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

Abstract

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 (ρRs/ρs,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.

Thermodynamic Charge-to-Mass Sensor for Colloids, Proteins, and Polyelectrolytes

“…The thermodynamic salt equilibrium between a macro-ion suspension and a salt solution reservoir has been analyzed 19 for arbitrary suspension and reservoir volumes. Here we will summarize the analysis for the limit of interest in this paper, namely, the sensor limit 19 in which the reservoir volume is much smaller than the suspension volume.…”

“…Construction and performance of the sensor are presented in the Results and Discussion section, including the measurements carried out on the three model systems. First we briefly review in the next section the predicted relation 19 between sensor salt concentration and macro-ion CMR.…”

“…17 Centrifugal analysis is further often hampered by sample turbidity 17,18 and macro-ion size polydispersity, complications that also affect other methods. 13,14 Mentioned obstructions impeding counterion counting can be circumvented, at least according to recent theory, 19 via a thermodynamic approach. The proposal 19 is to gauge counterions far away from unperturbed macro-ions that, consequently, do not affect the counterion counting.…”

“…13,14 Mentioned obstructions impeding counterion counting can be circumvented, at least according to recent theory, 19 via a thermodynamic approach. The proposal 19 is to gauge counterions far away from unperturbed macro-ions that, consequently, do not affect the counterion counting. The crux of the proposed method 19 is that counterion release by macro-ions to their surroundings triggers salt absorption by a sensor, essentially a tiny solution volume connected to the macro-ion suspension via a semipermeable membrane.…”

“…The proposal 19 is to gauge counterions far away from unperturbed macro-ions that, consequently, do not affect the counterion counting. The crux of the proposed method 19 is that counterion release by macro-ions to their surroundings triggers salt absorption by a sensor, essentially a tiny solution volume connected to the macro-ion suspension via a semipermeable membrane. The increase in the sensor's salt concentration is predicted 19 to yield the macro-ion CMR without any adjustable fit parameter.…”