Elastic moduli of highly stretched tie molecules in solid polyethylene Zdenko S ˇ pitalsky ´, Toma ´s ˇ Bleha * Department of Molecular Thermodynamics, Polymer Institute, Slovak Academy of Sciences, Dubravska cesta 9, 84236 Bratislava, Slovak Republic Received 19 July 2002; received in revised form 25 November 2002; accepted 7 December 2002 Abstract The elastic properties of interlamellar bridges in semicrystalline polyethylene (PE) were estimated from the molecular-mechanics calculations on the assumption that the energy loading of a chain backbone represents the principal deformation mechanism. The calculations result in the force – length functions featuring abrupt discontinuities due to sequential annihilation of the defects by the conformational transitions. The correlation of the chain elastic moduli E with the concentration of defects in the chain and with the chain extension ratio x were established. The distribution functions zðEÞ of Young’s moduli of interlamellar bridges in semicrystalline PE were calculated by using the literature data on the chain length distributions of tie molecules. The impact of the distribution function of moduli zðEÞ on the overall elastic response of solid PE materials was examined, particularly in cases of the stacked lamellae morphology involving so-called hard elastic PE. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Interlamellar phase; Mechanical properties; Semicrystalline polymers 1. Introduction Molecular description of elasticity of semicrystalline polymers is of considerable importance due to technical and biological applications of a variety of such materials, ranging from thermoplastics such as polyethylene to biological fibres such as spider silk. On a molecular scale the structure of semicrystalline polymers can be approxi- mated as consisting of two phases: crystalline regions and a noncrystalline matrix material. The quantitative modelling of mechanical properties of semicrystalline polymers is not a straightforward task because of the complexity in their structural and morphological hierarchy. Still, in recent years the theory and modelling provided new insights on the molecular mechanisms underlying the deformation of these materials [1–7]. The elastic properties of crystalline phase, typically consisting of thin crystal lamellae formed by folded chains, can be fairly well predicted [8]. According to the current view the Young’s elastic modulus and the strength of semicrystalline polymers are primarily affected by the structure of quasi-amorphous interlamellar (IL) regions where several types of molecules, such as loops, which start and end in the same lamella, tails with one free end, and bridges (tie molecules) which join up two lamellae, can be distinguished. Tie molecules that traverse the noncrystaline regions play a central role in transferring stress effectively from one lamella to the next when strained. Thus, the various models of deformation of semicrystalline polymers [9] are in large part focused on the properties of tie molecules, especially in polyethylene (PE). The concentration of tie molecules interconnecting crystallites in an undeformed solid PE can be estimated from the chain dimensions and the lamellar microstructure [10,11]. During tensile drawing of PE the spherulite-lamellar morphology of semicrystalline polymers is transformed into an oriented fibrous structure [9]. On drawing, tie molecules are pulled out and become more taut and the entire amorphous regions more oriented. In PE at high drawing ratios the intrafibrillar taut tie molecules involve long (zig-zag) sequences of all-trans bonds. It was argued that the fraction of the load-carrying taut tie molecules determines the elastic modulus of PE fibrils and of ultra-high molecular weight PE fibres [9,12]. Detailed atomistic modeling of elasticity of extended tie molecules in the noncrystalline IL phase is usually based on the axial mechanical loading of polymer chains containing the conformational defects [1,13 – 18]. In highly extended 0032-3861/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. PII: S0032-3861(02)00908-4 Polymer 44 (2003) 1603–1611 www.elsevier.com/locate/polymer * Corresponding author. Tel.: þ 421-2-54777414; fax: þ 421-2- 54775923. E-mail address: upoltble@savba.sk (T. Bleha).