The following sections provide details about the calculations performed to analyze the raw data measured in each of the experimental methods to yield the property values presented in the database. While this is not an exhaustive list, these methods are recommended by FSRI staff to extract property values or use in fire dynamics calculations and fire modeling.
STA data may be used to determine the temperature at which materials undergo physical transitions including melting and glass transition. By plotting together mass loss rate (MLR) data and heat flow rate data, sudden changes in the heat flow rate with no mass loss correspond to a physical transition.
Glass transition typically manifests as a step shift of the heat flow rate data. The glass transition temperature is determined by drawing two baseline curves: each consistent with the trend in the heat flow rate data before and after the transition. The glass transition temperature is defined as the mean of the temperatures at which the heat flow rate curve intersects each of the baseline curve. This analytical procedure is described in ASTM E1356 and ISO 11357-2.
Melting manifests in heat flow rate data as an endothermic curve that increases from the baseline, reaches a peak, and decreases back to the baseline. This peak is not accompanied by any change in mass. Analysis is similar to determination of glass transition temperatures, except it uses single baseline. The temperature at which the heat flow rate curve deviates from the baseline is considered the onset temperature for melting, and the temperature at which the maximum endothermic heat flow is measured is considered the peak melting temperature. Both quantities are typically reported. The enthalpy of fusion (heat of melting) is taken as the area between the melting peak and the melting baseline. This analytical procedure is described in ASTM E793, ASTM E794, and ISO 11357-3.
A variety of analytical methods have been used to determine reaction kinetics from normalized MLR data collected in thermal analysis experiments. The available methods are divided into model-based and model-free methods. The differentiation between the two sets of methods derives from the Arrhenius equation, which relates the reaction rate to the temperature of the material and some function of the instantaneous concentration of the reactant or the extent of reaction (conversion). Model-free methods do not presuppose the mathematical form of the function of the concentration of the reactant or extent of reaction. These methods include ASTM E698 (Ozawa), ASTM E2890 (Kissinger), and the Friedman (differential isoconversional) methods. These methods are also called isoconversional methods because they require data from several heating rates and conduct an analysis based on the temperature corresponding to several specific points of the extent of reaction (conversion). Kinetics yielded from isoconversional methods can be difficult to implement in fire models because the activation energy determined in these analyses are typically a function of temperature, and fire models currently do not have flexibility to accommodate reactions defined with kinetics that are temperature dependent.
Model-based methods are formulated with an a priori assumption of the form of the function of mass or concentration of the reactant. A commonly used reaction model assumes an nth-order model, which means the concentration of the reactant or the conversion is raised to the nth power. Some model-based methods use an approximate solution to the Arrhenius equation to directly estimate the kinetic parameters for one or more consecutive or parallel reactions. Methods have been proposed by Lyon et al., Lyon and Safronava, and by Bruns and Leventon, among many others. Another common approach is to use an optimization algorithm to fit one or more reactions to the MLR data. Lautenberger et al. popularized the use of a Genetic Algorithm (GA) Lautenberger et al. and the Shuffled Complex Evolution (SCE) algorithm Lautenberger and Fernandez-Pello, and Fiola et al. developed a method based on the Stochastic Hill Climber (SHC) algorithm Fiola et al. to determine the decomposition kinetics.
Research has shown that regardless of the method(s) used to determine the kinetic parameters, there is a strong linear relationship between the activation energy and the logarithm of the pre-exponential factor. This observation has been described as the kinetic compensation effect. This relationship helps us to define the uncertainty in the kinetic parameters for a given reaction. It also reveals that there is not a single pair of kinetic parameters that uniquely describe a MLR curve, but a range of values that may describe the same experimental curve.
Kinetics presented in the database were calculated assuming sequential mechanisms made up of first-order reactions.
Heat of Combustion
The heat of combustion is defined as the amount of energy per unit mass that is released when a gas, vapor, or the volatiles evolved from a condensed phase (solid) material undergoes combustion. The heat of complete combustion may be determined from data collected in MCC tests. The effective heat of combustion may be calculated from data collected in bench-scale flammability tests.
The procedure for calculating the heat of complete combustion from MCC data is described in ASTM D7309. The heat of complete combustion is calculated as the integral of the heat release rate curve with respect to time, divided by the total mass lost.
The procedure for calculating the average effective heat of combustion from cone calorimeter data is described in ASTM E1354. The procedure involves integrating the heat release rate curve over the length of the test to determine the total heat released. This quantity is divided by the total mass lost over the same time interval to get the effective heat of combustion.
Heat of Gasification
The heat of gasification is defined as the total amount of energy per unit mass required to convert a condensed phase (solid) material entirely to the gas or vapor phase. This quantity includes sensible enthalpy (energy required to increase the temperature of the material), heat absorbed during physical transitions, and heat absorbed during decomposition reactions. There are two main approaches to determining the heat of gasification which rely on heat flow rate data collected in thermal analysis experiments and burning rate data collected in bench-scale flammability tests.
Stoliarov and Walters describe a method for determining the heat of gasification using heat flow rate data collected in experiments conducted in a power compensation DSC. Although the data provided in this database are from experiments conducted with an STA, which incorporates a heat flux DSC, the analytical procedure is the same. The heat of gasification is calculated as the integral of the heat flow rate curve (presented in W/g) with respect to time in an experiment where the sample temperature is increased at a constant heating rate from room temperature until the temperature at which degradation is complete.
Hopkins and Quintiere describe a method for determination of the heat of gasification from cone calorimeter data. According to this method, the peak or quasi-steady burning rate from cone calorimeter tests conducted at a range of incident heat fluxes are plotted with heat flux on the abscissa and mass loss rate on the ordinate. Linear regression is performed and the inverse of the slope of the regression line is considered the effective heat of gasification for noncharring materials. For charring materials, this value must be corrected by dividing by the char mass fraction.
Specific Heat Capacity
Specific heat capacity may be calculated from data collected with the Heat Flow Meter (HFM) or through analysis of data collected in STA tests. The specific heat capacity is directly determined with HFM tests conducted according to ASTM C1784. The experimental and analytical procedure to determine the specific heat capacity of a material with the STA is outlined in ASTM E1269. According to the standard, three different types of tests with a heating rate of 20 K/min must be conducted in sequence: a correction, a test on a standard material with a known specific heat capacity, and a sample test. The heat flow rate measured for the sample is compared to the heat flow rate measured for the standard, and the specific heat capacity of the sample is related to the specific heat capacity of the standard.
In lieu of conducting tests strictly according to ASTM E1269, heat flow rate data collected at different heating rates in temperature ranges where no physical changes and no degradation reactions occur may be analyzed using the analytical procedure outlined in ASTM E1269 to determine specific heat capacity. The procedure involves dividing the heat flow rate [W/g] by the instantaneous heating rate [K/s] to yield effective specific heat capacity data [J/g/K]. This analysis provides the apparent specific heat capacity of the sample material.
Heats of Reaction
The heat of reaction (heat of decomposition) is the amount of energy absorbed by a material during a thermal degradation reaction. The heat of reaction may be determined from STA heat flow rate data according to ASTM E537. The mass loss rate (MLR) data vs time is plotted on the same plot as heat flow rate data vs time. To determine the heat of reaction, a baseline heat flow rate curve is first generated. The MLR data is used to determine the beginning and end of a reaction. The baseline is a curve drawn connecting the heat flow rate data at the start and end of the reaction (the simplest choice is a straight line). The absorbed energy is the difference between the baseline and the measured data. The heat of reaction is determined as the integral of the difference over the temperature range determined from the MLR data. Since the heat flow rate data is presented on an initial mass basis, the integral must be corrected for the total mass lost in the reaction by multiplying by the ratio of the initial sample mass to the mass lost during the reaction over the temperature range.
The true trend of the baseline during decomposition is unknown; therefore, the analysis must assume the shape of the curve over the temperature range that corresponds to the reaction. An alternative method of defining the baseline is described by McKinnon et al. With the alternative method, the reaction kinetics and the specific heat capacities of all defined components are used to parameterize a model of the thermal analysis experiment. With a simulation of the mass and composition as a function of temperature, a baseline that represents the sensible enthalpy may be constructed. There is a physical justification for the shape of the baseline when constructed with this procedure. The heats of reaction may be sensitive to the definition of the baseline, but the total heat of gasification is independent of this baseline definition.
The temperature at which a material ignites is not an intrinsic property (e.g. single value) of the material. This temperature is a complicated function of the material properties, geometry, orientation, exposure, and environmental conditions. The ignition temperature can be determined from either micro-scale combustion calorimeter data or a method relies on data collected with the cone calorimeter. DiDomizio et al. provide an excellent discussion of analytical methods that have been used to calculate ignition temperature and time to ignition.
The ignition temperature is determined from specific heat release rate data collected with the MCC. Lyon et al. present a correlation between a critical specific heat release rate and the temperature for sustained piloted ignition in bench-scale flammability tests. The mean critical specific heat release rate that corresponds to sustained ignition was found to be 25 ± 8 W/g for 20 different polymers. Ignition temperature was determined as follows: the mean ignition temperature was defined as the temperature where the average specific heat release rate over the three replicate tests was 25 W/g. The lower limit and upper limits for the ignition temperature were evaluated at specific heat release rates of 17 W/g and 33 W/g.