Glass-forming liquids: one or more ‘order’ parameters?

Abstract

Abstract. We first summarize the classical arguments that the vast majority of glass-forming liquids require more than one "order" parameter for their description. Critiques against this conventional wisdom are then presented, and it is argued that the matter deserves to be reconsidered in light of recent experimental developments. Out of the eight basic thermoviscoelastic frequencydependent response functions, there are generally three independent functions. For stochastic dynamics we show that there are only two independent response functions; for this case it is shown how analytic continuation may be utilized to express the third response functions in terms of two others. Operational criteria are presented for the linear thermoviscoelasticity being described by a single "order" parameter, in which case there is just one independent thermoviscoelastic response function. It is shown that a single "order" parameter description applies to a good approximation whenever thermal equilibrium fluctuations of fundamental variables like energy and pressure are strongly correlated. Results from computer simulations showing that this is the case for a number of simple glass-forming liquids, as well as a few exceptions, are briefly presented. Finally, we discuss a new conjecture according to which experiments at varying temperature and pressure follow the density-scaling expression for the relaxation time, τ = F (ρ x /T ) (ρ and T are density and temperature), if and only if the liquid is "strongly correlating," i.e., to a good approximation is described by a single "order" parameter. Glass-forming liquids: One or more "order" parameters?2

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

“…Taken together, Eqs. (19), (20), and (9) thus imply that from a single reference point (ρ * , T * , U * , W * ) we have a prediction for (ρ, T, U, W ) on the isomorph to which the reference point belongs. Figure 4 demonstrated that in the WU phase diagram, isochores to a good approximation are straight lines with slope γ , i.e., that one can write W (ρ, T ) = W 0 (ρ) + γ (ρ)U (ρ, T ).…”

“…(14) and (15), the entire isomorph to which this state point belongs is thus traced out in the WU phase diagram using Eqs. (19) and (20). Alternatively, given a collection of isomorphic state point generated, e.g., as described in Sec.…”

“…(2) The shape of the isomorphs depends only on the exponents, m and n. This means that all 12-6 LJ systems have the same isomorphs in the WU phase diagram -they may be scaled onto a single "master isomorph" (see also Eq. (27) (19) and (20). Two isomorphs belong to the KABLJ system, the third results from simulations of the Wahnström binary LJ liquid 46 (WBLJ), and the fourth (SCLJ) is the single component LJ liquid.…”

“…[8][9][10][11][12][13][14][15][16][17][18] Thus it has been shown that strongly correlating viscous liquids to a good approximation have all eight frequency-dependent thermoviscoelastic response functions [19][20][21] given in terms of just one 22 (i.e., are single-parameter liquids in the sense of having dynamic Prigogine-Defay ratio 19 close to unity 2,20,22 ). Strongly correlating viscous liquids moreover obey density scaling [23][24][25][26][27] to a good approximation, i.e., their dimensionless relaxation timeτ ≡ τρ 1/3 √ k B T /m (where m is the average particle mass) depends on density ρ = N /V and temperature as τ = F(ρ γ /T ).…”

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

“…In a series of papers published last year, [1][2][3][4][5] we introduced the concept of strongly correlating liquids and demonstrated by computer simulations that this includes a large class of model liquids. Specifically, the fluctuations, which are in many cases strongly correlated, are those of the configurational parts of pressure and energy, i.e., the parts in addition to the ideal gas terms, coming from the interatomic forces.…”