物理化学学报 >> 2001, Vol. 17 >> Issue (05): 422-426.doi: 10.3866/PKU.WHXB20010509

研究论文 上一篇    下一篇

端基被平面壁吸附的高分子链的Monte Carlo研究

罗孟波;陈英才;黄建花;许健民   

  1. 浙江大学物理系，杭州　310028;台州师范专科学校物理系，台州　317000;浙江大学化学系，杭州　310028
  • 收稿日期:2000-10-20 修回日期:2001-01-03 发布日期:2001-05-15
  • 通讯作者: 罗孟波 E-mail:mbluo@mail.hz.zj.cn

Monte Carlo Study on Polymer Chain with One End Attached to a Surface

Luo Meng-Bo;Chen Ying-Cai;Huang Jian-Hua;Xu Jian-Min   

  1. Department of Physics,Zhejiang University,Hangzhou　310028;Department of Physics,Taizhou Teacher's College,Taizhou　317000;Department of Chemistry,Zhejiang University,Hangzhou　310028
  • Received:2000-10-20 Revised:2001-01-03 Published:2001-05-15
  • Contact: Luo Meng-Bo E-mail:mbluo@mail.hz.zj.cn

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摘要： 运用Monte Carlo方法研究了端基被无限大平面壁吸附的线型无规飞行链的末端距矢量R的分布P(R)和链的形状，计算了末端距矢量R与z轴（垂直于平板）的夹角θ,链的最大主轴L3与z轴的夹角α,以及R与L3的夹角β的平均值 <θ>、<α>、<β>和各自的分布.得到如下结论： 　　1.端基吸附的高分子链的均方末端距≈(4/3)n，末端距矢量的径向分布为非高斯型，P(R)dR=2A4exp(－A2R2)R3dR，其中n为链长，A2=3/(2n).表明链受到限制后，较小的末端距R的分布概率减小，而较大的R的分布概率增大，导致链变得较为伸展. 　　2.角θ的平均值 <θ>≈45°，分布为P(θ)dθ =sin2θdθ ，表明吸附高分子链的末端极少处于平面附近，即平面对高分子链具有排斥作用 .但角α的平均值 <α>≈55.5°，分布近似为P(α )dα =sinαdα,均与自由链的情况相近，表面平面对最大主轴L3的方向的影响不大. 　　3.端基吸附的高分子链的末端距矢量R与最大主轴L3之间有较强的关联，它们的夹角β的平均值 <β>≈27°，其分布的峰值所对应的β值约为 10°. 　　4.吸附高分子链的形状更偏离球形，形状因子:: 约等于1:2.73:12.5.

关键词: 末端距矢量, 形状因子, 分布函数, 高分子链

Abstract: The endtoend vector distribution P(R) of a linear randomflight polymer chain with one end attached to an infinite large flat surface is investigated by Monte Carlo method.The meansquare endtoend distance can be given by =(4/3)n,and the mean angle by <θ>=45 ,where n is the chain length, θ is the angle between the endtoend vector R and Z axis normal to the surface.The radial distribution is P(R)dR=2A4 exp (－A2R2)R3 dR and the angular distribution isP(θ)dθ =sin 2θdθ ,here A2=3/(2n).The shape factor :: is about 1:2.73:12.5.The distribution of angle ,the angle between the longest principal axis L3 and Z axis,is approximately P(α)dα =sinαdα ,and its mean value <α> is nearly equal to 55.5 .

Key words: End-to-end vector, Shape factor, Distribution function, Polymer Chain excluded volume, real polymer chain