发表机构
National Institute for Materials Science (NIMS); University of Tsukuba（物质材料研究机构; 筑波大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对双层微悬臂梁瞬态弯曲中涂层厚度增加导致扩散与粘弹性松弛耦合的问题，提出专用有限元求解器，揭示厚度方向结构对瞬态响应的关键影响，并指出单一涂层无法同时优化稳态信号与瞬态过冲。
AI 中文摘要
静态模式微悬臂梁传感器通过双层梁的弯曲来检测化学分析物，其中聚合物涂层在吸收分析物后发生溶胀。瞬态弯曲通常被建模为涂层均匀吸收分析物，这对于薄涂层是足够的，但随着涂层增厚以及移动的扩散前沿与深度相关的粘弹性松弛耦合，该模型失效。我们通过一个专门构建的有限元求解器解决了这种耦合，该求解器每个时间步仅需一次线性求解，并展示了厚度方向的结构以均匀吸收模型无法捕捉的方式控制瞬态响应。该求解器经过已发表解析解的验证，能够重现从扩散相对于松弛较快时的显著曲率过冲（高达稳态值的近两倍）到扩散较慢时的单调上升的完整转变。在解析解无法达到的中间厚度区域，使稳态信号最大化的厚度与保持瞬态过冲的厚度受不同物理机制支配，一种为几何机制，另一种为动态机制，因此单一涂层无法同时优化两者。此外，过冲在现实表面传质阻力下仍然存在，这验证了全文所使用的理想化表面边界条件。
英文摘要
Static-mode microcantilever sensors detect chemical analytes through the bending of a bilayer beam whose polymer coating swells upon absorption. The transient bending is usually modeled as if the coating absorbed analyte uniformly, which is adequate for thin coatings but breaks down as the coating thickens and a moving diffusion front couples to depth-dependent viscoelastic relaxation. We resolve this coupling with a purpose-built finite-element solver requiring only one linear solve per time step, and show that the through-thickness structure controls the transient response in ways uniform-uptake models cannot capture. Verified against a published analytical solution, the solver reproduces the full transition from a pronounced curvature overshoot (up to nearly twice the steady-state value) when diffusion is fast relative to relaxation to a monotonic rise when it is slow. In the intermediate-thickness regime the analytical solution cannot reach, the thickness maximizing the steady-state signal and the thickness preserving the transient overshoot are governed by different physics, one geometric and one dynamic, so one coating cannot be optimized for both. The overshoot further survives realistic surface mass-transfer resistance, justifying the idealized surface boundary condition used throughout.
Comments26 pages, 8 figures
