Dipole systems

Capacitance as a function of charge was calculated.79 The capacitance curves showed a single hump, near qM = 0, and leveled off for qM about 10 /xC/cm2 on either side of the potential of zero charge, due to the dielectric saturation of the dipole system. The limiting values of the capacitance increased with increasing electron density of the metal. The nonideality of the metal was shown to... 

In the present book, we aim at the unified description of ground states and collective excitations in orientationally structured adsorbates based on the theory of two-dimensional dipole systems. Chapter 2 is concerned with the discussion of orientation ordering in the systems of adsorbed molecules. In Section 2.1, we present a concise review on basic experimental evidence to date which demonstrate a variety of structures occurring in two-dimensional molecular lattices on crystalline dielectric substrates and interactions governing this occurrence. 

The first step in studying the orientation ordering of two-dimensional dipole systems consists in the analysis of the ground state. If the orientation of rigid dipoles is described by two-dimensional unit vectors er lying in the lattice plane, then the ground state corresponds to the minimum of the system Hamiltonian... 

Thus, in a study on the properties of dipole systems, most promise is shown by the representation of chain interactions, which, first, reflects the tendency toward ordering of dipole moments along the axes of chains with a small interchain to intrachain interaction ratio. Second, this type of representation makes it possible to use, with great accuracy, analytical equations summing the interactions of all the dipoles on the lattice. Third, there are grounds for the use of the generalized approximation of an interchain self-consistent field presented in Refs. 62 and 63 to describe the orientational phase transitions. 

The description of phase transitions in a two-dimensional dipole system with exact inclusion of long-range dipole interaction and the arbitrary barriers AUv of local potentials was presented in Ref. 56 in the self-consistent-field approximation. The characteristics of these transitions were found to be dependent on AU9 and the number n of local potential wells. At =2, Tc varies from Pj /2 to Pj as AU9... 

An inference of fundamental importance follows from Eqs. (2.3.9) and (2.3.11) When long axes of nonpolar molecules deviate from the surface-normal direction slightly enough, their azimuthal orientational behavior is accounted for by much the same Hamiltonian as that for a two-dimensional dipole system. Indeed, at sin<9 1 the main nonlocal contribution to Eq. (2.3.9) is provided by a term quadratic in which contains the interaction tensor V 2 (r) of much the same structure as dipole-dipole interaction tensor 2B3 > 0, B4 < 0, only differing in values 2B3 and B4. For dipole-dipole interactions, 2B3 = D = flic (p is the dipole moment) and B4 = -3D, whereas, e.g., purely quadrupole-quadrupole interactions are characterized by 2B3 = 3U, B4 = - SU (see Table 2.2). Evidently, it is for this reason that the dipole model applied to the system CO/NaCl(100), with rather small values 0(6 25°), provided an adequate picture for the ground-state orientational structure.81 A contradiction arose only in the estimation of the temperature Tc of the observed orientational phase transition For the experimental value Tc = 25 K to be reproduced, the dipole moment should have been set n = 1.3D, which is ten times as large as the corresponding value n in a gas phase. Section 2.4 will be devoted to a detailed consideration of orientational states and excitation spectra of a model system on a square lattice described by relations (2.3.9)-(2.3.11). 

In an effort to understand the mechanisms involved in formation of complex orientational structures of adsorbed molecules and to describe orientational, vibrational, and electronic excitations in systems of this kind, a new approach to solid surface theory has been developed which treats the properties of two-dimensional dipole systems.61,109,121 In adsorbed layers, dipole forces are the main contributors to lateral interactions both of dynamic dipole moments of vibrational or electronic molecular excitations and of static dipole moments (for polar molecules). In the previous chapter, we demonstrated that all the information on lateral interactions within a system is carried by the Fourier components of the dipole-dipole interaction tensors. In this chapter, we consider basic spectral parameters for two-dimensional lattice systems in which the unit cells contain several inequivalent molecules. As seen from Sec. 2.1, such structures are intrinsic in many systems of adsorbed molecules. For the Fourier components in question, the lattice-sublattice relations will be derived which enable, in particular, various parameters of orientational structures on a complex lattice to be expressed in terms of known characteristics of its Bravais sublattices. In the framework of such a treatment, the ground state of the system concerned as well as the infrared-active spectral frequencies of valence dipole vibrations will be elucidated. 

The above procedure for finding the ground state of a dipole system on a complex lattice is a generalization of the technique used previously for simple Bravais lattices (see Sec. 2.2). 

The cathode receiver and the anode were composed into a dipole system, powered by a low voltage battery (Fig.3). The distance of the anode-cathode is about 30 40cm. The receiver (cathode) is buried in the soils at a depth of 30 40cm. The anode stainless steel is installed directly over the receiver at the ground surface. 

The second step of the evolution towards equilibrium is the Zeeman dipole-dipole relaxation. Hartmann and Anderson estimated this time using the hypothesis that p at any time is of the form (22). As a consequence of the shortness of the dipole-dipole relaxation time we may assume that the dipole-dipole system always remains in equilibrium we are thus led to treat the evolution of the Zeeman system as the Brownian motion of a collective coordinate in the dipole-dipole heat bath. We assume that the diagonal elements of p have the form... 

Substituting in Eq. (38) and taking the trace over the variables of the dipole-dipole system, we get a set of equations analogous to the Bloch equations (18)... 

Caspers relation r of Eq. (62) is in fact equal to the r12 of Eq. (64). But this author essentially looks for a closed equation for Mt without going into the details of the description of the energy exchange between the Zeeman coordinate and the dipole-dipole system. He therefore confuses r12 with the spin-spin relaxation time. 

A. Comparison of SACM and VTST for Isotropic Charge-Locked Permanent Dipole Systems... 

Of particular interest is the relation between the various forms of VTST and SACM. The charge-dipole system is particularly well suited to investigate this aspect in a quantitative way. In the following we show that, for potentials without pronounced energy barriers, VTST and SACM in general are not equivalent, the numerical differences depending on the chosen variant of VTST. Because SACM agrees well with classical trajectory calculations, the comparison of VTST with SACM may help to identify artifacts of the VTST treatment. 

Before evaluating Q and kcap for the charge-dipole system with its real anisotropy, we consider the hypothetical isotropic case with cos y in Eq. (4) replaced by unity. We understand this situation as that characterized by... 

---