Thank you for contacting C2C with your question on preservation storage of negatives.
Here is what the NEDCC Preservation Leaflet, Storage Enclosures for Photographic Materials…
Regardless of material or process, all enclosures used to house photographs should meet the specifications provided by the International Organization for Standardization (ISO). ISO 18902:2013 and ISO 18916:2007 provide specifications on enclosure formats, papers, plastics, adhesives, and printing inks, and require that storage materials pass the Photographic Activity Test (PAT). For more information, see http://www.iso.org/iso/home.htm.
Labels such as acid-free, lignin-free, or buffered do not guarantee that a material is safe to use with photographs. Even these chemically inert papers may be harmful to the photographic image; the only way to be certain of the stability of the paper is to purchase materials that have passed the Photographic Activity Test (PAT).
According to information on the Print File website, their enclosures are compliant with the PAT http://www.printfile.com/PAT-information.aspx thus the sleeves in a cardboard box will provide better environmental conditions than storing them in degrading paper envelopes. This said, if you store the negatives in the polyethylene sleeves in a regular cardboard storage box, you will have to account for off gassing of the box. You could do this by storing the sleeves in pH neutral envelopes or folders before placing them in the cardboard box. This would also add another layer of support and protection from mechanical damage if the box moves.
I hope this assists you in deciding what amount of control you want over the negative storage environment you want. Here are some additional resources:
Caring For Photographs, Connecting to Collections Care
Caring for Photographs