arXiv subjects
Publications and source records attributed to Daan Frenkel.
We report numerical calculations of the concentration of interstitials in hard-sphere crystals. We find that, in a three-dimensional fcc hard-sphere crystal at the melting point, the concentration of interstitials is 2 * 10^-8. This is some three orders of magnitude lower than the concentration of vacancies. A simple, analytical estimate yields a value that is in fair agreement with the numerical results.
We report a numerical simulation of the phase diagram of a simple model for membrane proteins constrained to move in a plane. In analogy with the corresponding three dimensional models, the liquid-gas transition becomes metastable as the range of attraction decreases. Spontaneous crystallization happens much more readily in the two dimensional models rather than in their three dimensional counterparts.
We propose an extension of the law of corresponding states that can be applied to systems - such as colloidal suspensions - that have widely different ranges of attractive interactions. We argue that, for such systems, the ``reduced'' second virial coefficient is a convenient parameter to quantify the effective range of attraction. This procedure allows us to give a simple definition of the effective range of attraction of potentials with different functional forms. The advantage of the present approach is that it allows us to estimate the relative location of the liquid-vapor and solid-fluid coexistence curves exclusively on basis of the knowledge of the pair-potential.
We investigate the possibility that freely rotating cylinders with an aspect ratio $L/D=0.9$ exhibit a cubatic phase similar to the one found for a system of cut-spheres. We present theoretical arguments why a cubatic phase might occur in this particular system. Monte Carlo simulations do not confirm the existence of a cubatic phase for cylinders. However, they do reveal an unexpected phase behavior between the isotropic and crystalline phase.
Temperature changes during the growth of lamellar polymer crystals give rise to steps on the surface of the crystals. It has recently been suggested that these steps could provide important insights into the mechanism of polymer crystallization. In particular, a characterization of the profiles of these steps might reveal the fixed-point attractor that underlies a recently proposed crystallization mechanism. Here we examine this hypothesis by performing simulations of such temperature jumps using the Sadler-Gilmer model. We find that for this model the step profiles do reveal the fixed-point attractor. However, for temperature decreases they also reflect the rounding of the crystal edge that occurs in this model and for temperature increases they also reflect the fluctuations in the thickness present in the crystal. We discuss the implications of these results for the interpretation of experimental step profiles.
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.
We consider the effect of intermolecular interactions on the optimal size-distribution of $N$ hard spheres that occupy a fixed total volume. When we minimize the free-energy of this system, within the Percus-Yevick approximation, we find that no solution exists beyond a quite low threshold ($η\thickapprox 0.260$). Monte Carlo simulations reveal that beyond this density, the size-distribution becomes bi-modal. Such distributions cannot be reproduced within the Percus-Yevick approximation. We present a theoretical argument that supports the occurrence of a non-monotonic size-distribution and emphasizing the importance of finite size effects.
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.
We have studied the structure and free energy landscape of a semi-flexible lattice-polymer in the presence of a surface. At low temperatures coexistence of two-dimensional integer-folded crystals is observed. As the temperature is increased there is a transition from these crystalline configurations to a disordered coil adsorbed onto the surface. The polymer then gradually develops three-dimensional character at higher temperatures. We compute the free energy as a function of increasing crystallinity and compare with the free energy profiles assumed by the Lauritizen-Hoffman surface nucleation theory of polymer crystallization. Our free energy profiles exhibit a `sawtooth' structure associated with the successive formation of chain folds. However, in the early stages of crystallization our profiles significantly deviate from those assumed by surface nucleation theory because the initial nucleus is not a single stem but two incomplete stems connected by a fold. This finding has significant implications for the theoretical description of polymer crystallization.
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. This description contrasts with those given by the two dominant theoretical approaches.
We have studied the thermodynamics of isolated homopolymer chains of varying stiffness using a lattice model. A complex phase behaviour is found; phases include chain-folded `crystalline' structures, the disordered globule and the coil. It is found, in agreement with recent theoretical calculations, that the temperature at which the solid-globule transition occurs increases with chain stiffness, whilst the $θ$-point has only a weak dependence on stiffness. Therefore, for sufficiently stiff chains there is no globular phase and the polymer passes directly from the solid to the coil. This effect is analogous to the disappearance of the liquid phase observed for simple atomic systems as the range of the potential is decreased.