Molecular Dynamics Simulation of Vitrification and Plastic Deformation of a Two-Dimensional Lennard-Jones Mixture (original) (raw)
A computer model of a two-dimensional atomic glass is generated by molecular dynamics. This model consists of 500 Lennard-Jones particles of two different diameters. A volume-temperature diagram is obtained. The bend found on this diagram at T = 0.288 is interpreted as the glass transition. Density fluctuations and changes in the particles coordination numbers at the glass transition are studied by means of Voronoy polygons. The spatial correlation functions for particle displacements in the liquid and glassy states are analyzed. It is found that the glass structure is always a frozen liquid structure. Below the glass transition particle displacements from their equilibrium positions become spatially correlated, and the correlation length is greater than the model's size. Unusual roton-like collective vibrational modes are found in the glass. The simulation of shear deformation shows that these modes may play an important role in the plastic deformation. No correlation is found between the diffusional mobility of particles and their local free volumes. This fact contradicts the main physical concept upon which a free volume approach is based. Ein Computermodell eines zweidimensionalen atomaren Glases wird mit Molekulardynamik generiert. Das Modell besteht aus 500 Lennard-Jones Teilchen mit zwei verschiedenen Durchmessern. Ein Volu-men-Temperaturdiagramm wird erhalten, in. dem die Krummung bei T = 0,28~ als Glasubergang interpretiert wird. Dichteschwankungen und Anderungen der Koordinationszahlen der Teilchen beim Glasubergang werden mit Voronoy-Polygonen studiert. Die raumlichen Korrelationsfunktionen der Teilchenverschiebung im flussigen und glasartigen Zustand werden untersucht. Es wird gefunden, daB die Glasstruktur immer eine eingefrorene Flussigkeitsstruktur ist. Unter dem Glasubergang werden die Verschiebungen der Partikel weg von den Gleichgewichtspositionen raumlich korreliert, und die Korrelationslange ist groBer als die ModellgroBe. Uniibliche rotationsahnliche kollektive Eigenschwin-gungen werden im Glas gefunden. Die Simulation von Scherung zeigt, daB die Eigenschwingungen eine wichtige Rolle in der plastischen Deformierung haben konnten. Es kann keine Korrelation gefunden werden zwischen Diffusionsmobilitat von Teilchen und ihrem freiem Volumen. Dies widerspricht dem grundlegenden physikalischen Modell, das auf dem Konzept des freien Volumens basiert.
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Microscopic Model of Glass transformation and Molecular Translation in Liquids I. Foundations
Based on free volume ideas of the liquid state a new spatial-kinetic model will be presented. Free volume is newly defined and its generation is supposed to arise from combined interactions of a critical number of vibrating elements generating temporary apertures bigger than the cross-section of a neighboring element or parts of it. Possible shifts of molecules or molecular parts through such gaps depend on size and axis orientation and do not need further energetic activation. After a displacement additional volume will be generated due to temporal delays in the occupation of abandoned sites and reconstitution of energetic equilibrium. The different possibilities of axis orientation in space lead in succession to different diffusive behavior of simple molecules and chain molecules, silicate network formers and associating liquids. Glass transformation takes place at a critical volume Vg0 when the cross-section of the apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg0 is assigned to Vg0 and, therefore, should be independent of molecular relaxation processes. Simple non-spherical molecular liquids change their behavior additionally above Vg0 at Vgl where the biggest gaps become as small as the largest molecular diameter. Vgl resp. Tgl is situated some degrees below the crystalline melting point Tm, probably in the region of fastest crystallization rate. Both regions, above and below Tm, are related to different physical states and have to be treated separately. In the region close to Vg0 resp. Tg0 the distribution of vibration amplitudes has to be taken into account. The evolution of transport properties depend on specific volume and not on temperature per se.
The glass transition is described as a time-and history-independent singular event, which takes place in an interval dependent on the distribution width of the molecular vibration amplitudes. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into the condensed matter and the resulting combined interactions between the vibration elements. This creates openings between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such gaps depend on the size and axis orientation and do not require further energetic activation. After a displacement additional volume is created by delays in occupying abandoned positions and restoring the energetic equilibrium. The different possibilities of axis orientation in space result in different diffusive behavior of simple molecules and chain molecules, silicate network formers and associating liquids. Glass transformation takes place at a critical volume Vg 0 when the cross-section of the apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg 0 is assigned to Vg 0 and is therefore independent of molecular relaxation processes. Tg 0 is well above the Kauzmann and Vogel temperatures, usually just a few degrees below the conventionally measured glass temperature Tg (qT). The specific volume at the two temperatures mentioned above cannot be achieved by a glass with an unordered structure but only with aligned molecular axes, i. e. in the crystalline state. Simple liquids consisting of non-spherical molecules additionally alter their behavior above Vg 0 at Vg l where the biggest gaps are as small as the largest molecular diameter. Tg l is located in the region of the crystalline melting point Tm. Both regions, above and below Tm, belong to different physical states and have to be treated separately. In the region close to Vg 0 resp. Tg 0 the distribution of vibration amplitudes has to be taken into account. The evolution of transport properties depend on specific volume and not on temperature per se. The boundary volume Vg 0 in conjunction with the distribution width of the molecular vibrations when approaching Vg 0 is the key to understanding the glass transition.
The glass transition is described as a time-and history-independent singular event, which takes place in an interval dependent on the distribution width of the molecular vibration amplitudes. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into the condensed matter and the resulting combined interactions between the vibration elements. This creates vacancies between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such gaps depend on the size and axis orientation and do not require further energetic activation. After a displacement additional volume is created by delays in occupying abandoned positions and restoring the energetic equilibrium. The different possibilities of axis orientation in space result in different diffusive behavior of simple molecules and chain molecules, silicate network formers and associating liquids. Glass transformation takes place at a critical volume Vg 0 when the cross-section of the apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg 0 is assigned to Vg 0 and is therefore independent of molecular relaxation processes. Tg 0 is well above the Kauzmann and Vogel temperatures, usually just a few degrees below the conventionally measured glass temperature Tg(qT). The specific volume at the two temperatures mentioned above cannot be achieved by a glass with an unordered structure but only with aligned molecular axes, i. e. in the crystalline state. Simple liquids consisting of non-spherical molecules additionally alter their behavior above Vg 0 at Vg l where the biggest gaps are as small as the largest molecular diameter. Tg l is located in the region of the crystalline melting point Tm. Both regions, above and below Tm, belong to different physical states and have to be treated separately. In the region close to Vg 0 resp. Tg 0 the distribution of vibration amplitudes has to be taken into account. The boundary volume Vg 0 and the creation of apertures larger than the cross-section of the vibrating elements or parts thereof, in conjunction with the distribution width of the molecular vibrations approaching Vg 0 and the molecular axis orientation, is the key to understanding the glass transition.
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