Black walnuts are in the genus Juglans and like all members of that genus, they produce a chemical called hydrojuglone in their roots which pervades the soil. This chemical is also in the leaves, nut hulls, and bark and is designed to prevent competing vegetation from growing near it. By itself it is non-toxic, however when exposed to soil or air it changes chemically and becomes toxic. They are especially toxic to plants like rhododendrons and many other ornamental plants. Most gardening books do not recommend planting any plants in close proximity to walnut trees as there is little to be done to combat the juglone chemicals. It even comes down from the canopy when it rains. There are SOME plants tolerant- vines, flowers, and groundcovers. You can read more about them here: http://pubs.ext.vt.edu/430/430-021/430-021.html at the Virginia Tech. Cooperative Extension.
The problem is the walnuts when they fall, are toxic to anything that tries to grow there! Beautiful trees, but messy as heck! They are also worth a LOT of money, so before they get too old, you might consider selling one or two of them!!!