Energy landscape of a lennard-jones liquid: statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well-defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy u(th), which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach u(th) at a temperature close to the mode-coupling transition temperature T(c).     

Mosaic multistate scenario versus one-state description of supercooled liquids

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.     

Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

Journal of Statistical Physics - A correction to this paper has been published: https://doi.org/10.1007/s10955-021-02770-w     

PMR configurational analysis of pinitol with the aid of lanthanide shift reagents and the homonuclear INDOR technique

The PMR spectrum of the peracetylated O-methyl-chiro-inositol (pinitol) could be analysed by employing lanthanide shift reagents and performing spin-decoupling and INDOR experiments. The 100 MHz theoretical spectrum has been simulated and good agreement with the experiment has been achieved. Analysis of the vicinal H? H-couplings yields the relative configuration.     

Proton-coupled 13C NMR and {14N}—1H-INDOR of highly-substituted 6-membered heterocycles. I—trisubstituted pyridones and isomeric aminopyrones; tetrasubstituted pyridines

The structural elucidation by NMR spectroscopy of trisubstituted α-pyridones and the isomeric 2-amino-γ-pyrones as well as their internal and external pyrylium salts is described. The most useful parameter for the differentiation between α-pyridones and isomeric γ-pyrones is the geminal coupling constant ²J(C-6, H-5) which changes from ～2.5 Hz to ～7 Hz whenever the cyclic amide group is replaced by an oxa-function; this applies to both the γ-pyrones and their pyrylium salts. The value of J(C-6, H-5) in the pyridones resembles that of the analogous coupling in N-vinylacetamide, whose sign determination by the selective population inversion (SPI) technique is reported. The ¹³C chemical shifts of seven pyridones, pyrones and pyrylium salts are reported and their structural correlations are discussed. Quick structural assignments in these classes of compounds may also be performed by evaluating the ¹⁴N chemical shifts, which often are accessible by the {¹⁴N}—¹H-INDOR technique. The proton coupled ¹³C NMR spectra of two tetrasubstituted pyridines are also reported, and empirical correlations between long range C? H coupling constants and substituent electronegativity are discussed.     

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e., at coexistence, where the critical nucleus becomes infinitely large.     

Dynamic relaxation of a liquid cavity under amorphous boundary conditions

The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set (PTS) correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between mode-coupling theory and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.