Based on nonlinear Poisson-Boltzmann equation (NLPB) and flexoelectric theory of liquid crystal thin films, with the help of Fogolari's correct formula, a nonlinear multiscale relation among single-stranded DNA (ssDNA) molecule structure feature, salt solution concentration and biofilm e-lectrostatic potential, chip macroscopic deformation is formulated. The flexoelectric coefficient is obtained by curve fitting based on existing experimental data. The linear and nonlinear predictions for biofilm electrostatic potential and chip deformation are compared to validate the present nonlinear multiscale relation. The influences of DNA fragment length, packing density on chip deformation are also investigated. The results show that chip deformation increase with the enhancement of DNA fragment length and packing density.%基于非线性Poisson-Boltzmann (NLPB)方程和液晶薄膜弯电理论,利用Fogolari修正公式,建立了单链DNA (ssDNA)分子结构特征、溶液离子浓度等因素与生物膜电势、芯片宏观变形之间的非线性多尺度关系.结合现有的实验数据,拟合了单链DNA生物薄膜的弯电系数,并将生物膜电势分布及芯片变形的线性预测和非线性预测进行了比较,阐明了非线性多尺度关系的有效性.考察了DNA链片断数和封装密度等因素对芯片变形的影响.结果表明:随着DNA链片断数和封装密度的增加,芯片变形逐渐增加.
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