropolymerized poly(3-hexylthiophene). Fitted (a) storage modulus (G ) and (b) loss modulus (C") as functions of charge and frequency. Frequency dependence obtained by use of harmonics of polished 10 MHz fundamental Au-coated TSM resonator open (filled) symbols for increasing (decreasing) potential measurement sequence (lines are merely a guide to the eye).

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