金刚石格点上自回避行走高分子链的构象熵

Conformational Entropy of SAW Polymer Chain on Diamond Lattice

计算了链长Ｎ为１０～１９的金刚石格点上自回避行走高分子链的构象熵Ｓ和平均ｇ态个数＜Ｗｇ＞。发现Ｓ和＜Ｗｇ＞均与Ｎ成线性关系，每键构象熵β（以ｋＢ为单位）和ｇ态密度μ都随参数κ（κ＝ｋＢＴ／ε）的变化而变化，参数κ是与温度、键构象能ε有关的量。β随参数κ的变化可划为三个区域，（１）｜κ｜≥２．０，β的值几乎与κ的大小无关，几乎接近于β的极值；（２）０．１６＜｜κ｜＜２．０，β的变化非常明显；（３）｜κ｜≤０．１６，β的值几乎不随κ的变化而变化，表明高分子链处于能量最低的构象。每键构象熵β和ｇ态密度μ随参数κ的变化是相互联系的，满足βκ＝κ－１μκ。

The conformational entropy S and mean number of state gauche (including g + and g -) <Wg> are calculated for polymer chains self-avoiding walk (SAW) on a diamond lattice by using exact enumeration method. We find that S and <W g> are in linear proportion to chain length N . Conformational entropy per bond β and the density of state gauche μ are varied with parameter κ, where κ = k B T/ε, ε is the bond energy of a gauche state relative to trans. Three regions can be divided for the relation of β on κ: (1) |κ| 2.0, β is nearly independent on κ and its value almost reaches the maximum. (2) 0.16<|κ|<2.0, the change of β is very obvious. (3) |κ| 0.16, β becomes insensitive to κ, indicating the polymer chain is in its minimum energy state. The relation between conformational entropy per bond β and the density of state gauche μ is revealed, it is βκ=κ -1 ·μκ.