Liquid-crystalline polymer equilibrium states

The preparation of fully aromatic polyesters is mostly performed by melt condensation. Complex phase equilibriums and states of aggregation are formed in this manner. This is in most cases not easy to control under laboratory conditions. Example 4.5 describes a polyester that is easy to prepare under laboratory conditions and allows the observation of typical properties of some thermotropic liquid crystalline polymers. 

In most cases, the flow properties of polymers in solution or in a molten state are Newtonian, pseudoplastic, or a combination of both. In the case of liquid crystal polymer solutions, the flow behavior is more complex. The profound difference in the rheological behavior of ordinary and liquid crystalline polymers is due to the fact that, for the flrst ones, the molecular orientation is entirely determined by the flow process. The second ones are anisotropic materials already at equilibrium (Acierno and Brostow 1996). The spontaneous molecular orientation is already in existence before the flow and is switched on, varying in space, over distances of several microns or less (polydomain). If one ignores the latter, one can discuss the linear case (slow flow) as long as the rate of deformation due to flow (the magnitude of the symmetric part of the velocity gradient) is lower than the rate at which molecules rearrange their orientational spread by thermal motions. 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

The aforementioned equilibria may be attained only in the liquid state, i.e., in the melt or solution. When the temperature is low enough to allow crystallization of the polymer, then the fraction of crystallized polymer does not take part in the equilibrium. Only the amorphous fraction of the polymer is involved in the monomer—polymer equilibrium and as a result, the monomer content decreases with increasing crystallinity [21]. In this way, the monomer content may be lowered substantially. The effect of crystallization or phase separation is very important in the polymerization of five- and six-membered lactams which can thus be forced to polymerize to higher yields. Dilution and lowering of the melting temperature, on the other hand, increases the equilibrium monomer content. 

Liquid diffusion in polymers is generally slower than gas diffusion, with diffusivities of the order of lO m s. The equilibrium solubility of liquids can be much larger than that of gases, and the liquid content can change the diffusion constant or even the physical state of the polymer. Semi-crystalline polymers are in general more resistant to organic liquids than glassy polymers, so the former are preferred. 

Mixtures of clay platelets and polymer chains compose a colloidal system. Thus in the melt state, the propensity for the clay to be stably dispersed at the level of individual disks (an exfoliated clay dispersion) is dictated by clay, polymer, stabilizer, and compatibilizer potential interactions and the entropic effects of orientational disorder and confinement. An isometric dimension of clay platelets also has implications for stability because liquid crystalline phases may form. In addition, the very high melt viscosity of polypropylene and the colloidal size of clay imply slow particulate dynamics, thus equilibrium structures may be attained only very gradually. Agglomerated and networked clay structures may also lead to nonequilibrium behavior such as trapped states, aging, and glassy dynamics. 

Transition from liquid to glass and crystallization are both phenomena responsible for polymer solidification at the end of a processing operation. Since they are kinetic phenomena, they lead to an out-of-equilibrium thermodynamic state glassy polymers present an excess of unstable conformations and free volume semi-crystalline polymers are not totally crystallized, their melting point being largely lower (usually some dozens of degrees) than the equilibrium value. 

The first class of blends to be analyzed is that of a homogeneous, disordered liquid phase in equilibrium with a pure crystalline phase, or phases. If both species crystallize they do so independently of one another, i.e. co-crystallization does not occur. With these stipulations the analysis is relatively straightforward. The chemical potentials of the components in the melt are obtained from one of the standard thermodynamic expressions for polymer mixtures. Either the Flory-Huggins mixing expression (7) or one of the equation of state formulations that are available can be used.(8-16) The melting temperature-composition relations are obtained by invoking the equilibrium requirement between the melt and the pure crystalline phases. When nonequilibrium systems are analyzed, additional corrections will have to be made for the contributions of structural and morphological factors. 

The phase equilibrium in systems containing rigid-chain polymers is characterized by the formation of a liquid-crystalline state, which fact can be illustrated by the diagram due to Flory reproduced in Figure 3. At x values below 0,the polymer-solvent system forms either an isotropic (one-phase) solution mixture of... 

In examining phase equilibria in polymer systems, until recently most of the attention has been focused on the transitions between amorphous and crystalline states alone and the transitions from one crystalline modification to another (polymorphic transitions). The detection and the subsequent study of the liquid-crystalline state of polymers showed that it is an independrat, tharoodynamically equilibrium state. In many phase transitions, it occupies an intermediate position between the amorphous and crystalline states, and the mutual transitions from these two states into the liquid-crystalline state and vice versa are phase transitions of the first kind. 

The first group includes liquid-crystalline systems based on polymers containing mesogenic groups in the main chain wh they alternate with flexible firagments, or in the side chains where they are joined to the main chain by flexible spacers. Phase equilibrium between these systems is due to thermal transitions from the crystalline state to some type of liquid-crystalline phase and subsequently to an isotropic melt. 

The possibility of the transition into the liquid-crystalline state for such samples (glassy amorphous and crystallized) is realized in the presence of solvents. The transition to the liquid-crystalline state can take place in two ways. The first is dissolution of the crystallized or dilution of the glassy amorphous polymer by the solvent. A concentrated solution of polymer is formed, and the mobility of the macromolecules in the solution is sufficient for the equilibrium state to be established and consequently for the transition into the liquid-crystalline phase, which naturally occurs if the critical concentration below which the system enters the region of the isotropic state, according to the theory, is not exceeded during dilution. 

Precipitation of the polymer on addition of a nonsolvent or with any changes in the thermodynamic parameters in solutions whose conc tration is below the critical point of the transition to the liquid-crystalline state is the most typical case of the intermediate phase equilibrium in rigid-chain polymer-solvent systems. Instead of the anticipated establishment of isotropic-anisotrqric phase equilibrium, equilibrium of two amorphous (isotropic) phases initially arises if the parameter x attains values greater than +0.5. 

It is known that the modulus and strength are a function of the degree of orientation of the polymer. The almost fivefold increase in the modulus and the more than twofold increase in the tensile strength should be attributed to passage of the polymer into a thermodynamically equilibrium, ordered state with elevated orientation, which also takes place in heat treatment. This transition is completed below the temperature at which crystallization could begin liquid-crystalline ordering apparently takes place here. 

In polymer science, the 1980s were marked by the birth and turbulent development of a new field the chemistry and physics of liquid-crystal polymers. This field, which includes synthesists, theoretical physicists, classic physical chemists, polymer chemists, and production engineers, has grown in an intensely developed new direction which has very rapidly led to practical successes in the creation of high-strength chemical fibers and is now drawing the attention of optical scientists and specialists in microelectronics. However, the main point is that the liquid-crystalline state in polymers and polymer systems is not only extremely common (many hundreds of polymeric liquids crystals have now been described) but is also a stable equilibrium phase state of polymeric substances. 

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