1210.5796 (Tieyan Si)
Tieyan Si
To find a quantitative understanding on the odd-even effect of melting finite polymer film, we proposed an equation for computing the melting temperature. For a dimer film covering a constant rectangular area but with different width, the melting temperature for odd number of width is always larger than that for even number of width. There is no experiment for melting two dimensional film so far. The existed experimental data of melting three dimensional powder reported the opposite phenomena. We computed the entropy growth rate of two dimensional confined dimer film on finite rectangle and torus. The entropy of two dimensional long belt with an even number of width is always larger than the entropy for an odd number of width. When the length of the rectangle goes to infinity, the speed of entropy growth shows a linear dependence on the width. This linear relationship originates from the constant melting temperature in thermal dynamic limit. Fusing two small rectangles with odd number of length into one big rectangle gains more entropy than fusing two small rectangles with even number of length. Fusing two small toruses with even number of length into one big torus reduces entropy. While fusing two small toruses with odd number of length increases the entropy. The entropy difference between covering a torus and covering a rectangle decays to zero when the lattice size becomes infinite. The correlation function between two topologically distinguishable loops on torus also demonstrate odd-even effect. We expect an experiment of melting two dimensional film to test this theory.
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http://arxiv.org/abs/1210.5796
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