Membrane Potential - McDaniel

The difference in the internal potential between the two solution phases when electrolyte solutions of different composition are in contact through a membrane. Membrane potential has been observed for various microporous membranes (parchment paper, collodion membranes, plastic membranes, gels, microporous silicates, biological membranes, etc.) and membranes of liquid layers that do not mix with the adjacent solution. Formally, the membrane potential can be considered as a special case of the liquid junction potential difference to explain its potential characteristics. According to this idea, the membrane potential E _m is given by the following equation.

Here, t _i ' is the transport number of ion i in the membrane, z _i is the charge of ion i (including sign), a _i ^Ⅰ and a _i ^Ⅱ are the activities of ion i in solution phase I and II, respectively, R is the gas constant, T is the absolute temperature, and F is the Faraday constant. There are two types of membrane potential: (1) concentration membrane potential and (2) heterogeneous ion membrane potential or the more general multi-ion membrane potential.
(1) The concentration membrane potential is the membrane potential that occurs when the same electrolyte solution with different concentrations is placed on both sides of a membrane. If the transport numbers of cations and anions in the membrane are t ₊ ' and t- _' , respectively, and it is assumed that they both show constant values ​​in the membrane, the concentration membrane potential can be immediately given by the above general formula as follows:

When a membrane is selectively permeable to ions, the transport number in the membrane differs significantly from that in the solution phase. For example, in an ideal selectively cation-permeable membrane,

t ₊ ′ = 1, t ₋ ′ = 0
Conversely, in the case of an anion-permeable membrane,

t ₊ ′ = 0, t ₋ ′ = 1
Therefore, the membrane potential of an ideal cation-permeable membrane is

In the case of an ideal anion-permeable membrane,

The following relationship holds. The membrane potential expressed by these two equations shows similar properties to the equilibrium electrode potential for membrane-permeable ions. Therefore, the membrane potential when the electrolyte concentration in one solution phase is constant acts reversibly on the activity of cations or anions in the other phase, and this property can be utilized to create so-called "membrane electrodes." Currently, membrane electrodes that act selectively for various cations (alkali metal and alkaline earth metal ions, NH ₄ ⁺ , etc.) and anions (F ^- , NO ₃ ^- , ClO ₄ ^- , CH ₃ COO ^- , etc.) have been created and are widely used for the analysis and activity measurement of these ions.
(2) [See alternative term] Membrane equilibrium

Source: Morikita Publishing "Chemical Dictionary (2nd Edition)" Information about the Chemical Dictionary 2nd Edition

膜を介して，組成の異なる電解質溶液を接触させたときの，両溶液相の内部電位の差．膜電位は各種の微細孔性膜(パーチメント紙，コロジオン膜，プラスチック膜，ゲル，細孔性ケイ酸塩，生体膜など)および隣接する溶液とまじり合わない液体層の膜について観測されている．膜電位は形式的には液間電位差の特別な場合と考えることにより，その電位特性を説明することができる．この考えによれば，膜電位 E_m は次式で与えられる．

ここで，t_i′はイオンiの膜中における輸率．z_i はイオンiの電価(符号を含む)，a_i^Ⅰおよび a_i^Ⅱはそれぞれイオンiの溶液相ⅠおよびⅡにおける活量であり，Rは気体定数，Tは絶対温度，Fはファラデー定数である．膜電位には(1)濃淡膜電位と(2)異種イオン間膜電位あるいはもっと一般的な多種イオン間膜電位がある．
(1)濃淡膜電位は膜の両側で濃度が異なる同種の電解質溶液をおいたときに生じる膜電位である．膜中におけるカチオンおよびアニオンの輸率をそれぞれt_＋′およびt_－′とし，それらはいずれも膜中一定値を示すものと仮定すると，濃淡膜電位は上記一般式よりただちに次のように与えられる．

膜がイオンに対して選択的透過性をもつ場合には，膜中輸率は溶液相中の値といちじるしく異なり，たとえば，理想的な選択的カチオン透過性の膜では

t_＋′ ＝ 1，t_－′ ＝ 0
となり，逆にアニオン透過性の膜では

t_＋′ ＝ 0，t_－′ ＝ 1
となる．したがって，理想カチオン透過膜の膜電位は，

で与えられ，理想アニオン透過膜の場合には，

の関係が成立する．これら二つの式で表される膜電位は，膜透過性のイオンについての平衡電極電位と類似の性質を示す．したがって，一方の溶液相の電解質濃度を一定にした場合の膜電位は，他方の相中のカチオンあるいはアニオンの活量に可逆的に作用するので，この特性を利用して，いわゆる“膜電極”をつくることができる．現在，種々のカチオン(アルカリ金属およびアルカリ土類金属イオン，NH₄^＋など)およびアニオン(F^－，NO₃^－，ClO₄^－，CH₃COO^－など)に対して選択的にはたらく膜電極がつくられており，これらイオンの分析に，また活量の測定に広く用いられている．
(2)[別用語参照]膜平衡

出典　森北出版「化学辞典（第2版）」化学辞典 第2版について　情報