This paper studies soygel transition of associating polymers with mult
iple cross-link junctions. Paying special attention to the multiplicit
y and sequence length of the network junctions, we derive phase diagra
ms and analyze molecular structure of the networks. The conventional E
ldridge-Ferry method is extended to evaluate multiplicity, as well as
enthalpy, of the cross links, and applied to the experimental gel melt
ing curves of poly(vinyl alcohol) in water. The effect of added surfac
tants on the formation of reversible gels in hydrophobically modified
polymer solutions is also studied under the assumption of the existenc
e of a minimum multiplicity required for stable cross-links. On the ba
sis of the transient network model with temporal junctions, we calcula
te dynamic mechanical moduli, average lifetime of a junction, the numb
er of elastically effective chains and of dangling ends as functions o
f the strength of the association constant, polymer concentration and
the temperature. We compare the results with the experimentally measur
ed moduli of hydrophobically modified poly(ethylene oxide). (C) 1998 E
lsevier Science B.V. All rights reserved.