Article
Inuence of physical properties on
polymer ammability in the cone
calorimeter
Patel, Parina, Hull, T Richard, Stec, Anna A and Lyon, Richard E.
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Influence of Physical Properties on Polymer Flammability in
the Cone Calorimeter
Parina Patel
a
, T. Richard Hull*
a
, Anna A. Stec
a
and Richard E. Lyon
b
a
Centre for Fire and Hazards Science, School of Forensic and Investigative Science, University Of
Central Lancashire, Preston, PR1 2HE, UK
b
Fire Safety, Federal Aviation Administration, William J. Hughes Technical Centre, Atlantic City
International Airport, NJ 08405, USA
* trhull@uclan.ac.uk
Abstract
The relationship between physical properties and fire performance as measured in the cone
calorimeter is not well understood. A number of studies have identified relationships between the
physical and chemical properties of polymeric materials and their gasification behaviour which can
be determined through numerical pyrolysis models. ThermaKin, a one-dimensional pyrolysis model,
has recently been employed to predict the burning behaviour in fire calorimetry experiments. The
range of thermal, chemical and optical properties of various polymers have been utilised to simulate
the processes occurring within a polymer exposed to a uniform heat flux, such as in a cone
calorimeter. ThermaKin uses these material properties to predict the mass flux history in a cone
calorimeter. Multiplying the mass flux history by the heat of combustion of the fuel gases gives the
HRR history and these have been calculated for cone calorimeter experiments at 50 kW m
-2
incident
heat flux for the lowest, average and highest values of physical parameters exhibited by common
polymers. In contrast with actual experiments in fire retardancy, where several parameters change
on incorporation of an additive, this study allows for the effect of each parameter to be seen in
isolation. The parameters used in this study are grouped into physical properties (density, heat
capacity and thermal conductivity), optical properties (absorption and reflectivity), and chemical
properties (heat of decomposition, kinetic parameter and heat of combustion). The study shows
how the thermal decomposition kinetic parameters effect the surface burning (pyrolysis)
temperature and resulting heat release rate history, as well as the relative importance of other
properties directly related to the chemical composition. It also illustrates the effect of thermal
inertia (the product of density, heat capacity and thermal conductivity) and of the samples’ ability to
absorb radiant heat.
1. Introduction
As the utilisation of polymeric materials steadily embraces a wider variety of potentially hazardous
applications, greater emphasis must be placed on mitigating the danger of fire. The physical
characteristics of polymers and a better understanding of the behaviour of such materials when
exposed to ignition sources is, therefore, a necessity. The ignitability and burning behaviour of
polymers is a complex process involving interactions between a number of physical and chemical
processes. Improved development of new fire safe materials would result from being able to
understand the effect on burning behaviour of altering each variable independently. Unfortunately
such studies are not practically feasible since any modification to the polymer, such as the
incorporation of an additive, results in changes to a range of physical and chemical properties and
processes. In many cases fire retardants (FRs) have chemical effects, such as intumescence,
This is the pre-peer reviewed version of the following article: Patel P, Hull T Richard, Stec Anna A, Lyon Richard E (2011)
Influence of physical properties on polymer flammability in the cone calorimeter. Polymers for Advanced Technologies 2011,
which has been published in final form at http://dx.doi.org/10.1002/pat.1943
c
arbonisation, ceramicisation or stabilisation of the polymer. These effects are masked by changes in
physical properties, resulting from the incorporation of FR additives, which are highlighted in this
study. Where the behaviour of the processes can be reliably predicted, these can be incorporated
into models of burning behaviour. Although state of the art models cannot yet make reliable
predictions of time to ignition or heat release rate (HRR) history, such predictions are of great value
in differentiating between expected, predictable behaviour and unexpected phenomena such as
different chemical pathways leading to inhibition of decomposition and pyrolysis.
The development of calorimetric techniques based on the principle of oxygen depletion has greatly
improved fire testing and research because it quantifies the heat release associated with real
burning [1] [2]. The cone calorimeter, [3] [4] developed at the National Bureau of Standards (NBS),
now the National Institute of Standards and Technology (NIST), has been widely used for assessing
the flammability of polymeric materials. This method was primarily developed for measuring the
rate of heat release from a burning object as a function of incident flux [5]. The external radiation
source is intended to simulate the effect of a burning object in close proximity. Interpretation of
cone calorimeter data has not been adequately addressed within the fire retardant community [6],
however, there is still a growing reliance on the instrument [7] [8] for the initial screening and
subsequent assessment of new flammability modified materials. For example, the use of mineral
fillers, such as aluminium hydroxide [9, 10] and nanofillers [11, 12
] will change both physical and
decomposition behaviour.
A number of studies [13] [14] [15] have effectively demonstrated that a numerical pyrolysis model
can be used to determine the relationships between the fundamental physical and chemical
properties of polymeric materials and their gasification behaviour. Typically, the model is used to
calculate the mass loss rate of a one-dimensional sample of solid fuel exposed to a uniform heat flux.
ThermaKin is an example of such a model, which has been effectively utilised as a practical tool for
the prediction and/or extrapolation of the results of fire calorimetry experiments [16] [17] [18] [19
].
The model, which combines the absorption and transfer of thermal energy with Arrhenius kinetics
for the decomposition of the polymer, predicts the overall behaviour of a pyrolysing object through
mass and energy conservation equations. These equations are formulated in terms of rectangular
finite elements, each element being characterised by component mass and temperature.
Additionally, the model describes the transport of gaseous products through the condensed phase
and follows changes in the volume of the bulk material.
For thermally thick solids (typically, thicknesses above 15 mm [20]) the thermal inertia, kρc, the
product of thermal conductivity (k), density (ρ) , and specific heat (c), of a material governs its
ignition and flame spread properties. This determines the rate of rise in surface temperature and
consequently, the time to ignition [21
]. The time to ignition (t
ig
) of a thermally thick solid exposed to
a constant net heat flux Q
R
= Q
ext
– CHF
,
where Q
ext
is the external heat flux from fire or radiant
heater and CHF is the critical heat flux for ignition, has been expressed in Equation 1.
[Equation 1]
where T
ig
and T
0
are the ignition and ambient temperatures, respectively. The time to ignition of a
thermally thin solid exposed to a constant net heat flux has also been expressed in Equation 2.
=
4
0
2
2
This is the pre-peer reviewed version of the following article: Patel P, Hull T Richard, Stec Anna A, Lyon Richard E (2011)
Influence of physical properties on polymer flammability in the cone calorimeter. Polymers for Advanced Technologies 2011,
which has been published in final form at http://dx.doi.org/10.1002/pat.1943
[E
quation 2]
Where
τ
refers to material thickness. Equations 1 and 2 follow from the concept of a constant
ignition temperature T
ign
and temperature-independent thermal inertia. Once ignition has occurred
and a flame is established on the surface, the net heat flux becomes Q
R
= Q
ext
+ Q
flame
- CHF
b
, where
Q
flame
is the additional heat flux supplied by the flame and CHF
b
≈ σ
T
b
4
is the critical heat flux for
burning in terms of the surface burning temperature T
b
and the Boltzmann radiation consant σ. It
has been shown that T
b
≈ T
p
where T
p
is the pyrolysis temperature measured in laboratory thermal
analysis experiments using small samples and constant heating rates [22]. Thus, polymers with high
pyrolysis temperatures reradiate more of the incident heat flux from the heater and flame back to
the surroundings, and the net heat flux that drives the burning process is reduced accordingly.
The Arrhenius rate constant, k(T) = A exp[-E
a
/RT] is a reasonable descriptor of the temperature
dependence of the rate of polymer thermal decomposition. The kinetic parameter A (s
-1
) represents
the frequency of chemical bond breaking reactions in the polymer at temperature T while the
activation energy E
a
represents the thermal energy barrier that must be overcome to break the
chemical bonds and produce fuel gases. It has recently been demonstrated for a range of common
polymers that the thermal decomposition temperature or peak pyrolysis rate temperature (T
p
)
measured in thermal analysis experiments such as pyrolysis combustion flow calorimetry (PCFC) [23]
or thermogravimetric analysis (TGA) has a large effect on ignition and burning [22][23
]. Equation 3 is
a derived result [22] that shows that the peak pyrolysis temperature in constant heating rate
experiments such as TGA or PCFC is defined by an activation energy (E
a
) and Arrhenius factor (A) that
are not independent:
[Equation 3]
In Equation 3, R is the gas constant and k
p
= k(T
p
) = Aexp[-E
a
/RT
p
] = βE
a
/R
T
p
2
is the value of the
kinetic rate constant at T
p
measured for a milligram-size sample at a constant rate of temperature
rise β = dT/dt derived from a semi-exact solution of the Arrhenius temperature integral [22]. Since
surface heating rates of polymers burning in a cone calorimeter at 50 kW/m
2
external heat flux are
comparable to those used to determine A and E
a
in PCFC or thermogravimetric analyses [22], β ≈ 1
K/s, and since R
T
p
2
/E
a
≈ 20K (typically), a constant value, k
p
= (1 K s
-1
)/(20K) = 0.05 s
-1
was used in
Equation 3 to calculate the pyrolysis temperatures in Table 1 for A and E
a
used in ThermaKin (also
shown in Table 1). It has been proposed that uncertainty in the Arrhenius parameters manifests
itself as uncertainty in modelling the fire response of polymers [22]. The processes modelled by
ThermaKin have been summarised in Figure 1. For this study, radiant heat from above the sample is
absorbed, emitted or reflected, and the condensed phase heat transfer process is modelled through
the solid. The resulting temperature increases drives endothermic decomposition processes, leading
to the gasification of volatile fuel components. When a critical mass flux for ignition is reached,
ignition will occur, and the incident radiant flux is augmented by radiation from the flame.
Thereafter, quasi-steady state conditions pertain, until the sample is so thin that it has no more
capacity to absorb heat, and the rate of pyrolysis increases.
=
(
0
)
=
ln
This is the pre-peer reviewed version of the following article: Patel P, Hull T Richard, Stec Anna A, Lyon Richard E (2011)
Influence of physical properties on polymer flammability in the cone calorimeter. Polymers for Advanced Technologies 2011,
which has been published in final form at http://dx.doi.org/10.1002/pat.1943
Figure 1. Schematic of processes occurring in the cone calorimeter, as modelled by Thermakin
This present study utilises ThermaKin as a means of relating the physical properties of a material to
its HRR history in a cone calorimeter.
2. Modelling
The effect of physical properties on the fire behaviour of non-charring polymers was investigated
using a one-dimensional pyrolysis model, ThermaKin; a complete description of the model’s
mathematical formulation and numerical algorithms has already been reported [16].
A sensitivity analysis has been carried out by the model’s developers to determine the relative
importance of individual properties [18]. Within ThermaKin, changes to the fuel are accounted for as
a change in the component. Each component is characterised by its physical state, density, heat
capacity, thermal conductivity, gas transfer coefficient, emissivity and absorption coefficient. The
model ignores changes in thermal conductivity resulting from changes in melt flow behaviour on
heating. The chemical processes occurring are characterised through the reaction’s activation energy
and Arrhenius factor. The energy balance assumes that radiant heat may be absorbed or reflected by
the sample, and then either conducted through it resulting in a localised temperature increase, or
re-radiated from the surface. Higher temperatures will result in gasification forming vapour phase
fuel which can b ignited and then burns, transferring some radiant heat back to the sample. From
the sensitivity analysis [18], it was established that for most synthetic polymers, the thermal, optical
and chemical properties varied only within limited ranges. To demonstrate this, the lower, average
and upper boundaries of each parameter were determined from experimental techniques and
reported values [18]. These are shown in
Table 1. The study also determined that some parameters
had a greater influence on time to mass loss, peak mass loss and average mass loss rate and
Emission
Absorption
Thermal Inertia kρc
Infrared Radiation – Absorption,
reflection, emission
Heat transfer through solid – thermal inertia kρC
Heat losses
Endothermic thermal decomposition and gasification -
First Order Arrhenius kinetics
Gas transport leading to critical mass flux
Ignition
Convective and Radiative Heat Transfer
Steady Burning – Rate of fuel pyrolysis controlled by
radiation from flame
radiation
convection
Reflection
Emission
Absorption
Thermal Inertia kρc
Infrared Radiation – Absorption,
reflection, emission
Heat transfer through solid – thermal inertia kρC
Heat losses
Endothermic thermal decomposition and gasification -
First Order Arrhenius kinetics
Gas transport leading to critical mass flux
Ignition
Convective and Radiative Heat Transfer
Steady Burning – Rate of fuel pyrolysis controlled by
radiation from flame
radiation
convection
Reflection
This is the pre-peer reviewed version of the following article: Patel P, Hull T Richard, Stec Anna A, Lyon Richard E (2011)
Influence of physical properties on polymer flammability in the cone calorimeter. Polymers for Advanced Technologies 2011,
which has been published in final form at http://dx.doi.org/10.1002/pat.1943
