Oddeven effect of melting finite polymer film on square lattice
Abstract
Twodimensional film system bears many exotic thermodynamics behaviors. We proposed a mathematical physics model to explore how the melting temperature of a twodimensional mathematical dimer film depends on the oddevenness of the finite width of dimer film. A weak external bond between dimers is introduced into the classical dimer model in this dimer film. We derived a general equation of melting temperature and applied it for computing the melting temperature of a dimer film covering a finite square lattice. The melting temperature is proportional to the external bonding energy that we assume it binds neighboring dimers together and proportional to the inverse of entropy per site. Furthermore, it shows fusing two small rectangular dimer film with odd number of length into one big rectangular film gains more entropy than fusing two small rectangles with even number of length into the same big rectangle. Fusing two small toruses with even number of length into one big torus reduces entropy. Fusing two small toruses with odd number of length increases the entropy. Thus two dimer films with even number of length repel each other, two dimer films with odd length attract each other. The oddeven effect is also reflected on the correlation function of two topologically distinguishable loops in a torus surface. The entropy of finite system dominates oddeven effect. This model has straightforward extension to longer polymers and threedimensional systems.
 Publication:

International Journal of Modern Physics B
 Pub Date:
 February 2015
 DOI:
 10.1142/S0217979215500629
 arXiv:
 arXiv:1210.5796
 Bibcode:
 2015IJMPB..2950062S
 Keywords:

 Mathematical physics model;
 critical melting temperature;
 dimer film;
 fusion of finite film;
 68.60.Dv;
 68.55.am;
 65.40.gd;
 64.70.qd;
 64.70.dj;
 Thermal stability;
 thermal effects;
 Polymers and organics;
 Entropy;
 Thermodynamics and statistical mechanics;
 Melting of specific substances;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter;
 Mathematical Physics
 EPrint:
 10 pages in two column, 15 figures in Int. J. Mod. Phys. B 2015