基于平均相位差法的液体离子竞争分析

Liquid Ion Competition Analysis Based on Average Phase Difference Method

摘要: 本研究基于数字全息显微技术，利用平均相位差法实现混合无机盐溶液折射率的高精度测量，旨在探究不同电解质溶液在混合过程中折射率变化是否遵循线性加权规律并验证是否存在离子拮抗效应。通过搭建透射式离轴数字全息系统，并设计等体积变浓度、等浓度变体积及不同离子体系三类实验，系统测量NaCl、KCl、CaCl₂等溶液的混合折射率，同时构建体积分数加权、摩尔分数加权与浓度加权三种理论模型进行预测比较。结果表明：体积分数加权模型的预测结果与实测值最为吻合，是预测混合折射率最稳定可靠的模型；摩尔分数加权次之，在含强水化或高价离子的体系中出现一定偏差；浓度加权误差最大，在等浓度变体积实验中甚至完全失效。部分体系(如NaCl-CaCl₂)出现明显非线性或折射率负偏差，推测源于离子竞争、水化壳层结构变化和活度系数的浓度依赖性。本研究揭示了多盐混合体系折射率的非理想行为及其机制，为电解质溶液折射率模型建立和数字全息液体检测技术的拓展应用提供重要参考。

Abstract: This study employs digital holographic microscopy technology to achieve high-precision measurement of refractive indices in mixed inorganic salt solutions using the average phase difference method. The objective is to investigate whether refractive index changes during electrolyte solution mixing follow linear weighting patterns and to verify the existence of ion antagonism effects. By constructing a transmissive off-axis digital holographic system and designing three experimental categories—equal volume with variable concentration, equal concentration with variable volume, and different ion systems—the refractive indices of mixed solutions such as NaCl, KCl, CaCl₂, were systematically measured. Concurrently, three theoretical models (volume fraction weighting, molar fraction weighting, and concentration weighting) were established for predictive comparison. Results indicate that the volume fraction weighting model exhibits the highest agreement with measured values, demonstrating the most stable and reliable prediction for mixed refractive indices. Molar fraction weighting follows, showing deviations in systems containing strong hydration or high-valence ions. Concentration weighting demonstrates the largest errors, even becoming completely invalid in experiments with equal concentration and variable volume. Some systems (e.g., NaCl-CaCl₂) exhibit significant nonlinear behavior or negative refractive index deviations, which are hypothesized to originate from ion competition, hydration shell structure changes, and concentration-dependent activity coefficients. This study elucidates the non-ideal behavior of refractive indices in multi-salt mixed systems and its underlying mechanisms, providing critical references for refractive index model development in electrolyte solutions and the expanded application of digital holographic liquid detection technology.