Orientation states

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

These two different approaches for attaining an oriented state in flexible-chain and rigid-chain polymers indicate that the fundamental property of macromolecules - their flexibility - is of great importance to the orientation processes. However, the mechanism of the transition into the oriented state and the properties of highly oriented systems exhibit many features characteristic of both rigid- and flexible-chain polymers. 

Anisotropy of Physical Properties as the Main Feature of the Oriented State of Polymers... 

The processes of ordering in polymer systems consisting of linear polymers are related, at least on one level of supermolecular organization, to the development of a predominant localization of macromolecules (or their parts) along some directions the orientation axes, i.e. to the transition of the system into the oriented state. The most simple and most widely spread type of polymer orientation is the uniaxial orientation, i.e. the one-dimensional orientation in the direction of the axes of macromolecules. 

Usually, the transition of polymer systems into the oriented state occurs as a result of deformation e.g. upon exposure to external stress. When the polymers undergo deformation both the macromolecule as a whole and its parts (segments) can undergo orientation. The rates of these orientation processes are very different and, hence, the orienting forces affect first of all the orientation of chain segments and subsequently that of a chain molecule as a whole. However, by varying the extension velocity and the temperature, only the overall orientation process may predominate, thus extension of all chains occurs in a single act. 

Hence, the transition of a polymer system into the oriented state is a result of the competition of two fundamental properties of a polymer molecule (1) its inherent anisotropy which is the main reason for the ability of polymer systems to form an oriented phase and (2) its flexibility which favours coiling of a long molecule. The result of this competition is determined by the chemical nature of the molecule however, kinetic hindrance can prevent the transition into the oriented state. 

Figure 2 shows the increase in the rigidity (1 - f) of macromolecules induced by the field as a function of the parameter x = e/kT + Fl/kT. As soon as the flexibility decreases to f < 0.63, a system of molecules flexible in the state of rest will undergo a spontaneous transition into a nematic oriented state upon the action of the stretching field, just as it occurs for rigid molecules at rest. 

Hence, the main aim of the technological process in obtaining fibres from flexible-chain polymers is to extend flexible-chain molecules and to fix their oriented state by subsequent crystallization. The filaments obtained by this method exhibit a fibrillar structure and high tenacity, because the structure of the filament is similar to that of fibres prepared from rigid-chain polymers (for a detailed thermodynamic treatment of orientation processes in polymer solutions and the thermokinetic analysis of jet-fibre transition in longitudinal solution flow see monograph3. ... 

One of the main methods for improving the mechanical properties of linear polymers is their drawing that can be uniaxial (fibres), biaxial (films), planar symmetrical (films-membranes) etc. As a result of polymer deformation, the system changes into the oriented state fixed by crystallization. 

A further increase in extension leads to irreversible changes which immediately precede the transition of the polymer into the oriented state. During this transition, the spherulites undergo considerable structural changes and are thus converted qualitatively into different structural elements i.e. macrofibrils4). After a certain critical elongation has been attained, the initial crystallites collapse and melt and a new oriented structure is formed in which the c axes of crystals are oriented in the direction of extension. 

The transition into the oriented state is accompanied by the formation of a neck , a sharp and abrupt local constriction of the sample, in which the extent of orientation and the degree of extension are mudh higher than in the rest of the polymer. After the neck has been formed, further orientation of the sample occurs by spreading of the neck to the entire length of the polymer. When the sample is extended after passing into the oriented state, it undergoes further deformation and at some critical extension it breaks. 

It should be noted that the relative accessibility of the transition into the oriented state observed for polymers of various rigidity under appropriate conditions is due to the internal anisotropy of macromolecules caused by their chain structure (see Sect. 1 of this paper and monographs2 3 ). 

A controversy exists over the interpretation of such a correlation. According to the simple two-state model for water at interfaces, the higher the preferential orientation of one of the states, the higher the value of BEa=Q/BT. If the preferentially oriented state is that with the negative end of the dipole down to the surface, the temperature coefficient of Ev is positive (and vice versa). Thus, in a simple picture, the more positive BEa=0/BTt the higher the orientation of water, i.e., the higher the hydro-philicity of the surface. On this basis, Silva et al.446 have proposed the... 

Ferroelasticity is the mechanical analogon to ferroelectricity. A crystal is ferroelastic if it exhibits two (or more) differently oriented states in the absence of mechanical strain, and if one of these states can be shifted to the other one by mechanical strain. CaCl2 offers an example (Fig. 4.1, p. 33). During the phase transition from the rutile type to the CaCl2 type, the octahedra can be rotated in one or the other direction. If either rotation takes place in different regions of the crystal, the crystal will consist of domains having the one or the other orientation. By exerting pressure all domains can be forced to adopt only one orientation. 

We now repeat the same exercise to show how we can create object-oriented state-space LTI models. In later chapters, all control toolbox functions take these objects as arguments. We first repeat the statements above to regenerate the state matrices a, b, c, and d. Then we use ss () to generate the equivalent LTI object. 

Rubinov AN, Tomin VI, Bushuk BA (1982) Kinetic spectroscopy of orientational states of solvated dye molecules in polar solutions. J Lumin 26 377-391... 

Polymer crystallization under flow or under highly oriented states is of prime importance in industrial polymer processing. We expected that the crystallization would be highly accelerated when the initial amorphous chains were highly orientated. Therefore, we dared to use a realistic molecular model of... 

Fig. 2.12. Dependences of the dipole energies of various orientational states (see Fig. 2.11) on the rhombic angle a.

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). 

Fig. 2.19. A phase diagram of orientational states for adsorbed molecules on a square lattice. Phase-separating solid and dash-dotted lines correspond to the case Ki = 0. The dotted line enclosed by the markers x specifies parameters of the system CO/NaCl(100) (K /Ki = 0.207, 0= 25°)...

Tunnel relaxation of orientational states in the phonon field of a substrate is considered in Appendix 2). When a molecule has a single equilibrium orientation (p = 1) the deformation potential is also characterized by a well-defined barrier AU which separates the equivalent minima. That is why, the subsystem Hamiltonian (4.2.12) used in the exchange dephasing model147,148 with... 

Thermally activated reorientations and tunnel relaxation of orientational states in a phonon field... 

The probability for a transition to occur between two states per unit time is determined by Fermi s golden rule and depends on the operator of interaction between the subsystem concerned and a thermostat. As orientational states are characterized by a low-energy spectrum, they will be substantially influenced by the... 

Calculate the probabilities for the transitions between orientational states a)... 

The book covers a variety of questions related to orientational mobility of polar and nonpolar molecules in condensed phases, including orientational states and phase transitions in low-dimensional lattice systems and the theory of molecular vibrations interacting both with each other and with a solid-state heat bath. Special attention is given to simple models which permit analytical solutions and provide a qualitative insight into physical phenomena. 

The fact that Tdhpz on Au is identical to that on Pt at pH 7 is evidence that ri1-N surface-coordinated DHPz is also formed on Au at this same pH. Since (i) the DHPz isotherm on Au at pH 0 is not stepwise unlike those exhibited by compounds attached in multiple orientational states, and (ii) it has already been shown above that hydroquinone, the homoaromatic analogue of DHPz, is not chemisorbed on Au, it can be argued that i -N surface-coordination of DHPz occurs on Au at pH 0 even at coverages below the saturation value. It can be inferred further that the driving forces for protonation and Au-surface-coordination of the N heteroatom are equally competitive in molar acid. 

---