Estimation of Crystalline Junction Size of Linear High-Density Polyethylene Gel Comprised of Lamellae

Abstract

ABSTRACT:A method for estimating junction point size in a thermoreversible gel made up of overlapping lamellae with disc-like morphology is proposed by combining the theory of melting temperature depression of copolymer-diluent system with the continuum percolation theory which takes account of the excluded volume of disc. According to our method, junction point size of gel can be estimated from measurement of gel-melting temperature Tmg* at the critical gelation concentration v,.This method was applied to linear high-density polyethylene (LHDPE)Ixylene gel. The junction point size estimated by the present method, i.e., diameter and thickness of disc-like lamellae in a LHDPE gel, was in reasonable agreement with measurement by scanning electron microscopy (SEM) and small-angle X-ray scattering (SAXS) measurement.KEY WORDS Thermoreversible Gel I Polyethylene I Linear High-Density Polyethylene I Continuum Percolation Theory I Junction Size of Lamella I Gel-Melting Temperature IThe sol-gel transition of polyolefin in organic solvents is well known. 1 • 2 Gelation of such crystalline polymer takes place through formation of a network structure with crystalline junctions. In the case of semi-crystalline polymer gels such as random copolymer gel of ethylene and propylene including high content of propylene units (i.e., lots of methyl branchings), fringed micelle-type crystallite was appropriate morphology for the junction point. 3 In the case of highly crystalline polymer gels such as linear high-density polyethylene (LHDPE) gel, junction points were disc-like lamellae with diameter 2r and thickness d, which were three-dimensionally in contact with the others at random array as shown in Figure 1. 4 Recently, site-bond percolation process was applied to gelation, because percolation has close similarity to sol-gel transition. Elastic behavior near the threshold ( C*) of gelatin or casein gel has been investigated 5 • 6 in detail by the bond percolation theory using the relation Eoc[(C-C*)/C*J and critical exponent (t) has been compared with that by the classical theory (i.e., the tree approximation), where E is the elastic modulus and C* is the critical gelation concentration.The site-bond percolation theory was developed basing upon a lattice model. Thus this theory cannot be applied directly to the system where particles such as lamellar or spherulitic crystals behave as junction points or loci, because the theory does not take the excluded volume effect of the particles into consideration. To such a system that contains the particles, application of the continuum percolation theory is more appropriate. In this theory, the excluded volume of the particles is taken into account.This study proposes a new method for estimating the size of lamellar junction in a thermoreversible gel by combining the theory of melting temperature depression of crystallites, formulated by Takahashi and co-workers, 7 with the continuum percolation theory. The present method is applied to the LHDPE/xylene gel in order to 1 To whom all corre...

The Flory-Huggins Interaction Parameter and Thermoreversible Gelation of Poly(vinylidene fluoride) in Organic Solvents

“…The gel-melting temperature (T m g ) of each sample increases gradually with increasing polymer concentration similar to highly crystalline polymer gel such as polyethylene or isotactic polypropylene gel. [28][29][30] The molecular weight dependence of T m g is not observed in Figure 4a and 5a. It is likely seen that the gel→sol transition curve becomes higher with increasing X c of sample, though the difference in X c of the present PVdF samples is not so large.…”