(181c) Glass Transition Temperature of a Polymer Thin Film: Simulation Methodology and Statistical Variation

Glass
transition temperature of a polymer thin film: simulation methodology and
statistical variation

David
McKechnie, Jordan Cree, and Karen Johnston

Department of Chemical
and Process Engineering, University of Strathclyde, 75 Montrose Street,
Glasgow, UK

Carbon fibre reinforced polymer composites are used in a wide variety of applications that take advantage of their mechanical, thermal and electrical properties, for example, "light weighting" aircraft and automobiles to reduce their energy consumption and emissions. An important polymer
property is the glass transition temperature, T_g, below which the
polymer exhibits hard and relatively brittle glassy properties. This makes the
glass transition an important property in the design and processing of polymer
composites. The properties of the resulting polymer composite depend on not
only the individual properties of the polymer and fibre but also on the interfacial
properties, which depend on the interaction between the polymer and the fibre
surface.

The effect of a surface
on the polymer T_g is a source of controversy in literature with
experiments predicting a wide range of shifts in T_g [1]. Classical molecular
dynamics (MD) simulations provide insight into the interfacial properties at a
molecular level that is not easily accessible using current experimental
techniques, and have, therefore, been employed to investigate T_g for
a variety of polymeric systems [2]. One study of supported
thin films of atactic-polystyrene showed that confinement increases T_g
and reduces the mobility of polymer chains close to the substrate [3], whilst another study
finds that free-standing thin polystyrene films see a reduction in T_g
of 60 K in comparison to the bulk [4]. In this work we use MD
simulations to investigate the glass transition of a united atom model of
polyethylene (PE) in contact with a graphene surface. Simulations were
performed with 50 monomer PE chains in both bulk and a 9 nm film between
two graphene surfaces (see Figure 1).

T_g is often
determined by cooling an equilibrated polymer melt at a specified cooling rate
and measuring where the density vs temperature undergoes a gradient change (see
bottom Figure 2). T_g
is known to depend on the cooling rate [5,6], but cooling can be simulated in
several ways: linearly [5] , stepped [3,5], and sampled cooling [6]. Under
linear cooling the temperature is gradually reduced at a constant rate, while
stepped cooling reduces the temperature in a stepwise fashion with time between
the steps of constant temperature simulation to allow for equilibration.
Sampled cooling involves cooling linearly and taking snapshots
of the system to be simulated further at a constant temperature to improve
statistics. Schematic graphs of temperature vs time for each cooling method are
shown in Figure 2 (top). T_g can then be found by fitting straight
lines to the fluid and glassy branches of the temperature-density curves as
shown in Figure 2 (bottom). T_g is then defined as the temperature where
the straight lines intersect. The sensitivity of the results on the cooling
method and fitting ranges is unknown, and often these details are not reported
in literature. Moreover,
it has been reported that the statistical variation associated with T_g
is significant and that a large number of independent simulations are required [7]. In this study we
investigate the effect of the cooling and fitting methods, and the statistical
variation in calculations of T_g.

To
test the statistical variation for bulk PE we produced 100 independent starting
configurations by randomly inserting pre-coiled polymer chains into a
simulation box and simulating them in NPT at 500 K and 1 atm until
the radius of gyration reached a stable value (~ 10 ns). Using stepped cooling,
we found that 20 independent simulations were necessary to reduce the standard
error in T_g to 6 K. We compared this result to linear or
stepped cooling using 20 independent simulations, and found there was no significant
effect of the cooling method on T_g. Work is ongoing to test the
sensitivity to the fitting ranges.

We
investigated the glass transition of bulk PE and PE thin films using stepped
cooling over a range of cooling rates from 0.015 – 1.3 K/ps, and
20 independent starting configurations for each cooling rate. We found that the
graphene surfaces increase T_g by approximately 25 K, which is a
statistically significant difference from the bulk T_g.

Acknowledgements

Results
were obtained using the ARCHIE-WeSt High Performance Computer
(www.archie-west.ac.uk) based at the University of Strathclyde. David McKechnie was
supported by an EPSRC Institutional
Sponsorship Award (Grant Ref: EP/P511420/1). Jordan Cree
received funding from CCP5 (www.ccp5.ac.uk) for a vacation bursary. We thank Dominic Wadkin-Snaith and Peter Mills at Solvay Composites
Group, U.K. for useful discussions.  

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