双电层和薄膜电容器理论模型中的负电容及其不稳定性
Negative capacitance and related instabilities in theoretical models of the electric double layer and membrane capacitors
摘要：
各种模型导致预测的负电容，C，简要回顾。讨论了它们与电气控制性质的关系。我们再次确认，计算的双电层电容可以是负的S-控制下-一个人工构造，需要均匀分布的电极表面电荷密度，S。结果表明，即使对于具有严格正扩散层电容的局部统计离子模型，离子和电子贡献的联合弛豫也可以导致C<0。然而，实际上，在隔离电池研究中，只有总电荷q（或平均表面电荷密度S）可以通过实验固定（q控制）。对于在S控制下C变为负值的那些S，向q控制的转变（即，放宽横向电荷密度分布，将其平均值固定到S）导致均匀分布的不稳定性和向非均匀相的转变。作为一个例子，“膜电容器”模型进行了讨论。这个完全可解的模型，允许均匀和不均匀的双电层松弛，有助于证明发病和一些重要的功能的不稳定性。进一步发展的前景进行了简要讨论。
英文摘要：
Various models leading to predictions of negative capacitance, C, are briefly reviewed. Their relation to the nature of electric control is discussed. We reconfirm that the calculated double layer capacitance can be negative under S-control - an artificial construct that requires uniform distribution of the electrode surface charge density, S. It is shown that the combined relaxation of the ionic and electronic contributions can result in C<0 even for the local statistical ionic models with strictly positive diffuse layer capacitance. In reality, however, only the total charge q (or the average surface charge density S) can be experimentally fixed in isolated cell studies (q-control). For those S where C becomes negative under S-control, the transition to q-control (i.e. relaxing the lateral charge density distribution, fixing its mean value to S) leads to instability of the uniform distribution and a transition to a non-uniform phase. As an illustration, a "membrane capacitor" model is discussed. This exactly solvable model, allowing for both uniform and inhomogeneous relaxation of the electrical double layer, helps to demonstrate both the onset and some important features of the instability. Perspectives for further development are discussed briefly.
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