The thermodynamics of homopolymers and clusters with square-well interactions of up to 64 particles are studied with constant-temperature discontinuous molecular dynamics ͑DMD͒ simulations; for comparison Monte Carlo ͑MC͒ simulations are also reported. Homopolymers composed of more than five beads are found to exhibit two or more equilibrium transitions. In the long chain limit, these multiple transitions correspond to gas-to-liquid, liquid-to-solid, and solid-to-solid transitions. In particular, the liquid-to-solid-like disorder-to-order transition for isolated 32mers and 64mers is strongly first order ͑bimodal energy distribution͒ at the reduced square-well diameter ϭ1.5. As decreases from 1.5 to 1.3, the bimodal distribution becomes unimodal. The use of Lindemann's rule for solids indicates that the structure formed right below the liquid-to-solid transition temperature has a solid core but a liquid surface. Comparing the homopolymer results with those for square-well clusters indicates that the bonding constraint in homopolymers increases the temperatures of transitions but decreases their strength. The solid structure of an isolated 64mer is nearly identical to that of a cluster of 64 beads. Possible approaches to the experimental observation of the solid-state for an isolated chain are discussed.

In this series of two papers we study the thermodynamics of binary hard chain mixtures. Here, a generalized Flory-dimer (GF-D) equation of state is derived for binary hard chain mixtures composed of chains of variable length and segment diameter. Compressibility factors predicted by the GF-D equation of state developed here and by the previously derived generalized Flory equation of state are compared to previous Monte Carlo results for hard monomer/hard chain mixtures, and to new molecular dynamics (MD) hard monomer/hard chain and hard chain/hard chain mixture simulation results. Compared to the MD simulations, the GF-D theory is found to be quite accurate, with an average error of about 3% at liquid-like densities.

The second virial coefficient, Bz, has been calculated for square-well chain molecules of lengths n = 2-50 and well widths of X = 0.25-1.0 by Monte Carlo integration. The theta temperature, at which Bz = 0, is independent of chain length around X = 0.5, increases with chain length for X > 0.5, and decreases with chain length for X < 0.5. A scaling relation, Te*(n) -To*(-) a n", accurately describes the departure of the theta temperature from the infinite chain length value for X 1 0.6. A closed-form expression for the second virial coefficient of square-well chains is presented which accurately fits the Monte Carlo data for n = 2-50 and X = 0.25-0.75. When compared to the Monte Carlo results, the second virial coefficient predicted by the generalized Flory-dimer theory for square-well chains is found to be increasingly inaccurate as chain length increases. If we correct the generalized Flory-dimer equation of state by forcing it to have the correct second virial coefficient, the compressibility factor is accurately predicted at densities below 7 = 0.04.

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The generalized Flory (GF) and generalized Flory-dimer (GFD) equations of state have been extended to fluids containing hard heteronuclear chain-like molecules. Compressibility factor expressions have been derived for block, alternating and random ‘‘copolymer’’ fluids. The effect of composition and the relative size of the segments of a heteronuclear chain on the compressibility factor are studied. We have also performed molecular dynamics computer simulations on these systems using an extension of Rapaport’s algorithm in which the chains are effectively treated as hard spheres of different sizes held together by invisible strings. The compressibility factors predicted by the GFD theory for heteronuclear chain fluids are in very good agreement with our computer simulation results. The predictions of Chiew’s Percus Yevick theory are also in very good agreement with our computer simulation results on block copolymers.