The present invention provides absorbent articles, such as disposable diapers, which utilize substantially water-insoluble hydrogel material to enhance the absorbent capacity of such articles. In these articles, the hydrogel material, combined in particulate form with hydrophilic fiber material, is primarily placed in a lower fluid storage layer of the absorbent core of the article. Such a fluid storage lower layer of the absorbent core is placed underneath an upper, preferably larger, fluid acquisition/distribution layer containing little or no hydrogel. This lower fluid storage layer is positioned in such a manner that at least about 75% of the hydrogel in the lower layer is found in the front two-thirds of the absorbent article and such that at least about 55% of the hydrogel in the lower layer is found in the front half of the absorbent article. Absorbent articles of this type make especially effective and efficient use of the hydrogel material and may also provide a diaper rash control benefit. Absorbent cores of the type utilized in such articles are also disclosed.