Supplementary material

Plasma Chemistry and Plasma Processing

Enhanced adhesion properties, structure and sintering mechanism of hydroxyapatite coatings obtained by plasma jet deposition

Vukoman Jokanović1(), Miroljub Vilotijević1,Božana Čolović1, Monika Jenko2, Ivan Anžel3, Rebeka Rudolf3,4

1 University of Belgrade, Vinča Institute of Nuclear Sciences, Mike Petrovića Alasa 12-14, 11001 Belgrade, Serbia

2Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia

3University of Maribor, Facultyof Mechanical Engineering, Smetanova 17, 2000 Maribor, Slovenia

4Zlatarna Celje d.d., Kersnikova 19, 3000 Celje, Slovenia

Supplement 1. Parameters for calculation of sintering time

Table S1.1. Initial-stage sintering equations [41, 42]

Mechanism of matter transfer / The values of coefficients in equations
m / n / C(T)
Volume diffusion / 5 / 3 / 80DvγΩ/kT
Grain boundary diffusion / 6 / 4 / 20δbDbγΩ/kT
Surface diffusion / 7 / 4 / 56δsDsγΩ/kT

Table S1.2. Numerical data used for calculation of sintering time of HA [41]

Parameters / Numerical data
θ, K/s / 0.17
D, m / 6·10-8
Dv0, m2/s / 5·10-11
δbDb, m3/s / 4·10-21
δsDs, m3/s
Qv, J/mol / 1.4·105
Qb, J/mol / 8.4·104
Qs, J/mol
Surface tension, γ, J/m2 / 4.67·10-2
Atomic volume, Ω, m3 / 5.28·10-28

Supplement 2. Calculation of the particles velocity and residence time inside of plasma torch

For the calculation of the particles velocity and residence time, the velocity of carrier gas in the hose should be determined firstly using eq.(S2.1) [43]:

, (S2.1)
where qcg is flow rate and Dhis hose diameter.

Time residence in hose is given by the following equation:

, (S2.2)

where Lh is hose length and k is defiend as:

, (S2.3)

where ηcg is dynamic viscosity of the carrier gas, ρp is density of particle material and dp is particle diameter. At the end of the hose the velocity of particles is:

, (S2.4)

while the residence time of the particle in the injector ti is:

, (S2.5)

where Li is injector length and Ui-cg is the carrier gas velocity in the injector given by:

, (S2.6)

where Di is injector diameter.

Finally, initial velocity of the particle in plasma jet is:

. (S2.7)

After replacement the values of hose diameter Dh=3 mm and flow rate of Ar carrier qcg=38.5 l/min in eq.(S2.1) the velocity of carrier gas inside of hose was calculated to be 91 m/s. Taking into account the values of dynamic viscosity of carrier gas at temperature close to 10000 K and higher: ηcg=2.5·10-4 kg/m·s, particle density - the density of sprayed spherical agglomerates ρp=2.52 g/cm3 and particle diameter dp=90 μm, constant k was obtained using eq.( S2.2). Using so obtained value for k and previously obtained value for velocity of carrier gas inside of hose, for the hose length of 1.5 m the obtained residence time of particle in the hose was 1.2·10-5 s. The residence time of particle in the injector, obtained using eq.(S2.5), was almost the same. The initial and final velocities of particle in the plasma jet were almost equal, because the correction values obtained using eq. (S2.5) and (S2.7) can be neglected.