Popova Hristina, Milchev Andrey
Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.
J Chem Phys. 2008 Dec 7;129(21):215103. doi: 10.1063/1.3028055.
Adsorption of self-avoiding tethered membranes of hexagonal orientation on a solid impenetrable plane is studied by means of Monte Carlo computer simulations of a coarse-grained continuum model, varying the membrane linear size L and the strength epsilon of the short-range attractive wall potential. A second-order adsorption transition is found to take place at a critical strength of the adsorption potential epsilon(c), as predicted earlier for binding manifolds in the so-called strong fluctuating regime. By means of finite-size scaling analysis for membranes of size 5<or=L<or=30, containing 61<or=N<or=2611 monomers, we find that the critical crossover exponent for adsorption phi approximately 0.60+/-0.01. Thus the fraction m of adsorbed segments at epsilon(c) is found to scale as m proportional to N(phi-1)=N(-0.4). The membrane thickness lambda(min) decreases with growing strength epsilon of the adhesive potential as lambda(min) proportional to mid R:epsilon/epsilon(c)-1mid R:(-psi), where psi approximately 0.58+/-0.02. The monomer density profiles of adsorbed membranes decay exponentially with the distance z from the substrate rho(z) proportional to exp[-(z/xi)], where the correlation length xi proportional to mid R:epsilon/epsilon(c)-1mid R:(-psi) with psi approximately 0.70+/-0.01. We also investigate the kinetics of adsorption of a polymerized membrane in the regime of strong adsorption and find that the order parameter variation with elapsed time during the adsorption process is given by a power law m(t) proportional to t(omega), where omega approximately 1.0, regardless of the strength of the adsorbing potential epsilon>>epsilon(c). The characteristic time for complete adsorption in this regime scales as tau(ads) proportional to L(2). Regarding the strength epsilon of the substrate potential, tau(ads) is found to diminish linearly as the respective equilibrium value of the order parameter increases. A simple analytic model yields also tau(ads) proportional to L(2) while suggesting that the process of adsorption cannot be identified by simple "unrolling."
通过粗粒化连续介质模型的蒙特卡罗计算机模拟，研究了具有六边形取向的自回避拴系膜在固体不可穿透平面上的吸附情况，改变了膜的线性尺寸(L)和短程吸引壁势的强度(\epsilon)。如先前针对所谓强波动 regime 中的结合流形所预测的那样，发现二阶吸附转变发生在吸附势(\epsilon(c))的临界强度处。通过对尺寸为(5\leq L\leq30)、包含(61\leq N\leq2611)个单体的膜进行有限尺寸标度分析，我们发现吸附的临界交叉指数(\phi\approx0.60\pm0.01)。因此，发现在(\epsilon(c))处吸附链段的分数(m)按(m\propto N^{(\phi - 1)} = N^{-0.4})标度。膜厚度(\lambda(min))随着粘附势强度(\epsilon)的增加而减小，即(\lambda(min)\propto |R:\epsilon / \epsilon(c) - 1|^{R:(-\psi)})，其中(\psi\approx0.58\pm0.02)。吸附膜的单体密度分布随离基底的距离(z)呈指数衰减，(\rho(z)\propto \exp[-(z / \xi)])，其中关联长度(\xi\propto |R:\epsilon / \epsilon(c) - 1|^{R:(-\psi)})，(\psi\approx0.70\pm0.01)。我们还研究了强吸附 regime 中聚合膜的吸附动力学，发现吸附过程中序参量随时间的变化由幂律(m(t)\propto t^{\omega})给出，其中(\omega\approx1.0)，与吸附势强度(\epsilon\gg\epsilon(c))无关。在此 regime 中完全吸附的特征时间按(\tau(ads)\propto L^{2})标度。关于基底势的强度(\epsilon)，发现(\tau(ads))随着序参量的相应平衡值增加而线性减小。一个简单的解析模型也得出(\tau(ads)\propto L^{2})，同时表明吸附过程不能通过简单的“展开”来识别。
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