Simulation of chemical bond distributions and phase transformation in carbon chains

Abstract

In the present work we develop a Monte Carlo algorithm of the carbon chains ordered into 2D hexagonal array.The chemical bond of the chained carbon is computed from 1K to 1300K. Our model confirms that the beta phase is more energetic preferable at low temperatures but the system prefers the alpha phase at high temperatures. Based on the thermal effect on the bond distributions and 3D atomic vibrations in the carbon chains, the bond softening temperature is observed at 500K. The bond softening temperature is higher in the presence of interstitial doping but it does not change with the length of nanowire. The elastic modulus of the carbon chains is 1.7TPa at 5K and the thermal expansion is +7 x 10 -5 K -1 at 300K via monitoring the collective atomic vibrations and bond distributions. Thermal fluctuation in terms of heat capacity as a function of temperatures is computed in order to study the phase transition across melting point. The heat capacity anomaly initiates around 3800K.

Electron–electron interactions of the multi-Cooper-pairs in the 1D limit and their role in the formation of global phase coherence in quasi-one-dimensional superconducting nanowire arrays

“…If the random number is greater than or equal to 0.5, the sign of the preferable axis is positive. Otherwise, the preferred direction becomes opposite [30]. In our simulation, four rotational states, i.e.…”

Revisiting the Entangled Chains of Polymer in the Carbyne Model

“…According to figure 4, the thermal expansion in the thinner polymer films is larger and therefore generating the critical void [9] is relatively easier than the case of thicker film. In other word, more voids give a bigger space to monomer diffusion upon heating to lower the glass transition temperature.…”

“…The box size of 1000 x 1000 x 1000 contains 6 polymer chains where each chain is made up of 100 spherical monomers. The original carbyne model [9] is slightly modified in the following. The initial condition sets the 600 monomers to occupy within the size of 5 x 5 x 5 in random manner.…”

“…During the thermal expansion, the bond length energy becomes more positive in spite of the existence in the approximated Lennard-Jones potential. The bond angle is thus readjusted where three consecutive monomers form a pivot [9]. However, the monomers may collide on each other to weaken the effect of volume expansion through the hard potential in the unit of 2 (unless we specify) per collision.…”

“…It is used to examine the directed assembly of copolymer blends and nanoparticles on nanopatterned substrates where the simulation results are in good agreement with experiment [7] In addition, D. P. Landau et al proposed a methodology [8] to simulate a semi-flexible polymer chain. However, if there is more than one semi-flexible chain in the system, the entanglements play an important role to the glass transition temperature and therefore we are going to test whether the newly developed Monte Carlo carbyne model [9] can simulate the Tg of semi-flexible multi-chains of polymer or not. The Tg of our polymer system is estimated by plotting the volume as a function of temperature where Tg is defined by finding the point of intersection [10,11] for two extrapolated straight lines in the frozen glassy (below Tg) and soften states (above Tg) respectively.…”