关键词: 有效电荷/
剪切模量/
孔隙/
胶体晶体
English Abstract
Theoretical improvement on the determination of effective elasticity charges for charged colloidal particles
Wang Lin-Wei1,2,Xu Sheng-Hua2,3,
Zhou Hong-Wei2,
Sun Zhi-Wei2,
Ouyang Wen-Ze2,
Xu Feng1
1.School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China;
2.Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
3.School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11302226, 11572322, 11672295).Received Date:22 November 2016
Accepted Date:17 December 2016
Published Online:05 March 2017
Abstract:According to the existing shear modulus-pair potential relationship model for colloidal crystal comprised of highly charged colloidal particles, the calculated shear moduli of colloidal crystals are much larger than the measured values by the torsional resonance spectroscopy (TRS). Moreover, by using the relationship model, the effective surface charge of colloidal particles, obtained by fitting values of shear moduli measured by TRS (effective elasticity charge), is smaller than that obtained through the experimental method of conductivity-number density relationship (effectively transported charge). So far there has been no practical explanation to this discrepancy. Our analysis shows that this discrepancy is because the existing relationship model is for the perfect crystals and does not include the defects such as voids which can result in the decrease of mechanical properties of materials. The existing shear modulus-pair potential model will be improved by introducing the effect of voids, which is inspired from the Gibson-Ashby model in the study of cellular solid. The Yukawa potential, which considers Coulomb repulsions between colloidal particles and is usually used in the model expressions, will be substituted by Sogami-Ise potential, which considers a long-range attraction in addition to that Coulomb repulsions and accepts the existence of voids inside the colloidal crystals. For five different kinds of highly charged colloidal particles, the shear moduli with different volume fractions are measured by TRS. Then the fitted effective surface charges using the original and improved model respectively are compared with each other. It can be concluded that the effective elastic charge obtained by the improved model is more suitable and much closer to the renormalized charge obtained from Alexander's method. It is also clear that neither the effectively transported charge nor the Alexander's renormalized charge can be used to evaluate the shear moduli of colloidal crystals with voids inside. These results can also let us further understand and use the effective surface charge in the colloid studies.
Keywords: effective charge/
shear modulus/
voids/
colloidal crystal
