The Chemistry of Tie-Dye

This video demonstrates the chemistry behind why some dyes used for tie-dying fabric can be made to bind quite strongly to cotton fabric, but hardly at all to polyester. Below is a step-by-step guide to doing the experiment yourself. Please do try this at home!
Step-by-step instructions, courtesy of Dr. Elizabeth Migicovsky:
1. Add 2 tablespoons baking soda to your plastic cup. Fill the cup up with very hot water from your faucet. Carefully stir the baking soda with a spoon to make sure it is fully dissolved.
2. Put the fabric in the plastic bag. Pour the baking soda solution onto the fabric in the bag. Let the fabric soak for 20 minutes. Squeeze the fabric out by hand in your sink.
3. Fold and tie the fabric to make your desired pattern. Bind the fabric tightly with the rubber bands.
4. The squeeze bottles contain blue and red dye. Fill each bottle up with tap water. Cap the bottle and shake it to fully dissolve the dye.
5. Squeeze the dye mixture onto the tied fabric. Turn the fabric over and repeat the same pattern on the other side.
Hint 1: even though you want to make red, white, and blue, there is no need to leave too much white space. The creases will be white when the rubber bands come off.
Hint 2: The colors will run together if you oversaturate, and you will get red, white, blue, and purple. Try to keep the colors distinct.
6. Do not untie the fabric yet. Put the fabric into your plastic bag and let it stand for 12-24 hours.
Hint 3: The longer the fabric stands, the brighter the color will be.
7. The next day, untie the fabric and behold your art!
8. While wearing gloves, rinse the fabric with cool water once, then rinse by warmer water two or three times. When the water is clear (after about 3-4 rinses), wash the fabric with soap (separate from other clothes).
9. Is the cotton fabric still bright with color? What about the polyester fabric?