The use of synthetic polymers in buildings or construction applications is steadily increasing and every year more emphasis is placed on the hazards that result from the burning of such materials. The majority of polymer-containing end products must now pass regulatory tests and there is therefore considerable interest in the design of materials that can pass such tests. Although halogenated flame retardant systems have proven very effective, environmental concerns have prompted the development of alternative flame retardant systems. Research into new fire-retardant systems covers a broad range of approaches, including the systematic investigation into combinations of additives that promote synergy [Weil et al 1996], intumescent systems [Weil et al 1996; Horrocks 1996; Bras et al 1998], char formation [Weil et al 1996; Horrocks 1996; Wilkie et al 1996], the use of heat sink additives such as aluminium trihydrate and magnesium hydroxide etc. Kashiwagi has identified char formation as the most promising of these and has reviewed the benefits of char formation in improving the fire resistance of polymers [Kashiwagi 1994].
The advantages of char formation are:
The charring of a thermally-thick sample leads to the formation of three zones: a surface charred zone, comprising char and no polymer; an interfacial (pyrolysis) zone, containing a mixture of char and polymer; and a polymer zone, comprising virgin polymer and no char. The physical and chemical behaviour of these zones can be quite complicated and distinct from one another. For example, the char layer may be anisotropic, and properties such as porosity and thermal conductivity can be significantly different in each layer. The burning of synthetic polymers introduces another complication: the introduction of a moving boundary. Unlike wood, the sample size is not constant through the burn but contracts (if intumescent retardants are present expansion may occur). In practice the pyrolysis layer may be very thin, separating two zones, comprising respectively polymer and char only. If the sample is thermally-thin, then it effectively comprises the pyrolysis zone.
We distinguish between two general mechanisms, competitive and non-competitive, of char-formation. By non-competitive char formation we mean the scheme
P --> c C + (1-c) V, Equation 1
where P is the polymer, C is char and V represents gaseous volatiles. By competitive char formation we mean the reaction scheme
| P | --> | V | Equation 2 |
| P | --> | c C + (1-c) V | Equation 3 |
In the non-competitive scheme the fraction of char formed is independent of the heating history of the sample and is represented by c (0 <= c <= 1). In the competitive scheme the fraction depends upon the heating history and is at most c. (In the ideal case c is unity for competitive char-formation). The attraction of non-competitive char formation is that only three parameters are required to define the reaction kinetics, whereas competitive char formation requires five. It is much more difficult to investigate parameter space in a meaningful way for the competitive scheme and, in general, comments can only be made for specific values of the kinetic parameters.
Although highly simplified, the competitive mechanism represents a prototype scheme for char formation in polymers in which char formation is based upon competition between dehydration to char, equation (3), and depolymerisation, equation (2). The detailed chemistry of char formation is more complicated than either of these schemes. However, detailed chemistry can only be incorporated into models when reliable kinetic parameters have been obtained for all the reaction steps in a mechanism. This is almost invariably not the case. The few kinetic models for which parameter values are available are almost exclusively for cellulosic materials. Kinetic models for the pyrolysis of cellulose in non-oxidising environments have been extensively reviewed by Di Blasi [1993]. Kandola et al [1996] provide a more detailed discussion of the chemistry of cellulose pyrolysis, with emphasis on the implications for the design of effective fire retardants.The development of one-dimensional (1-D) models for wood pyrolysis dates back to Bamford et al [1946]. Starting with Kung [1972], detailed models have been developed describing the charring of wood. Di Blasi [1993] has reviewed subsequent development in this field. More recent models include those of Ritchie et al [1997] and Yuen et al [1997], the latter contains a succinct review of the development of 1-D, 2-D and 3-D models. These models often employ temperature dependent thermal properties and modelling assumptions specific to wood. For instance, anisotropic properties due to the grain structure of wood influence heat and mass transfer during pyrolysis. The existence of a consolidated porous structure means that the transport of gases and vapour can be modelled using Darcy's Law. Such detailed models have little relevance to investigations into char formation/degradation in non-cellulosic materials.
There have been few investigations of charring in non-cellulosic materials. In particular, there has been very little work investigating the efficiency of char formation in reducing flammability. This is also, surprisingly, the case for cellulose.
Note that in the models described in sections 3.1 & 3.2 the pyrolysis gases reach the exposed surface as soon as they are formed (i.e. no pressure builds up inside the material) and that once the char is formed it is assumed to be inert.
In the thermal pyrolysis approach char-formation is assumed to occur at a fixed temperature and at a moving boundary separating regions of char and virgin polymer.
Chen et al [1993] consider the transient pyrolysis of a one-dimensional charring slab. The model is reduced from two partial differential equations, one in each of the char and virgin polymer layers, to four ordinary differential equations, two in each layer, by assuming exponential temperature profiles within the layers. The heat-loss mechanism on the heated surface is purely radiative. This model was subsequently used as the basis for a methodology for determining material pyrolysis properties from flammability measurements under an inert atmosphere [Chen et al 1995]. The latter paper shows that the thermal capacity of the char (\rho_{c}cp,c)) has a negligible effect on the mass loss rate. This is explained by identifying radiative heat losses from the hot char as the dominant mechanism causing the reduction in pyrolysis rates. In these papers the sample is assumed to be of fixed length throughout the burn; pyrolysis does not produce a moving boundary between the char and inert atmosphere.
Leung et al [1996] model a char-forming ablation process in a semi-infinite solid under an inert atmosphere. Three heat-loss mechanisms on the heated boundary are considered: no heat-loss, purely convective, and purely radiative. For all three mechanisms the mass-loss rate increases to a global maximum before decreasing to zero. This happens because, as the amount of char builds up, a greater proportion of the heat input is used in raising the heat content of the char layer. The density of the char has little effect on the mass-loss rate, and no effect in the limiting case of no heat-loss. The maximum mass-loss rate increases with increasing thermal conductivity of the char. A useful long-time asymptotic solution is found whose percentage error increased with increasing time. A subsequent paper [Leung et al 1997] investigates how the choice of a non-combustible substrate base effects the mass loss rate of a sample. Pyrolysis of char-forming and non char-forming polymers under an inert atmosphere is studied. The physically unlikely case of no heat loss on the heated boundary is considered. Unlike the model of Chen et al [1993,1995] the sample length is not fixed during the burn. Thus in the char-forming case there are two moving boundaries: one representing the heated boundary and the other the char-polymer boundary. For thermally-thin samples the mass-loss rate increases monotonically until the polymer is completely pyrolysed. For thermally thick samples the mass-loss rate increases to a local maximum before decreasing to a local minimum. Eventually the polymer layer becomes thermally thin and at this point the mass-loss rate increases to a global maximum at the end of ablation. The global maximum decreased with increasing sample size.
Although the substrate-pyrolysis model of Leung et al could be used to investigate the effect of char-formation in reducing mass-loss rate, the exclusion of heat-loss mechanisms on the heated boundary precludes any meaningful comparison.
Staggs [1999] considers a char-forming ablation process in which there are no heat losses on the heated boundary and the temperature is constant on the rear boundary. The model contains two partial differential equations, one in each layer, and is reduced to two ordinary differential equations, one for the mass-loss rate and one for the thermal penetration depth, by assuming polynomial temperature distributions.
Historically much of the work on charring materials has been concerned with wood. However, in the 1960s there was considerable interest in the potential use of ablating materials to protect a space vehicle against overheating when re-entering the earth's atmosphere. An early model is due to Matsumoto et al [1969] who modelled the decomposition of charring materials subject to very large heat flows, including the heterogeneous oxidation of the char layer. A priori the ablating material is divided into three zones (char layer, pyrolysis zone and virgin polymer) and three sets of partial differential equations are used to describe the regions. A serious defect in this model is the absence of heat-loss mechanisms on the char surface. The width of the pyrolysis zone was found to be very narrow. Kung [1972] notes that only one set of equations should be required to describe the entire problem and the three zones should naturally arise from the resulting solution.
The pioneering work of Kung [1972] investigates the dependence of the mass-loss rate upon the thermal conductivity of the char using a non-competitive scheme. There is a pronounced increase in the mass-loss rate with increasing thermal conductivity, this is particularly noticeable in the global maximum. For thermally-thick samples the mass loss rate initially increases to a local maximum before decreasing to a local minimum. Eventually the polymer layer becomes thermally thin and the mass loss rate increases to a global maximum before finally decreasing towards zero. For thermally thin samples the mass loss rate curve exhibits one global maximum. This type of behaviour has been exhibited in a thermal pyrolysis model [Leung et al 1997]. However, there is a subtle difference: in the thermal pyrolysis models the global maximum occurs at the end of the burn, in the finite-rate kinetics model the mass-loss rate decays to zero after the global maximum.
Kung suggests that in thermally thick samples the decline in mass loss rate after the first local maximum is primarily due to convective heat losses within the material caused by the outward flow of the volatiles. In fact this decrease is a structural effect entirely due to the char layer [Leung et al 1997], which acts as an insulating layer for heat conduction and inhibit mass transfer of decomposition products.
Sibulkin [1986] investigates how the heat of gasification varies during the burning of charring materials using a non-competitive scheme. The mass loss rate increases to a local maximum, decreases to a local minimum, and towards the end of the burn starts to increase again as the sample becomes thermally thin. Sibulkin calculates that the net flux into the solid decreases by 20% of its initial value after the char layer is formed because of increased surface heat losses --- the surface temperature of a charring material is considerable higher than that of an equivalent non-charring material.
Staggs [1999] considers competitive char formation in thermally thick samples under an inert atmosphere. The mass-loss rate is found to be sensitive to the rate of char formation and is greatly reduced by ensuring that the char-forming reaction switches on before the volatile-forming step. Chars with low density and thermal conductivity are the most beneficial at providing thermal protection.
The evolution of the mass-loss rate with time is now understood for both thermally thin and thermally thick materials. However, there has been no attempt to systematically quantify the contributions made by specific physical mechanisms to the decreased flammability of char-forming materials. Moreover there is some inconsistency in the results. Chen et al [1995] state that the thermal capacity of the char ($\rho_{c}cp,c$) has a negligible effect on mass-loss rate. Leung et al [1996] also notes that char density has little effect on mass loss rate. However, Staggs [1999] identifies low density as a desirable property in providing enhanced thermal protection. Other authors consider the pyrolysis of a given material and do not investigate the dependence of flammability upon physical properties, as these are assumed to be fixed.
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