Wrinkles - Physics of wrinkles

Heat and water cause wrinkles. Heat breaks the bonds holding polymers in place within the fibers of a fabric. When the bonds are broken, the fibers are less rigid with respect to each other, so they can shift into new positions. As the fabric cools, new bonds form, locking the fibers into a new shape. This is both how ironing gets wrinkles out of your clothes and why letting clothes cool in a heap fresh from the dryer will instill wrinkles. Not all fabrics are equally susceptible to this type of wrinkling. Nylon, wool, and polyester all have a glass transition temperature, or temperature below which the polymer molecules are almost crystalline in structure and above which the material is more fluid, or glassy.
Water is the key culprit behind wrinkling of cellulose-based fabrics, such as cotton, linen, and rayon. The polymers in these fabrics are linked by hydrogen bonds, which are the same bonds that hold together molecules of water. Absorbent fabrics allow water molecules to penetrate the areas between the polymer chains, permitting the formation of new hydrogen bonds. The new shape becomes locked in as the water evaporates. Steam ironing works well on removing these wrinkles.
Permament Press Fabrics
In the 1950s, Ruth Rogan Benerito, of the Department of Agriculture, came up with a process for treating a fabric to render it wrinkle-free, or permanent press. This worked by replacing the hydrogen bonds between polymer units with water-resistant cross-linked bonds. However, the crosslinking agent was formaldehyde, which was toxic, smelled bad, and made the fabric itchy, plus the treatment weakened some fabrics by making them more brittle. A new treatment was developed in 1992 that eliminated most of the formaldehyde from the fabric surface. This is the treatment used today for many wrinkle-free cotton garments.