# How does the surface to volume ratio of ions and their distribution in solution compare to that of suspended nanoparticles in nanofluids?

I am interested in understanding the heat transfer capabilities of fluids.

Nano-fluids are suspensions of nanoparticles (1-100nm sized particles) in a base fluid, often water, oil or glycol. These provide anomalously enhanced heat transfer capabilities on account of the surface area to volume ratio of the particles. The percentage of atoms present on the surface of nanoparticles far exceeds that of the percentage of atoms in bulk materials.

Smaller particle sizes (with larger surface areas) have been shown to correlate with higher specific heat capacities (see Ref. 1).

What I would like to understand is how ions are distributed in a solution, and its impact on heat transfer. Are ions in solution smaller than nano-particles? What is the surface area of an ion in solution, and what volume does it occupy?

If I were to dissolve silver nitrate in water, I would get $$\ce{Ag+}$$ and $$\ce{NO3-}$$ ions distributed in the solution. Will they be distributed as aggregates of positively charged silver and negatively charged nitrate ions or as uniformly distributed individual ions?

If the latter, would not these ions have very large surface area to volume ratios, more so than that of nanoparticles? I do not know. Intuitively it seems so. If so, specific heat capacities of solutions should reflect this.

However, this does not appear to be the case. Experimental data and theoretical calculations and models for calculating heat capacities for solutions reflect bulk properties. A common and simple method of estimating specific heat capacity of solutions was proposed by Dimoplon as the sum of the component fractions of individual specific heat capacities:

$$C_p(\textrm{soln}) = w_\textrm{solid} C_p(\textrm{solid}) + w_\textrm{water} C_p(\textrm{water})$$

where $$C_p(\textrm{soln})$$= Heat capacity of the solution, $$C_p(\textrm{solid})$$= Heat capacity of the dissolved solid, $$C_p(\textrm{water})$$ = Heat capacity of water, $$w_\textrm{solid}$$ = Weight percent of dissolved solid, $$w_\textrm{water}$$ = Weight percent of water.

This calculation (which agrees closely enough with experimental data) makes use of specific heat capacities of bulk material, so obviously it appears that the surface area to volume ratio of ions is not very high with respect to nanoparticles.

How then are ions distributed in solution?

I would appreciate if anyone could explain the theory/mechanism behind this or point me to a place where I can obtain a better understanding.

References

1. Madan Singh, Sekhants o'Lara, Spirit Tlali. Effects of size and shape on the specific heat, melting entropy and enthalpy of nanomaterials. Journal of Taibah University for Science. Volume 11, Issue 6, November 2017, Pages 922-929. https://doi.org/10.1016/j.jtusci.2016.09.011
• – Poutnik May 12 at 10:10
• Why would "uniformly distributed individual ions" result in "very large surface area to volume ratios". Specifically, surface and volume of what exactly? – Buck Thorn May 13 at 6:05
• @Buck Thorn: Nano-particles when suspended in a fluid act as excellent heat transfer media because their surface area to volume ratio is extremely high, allowing for heat to be absorbed and circulated by the large number of surface atoms vis à vis volume. When a salt is dissolved in water, it forms ions. Ions individually are smaller than nanoparticles, thus when dissolved in water as non-aggregates they should have larger surface areas. Should they not have better heat transfer capability? Why is this not the case? I would like to understand how salt ions are distributed in a solution. – R2B2 May 13 at 6:58
• Remember that molecules and ions do not have temperature, which is statistical parameter defined for (very) large sets of atoms/molecules/ions only. – Poutnik May 13 at 8:36