Five commercial tattoo inks of different colorations (black,
blue,
red,
yellow,
white) were subjected to measurement of electric and magnetic parameters and were then let dry,
in order to measure the same parameters on pigments alone.
The electric conductivity measurement on liquid inks was carried out through an “Agilent” electrical impedance analyzer combined with a "16452A Liquid Test Fixture".
The 16452A employs the parallel plate method,
which sandwiches the liquid material between two electrodes to form a capacitor.
An impedance analyzer is then used to measure the capacitance created from the fixure.
The described fixture was filled with different inks,
so impedance was measured and memorized as a function of the frequency (ranging between 40 Hz and 110 Hz).
The measurements were then analyzed by a software codified in Python language and a first estimation of electric conductivity was delivered.
This estimation was obtained by assimilating the ink’s impedance beahaviour to the one of a parallel RC circuit.
Electric conductivity σ was therefore obtained in (S/m) as :
σ = ϵ0 / RL C0
-ϵ0 represents the in vacuum-electric permittivity
-RL represents the ink’s paralel resistance at a proper frequency,
measured in Ohm
-C0 represents the capacity of the empty fixture,
measured in Farad
A second estimation of the electric conductivity was obtained by considering an equivalent circuit,
more complex than the paralel RC.
This circuit permits to take into account “non ideal conditions” effects,
such as “bouble layer” effect,
polarization and electric charge resistance and diffusion phenomena.
The circuit parameters were elicited through a process of fitting with the measured impedance curves.
The value of electric conductivity was obtained similarly to the previous case,
using the RL value derived from the fitting process.
Magnetic properties measurements of the five inks were performed through a “vibrating-sample magnetometer” (VSM) .Five different specimens were obtained by filling special capsules with the inks.
Specimens’ magnetic moment was measured by performing a single static magnetic field cycle within a ± 1 T interval.
A preliminary measurement of the empty capsule enabled the examinator to purify the analysis performed on liquids from the effects due to the case.
Magnetic moment measured during the cycle was then normalized for the mass of ink present in the specimen,
whose measurement was carried out through a precision balance and before the measurement of magnetic moment.
In a second moment,
the five inks were subjected to a process of exsiccation by using an electric oven in order to extract the pigments.
Impedance and magnetic properties of ink powders so obtained,
were measured.
Impedance of pigments was measured through an Agilet impendance analyzer combined with a "16451B Dielectric Test Fixture" and memorized as a function of the frequency (ranging between 40 Hz and 15 MHz).
As for the liquids,
values of electric conductivity were obtained in reference to in vacuum-capacity C0.
An estimation of the relative electric permittivity was also obtained through in vacuum-capacity as it follows:
ϵr= CL / C0
Where CL represents the measured powder’s capacity.
Methodologies adopted for the magnetic characterization of pigments completely reflect the ones exposed above for liquid inks.
Finally thermic effects of pigments were mathematically evaluated through specific calculation codes,
by utilizing a cubic sample with magnetic and electric properties similar to the ones of human epithelial tissue.
One face of the cube was partially covered with a 1 mm layer of a material carrying the most unfavourable properties among the ones measured in all pigments.
The sample was irradiated with a “Birdcage” type antenna,
at a frequency of 128 MHz (corresponding to a 3T MR scanner) and the SAR distribution was obtained by solving the related electromagnetic field problem.
This distribution was used as source of the thermic problem in order to determine temperature increment through Pennes equation.