What kinds of chemical bonds attach dyes to fibers?

This isn't just a trivia question. The types of bonds directly determine the properties of the dyes. The most permanent, wash-fast dyes are the most tightly attached to the fiber molecules. In addition, the requirements for forming the chemical bonds are what determine the ingredients and method for each recipe for dyeing.

Fiber Reactive Dyes

Fiber reactive dyes, such as the dichlorotriazines (Procion MX type dyes), are attached to the fiber by the same strong covalent bonds that hold the atoms within the dye molecule together. The dye actually becomes one molecule with the fiber molecule to which it attaches. Covalent bonds are formed by electron sharing between atoms.

Direct Dyes

Direct dyes, including that portion of "all purpose" dyes that is left in cotton that has been dyed with them, are only loosely associated with the fiber molecule through the property called substantivity, which is the tendency of the dye to associate with the dye without strong bonds. This substantivity is increased by increasing the size of the dye molecule, so direct dyes tend to be large. Small dye molecules tend to be bright, while large dye molecules tend to be duller (as there are more parts that can absorb additional wavelengths of light), so direct dyes are generally much less bright in color than fiber reactive dyes. Substantivity is said to result from a combination of the relatively weak Van der Waals forces and some hydrogen bonding.

Disperse Dyes

Disperse dyes, used for synthetic fibers such as polyester, work by being vaporized by the heat of an iron or heat transfer press and then condensing onto and into the fiber. (They can also by induced to migrate into the fiber by boiling with a special carrier chemical.) Unsurprisingly, such loosely associated dye may rub off, though not visibly so. The fact that the dye can rub off on the wearer makes this class of dye more allergenic than other types of dye, though this is a problem for only a minority of people. Such people are happier wearing natural fibers that have been dyed with fiber reactive dye.

Acid Dyes

The attachment between acid dyes and the protein fibers that they join to are the most complex of all. Proteins are made of up to twenty different amino acids, each of which has a different side chain. At different pHs, different dyes can form rather strong hydrogen bonding to various of these side chains. Many acid dyes contain a sulfonic group, or, in some cases, a carboxylic group, which can form a strong 'salt linkage' to a basic group in the wool molecule. (See Ingamells, under "Further Reading", below.) A salt linkage is an ionic bond between fixed ions of opposite charges, due to Coulombic interaction. The strength of this bond is considered to be responsible for the washfastness of good acid dyes.

Note that certain specialized fiber reactive dyes are also used for wool, though the fiber reactive dyes commonly used for cotton, such as Procion MX dye, is said to not react appreciably with wool under acid conditions; instead, the types of fiber reactive dyes used on cotton can be used simply as acid dyes with wool, even if the reactive groups on the dye have 'gone bad' by reacting with water. (The alkaline conditions normally used with Procion MX dye on cotton will damage wool, though they work fine on silk.)

Vat Dyes

Vat dyes, such as indigo, are trapped within the fiber by having been converted to a form that is insoluble in water. The vat dye is insinuated into the fiber while in a water-soluble form. This is a purely physical form of attachment, and not a chemical bond at all. Vat dyes are very wash-fast, but have the opposite reputation due to ring-dyeing. Ring dyeing is what happens when the dyer fails to make sure that the dye thoroughly penetrates the fiber shaft, but leaves only the surface of each fiber coated, so that even a little bit of wearing removes the dyed layer. Normally this is a sign of bad dye procedure, but the fading of blue jeans due to abrasion is generally appreciated, as it implies greater age for a garment than is actually the case.

Naphthol Dyes

Like Vat dyes, Naphthol dyes are held in the fiber in a water insoluble form. The technique is quite interesting: any of a range of diazo salts are combined on the fabric with any of a range of naphthols (azoic coupling agents). Their reaction results in the formation of a water insoluble dye, typically of a very different color than either of the two components. Various combinations result in different colors. These dyes are widely used in batik producting in southeast Asia; the use of wax in batik requires that dye reactions not involve heat, so both naphthol dyes and cool water fiber reactive dyes are suitable for this purpose. Naphtol dyes are less expensive than many fiber reactive dyes, and peculiarly suited to painting different colors immediately adjacent to one another on fabric. Unfortunately, naphthol dyes are quite toxic, and probably significantly carcinogenic, and are thus not considered suitable for use at home or in the artist's studio.

Natural Dyes

Natural dyes are, in most cases, acid dyes, which is why they will bond to wool and other animal fibers, but not to cotton. A way to improve attachment to wool, and to make some weak attachment to cotton possible, is to use metal ions, sometimes including toxic heavy metal ions, to form a bridge between the dye and the fiber; this is called mordanting. Cotton is typically mordanted with tannins in addition to metal ions

Indigo is a natural dye, but it is quite different from other natural dyes, in that it is a member (the very first member) of the class of dye known as vat dyes, see above.