The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function F(S)(k,τ;t), where τ is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the α-relaxation time τ(α)(t) as a function of t allows us to define the equilibration time t(eq)(φ), as the time after which τ(α)(t) has attained its equilibrium value τ(α)(eq)(φ). It is predicted that both, t(eq)(φ) and τ(α)(eq)(φ), diverge as φ→φ((a)), where φ((a)) is the hard-sphere dynamic-arrest volume fraction φ((a))(≈0.582), thus suggesting that the measurement of equilibrium properties at and above φ((a)) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of τ(α)(t;φ) as a function of φexhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (φ≤φ((c))(t)), and to samples for which equilibration is not yet complete (φ≥φ((c))(t)). The crossover volume fraction φ((c))(t) increases with t but saturates to the value φ((a)).

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a non-equilibrium state with the desired final volume fraction φ for which we can obtain a well-defined non-equilibrium static structure factor S0(k; φ). The evolution of the α-relaxation time τα(k) and long-time self-diffusion coefficient DL as a function of the evolution time tw is then monitored for an array of volume fractions. For a given waiting time the plot of τα(k; φ, tw) as a function of φ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time (φ ≤ φ (c) (tw)), and to samples for which equilibration is not yet complete (φ ≥ φ (c) (tw)). The crossover volume fraction φ (c) (tw) increases with tw but seems to saturate to a value φ (a) ≡ φ (c) (tw → ∞) ≈ 0.582. We also find that the waiting time t eq w (φ) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time,1.43 , and that both characteristic times increase strongly as φ approaches φ (a) , thus suggesting that the measurement of equilibrium properties at and above φ (a) is experimentally impossible. exp ≈ 0.58 [6,7], although a number of intrinsic experimental uncertainties render the precise determination of φ (a) exp a topic of recurrent scientific discussion [4,[6][7][8][9][10].

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both, an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids [Phys. Rev. Lett. 70, 1557(1993]. We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the "hard-sphere" dynamic universality class. One of the fundamental challenges in understanding the relationship between dynamic arrest phenomena in colloidal systems [1], and the glass transition in simple glass-forming atomic liquids [2], is to determine the role played by the underlying (Brownian vs. Newtonian) microscopic dynamics. It is a widespread notion that colloidal systems constitute a mesoscopic analog of atomic systems regarding the relationship between inter-particle forces and macroscopic properties [3,4]. The molecular dynamics simulation of an atomic liquid, for example, is expected to yield the same equilibrium phase diagram, and a similar dynamic arrest scenario, as the Brownian dynamics simulation of a colloidal liquid, when referring to the same model system [5,6]. Important questions, however, remain unanswered, even at normal liquid states, far from the neighborhood of the conditions for dynamic arrest. For example, while it is well-known that monodisperse Brownian liquids will freeze when the longtime self-diffusion coefficient D L reaches about 0.1×D S , with D S being the short-time self-diffusion coefficient ("Löwen's dynamic freezing criterion" [7]), no analogous criterion has been identified for the corresponding atomic liquids.In the attempt to develop the extension to atomic liquids, of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [8], we have discovered that a well-defined long-time dynamic equivalence between atomic and colloidal liquids emerges upon the identification of the kinetic-theoretical self-diffusion coefficient D 0 of an atomic fluid [9], as the analog of the short-time self-diffusion coefficient D S of a colloidal liquid. In this short communication we describe the physical foundations of this extended SCGLE theory, which also constitute the physical basis of the referred dynamic equivalence. One of the most important manifestations of the latter is that the ratio D * ≡ D L /D S must then be the same for an atomic and a colloidal system characterized by the same inter-par...

Using small angle neutron scattering, we conducted a detailed structural study of poly(3-alkylthiophenes) dispersed in deuterated dicholorbenzene. The focus was placed on addressing the influence of spatial arrangement of constituent atoms of side chain on backbone conformation. We demonstrate that by impeding the π-π interactions, the branch point in side chain promotes torsional motion between backbone units and results in greater chain flexibility. Our findings highlight the key role of topological isomerism in determining the molecular rigidity and are relevant to the current debate about the condition necessary for optimizing the electronic properties of conducting polymers via side chain engineering.Conjugated polymers are synthetic macromolecules that are characterized by a backbone consisting of alternating doubleand single-bonds. [1][2][3][4] This conjugated structure provides overlapping -orbitals for delocalised -electrons and allows them to be electrically conducting upon properly doping. 5 Conjugated polymers are found in a variety of applications. [6][7][8][9] The most exploited one is their use as organic electronics including photovoltaic cells and organic field-effect transistors 10-11 ; they are also proposed for many other applications, such as in the molecular imaging 12 and pharmaceutical fields 13 .