Unbuffered, acid-free tissue paper should be used for storing heirloom garments and fibers, just the same way acid-free photo albums protect your keepsake pictures from color change and decay. From the review on Cool Tools:

For years I’ve been relying on inexpensive, unbuffered acid-free tissue paper to ensure some dear family heirlooms will remain in tact for years to come, including a piece of beaded silk from my step-grandmother’s dance costume from the ’20s. Regular tissue paper is acidic and will yellow over time and damage fragile fabrics, especially silk. Unbuffered, acid-free tissue paper is completely PH neutral.

It is available from Light Impressions and University Products.

Acid-free tissue paper and heirloom garment storage advice – Link.