P - Technische Universiteit Eindhoven

8. NMR combined with accelerated weathering 94
In case of hydrated crystals, the crystallization pressure has to be corrected and is
given by [42]:
P c = RT [ ( ) ( c N 1 − (N − 1)cMH2 O
ln
· 1 + cM ) νw
]
H 2 O
, (8.2)
V m c s 1 − (N − 1)c s M H2 O 1 + c s M H2 O
where M H2 O is the molar mass of water, ν w is the hydration factor (for heptahydrate
ν w = 7 and for decahydrate ν w = 10, i.e., the amount of water molecules incorporated
into one chemical unit of the crystal). Here the additional term takes into account the
excess of supersaturation caused by consumption of water from a solution by the growth
of a hydrated crystal.
The crystallization pressure is determined directly by the crystalline phase that is
formed via c s . For example, according to the phase diagram given in figure 8.1, for a temperature
of 22 ◦ C the ratio c t s/c d s ≈ 2.37, where c t s and c d s are the solubility concentrations
for thenardite and decahydrate, respectively. Hence, if a transformation from thenardite
to decahydrate occurs, the ratio c/c s will increase and as a result a thermodynamic crystallization
pressure will be generated.
The macroscopic poromechanical crystallization pressure can be evaluated by analyzing
the actual expansion of a sample induced by salt crystallization. Assuming that
the crystals are uniformly distributed within the porous material and there is no preferred
direction of crystal growth in the pores, the poromechanic crystallization pressure, P m ,
for a saturated sample in the isothermal case, is given by [42],:
∫
P m =
3K
dε, (8.3)
bϕ
where P m is the pore pressure exerted by confined crystals in the porous material, ε [µm] is
the expansion of a sample resulting from salt crystallization, K [GPa] is the bulk modulus,
b is the Biot-coefficient, and ϕ (0 < ϕ < 1) is the pore filling coefficient. This pore filling
coefficient can be directly evaluated from the concentration (see the appendix).
8.3 Experimental setup
In order to find out which crystallization pathway in sodium sulfate weathering generates
most damage we have performed a weathering experiment in a Nuclear Magnetic Resonance
(NMR) setup. We use NMR in combination with an optical displacement sensor
for measuring simultaneously both the concentration of the solution in the samples and
the expansion of samples caused by crystallization. The experimental setup is presented
in figure 8.3. The NMR system used in this study contains an electromagnet generating
a static magnetic field of 0.78 T. This setup has the possibility to measure quantitatively
both the amount of H and Na nuclei in a sample. No signal from Na and H nuclei incorporated
into the crystals or the porous material itself is obtained. Hence the measured
signal can be directly related to the concentration of a solution in the material, giving the
possibility to measure this concentration non-destructively. A more detailed explanation
of the NMR setup can be found in [40] and [57].
The sample is centered with PTFE rings, which allow the sample to expand almost
frictionless. A fiber-optic displacement sensor is used to measure the length of the sample.