Solubility of solvents in polyethylene below the melt temperature

• 05 Mar 2023

Globally polyethylene (PE) is the most abundant polymer found
in everyday life [1]. Some of the most common uses for PE included
plastic bags, plastic film, bottles, and piping. Below its melting point
polyethylene is a semi-crystalline polymer, i.e., some of the chains
form an ordered dense crystalline phase while others are in an
amorphous phase of lower density. In general, solvents are
excluded from the crystalline phase [2]. To improve the ability of
current models to predict the solubility in polyethylene the effect of
the amount of crystallinity needs to be characterized.
The first type of polyethylene that was commercially produced
was known as low-density polyethylene (LDPE) [3]. The production
of this type of PE is done without the use of a catalyst. In the
absence of a catalyst, the radical site can move from a location at the
end of the chain to a more stable location in the middle of the chain.
This causes a new ethylene monomer to polymerize at the radical
site and form a branch in the middle of the PE chain. As this process
continues a non-linear, highly branched PE chain is formed. In LDPE
the large amount of chain branching prevents a portion of the
chains from crystallizing [4]. Since the amorphous phase of PE has a
much lower density than the crystalline phase, the reduction in
crystallinity results in an overall product that has a lower density
than when the chains are completely linear.
Once catalysts were introduced into PE production high-density
polyethylene (HDPE) was commercially produced. PE polymerization using a catalyst, such as a Zeigler-Natta or a metallocene
catalyst, ensures that the radical site stays at the end of the PE
chain, resulting in a final product that is a linear chain with little to
no branching. These chains have a higher tendency to crystallize
resulting in a high density PE [3].
Soon after the introduction of polymerization catalysts, longer
a-olefins such as 1-butene, 1-hexene, and 1-octene were added to
the polymerization process. This addition of a co-monomer results
in a polyethylene chain that has a linear backbone with short side
chains distributed along its length. As these side chains cannot be
included in the crystal structure [2], they act to reduce the crystallinity of the polyethylene. The resulting linear low-density
polyethylene is sometimes divided into subgroups: mediumdensity PE (MDPE) having a density between 0.94 and 0.926 g/
cm3
, linear-low-density PE (LLDPE) having a density between 0.926
and 0.915 g/cm3 and very-low-linear-density PE (VLLDPE) having a
density below 0.915 g/cm3
.
2. Semi-crystalline structure models
There are three common models in the literature used to
describe the semi-crystalline structure of PE [5]. The first was Flory's switchboard model [6] which proposes that the majority of
polyethylene chains leave the crystalline surface and cross over the amorphous region to a different crystalline surface rather than reenter the same crystal. The second is the adjacent reentry model of
Hoffman and Lauritzen [7]. They propose two forms: a smooth
surface in which almost all the chains that leave the crystalline
surface immediately bend and reenter adjacent to where they
exited, and a rough surface model in which the majority of chains
still enter adjacent to where they exited the crystalline phase, but
the fold length is not uniform. The third model was originally
suggested by Stamm et al. [8] and later adapted by Strobl [9]. In
either version crystallization from the melt occurs by formation of
an aligned, long-range, ordered state, which then proceeds to
develop into the long-range ordered crystalline phase.
In the past thirty years, numerous studies have been performed
to study the effect of tie chains on the properties of semi-crystalline
polymers. Most of these focus on mechanical properties [10,11]. A
good review of the relationships between tie chains and mechanical properties in semi-crystalline polymers is provided by Seguela
[12]. Only a few studies have focused on solvent solubility [13e16].
3. Solubility in PE
Unlike amorphous polymers, where the penetrant is evenly
distributed throughout the polymer phase at equilibrium, semicrystalline polymers, like PE, restrict the penetrant from entering
the crystalline phase due to dense chain packing [2]. While the
penetrant is not evenly distributed throughout the entire polymer
domain, it is assumed to be evenly distributed within the amorphous domain of the polymer. Thus, when comparing the solubility
between polyethylene samples with different crystallinity, the
weight fraction of penetrant should be normalized in terms of the
amount of penetrant in the amorphous phase of the polymer rather
than on a total polymer basis. Above the melt temperature, where
PE is entirely amorphous, models like the Group Contribution
Lattice Fluid-Equation of State (GCLF-EoS) [17], UNIFAC-FV [18], and
UNIFAC-vdw-FV [19] have been shown to accurately predict the
solubility of solvents in PE [15]. Below the melt temperature
application of these models to PE needs to be evaluated.
Michaels and Hausslein [20] were one of the first to propose an
explanation for the reduction in solubility in the amorphous phase
in semi-crystalline polymers like PE. Their model, which was
originally proposed in 1965, is still the most successful model. They
postulated that the cause for the large temperature dependence in
penetrant solubility in polyethylene is due to the tie chains. As the
penetrant enters the amorphous phase these tie chains act like
springs and apply an elastic force on the amorphous region which
reduces the equilibrium concentration of penetrant within the
amorphous phase. The most important assumptions of their derivation are:

The amorphous phase is composed of two types of tie chains:
elastically effected and inelastically effected chains. The elastically effected chains extend across the amorphous region,
tethering two crystalline domains. The inelastic portion consists
of chains which exit and reenter the same crystal phase, as well
as chain ends and other short segments excluded from the
crystal.

The amount of tie chains is constant in the temperature range in
which the polymer's crystalline structure does not change. Thus,
the temperature dependent behavior of the tie chains is
reversible as long as the crystalline structure does not change.

The collective properties of the tie chains, such as length, can be
accurately captured by an average of those properties.

The deformation is uniform in all directions, i.e., isotropic.
By assuming that the force required to stretch the chains can be
approximated by Hooke's Law, the final expression lacked any
terms that require the number of monomers in the tie chains, the
length of the chains, or directly evaluating the Hookian spring
constant. Dong and Ho [21] used Michaels and Hausslein's
expression for the chemical potential that the tie chains exert on
the amorphous phase and converted it into an activity.