Retardation functions

The mechanism by which tin flame retardants function has not been well defined, but evidence indicates tin functions in both the condensed and vapor phases. In formulations in which there is at least a 4-to-l mole ratio of halogen to tin, reactions similar to those of antimony and halogen are assumed to occur. Volatile stannic tetrahaUde may form and enter the flame to function much in the same manner as does antimony trihaUde. 

Protective Coatings. Some flame retardants function by forming a protective Hquid or char barrier. These minimize transpiration of polymer degradation products to the flame front and/or act as an insulating layer to reduce the heat transfer from the flame to the polymer. Phosphoms compounds that decompose to give phosphoric acid and intumescent systems are examples of this category (see Flame retardants, phosphorus flame retardants). 

Effects on Visible Smoke. Smoke is a main impediment to egress from a burning building. Although some examples are known where specific phosphoms flame retardants increased smoke in small-scale tests, other instances are reported where the presence of the retardant reduced smoke. The effect appears to be a complex function of burning conditions and of other ingredients in the formulation (153,156,157). In a carehil Japanese study, ammonium phosphate raised or lowered the smoke from wood depending on pyrolysis temperature (158). Where the phosphoms flame retardant functions by char enhancement, lower smoke levels are likely to be observed. 

Note that the term y in Eqs. 2-15 and 2-16 has a different significance than that in Eq. 2-14. In the first equation it is based on a concept of relaxation and in the others on the basis of creep. In the literature, these terms are respectively referred to as a relaxation time and a retardation time, leading for infinite elements in the deformation models to complex quantities known as relaxation and retardation functions. One of the principal accomplishments of viscoelastic theory is the correlation of these quantities analytically so that creep deformation can be predicted from relaxation data and relaxation data from creep deformation data. 

Crystal growth retardation, function of all-organics 443 Crystal modification, function of all-organics 443... 

The use of copolymers is essentially a new concept free from low-MW additives. However, a random copolymer, which includes additive functions in the chain, usually results in a relatively costly solution yet industrial examples have been reported (Borealis, Union Carbide). Locking a flame-retardant function into the polymer backbone prevents migration. Organophosphorous functionalities have been incorporated in polyamide backbones to modify thermal behaviour [56]. The materials have potential for use as fire-retardant materials and as high-MW fire-retardant additives for commercially available polymers. The current drive for incorporation of FR functionality within a given polymer, either by blending or copolymerisation, reduces the risk of evolution of toxic species within the smoke of burning materials [57]. Also, a UVA moiety has been introduced in the polymer backbone as one of the co-monomers (e.g. 2,4-dihydroxybenzophenone-formaldehyde resin, DHBF). 

Retarders of opposite ionic charge to the dyes can be used [33,36,48-51]. Anionic retarders function by forming a thermally labile complex with the dye and thus lowering the substantivity of the dye for the fibre. Undesirable precipitation of this complex, which is one of the drawbacks of the system, can be inhibited ... 

In modified polyphenylene oxide, the preponderance of evidence suggests that the phosphate ester flame retardant functions mainly in the gas phase (2) as a radical trap to help quench the flame. 

Once again, Heras [13] gave another formulation of Helmholtz theorem now based on Green s retarded function G = 8(f — ts — R/c)/R for a value B5(r5. ts) function of space and retarded time ts = t — R/c. Heras obtained the following equation ... 

From the definitions it is clear that the retarded function can be combined from lesser and greater functions... 

Following the same way, as for the retarded functions (using only the definitions of NGF and Heisenberg equations of motion) one derives instead of (384)-(386)... 

It might be assumed that, as condensed-phase flame retardants function by modifying the normal thermal degradation processes of polymers, they would also function as thermal stabilizers and that thermal antioxidant stabilizers would show flame-retardant properties. However, these statements are rarely the case, and to understand why, it is necessary to compare the mechanistic aspects of flame retardance as discussed earlier with those of thermal degradation and thermal oxidation as well, briefly alluded earlier, and in the case of the latter, the Bolland and Gee mechanism,17 in Scheme 2.1. 

PROBLEM L1.6 How does convergence of the sum under the influence of only the retardation function R (l ) create the appearance of the 1/Z3 variation of free energy ... 

The final manifestations of abnormal development are death, malformation, growth retardation, functional disorder. 

The relaxation and retardation functions for these models in the case of a discrete distribution of relaxation or retardation times are obviously given by... 

A theory of thermoviscoelasticity that includes the temperature dependence of the relaxation or retardation functions is necessarily nonlinear, and consequently the elastic-viscoelastic correspondence principle is not applicable. Nevertheless, a linear theory of thermoviscoelasticity can be developed in the framework of rational thermodynamics with further constitutive assumptions (Ref. 5, Chap. 3 see also Ref. 10). 

This and many similar results lead to the conclusion that in this sort of system, with typical pollution incident parameter choices, it b the soil heterogeneity present that dominates the breakthrough behaviour. Equally, the laboratory data for retardation factors can only be applied to field scale calculations with great care and there is a real danger of wildly overestimating the retardation function of a heterogeneous system. 

TA f (t)B (t )) is thus always a retarded function. This follows from the definitions (8) since a superoperator corresponds to a commutator in Hilbert space, this implies that... 

Flame-retardant textiles are textiles or textile-based materials that inhibit or resist the spread of fire. Factors affecting flammability and thermal behavior of textile include fiber type, fabric construction, thermal behavior of textile polymer and its composition as well as the presence or absence of flame additives. On the other hand, flame-retardant additives can be classified by their chemical composition or by mode of action, i.e., gas phase action or by the formation of protective barrier [49, 50]. Moreover, flame-retardant functional finishes of cellulose-based textiles can be accomplished by [i] using inorganic phosphates, (ii) with organophosphorous compounds, [iii) with sulfur-derivatives or (iv) by grafting flame retardants monomers [49,50]. 

Van der Waals forces were calculated on the basis of Hamaker s theory with a retardation function introduced by Schenkel and Kitchener (5). The Hamaker constant of water-toluene-water was taken from Ref. 6. Both the... 

From the common line in the retardation functions shown at Tg in Fig. 12.27 the Andrade coefficient /3xg can be calculated. Smith showed [157] that when Andr e creep is observed... 

---