Liquid-crystalline polymers, free volume

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

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... 

Hsieh et al [62] found that for a range of thermotropic liquid crystalline polymers, the greater the free volume measured by PAL the greater the chain mobility at Tg and the higher the value of tan S (damping strength) measured by dynamic mechanical analysis. 

Priest (1973) and Straley (1973), in terms of the classical virial expansion, the Onsager theory (referred to in Section 2.1) and the curvature moduli theory, derived the elastic constants of rigid liquid crystalline polymers. The free energy varies according to the change of the excluded volume of the rods due to the deformation. The numerical calculation of elastic constants (Lee, 1987) are shown in Table 6.2. 

The influence of chain packing (Le. free volume) on solubility, diffusivity and permeability in liquid crystalline polymers can be studied by comparing properties of LCPs in the disordered, isotropic state with those in the ordered, liquid crystalline state. HIQ-40 is a random, glassy, thermotropic, nematogenic terpolymer synthesized from 40 mole percent p-hydroxybenzoic acid and 30 mole percent each of isophthalic acid and hydroquinone. The chemical structures of the constituent monomers for fflQ-40are ... 

The free volume of thermoplastic miscible blends has also been determined as a function of blend composition (Zhou et al. 2003 Campbell et al. 1997 Roland and Ngai 1991). Those studies have shown that the degree of blend miscibility alters the free volume behavior as a function of blend composition. On the other hand, Hsieh et al. (2000) have studied a number of blends containing only thermotropic liquid crystalline polymers TLCP s as the only components. That work showed that regardless of their various miscibilities, TLCP blends tend to display smaller, fewer free volume sites than expected from a weighted average. This observation has been ascribed to the intrinsic affinity of nematic TLCP s. 

Kietzmann C, Van der Walt JP, Morsi YS (1998) A free-front tracking algorithm for a control-volume-based Hele-Shaw method. Int J Numer Methods Eng 41 253-269 Kim SH, Kim CH, Oh H, Choi CH, Kim BY, Youn JR (2007) Residual stresses and viscoelastic deformation of an injection molded automotive part. Korea-Australia Rheol J 19 183-190 Klein DH, Leal LG, Garcfa-Cervera CJ, Ceniceros HD (2008) Three-dimensional shear-driven dynamics of polydomain textures and disclination loops in liquid crystalline polymers. J Rheol 52 837-863... 

The vacant sites of the solid polymer (amorphous) are called free volume no long range order in extensive regions occurs in the amorphous state (e.g., amorphous material is not x-ray crystalline) although indications are that these regions possess a certain order and theoretically a certain number of vacant sites must be present in the solid polymer. Free volume is mainly responsible for the compressibility of liquids and solids. Also called Free Volumes f. Vacant Free Volume f, Williams-... 

Hsieh T-T, Tin C, Simon GP. Miscibility and free volume behaviour of a number of polymer blends containing only thermotropic liquid crystalline polymers. Polymer 2000 41 4737-42. 

Uedono, A., Sadamonto, R., Kaqano, T., Tanigawa, S., Uryu, T. (1995) "Free volumes in liquid-crystalline main-chain polymer probed by positron annihilation . J. Poly. Sci. B Poly. Phys. 33, 891. 

In conclusion regarding the results obtained with polymer-bound azobenzene chromophores, establishing liquid crystalline phases that combine order and flexibility in the side chain region of the polymer seems to be the best way to obtain materials with a strong photoresponse. This is because a high density of chromophores can be combined with sufficient flexibility that the chromophores still can be photoisomerized in the dense packing of an LBK film. When a low density of chromophores is acceptable, however, the chromophores can be diluted along the polymer chain to reduce their interaction and secure sufficient free volume. 

However, the derivation of Equation 16 failed to take into account the free-volume ("structural") contribution to xy"(35), nor is the effect negligible with some polymer phases (36). In addition, there remains considerable doubt even as to what constitutes a "family" set of data e.g., with polymers that are liquid-crystalline. The characterization of polymer stationary phases via family-plot regressions of "inverse" gas-chromatographic retentions therefore invites further and comprehensive study. 

Table II presents PALS results and other physical property data for an as-cast HIQ-40 sample and for a sample that was annealed for one hour at 200 C. The annealing protocol results in a 2,5% increase in density, which corresponds to a 17% decrease in fractional free volume. The acetone diffusion coefficient decreases almost five-fold and acetone solubility decreases by approximately 90% as a result of the ordering induced by the annealing protocol. The oPs lifetime decreases by 14%, suggesting that the average free volume cavity size decreases due to annealing. Based on the oPs lifetime, the mean free volume cavity diameter may be estimated (36) these values are reported in parentheses in Table n. The PALS I3 parameter, which reflects the relative concentration of free volume elements in the polymer matrix, is approximately 22% lower in the annealed, liquid crystalline sample.

As discussed in Chapter 2, the moleeular structure of polymers, whether glassy or semi-crystalline, incorporates a signifieant component of disordered material containing a certain fraction of free volume or a liquid-like material environment, depending on the thermal history of the polymer. The subject of this chapter is the small-strain reversible response of sueh polymeric materials and structures under stress that we refer to as linear viscoelasticity. 

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