The exact theory of the ``wavelength exponent'' of the turbidity is developed for Rayleigh scattering and ``Debye scattering'' and, particularly, for Mie scattering by nonabsorbing spheres. The basic exponent, n, defined by {α[∂ln(τ/c)0/∂α]+1} is computed from Mie turbidity data, reported previously, for α=0.40 (0.04) 0.68, 0.80 (0.2) 25.0 and m=1.05 (0.05) 1.20. For m=1.25 and 1.30, the smallest α values and the Δα intervals are the same, but the upper limiting α values are 14.0 and 11.6, respectively. In addition, α values<0.40 are considered for m=1.05. The actual exponent to be expected in a given dispersed system n0 is found to depend on three additional factors: (1) The rate of change of the turbidity with the relative refractive index of the spheres [this factor is evaluated for α=0.4, 1.0 (1.0) 7.0 and m=1.05 (0.05) 1.30 and approximating equations are given for purposes of interpolation]. (2) The dispersion of the relative refractive index of the spheres. (3) That of the refractive index of the medium. The advantages and limitations of an application of the wavelength exponent to particle size determinations are discussed and labor saving approximating n(α) relations, suitable for first approximation results on particle size, are given. The effect of heterodispersion upon the wave length exponent is briefly discussed.
SynopsisThe thermal degradation of cellulose and its phosphorylated products (phosphates, diethylphosphate, and diphenylphosphate) were studied in air and nitrogen by differential thermal analysis and dynamic thermogravimetry from ambient temperature to 750°C. From the resulting data various thermodynamic parameters were obtained following the methods of Broido and Freeman and Carroll. The values of E, for decomposition for phosphorylated cellulose were found to be in the range 55-138 kJ mol-I in air and 85-152 kJ mol-' in nitrogen and depended upon the percent of phosphorus contents in the samples. The mass spectrum of cellobiose phosphate indicated the absence of the molecular ion, indicating that the compound was thermally unstable. The IR spectra of the pyrolysis residues of cellulose phosphate gave indication of formation of a compound having C = O and P=O groups. A fire retardancy mechanism for the thermal degradation of cellulose phosphate has been proposed.
Reaction of cellulose with hexamethylphosphoric acid triamide has been investigated under various physical conditions. Dimethylamine hydrochloride was found to be an efficient catalyst for the system. The thermal degradation of cellulose and its phosphoramide products in air was studied by DTA, TG, and DTG techniques from ambient temperature to 500°C. The data were processed for the various thermodynamic parameters following the methods of Freeman and Carroll, of Broido, and of Dave and Chopra. The energies of activation, Ea, for the degradation for various cellulose phosphoramide samples were found to be in the range of 92–136 kJ mol−1. These values were found to decrease with increase in the degree of substitution. A mechanism for the thermal degradation of cellulose phosphoramide has been proposed. The IR spectra of char residues of cellulose phosphoramide gave an indication of the formation of compounds containing CO and PO groups.
Cotton cellulose has been treated with tetrakis(hydroxymethy1)phosphonium chloride (THPC), urea and small amounts of ammonium dihydrogen orthophosphate (ADP) to impart flame retardancy. Complexes of cell-THPCurea-ADP with transition metals such as chromium, manganese, iron, cobalt, nickel, copper and zinc have been characterized by reflectance UV-visible spectra. The samples were subjected to differential thermal analysis and thermogravimetry from ambient temperature to 700°C in air to study their thermal behaviour. From the resulting data, various kinetic parameters for different stages of thermal degradation were obtained following the method of Broido. For the decomposition of cellulose and flame-retardant celluloses, the activation energy was found to increase from 242 to 322kJmol-', the entropy of activation from 140 to 307 J K -' mol-* and the char yield from 2 5 to 31 %. The free energy of activation for decomposition of cellulose and its derivatives was almost the same, viz.148-162 kJ mol-', indicating that the basic steps in the decomposition of cellulose and its derivatives are the same. The IR spectra of the thermally degraded residues of cell-THPC-urea-ADP and its metal complexes indicate that dehydration takes place and a compound containing the carbonyl group is formed. The electron paramagnetic resonance signals indicate the formation of trapped and stable free radicals in the thermal degradation of cellulose and its derivatives.
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