Dielectric Characterization of a Thermotropic Liquid Crystalline Copolyesteramide: 2. Orientation and Crystallinity A. Boersma, J. van Turnhout,* and M. Wu 1 bbenhorst Department of Polymer Technology, Faculty of Applied Science, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received August 3, 1998; Revised Manuscript Received August 3, 1998 ABSTRACT: The dielectric characterization of a thermotropic liquid crystalline copolyesteramide was extended. The influence of orientation and crystallization was studied. An effect of the draw ratio on the dielectric properties in the transverse direction was hardly found. However, the orientation of the sample in the electric field (parallel or perpendicular) showed a significant effect. The birefringence predicted from the dielectric data at high frequencies agrees well with the optical value. Annealing of extruded and compression-molded samples resulted in an increase of the R relaxation peak. I. Introduction Dielectric spectroscopy on the thermotropic liquid crystalline copolyesteramide Vectra B950, discussed in the previous paper, 1 revealed the existence of four relaxations. The effect of orientation and crystallization on the relaxations was not discussed. However, it is known that these parameters can have a large influence on the magnitude and position of the relaxations. In the present paper we will deal with this influence. Several authors have discussed the influence of the draw ratio on the mechanical properties of main chain LCPs. For instance, Choy et al. 2 correlated the molec- ular orientation, obtained by X-ray diffraction, to the elastic moduli as a function of the draw ratio. The dependence of the dielectric properties on the molecular orientation in main chain LCPs is described by only a few authors (e.g. Liu 3 and Willems 4 ). They both found an increase of the relaxation strength perpendicular to the orientation direction with increasing draw ratio. II. Theory Relation between Relaxation Strength and Or- der Parameter. Liquid crystalline polymers are by nature highly anisotropic materials. For the interpreta- tion of dielectric data of liquid crystalline polymers, it is important to consider the molecular orientation with respect to the applied electric field. Several authors have published experimental and theoretical results on side-chain LCPs. The papers on main chain LCPs considering molecular alignment are however limited. For side-chain LCPs it is common to account for orientation phenomena, but for main-chain LCPs not many data are available. An interesting approach has been suggested by Attard et al. 5 They assumed that the polymer is built up of domains and derived expres- sions for the dielectric permittivity as a function of the order parameter, under the assumption that the orien- tation is uniaxial. where ǫ x , ǫ y and ǫ z are the dielectric permittivities in the x, y and z directions. The z axis is parallel to and the x and y axis are perpendicular to the draw direction of the samples (Figure 1). ǫ | and ǫ ⊥ are the permittivi- ties parallel to and perpendicular to the director of the domains. The order parameter of the director S d is related to the angle θ between the director and the z-axis by Hermans’s relation S d ) (3〈cos 2 θ〉 - 1)/2. Equations for the low frequency or static permittivi- ties ǫ | s and ǫ ⊥ s of the domains were derived by Maier et al. 6 as a function of the local order parameter inside the domains. in which µ is the permanent dipole moment, Ψ the angle between each dipolar vector and the director of the domains. S l the local order parameter inside the domains, and G | and G ⊥ combine the number of dipoles, the cavity field factor and the reaction field factor in the parallel and perpendicular direction, respectively. Maier et al. derived these equations neglecting the influence of the dielectric anisotropy on both the cavity and the reaction field, thus using G instead of G | and G ⊥ . Furthermore, since we are dealing with a semi- crystalline polymer, the effect of the crystallinity is also incorporated in the parameter G. Combination of eqs 1-4 leads to the following equations for the three dielectric permittivities: The parameters G z and G xy incorporate the cavity and reaction field in the direction of respectively the z and ǫ z ) ǫ | (1 + 2S d )/3 + ǫ ⊥ 2(1 - S d )/3 (1) ǫ x ) ǫ y ) ǫ | (1 - S d )/3 + ǫ ⊥ (2 + S d )/3 (2) ǫ | s ) ǫ | ∞ + G | µ 2 3kT [1 - S l 〈1 - 3 cos 2 Ψ〉] (3) ǫ ⊥ s ) ǫ ⊥ ∞ + G ⊥ µ 2 3kT [1 + S l 〈1 - 3 cos 2 Ψ〉/2] (4) ǫ z s ) ǫ | ∞ 1 + 2S d 3 + ǫ ⊥ ∞ 2(1 - S d ) 3 + G z µ 2 3kT [1 - S d S l 〈1 - 3 cos 2 Ψ〉] (5) ǫ x s ) ǫ y s ) ǫ | ∞ 1 - S d 3 + ǫ ⊥ ∞ 2 + S d 3 + G xy µ 2 3kT [ 1 + S d S l 2 〈1 - 3 cos 2 Ψ〉 ] (6) 7461 Macromolecules 1998, 31, 7461-7466 10.1021/ma981287b CCC: $15.00 © 1998 American Chemical Society Published on Web 10/02/1998