# 8.1 Measuring the specific surface area of nanoparticle suspensions  (Page 3/4)

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## Calculations

From an atomic stand point, T 1 relaxation occurs when a precessing proton transfers energy with its surroundings as the proton relaxes back from higher energy state to its lower energy state. With T 2 relaxation, apart from this energy transfer there is also dephasing and hence T 2 is less than T 1 in general. For solid suspensions, there are three independent relaxation mechanisms involved:-

1. Bulk fluid relaxation, which affects both T 1 and T 2 relaxation.
2. Surface relaxation, which affects both T 1 and T 2 relaxation.
3. Diffusion in the presence of the magnetic field gradients, which affects only T 2 relaxation.

These mechanisms act in parallel so that the net effects are given by [link] and [link]

$\frac{1}{{T}_{2}}=\frac{1}{{T}_{2,\text{bulk}}}+\frac{1}{{T}_{2,\text{surface}}}+\frac{1}{{T}_{2,\text{diffusion}}}$
$\frac{1}{{T}_{1}}=\frac{1}{{T}_{1,\text{bulk}}}+\frac{1}{{T}_{1,\text{surface}}}$

The relative importance of each of these terms depend on the specific scenario. For the case of most solid suspensions in liquid, the diffusion term can be ignored by having a relatively uniform external magnetic field that eliminates magnetic gradients. Theoretical analysis has shown that the surface relaxation terms can be written as [link] and [link] , where ρ = surface relaxivity and s/v = specific surface area.

$\frac{1}{{T}_{1,\text{surface}}}={\rho }_{1}\left(\frac{S}{V}{\right)}_{\text{particle}}$
$\frac{1}{{T}_{2,\text{surface}}}={\rho }_{2}\left(\frac{S}{V}{\right)}_{\text{particle}}$

Thus one can use T 1 or T 2 relaxation experiment to determine the specific surface area. We shall explain the case of the T 2 technique further as [link] .

$\frac{1}{{T}_{2}}=\frac{1}{{T}_{2,\text{bulk}}}+{\rho }_{2}\left(\frac{S}{V}{\right)}_{\text{particle}}$

One can determine T 2 by spin-echo measurements for a series of samples of known S/V values and prepare a calibration chart as shown in [link] , with the intercept as $\frac{1}{{T}_{2,\text{bulk}}}$ and the slope as ${\rho }_{2}$ , one can thus find the specific surface area of an unknown sample of the same material.

## Sample preparation and experimental setup

The sample must be soluble in the solvent. For proton NMR, about 0.25-1.00 mg/mL are needed depending on the sensitivity of the instrument.

The solvent properties will have an impact of some or all of the spectrum. Solvent viscosity affects obtainable resolution, while other solvents like water or ethanol have exchangeable protons that will prevent the observation of such exchangeable protons present in the solute itself. Solvents must be chosen such that the temperature dependence of solute solubility is low in the operation temperature range. Solvents containing aromatic groups like benzene can cause shifts in the observed spectrum compared to non-aromatic solvents.

NMR tubes are available in a wide range of specifications depending on specific scenarios. The tube specifications need to be extremely narrow while operating with high strength magnetic fields. The tube needs to be kept extremely clean and free from dust and scratches to obtain good results, irrespective of the quality of the tube. Tubes can cleaned without scratching by rinsing out the contents and soaking them in a degreasing solution, and by avoiding regular glassware cleaning brushes. After soaking for a while, rinse with distilled water and acetone and dry the tube by blowing filterened nitrogen gas through a pipette or by using a swob of cotton wool.

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