## 4 Conclusions  
The research described in this paper shows that the hydrogenation of the grain boundaries of PCD films is directly related to the density of dangling bonds per unit volume. The H atom concentration measured by SIMS was in accordance with the calculated dangling bonds available in the grain boundaries. The simplifying assumptions are that there are two dangling bonds per unit cell at the grain boundary, and the PCD films are homogenous (same grain size throughout the film), providing a first approximation regarding the makeup of the grain boundaries. The surface concentration of the dangling bonds was calculated to be 1.56 \(\times\) 10\({}^{15}\) sites/cm\({}^{2}\). The hypothesis to explain the results is that the surface of the diamond crystalline grains forms either a C-H bond or C=C bond The C=C bond is formed between two non passivated C atoms within the same crystalline grain at the boundary or between two adjacent crystallites at the boundary. The combination of the C-H and C=C bonded atoms at the grain boundaries, randomly located, could produce the characteristic Raman spectrum. (There is no room for strands of TPA molecules to be present in the interface). From the model presented, it is expected that the UNCD films would have a larger concentration of v1 and v2 signals. However, UNCD growth complexity allows for the formation of disordered and graphitic carbon between the cluster growths, represented as D* and G peaks in the Raman spectrum. This effect will have to be further investigated with HRTEM. The grain boundary nature (or make up), regardless of grain size is similar for all PCD films in the studies. Electrical measurements in an MCD film showed that the grain boundaries are conductive. Conductive atomic force microscopy (CAFM) measurements showed that electrical conduction through PCD films is mainly controlled by the grain boundaries, most probably due to electron insertion into the gran boundaries via H atom bonding to dangling bonds of C atoms, resulting in the release of electrons. UPS measurements showed that the work function for the electrons in the PCD films is independent of grain size, reinforcing the idea that the makeup of the grain boundaries is the same for all PCD films.  
Conceptualization, E.I.d.O. and J.J.A.-P.; methodology, E.I.d.O., J.J.A.-P., F.P.W., J.F.V., S.G.-H. and Y.K.; formal analysis, E.I.d.O., J.J.A.-P., F.P.W. and O.A.; investigation, E.I.d.O., J.J.A.-P. and S.G.-H.; data curation, E.I.d.O., J.J.A.-P. and J.F.V.; writing--original draft preparation, E.I.d.O., J.J.A.-P. and F.P.W.; writing--review and editing, S.G.-H., D.B.-M. and O.A.; supervision, Y.K., D.B.-M. and O.A.; funding acquisition, E.I.d.O., J.J.A.-P., D.B.-M. and O.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Consejo Nacional de Ciencia y Tecnologia-Mexico (CONACYT) and the Secretaria Nacional de Ciencia y Tecnologia-Panama (SENACYT).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **B\({}_{\text{E}}\) (eV)** & **E\({}_{\text{cut-off}}\) (eV)** & **\(\Phi\) (eV)** \\ \hline A & 3.3 & 16.6 & 4.6 \\ B & 4.3 & 16.7 & 4.5 \\ C & 4.9 & 16.6 & 4.6 \\ D & 4.6 & 15.8 & 5.5 \\ E & 5.0 & 16.1 & 5.2 \\ F & 5.2 & 16.4 & 4.8 \\ G & 5.1 & 15.9 & 5.3 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fermi energy, low energy cutoff, and work function calculations from Figure 9 for all the PCD films.  
**Acknowledgments:** [PERSON] acknowledges support from the University of Texas at Dallas through his Distinguished Endowed Chair Professor position. This research was made possible in part thanks to the support of the Sistema Nacional de Investigacion (SNI) of SENACYT, Panama, awarded to Elida de Obaldia, and the Vicerrectoria de Investigacion Postgrado y Extension de la Universidad Tecnologica de Panama. [PERSON] acknowledges the support of CONACYT-FORDECyT through the project FORDECYT-297497.  
**Conflicts of Interest:** The authors declare no conflict of interest.