Extending the Use of Diffusive Gradients in Thin Films (DGT) to Solutions Where Competition, Saturation, and Kinetic Effects Are Not Negligible

DGT (Diffusion Gradients in Thin films) was designed to sample trace metals in situ at their natural concentrations. The setup and the experimental deployment conditions were established to allow interpretation of a linear accumulation of metal with time, using a simple expression based on a steady-state flux under perfect sink conditions. However, the extension of DGT to a wide range of analytes and its use under varied conditions has shown that, in some situations, these conditions are not fulfilled, so that accumulations with time are nonlinear. Previously, when such curvature was observed, concentrations in solution could not be reliably calculated. Here, we present fundamentally derived equations that reproduce the time accumulation for three situations: (i) kinetic limitations in the binding to the resin, (ii) saturation or equilibrium effects, or (iii) non-negligible competitive effects. We show how the accumulations can be quantified, in terms of the required kinetic and thermodynamic constants, and provide practical guidance for their use to obtain reliable estimates of solution concentrations. Solutions containing Mg or Mn, where all three situations can prevail, are used as examples. Calculated concentrations show reasonable agreement with the experimentally known values and with the results of a numerical model of the system, significantly improving the estimations based on perfect sink conditions. Such an approach opens up the possibility of using DGT more widely in challenging systems and allows DGT data to be interpreted more fully.DGT（薄膜扩散梯度技术，Diffusion Gradients in Thin films）旨在原位采样处于自然浓度水平的痕量金属。该装置的搭建方案与实验部署条件均经过设定，可基于完美汇条件（perfect sink conditions）下的稳态通量（steady-state flux），通过简洁表达式推导出金属随时间线性累积的结论。不过，将DGT拓展至覆盖多种分析物（analytes）的范围并在多变实验条件下应用后发现，部分场景中上述理想条件无法满足，此时金属随时间的累积过程呈现非线性特征。此前当观测到这类累积曲线出现曲率时，无法可靠计算溶液中的金属浓度。本文推导了可复现三种场景下时间累积规律的基础方程：（i）树脂结合过程中的动力学限制；（ii）饱和或平衡效应；（iii）不可忽略的竞争效应。本文还阐明了如何通过所需的动力学与热力学常数量化累积过程，并为实际应用中可靠获取溶液浓度提供实操指南。以同时可能出现上述三种效应的含镁（Mg）或锰（Mn）溶液作为示例开展验证，计算得到的浓度与实验已知值及系统数值模型（numerical model）的结果均具有良好一致性，显著优化了基于完美汇条件的浓度估算方法。该方法为DGT技术在复杂体系中的更广泛应用提供了可能，并可实现对DGT数据更全面的解读。