Volume crystalline polymer

For liquid crystalline polymers and volume, crystalline polymers, most of the scattering arises from orientation fluctuations. 

Crystalline polymers undergo a discontinuous decrease in volume when cooled through (Fig. 4). This can lead to nonuniform shrinkage and warping in molded objects. On the other hand, it also causes the polymer to "lock on" to reinforcing fibers, eg, glass (qv), so that crystalline thermoplastics benefit much more than amorphous thermoplastics from fiber reinforcement. 

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

In principle the heat required to bring the material up to its processing temperature may be calculated in the case of amorphous polymers by multiplying the mass of the material (IP) by the specific heat s) and the difference between the required melt temperature and ambient temperature (AT). In the case of crystalline polymers it is also necessary to add the product of mass times latent heat of melting of crystalline structures (L). Thus if the density of the material is D then the enthalpy or heat required ( ) to raise volume V to its processing temperature will be given by ... 

The fact that crystalline polymers are multiphase materials has prompted a new approach in characterizing their internal structure (lamellar thickness, perfection, etc.) and relating it to the hardness concept (volume of material locally deformed under a point indenter). In lamellar PE microhardness is grossly a given increasing function of lamellar thickness. In using the composite concept care must be exercised to emphasize and properly account for the non-crystalline phase and its various... 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

Many of the properties of a polymer depend upon the presence or absence of crystallites. The factors that determine whether crystallinity occurs are known (see Chapter 2) and depend on the chemical structure of the polymer chain, e.g., chain mobility, tacticity, regularity and side-chain volume. Although polymers may satisfy the above requirements, other factors determine the morphology and size of crystallites. These include the rate of cooling from the melt to solid, stress and orientation applied during processing, impurities (catalyst and solvent residues), latent crystallites which have not melted (this is called self-nucleation). 

Volume and mass-based expressions for the degree of crystallinity are easily derived from the experimentally measured density (p) of a semi-crystalline polymer. The method is based on an ideal crystalline and liquid-like two-phase model and assumes additivity of the volume corresponding to each phase... 

Vc crystalline Va, amorphous). The densities of the pure crystalline (pc) and pure amorphous (pa) polymer must be known at the temperature and pressure used to measure p. The value of pc can be obtained from the unit cell dimensions when the crystal structure is known. The value of pa can be obtained directly for polymers that can be quenched without crystallization, polyfethylene terephtha-late) is one example. However, for most semi-crystalline polymers the value of pa is extrapolated from the variation of the specific volume of the melt with temperature [16,63]. 

Holmes P (1988) Biologically Produced (R)-3-hydroxyalkanoate Polymers and Copolymers. In Development in Crystalline Polymers, Volume 2. Elsevier, London... 

Molecularlv Doped Thermotropic Liquid Crystalline Polymer. The idea of the nonlinear optical medium which is the subject of this paper results from a synthesis of the ideas of the discussion above and a few concepts from nonlinear optical molecular and crystal physics. As discusssed several places in this volume, it is known that certain classes of molecules exhibit tremendously enhanced second-order... 

Haze is generally caused by the scattering of light in crystalline polymers. Optical inhomogenities with dimensions in the wavelength range of visible light cause haze. The latter often corresponds to the spherulite volume fraction, spherulite size and crystallinity. An increased size of spherulites results in... 

Free radical vinyl polymerization, the oldest process, leads to branched low density polyethylene (LDPE). Macromolecules have numerous short branches, which reduce the melting point, tensile strength and crystallinity. Polymers are relatively flexible because of the high volume of the branched molecule and the low crystallinity. 

PE, PP and PA are semi-crystalline polymers melting and solidification go accompanied by a (though gradual) volume jump. PS, PVC and PC are amorphous thermoplastics upon solidification they show no volume jump, but only a bend in the V-T relation. 

Here, Da is diffusion coefficient in the amorphous phase alone, oc is the volume fraction of crystalline polymer, and t is a scalar quantity that denotes the tortuosity of diffusional path of the solute. The value of Da may be estimated by the Peppas-Reinhart model if the amorphous regions of the polymer are highly swollen. This substitution yields... 

Is a crystalline polymer in which the chains are present in helical conformations, with three repeating units per turn. Because of the added volume which is left between the pendant methyl groups, this opaque polymer has a low specific gravity (0.90) as cited in Table 112. Its index of refraction is 1.49. 

The diameter d of a polymer chain can be estimated from (1) hydrodynamic quantities such as intrinsic viscosity and sedimentation coefficient, (2) the partial specific volume vgp of the polymer, and (3) X-ray crystallographic data of the polymer. Table 2 lists the values of d for liquid-crystalline polymers estimated by different methods. Those determined from hydrodynamic data are close to but slightly larger than those from vsp and crystallographic data, though this may not always be the case. 

We begin by formulating the free energy of liquid-crystalline polymer solutions using the wormlike hard spherocylinder model, a cylinder with hemispheres at both ends. This model allows the intermolecular excluded volume to be expressed more simply than a hard cylinder. It is characterized by the length of the cylinder part Lc( 3 L - d), the Kuhn segment number N, and the hard-core diameter d. We assume that the interaction potential between them is given by... 

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