Publication Date:
2014-11-07
Description:
Extensive numerical solutions of the hypernetted-chain (HNC) and Rogers-Young (RY) integral equations are presented for the pair structure of a system of two coupled replicae (1 and 2) of a “soft-sphere” fluid of atoms interacting via an inverse-12 pair potential. In the limit of vanishing inter-replica coupling ɛ 12 , both integral equations predict the existence of three branches of solutions: (1) A high temperature liquid branch ( L ), which extends to a supercooled regime upon cooling when the two replicae are kept at ɛ 12 = 0 throughout; upon separating the configurational and vibrational contributions to the free energy and entropy of the L branch, the Kauzmann temperature is located where the configurational entropy vanishes. (2) Starting with an initial finite coupling ɛ 12 , two “glass” branches G 1 and G 2 are found below some critical temperature, which are characterized by a strong remnant spatial inter-replica correlation upon taking the limit ɛ 12 → 0. Branch G 2 is characterized by an increasing overlap order parameter upon cooling, and may hence be identified with the hypothetical “ideal glass” phase. Branch G 1 exhibits the opposite trend of increasing order parameter upon heating; its free energy lies consistently below that of the L branch and above that of the G 2 branch. The free energies of the L and G 2 branches are found to intersect at an alleged “random first-order transition” (RFOT) characterized by weak discontinuities of the volume and entropy. The Kauzmann and RFOT temperatures predicted by RY differ significantly from their HNC counterparts.
Print ISSN:
0021-9606
Electronic ISSN:
1089-7690
Topics:
Chemistry and Pharmacology
,
Physics
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