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CAPÍTULO 3. MODELO MATEMÁTICO Y GEOMETRÍAS DE

3.1. MODELO MATEMÁTICO DEL PROCESO DE FUSIÓN/SOLIDIFICACIÓN

3.1.1. Ecuaciones que gobiernan la transferencia de calor y el flujo

3.1.1.2. Convección

Chitin is the second most important natural polysaccharide produced by biosynthesis, exceeded only by cellulose, to which it is closely related in structure. It was first isolated by Braconnot in 1811 and thus its ‘original and spectacular’ properties have been recognised for a long time [64]. Chitin is found in crabs, lobsters and other crustaceans, spiders and other arthropodic insects, and the cell walls of fungi. Like cellulose (10.53), chitin (10.54) is a 1,4-β-D-glucopyranose. Both have a linear sequence of pyranose rings linked by 1,4-glycosidic bonds, a non-reducing end group and a reducing end group in the cyclic hemiacetal form.

The characteristic difference between them is that chitin has an acetylamino group in the 2-position, compared with the 2-hydroxy group in cellulose. Chitin exists in three polymorphic forms, depending on the directions of adjacent polymer chains, the alternating α-chitin structure being the most common [64].

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Chitosan (10.55) is a derivative of chitin made by alkaline hydrolysis resulting in deacetylation to give a primary amino group in the 2-position. Chitin is less hydrophilic than cellulose, whilst chitosan is more basic than either of the others. Structures 10.53–10.55 are representative only. Variations occur, depending on the source of the chitin and its treatment during and after harvesting. Chain length, average molecular mass and molecular mass distribution vary. There is also the question of impurities and the degree of deacetylation of chitosan, which is usually 75–95% [65]. Knittel and Schollmeyer [65] have outlined the nature, properties and uses of chitin and chitosan, including indications of their uses in textile processes [65]. Roberts has provided an excellent textbook [64]. There are also the proceedings of two symposia, although these do not deal with textile processing applications [66,67].

Numerous substituted derivatives of chitin and chitosan are known [67]; some important examples are shown in Scheme 10.9. The possibility of forming either anionic (5,7,8,11) or cationic (9,12) derivatives should be noted. The O-carboxymethyl (5) and N-carboxymethyl (11) polymers are of particular interest as they have stronger complex-forming capabilities with metal ions than either unsubstituted chitosan or EDTA [65]. In practice, derivatives formed by substitution via the 2-amino group of chitosan are more common than those substituted via the 6-hydroxy position of the glucopyranose grouping [65].

Chitosan features far more than chitin in research into applications. This is largely due to their difference in solubility characteristics, chitosan being more amenable to practical manipulation. Chitin is in fact rather more intractable than cellulose, since it is insoluble in those solvents, such as cuprammonium hydroxide, that are commonly used to dissolve cellulose. Chitin is soluble in hot concentrated solutions of certain inorganic salts capable of

a high degree of hydration, the order of effectiveness being: lithium thiocyanate > calcium thiocyanate > calcium iodide > calcium bromide > calcium chloride. Chitin also dissolves, with some degradation, in concentrated hydrochloric acid, sulphuric acid (some O-sulphation taking place) or phosphoric acid, but not in nitric acid. Certain organic carboxylic acids, such as formic, dichloroacetic or trichloroacetic, will also dissolve chitin.

Chitosan, on the other hand, interacts with inorganic acids to yield cationic polyelectrolytes, their solubility depending on the nature of the anion. Thus it is soluble in dilute hydrochloric, hydrobromic, hydroiodic, nitric or perchloric acid, but may be precipitated from hydrochloric or hydrobromic solutions as the acid strength is increased.

Chitosan forms water-soluble salts with most carboxylic acids. Hence it is chitosan, rather than chitin, that has come to the fore in a remarkably wide range of end-uses, including such diverse fields as medicine, personal care, contact lenses, biotechnology, food, agriculture, effluent treatment, analysis, textile finishes and coatings. Although usage in textiles is relatively small as yet, its availability, environmental compatibility and remarkable versatility offer considerable potential.

Both chitin and chitosan are manufactured commercially on a large scale. Chitosan is available in powder, gel, solution, film, membrane, fibre and bead forms. Interest in all forms and levels of purity is high and continuing to expand [67]. Chitosan is produced from amply replenishable biological sources and is readily biodegradable, non-toxic and non-allergenic.

It has bactericidal and fungicidal properties and actively promotes wound-healing.

The ability of chitosan to form complexes is of particular interest. Being slightly basic, it will readily form complexes with anionic compounds. Initially it forms into micelles with small amounts of anionic surfactants, leading to precipitation of a complex as the concentration of the anionic surfactant increases. Chitosan will complex with anionic

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Typical derivatives of chitin (1) and chitosan (2) [67]: alkali-chitin (3), O-acylchitin (4),

O-carboxymethylchitin (5), O-hydroxyethylchitin (6), chitin O-sulphate (7), chitin O-phosphate (8), chitosan salt (9), N-acylchitosan (10), N-carboxymethylchitosan (11), trialkylammonium salt (12) Scheme 10.9

polyelectrolytes leading to the formation of polycationic/polyanionic complexes of high molecular mass. This capability to complex with anionic substances is further enhanced if cationic derivatives of chitosan are used. The degree and strength of complexing depends on:

– the nature and ionic strengths of the cationic and anionic species

– the spacing of the charged ionic groups, as influenced by the relative molecular masses and spatial configurations of the components.

This property is clearly of interest for the removal of anionic substances from effluent streams, for example. However, since such complexing often results in an increase in viscosity as complexing proceeds, such systems can be used to produce gels or viscous liquids. Hence there is the possibility of using these complexes as print–paste or pad–liquor additives to control migration. Weakly basic chitosan or its more strongly basic derivatives will complex with anionic fibres and can therefore be used as finishes or pretreatments to modify selected properties of the fibres. They are already used, for example, in hair sprays or for complexing with and isolating proteins.

It is not surprising, therefore, that chitosan and its basic derivatives will complex with anionic dyes. Giles et al. [68,69] researched the use of chitosan for the removal of dyes from effluent as long ago as 1958. The binding capacity of chitosan for anionic dyes is pH-dependent, but it has been reported [65] that in effluent treatment as much as 10 g dye per kg chitosan can be complexed at pH values above about 6.5. Similarly, chitosan has been used for the aftertreatment of direct dyeings on cotton to improve their fastness.

The complexing of chitosan and its basic derivatives with anionic substances is paralleled by compatibility with cationic and nonionic compounds. Similarly, the anionic derivatives of chitosan show complex formation with cationic agents and are compatible with anionic and nonionic compounds. The capability of these chitosan derivatives to complex with certain metal ions, notably those of the transition series, is also important, having possibilities for the removal of metal salts from effluent. The hierarchy in terms of binding capacity is:

Cr(III) < Cr(II) < Pb(II) < Mn(II) < Cd(II) < Ni(II) < Fe(II) < Co(II).

Chitosan will readily react with formaldehyde via its primary amino groups [65]. The capability of chitosan and its basic derivatives to complex with anionic fibres has already been mentioned. In this context, the bactericidal and fungicidal properties of these chitosan compounds are useful. The fact that fibre-reactive chitosan derivatives can be prepared further increases these possibilities. Chitosan compounds containing long-chain alkyl groups exhibit fabric-softening properties and can be incorporated into finishing formulations for this purpose. The fact that charged chitosan derivatives can interact with appropriate fibre types gives scope for their use as levelling agents and to modify dye absorption in either a positive or negative sense, depending on circumstances and dyeing requirements. For example, they are claimed to reduce dye uptake variations between mature and dead cotton.

The use of chitosan derivatives in print pastes, to reduce the content of the environ-mentally unfavourable hygroscopic agent urea necessary when applying reactive dyes, has been evaluated [43]. It was found that in recipes normally requiring 300 g/kg urea this could be reduced to 75 g/kg by adding either 20 g/kg chitosan or 4 g/kg N-hexylchitosan. Although this did not give a significant increase in dye yield, the replacement of most of the urea by a biodegradable chitosan polymer offered significant promise.

10.3.6 Summary

In conclusion, it is noteworthy that cyclodextrins, liposomes and chitin derivatives are all readily available from renewable biochemical sources and offer advantages of biodegradability and safety in use. However, it needs to be borne in mind that this fact alone does not necessarily mean that they are entirely environmentally innocuous in the long run.

Demands on resources for the husbanding and processing of bioforms that may be necessary in order to sustain demand for commercially viable qualities and quantities can exert deleterious effects, not least because they may give by-products that present problems of utilisation or disposal [70].

10.4 ENZYMES