A thermodynamic gauge for mobile counter-ions from colloids and nanoparticles

Albert P. Philipse*, Bonny W M Kuipers, Agienus Vrij

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


A thermodynamic equilibrium sensor is proposed that measures the ratio of the number of elementary charges z to the mass m of charged solutes such as charged colloids and nanoparticles. The sensor comprises a small, membrane-encapsulated salt solution volume that absorbs neutral salt molecules in response to the release of mobile counter-ions by charge carriers in the surrounding suspension. The sensor state emerges as a limiting case of the equilibrium salt imbalance, and the ensuing osmotic pressure difference, between arbitrary salt and suspension volumes. A weight concentration of charge carriers c is predicted to significantly increase the sensor's salt number density from its initial value ρs,0 to ρRs, according to the relation (ρRss,0)2 - 1 = zc/mρs,0, under the assumption that the mobile ions involved in the thermodynamic sensor-suspension equilibrium are ideal and homogeneously distributed.

Original languageEnglish
Pages (from-to)103-121
Number of pages19
JournalFaraday discussions
Publication statusPublished - 1 Aug 2015


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