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Mechanical properties of semicrystalline polymers

The molecular models of the deformation mechanisms in the semicrystaline polymers such as polyolefins and aliphatic polyesters are examined. The stretching of tie chains, which transfer the stress in the interlamellar phase, is estimated from the molecular mechanics calculations of molecules with conformational defects. The deformation behaviour of biopolyester PHB, including the problem of its physical aging, is studied by the combination of experimental and computational approaches. Recent Publications

Introduction

The structure of semicrystalline polymers on a molecular scale can be approximated as consisting of two phases: (a)- crystalline regions and (b)- disordered quasi-amorphous interlamellar (IL) regions. Crystal regions typically consist of crystal lamellae by regular folding chains. Within the IL regions four types of molecules are present (Picture 1): (a)- tails with one free end; (b)- loops, which start and end in the same lamellae; (c)- bridges (tie molecules) which join up two lamellae and (d)- floating molecules which are unattached to any lamella.

Elastic properties of the crystalline phase can be predicted fairly well. However, the response of the IL region to mechanical load is much less understood. Clearly, mechanical properties of the IL phase depend on the distribution of chains into all four categories. Still, it is believed that tie chains bridging the crystal lamellae and threading the disordered IL region, is crucial for the transfer of stress between crystal lamellae (Picture 2). Thus, the modelling of deformation of semicrystalline polymers is in large part focused on the elastic properties of tie chains in the disordered IL phase.

Picture 1: Sketch of the different types of chains in the IL phase: tie molecules (full line), loops (dashed), free ends (dotted) and floating chains (dash-dotted line). Picture 2: Stretching of tie molecules in the interlamellar phase.


Results

The interlamellar phase is disordered even in highly oriented polymers. Chains are not in crystallographic registry and contain conformational defects. It is common belief that the kink defect, a three-bond sequence g+tg- in poly(methylene) segments is best suited to be accommodated into the interlamellar phase. An insertion of the conformational defect into the full trans molecule (T-form) decreases the length and increases the potential energy of molecule. By axial stretching of a defect chain the static energy is modified by the force - length (elastic) energy term that is always positive. At first, the energy of a defect molecule increase with length R, or with strain ε. Then an abrupt decrease of the energy is observed at some critical strain.

Picture 3 shows a stretching of a three-kink chain. The 3K defect chain is interconverted in the sequence 3K ->1K->T, i.e. at first into the 1K defect (a two kink annihilation)and subsequently transformed into the T-form (one-kink annihilation).The data in Picture 3 confirm that the path followed by interconversions is indepedent of the "stretching history". The stretching of an "intermediate" 1K defect in the above sequence follows the same U(R) potential curve as the stretching of the monokink 1K structure.

Picture 3: Deformation potentials of the defect PE chains with one, two and three kinks.

The force - length functions of multikink chains are investigated. Depending on the number of defects, the F(R) curves are comprised of several essential linear segments separated by the sudden drops in force. Superimposing of individual F(R) functions generates a distinct sawtooth-like pattern in the consolidated F(R) curve. The chain defects are sequentailly annihilated by stretching, with the weakest elements yielding first. Alternatively, the defect chain loading can be describe by the stress - strain function σ(R), a usual representation of the static mechanical properties of polymer materials. From their slopes at ε = 0 the longitudinal Young`s moduli E of PE chains are determined.

The moduli of PE tie chains determined from the initial parts of the stress - strain curves were correlated with the respective chain extension ratio x (Picture 4). The plot in this picture validates the notion that an introduction of a defect into the all-trans chain brings about a shortening of the molecule and a reduction of the modulus. The data in picture can be fitted by the power-law expression E/ET = kxa, where E/ET is relative modulus. Three regions can be identified in the plot: the low-module region (x<0.85) where partly coiled chains are located, the high-modulus region (x>0.95) formed by the highly extended kink defects and the region in-between. In this intermediate region mainly the the chains with a high concentration of kink defects are situated. The calculated correlation E/ET vs x should apply for tie molecules of any length, i.e. for any interlamellar thickness in solid PE.


Picture 4: Variation of the relative modulus E/ET of PE tie molecules with their chain extension ratio x.

Tie molecules represent only one of four categories of chains assumed in the IL phase (Picture 1). Usually only a small portion of chains in the IL region belongs to this category, their population is defined by the number fractionτ. However, the chain length, given by the polymerisation degree N, differs in individual tie molecules and the chain length distribution τ(N) has to be introduced. From such a distribution function the populations of the taut and coiled bridges in the IL layer can readily be find out. The function τ(N) for PE tie chains was already determined from the wide-line NMR measurements or from Monte Carlo simulations. The length distribution of tie molecules τ(N) can be converted into a related distribution of moduli ζ(E) by using the correlation between the chain extension ratio x and the relative chain modulus E/ET from Picture 4. The ζ(E) function resulting from such a transformation of the oriented samples of PE of M = 1.05x105 is plotted in Picture 5.

Picture 5: The length distribution of PE tie molecules, expressed through the inverse of the chain extension ratio x, replotted from the experimental data (a) and the corresponding distribution function ζ of relative chain moduli E/ET (b).

The whole spectrum of shapes of τ(N) function can be envisaged, differing in the peak maximum, width and asymmetry of the distribution. In this way the distribution τ(N) represent an essential parameter affecting the properties of the IL phase and of the PE samples as a whole. The distribution τ(N) should depends on the sample preparation, modification, morphology, history, etc. In all cases, the transformation of the chain length distribution τ(N) into the chain modulus distribution ζ(E) via the E vs x correlation in Picture 4, should be viable.

It is believed that the above description of the energy elasticity and the estimation of the chain modulus is relevant also to other situations of highly stretched molecules connecting two surfaces, such as bridging two adjacent surfaces in the adhesion joints or in the domains of block copolymers, in cases of fibrillar structures bridging crazes, bimodal polymer networks with one component stretched almost to the full length, filled reinforced elastomers, etc.


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