简立方格点自避行走所模拟的高分子链吸附和塌缩

采用复合Markov链法 ,针对简立方格点上的自避行走模型 ,研究了同时具有对壁的吸附作用ε1 和最近邻相互作用ε2 的高分子链的热力学性质 .相互作用能量参数ε1 和ε2 分别联系于参数α和 β .令链长N=10 0 ,由这种MonteCarlo方法可得出链的自由能FN(α ,β) ,热容2 FN(α ,β) /2 α和2 FN(α ,β) /2 β ,吸附点平均数〈m〉/N ,最近邻相互作用对平均数〈n〉/N和均方末端距对壁的垂直分量RZ2 .除已有方法由热容数据可绘出α β相图外 ,建议由结构参数〈m〉/N ,〈n〉/N和RZ2 绘制相图 ,并发现二者基本一致 .所得相图表明 ,存在 4个相区 ,分别是解吸 膨胀相 (DE) ,吸附 膨胀相 (AE) ,解吸 紧密相 (DC)和吸附 紧密相 (AC) .在伸展区和塌缩区 ,随着吸附作用的增强 ,会出现吸附相转变 .在解吸区和吸附区 ,随着自相互作用的增大 ,也将出现塌缩相转变 .相图出现了两个三相点 ,即AE AC DC三相点和AE DE DC三相点

ADSORPTION AND COLLAPSE OF A POLYMER CHAIN MODELED BY A SELF-AVOIDING WALK ON THE CUBIC LATTICE

The thermodynamic properties of a polymer chain with a length of N =100 near an adsorbed surface,modeled by a self avoiding walk on the simple cubic lattice in addition to both the vertex plane interaction energy ε 1 and the vertex vertex interaction energy ε 2 ,were calculated by means of the multiple Markov chains method.These two interaction energy terms ε 1 and ε 2 were related to the vertex plane interaction parameter α and the vertex vertex interaction parameter β .The statistical physical quantities obtained by Mont Carlo simulations include the free energy F N(α,β), the heat capacities  2F N(α,β)/ 2α and  2F N(α,β)/ 2β ,the mean number of visits per edge 〈m〉/N ,the mean number of contacts per edge 〈n〉/N and the mean square z component R Z 2 of the end to end distance.It suggests a new method to construct the α β phase diagram by structure parameters 〈m〉/N,〈n〉/N and R Z 2,which is very similar to that obtained by the traditional method using peaks of the heat capacity.The α β phase diagrams indicated that there are four regions of phases,which are desorbed expanded (DE),adsorbed expanded (AE),desorbed compact (DC) and adsorbed compact (AC).In both expanded phase and compact phase,there were adsorption transitions as the surface interaction increased.In both desorbed and adsorbed phases,there were collapse transitions as the nearest neighbor interaction increased.It is also found that there are two triple points in the α β phase diagram,which represent the coexistance of the three phases AE AC DC and AE DE DC,respectively.and AE DE DC,respectively.