A model for infinitely long twohyphen;stranded macromolecules, previously shown to exhibit phase transitions in association with the helixndash;coil equilibrium, is examined further. It is found that phase transitions of all orders from one to infinity are formally possible, depending on the value ofa, which is defined by the fact that the probability of loop closure for a random flight ofksteps is proportional tokminus;a. Defininghthinsp;equals;thinsp;athinsp;minus;thinsp;1for the ldquo;matching caserdquo; andhthinsp;equals;thinsp;athinsp;minus;thinsp;2for the ldquo;mismatching case,rdquo; a phase transition of orderm lpar;mthinsp;equals;thinsp;2, 3,middot;middot;middot;,rpar;is predicted if1thinsp;sol;thinsp;mthinsp;le;thinsp;hthinsp;thinsp;1thinsp;sol;thinsp;lpar;mthinsp;minus;thinsp;1rpar;. The transition is of infinite order ifhthinsp;le;thinsp;0and of first order ifhthinsp;thinsp;1. From calculated transition curves it is found that the apparent order may be lower than the true order if the stacking parameterbis sufficiently small. The maximum slope of the transition curve is found to vary asbminus;1sol;lpar;1minus;hrpar;forbthinsp;Lt;thinsp;1, hthinsp;le;thinsp;12, in agreement with previous studies of certain special cases. An examination of mean sequence lengths shows that, for phase transitions of low order, the mean length of a helical sequence remains near a critical minimum value over a considerable range of the degree of bonding, while the mean loop size varies greatly over the same range. Experiments on the helixndash;coil equilibrium in twohyphen;stranded polyriboadenylic acid are reported, demonstrating the existence of a true equilibrium under certain conditions, and confirming the occurrence of an apparent secondhyphen;order phase transition under these conditions. Attempts to fit the experimental data to the theory lead to the conclusion thatais in the range 2.3ndash;2.5 if the mismatching model is correct but thatawould be lower if some bias exists toward the matching condition.
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