Extended-range order, diverging static length scales, and local structure formation in cold Lennard-Jones fluids

We report molecular-dynamics simulations on a three-dimensional, two-component Lennard-Jones fluid. We used 125 000 particles (equal numbers of A and B) at density N/V=1.29 and 34 temperatures T covering 5 x 10(4) > or =T > or =0.56. The pair potential was 4epsilon[(sigma(ij)/r)(12)-(sigma(ij)/r)(6)] with sigma(AA)=1, sigma(AB)=11/12, and sigma(BB)=5/6. We computed specific and generic radial distribution functions g(ij)(r), and several density-momentum dynamic correlation functions whose static (t=0) parts vanish by symmetry. Evidence is presented that our systems were adequately annealed to eliminate remnant initial order and were adequately equilibrated at each temperature. Static spatial correlations in cold Lennard-Jones liquids have longer ranges than are often reported: g(r)-1 unequal to 0 is found out to r > or =7 at T=2 and out to r > or =10 at T=0.56. |g(r)-1| has an envelope function that simultaneously fits both crests and troughs of g(r). The envelope function implies a temperature-dependent static length scale l(1); over (0.56 < or =T< or =100), l(1) approximately T(-0.3), contrary to suggestions that g(r) is temperature independent as the glass is approached. The highest-melting-point crystal that we identified melts at T(m) approximately 1.08. In the fluid phase, we observe short-range noncrystalline local structure formation in g(r) as the glass is approached. Local structure is only found below a local structure melting temperature T(mc)=2.0. Local structure vanishes above T=2. Local structure becomes more pronounced as temperature is reduced. However, at all temperatures at which there is local structure in g(r), the local structure is confined to r < or =4. Within the region r < or =4, the amplitude of the local structure diminishes with distance r from the central atom approximately as exp(-r/l(2)), thereby defining a second distance scale in the fluid. l(2), while more difficult to measure, appears to scale with temperature as l(2) approximately T(-0.6); l(2) is not the same as l(1). The static and dynamic properties of the local structure match properties assigned by Kivelson's glass model [S. A. Kivelson et al., J. Chem. Phys. 101, 2391 (1994)] to that model's frustration-limited local clusters.