The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l_min. This convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavourable for a stem to be shorter than l_min and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behaviour of the Sadler-Gilmer model when an energetic contribution from chain folds is included.Comment: 15 pages, 13 figures, revte

Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]

Recently, the properties of supercooled liquids have been studied by mapping instaneous configurations onto minima of the gradient squared. It was originally suggested that this mapping would probe higher-order saddle points of the potential energy surface. However, it was subsequently shown that the majority of the minima of this function are only local minima and so do not correspond to saddles. In this comment, we provide a critique of the suggestion made by Angelani et al. [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301] that although these minima are not true saddles, they are almost saddles (hence the term quasisaddles). This issue has important implications for the interpretation of the results obtained by this approach.Comment: 2 page

New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster

A new atomic cluster structure corresponding to the global minimum of the 98-atom Lennard-Jones cluster has been found using a variant of the basin-hopping global optimization algorithm. The new structure has an unusual tetrahedral symmetry with an energy of -543.665361, which is 0.022404 lower than the previous putative global minimum. The new LJ_98 structure is of particular interest because its tetrahedral symmetry establishes it as one of only three types of exceptions to the general pattern of icosahedral structural motifs for optimal LJ microclusters. Similar to the other exceptions the global minimum is difficult to find because it is at the bottom of a narrow funnel which only becomes thermodynamically most stable at low temperature.Comment: 3 pages, 2 figures, revte

Melting of aluminium clusters

The melting of Al clusters in the size range 49 <= N <= 62 has been studied using two model interatomic potentials. The results for the two models are significantly different. The glue potential exhibits a smooth relatively featureless heat capacity curve for all sizes except for N = 54 and N = 55, sizes at which icosahedral structures are favoured over the polytetrahedral. Gupta heat capacity curves, instead, show a well-defined peak that is indicative of a first-order-like transition. The differences between the two models reflect the different ground-state structures, and neither potential is able to reproduce or explain the size dependence of the melting transition recently observed in experiments

Power-law distributions for the areas of the basins of attraction on a potential energy landscape

Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.Comment: 4 pages, 3 figure

Structural relaxation in Morse clusters: Energy landscapes

We perform a comprehensive survey of the potential energy landscapes of 13-atom Morse clusters, and describe how they can be characterized and visualized. Our aim is to detail how the global features of the funnel-like surface change with the range of the potential, and to relate these changes to the dynamics of structural relaxation. We find that the landscape becomes rougher and less steep as the range of the potential decreases, and that relaxation paths to the global minimum become more complicated.Comment: 21 pages, 3 tables, 5 figure

Kinetic Monte Carlo simulations of the growth of polymer crystals

Based upon kinetic Monte Carlo simulations of crystallization in a simple polymer model we present a new picture of the mechanism by which the thickness of lamellar polymer crystals is constrained to a value close to the minimum thermodynamically stable thickness, l_{min}. The free energetic costs of the polymer extending beyond the edges of the previous crystalline layer and of a stem being shorter than l_{min} provide upper and lower constraints on the length of stems in a new layer. Their combined effect is to cause the crystal thickness to converge dynamically to a value close to l_{min} where growth with constant thickness then occurs. This description contrasts with those given by the two dominant theoretical approaches. However, at small supercoolings the rounding of the crystal profile does inhibit growth as suggested in Sadler and Gilmer's entropic barrier model.Comment: 12 pages, 13 figures, revte

Structural Transitions and Global Minima of Sodium Chloride Clusters

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we determine reaction pathways between the low energy isomers of one of these clusters, (NaCl)35Cl-. The key process in these structural transitions is a highly cooperative rearrangement in which two parts of the nanocrystal slip past one another on a {110} plane in a direction. In this way the nanocrystals can plastically deform, in contrast to the brittle behaviour of bulk sodium chloride crystals at the same temperatures; the nanocrystals have mechanical properties which are a unique feature of their finite size. We also report and compare the global potential energy minima for (NaCl)NCl- using two empirical potentials, and comment on the effect of polarization.Comment: extended version, 13 pages, 8 figures, revte

Coordination motifs and large-scale structural organization in atomic clusters

The structure of nanoclusters is complex to describe due to their noncrystallinity, even though bonding and packing constraints limit the local atomic arrangements to only a few types. A computational scheme is presented to extract coordination motifs from sample atomic configurations. The method is based on a clustering analysis of multipole moments for atoms in the first coodination shell. Its power to capture large-scale structural properties is demonstrated by scanning through the ground state of the Lennard-Jones and C$_{60}$ clusters collected at the Cambridge Cluster Database.Comment: 6 pages, 7 figure

Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids

We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.Comment: 16 pages, 2 figure