Polarisation macroscopic

Second, after an appropriate time interval to allow the gas pulse to reach an optimum position between the cavity mirrors, a 1 qs pulse of monochromatic microwave radiation is introduced into the cavity, which is itself tuned to the correct matching resonant frequency. The pulse carries with it a band of frequencies Av 1 MHz, centred at the resonant frequency v of the cavity. The cavity has a bandwidth of approximately 1 MHz, so that the microwave radiation density is high. If the molecular species under investigation has one or more resonant frequencies within this bandwidth, an appreciable macroscopic polarisation is induced, corresponding classically to a phase-coherent oscillation of the molecular electric dipole moments. The microwave pulse must arrive at the correct time interval after the gas pulse. 

An essential requirement is that the characteristic time, T2, for the decay of the macroscopic polarisation must be much longer than the time taken for the polarising radiation pulse to dissipate. This requirement is readily satisfied the pin-diode S2 is held closed until the pulsed radiation has dissipated, and is then opened to capture the coherent radiation emitted by the polarised gas, due to one or more rotational transitions producing spontaneous emission. If all is well, the emission is detected against a near-zero radiation background. 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

Spontaneous polarisation can also be observed for chiral discotic metallomesogens forming columnar mesophases, when the chiral molecules are tilted with respect to the column axis. The tilt induces a dipole moment within the plane of the molecule. A net macroscopic polarisation can be obtained for rectangular columnar phases with Cz or P2i symmetry. Serrano and Sierra reported on ferroelectric switching in the columnar mesophase for chiral /3-diketonate complexes (Figure 2.52). ... 

Table 4 Equilibrium structure for the tetragonal phase of BaTi03 and KNb03 for different Hamiltonians, a represents the mixing parameter in the hybrid F -BLYP functionals. V is the equilibrium volume (A ), Vq the ratio between optimised volume of tetragonal and cubic phases, Z the fractional coordinates, P the macroscopic polarisation (Cm ) calculated at the experimental and optimised geometries... 

Fig. 11 Variation of the macroscopic polarisation P(Cm in the optimised tetragonal phase of BaTiOa, as a function of the mixing parameter a in the hybrid F-BLYP series...

Hulliger, J. New physical methods for a space resolved mapping of the macroscopic polarisation in molecular crystals and a stochastic theory for understanding. Chimia... 

As we have seen, locally the smectic C layers are polar, belonging to pyroelectric class C2. Macroscopically SmC either forms a helical structore or does not. So, we can discuss a structure without helicity. In a sense, the formation of a helix is equivalent to formation of ferroelectric domains which would reduce overall macroscopic polarisation. Thus we can consider the (1) (very important) and (2) (additional) requirements fulfilled. As to the phase transition (3), we know that in the smectic A phase, even chiral, there is no polar axis, therefore that phase can be considered as a paraelectric phase. The two-component order parameter of the A -C transition is the same as the parameter of the A-C transition in an achiral substance, namely 9exp (i(p), where we recognise the tilt 9 and azimuth (p angles. The spontaneous... 

Figure 5.6 shows the basic concept. The two polarised insulators shown in the central and lower parts of the Figure have identical electron densities, but different Kohn-Sham potentials the two systems differ in their macroscopic polarisation. In order to reproduce the correct macroscopic polarisation, the exact Kohn-Sham xc potential must acquire a part which varies linearly in space the xc field. 

When a (polar) molecule is placed in an electric field, two types of molecule/field interactions take place, namely reversible storage and irreversible dissipation of field energy. The first interaction is a capacitive effect, caused by the polarisability of a molecule. Molecules placed in an electric field are polarised. Various polarisation mechanisms are distinguished (atomic, electrical and macroscopic polarisation, and dipole orientation). When the electric field is removed the molecules will return to... 

As the metallic particles are assumed to be sufficiently large for macroscopic dielectric theory to be applicable, we can substitute for a the expression for the polarisability of metallic particle immersed in an insulator. The dipole moment is given by the integration of the polarisation over the volume V. Thus, if the polarisation is uniform ... 

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

In this equation a is the usual linear polarisability, whilst the others are the hyperpo-larisability terms, P, y etc. Macroscopically this equation turns into... 

The results discussed in this chapter demonstrate that 2H NMR is a powerful technique for investigating microscopic properties in rubber networks. Most of the experiments described here are easy to handle on standard NMR equipment. Due to the absence of interactions between 2H nuclei, spectra and line shapes are easy to interpret and give quite direct information, at least in the first step of analysis, which is that generally required to correlate microscopic to macroscopic properties in these systems. Additionally, in contrast to optical techniques (as birefringence, infrared dichroism, fluorescence polarisation) the information which is obtained is very specific, because spatial and temporal averaging processes are clearly distinguishable in NMR. 

Fig. 51 Schematic macroscopic hysteresis loop of a ferroelectric material. Therein Ec denotes the coercitive field strength, Prei the remanent polarisation and P ei the saturation polarisation...

The macroscopic alignment of polymer chains was also achieved by depositing soluble poly(p-phenylenes), such as 37 or poly(3-thiophenes) such as 26, from solution by the Langmuir-Blodgett technique. However, low polarisation ratios ( u/ x) were found for electroluminescence (3 1). 

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