Ferroelectric system dependence

Mesogenic groups can be incorporated into polymeric systems [7]. This results in materials of novel features like main chain systems of extraordinary impact strength, side-chain systems with mesogens which can be switched in their orientation by external electric fields or—if chiral groups are attached to the mesogenic units—ferroelectric liquid crystalline polymers and elastomers. The dynamics of such systems depends in detail on its molecular architecture, i.e. especially the main chain polymer and its stiffness, the spacer molecules... 

Typical property of a ferroelectric system, the hysteresis loop, shows marked dependence on the pressure (Fig. 29). Observations of the hysteresis loops have shown that the spontaneous polarization abruptly increases at the Sm A-Sm C transition point when T decreases at p = const (Fig. 30a) or when p increases at T = const (Fig. 30b). That is accompanied by an increase of the tilt angle (Fig. 30c). 

To summarize the ferroelectric and piezoelectric properties of the discussed polymers, some important ferroelectric and piezoelectric parameters are tabulated in Table 4. As discussed in the previous sections, the ferroelectric and piezoelectric properties of polymeric and polymeric composite systems depend on various factors, such as crystallinity, pohng conditions, glass transition temperature, and before and after electrical poling treatments (electrical, mechanical, and thermal treatments). In addition to the factors mentioned above, for composite systems, laminates or blends, fraction of constituents, and interfacial polarization are also important. Therefore, the... 

Least-root-mean-square linearization of the measured size-dependent Tc represented by Eq. (14.20) gives the slope B and an intercept that corresponds to the bulk TcCoo). The B = TAcoh for a ferroelectric system. For a ferromagnetic system, B = TAb is a constant without needing numerical optimization. Calculations based on Eq. (14.20) were conducted using the average bond length (appendix A2) and the known Tc(oo) values listed in Table 14.4. 

The introduction of a polymer network into an FLC dramatically changes phase and electro-optic behavior. Upon addition of monomer to the FLC, the phase transitions decrease and after polymerization return to values close to that observed in the neat FLC. The phase behavior is similar for the amorphous monomers, HDD A and PPDA. The electro-optic properties, on the other hand, are highly dependent on the monomer used to form the polymer/FLC composite. The ferroelectric polarization decreases for both HDDA and PPDA/FLC systems, but the values for each show extremely different temperature dependence. Further evidence illustrating the different effects of each of the two polymers is found upon examining the polarization as both the temperature and LC phase of polymerization are changed. In PPDA systems the polarization remains fairly independent of the polymerization temperature. On the other hand, the polarization increases steadily as the polymerization temperature of HDDA systems is increased in the ordered LC phases. 

Two other important points have to be stressed. The first is that above Tc = 210 K, T2 does not depend on the frequency offset so that the nanocluster dynamics is similar in different parts of the crystal. Below Tc, on the other hand, T2 depends on the frequency offset and the nanocluster dynamics is different in different parts of the crystal, as expected for a two-component system consisting of ferroelectric regions and a spherical glass-type matrix. The second point is that in the FC T2 data around 140-150 K, a second flat T2... 

In Table 1 we compare performance data for reported MRAM and FRAM prototypes. The small Fujitsu FRAM is not a prototype it is in large-scale production and found in the memory board of every Sony Playstation 2, as part of the Toshiba memory system. The main advantages of FRAMs over EEP-ROMs or Elash memory are in the WRITE times (100 ns for FRAM, versus 1 xs for Flash and 10 xs for EEPROM), and energy per 32-bit WRITE (1 nj for ERAM versus 1 or 2 mj for EEPROM or Plash). Note that parameters such as READ time or WRITE time for PRAMs are dependent upon actual cell architecture they are not limited by the intrinsic switching time of the ferroelectric thin film, which is typically 220 ps [3]. 

Finally we can conclude that confinement could be responsible for nonmonotonic relaxation kinetics and could provide a specific saddle-like temperature dependence of the relaxation time. The experimental examples discussed show that this type of kinetics may be inherent in systems of completely different natures confined liquids, ferroelectric crystals, and it was even demonstrated recently macromolecular folding kinetics [78]. In each case, the specific interpretation of the parameters of model (129) depends on the discussed experimental situation. We are far from the opinion that confinement is the only reason for nonmonotonic relaxation kinetics. However, for all the examples discussed in this paper, the nonmonotonic dependence of the relaxation time on temperature has the same origin, that is, confinement either in real or configurational space. 

Gradient coefficients > 0 and q > 0 the expansion coefficient an>0 for the second order phase transitions. Coefficient ai(T) = ar T — Tc), E is the transition temperature of a bulk material. Note, that the coefficient flu for displacement type ferroelectrics does not depend on T, while it is temperature dependent for order-disorder type ferroelectrics (see corresponding reference in [117]). Eq is the homogeneous external field, the term Ed (P3) represents depolarization field, that increases due to the polarization inhomogeneity in confined system. Linear operator Ed P3) essentially depends on the system shape and boundary conditions. Below we consider the case when depolarization field is completely screened by the ambient free charges outside the particle, while it is nonzero inside the particle due to inhomogeneous polarization distribution (i.e., nonzero divP 0) (see Fig. 4.35b). 

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