## 4 Discussion  
Comparing the data on average specific conductivity \(\sigma\)(e) (Figure 4) and on microstructure (Figure 5, Table 2) of silver NP arrays sintered by four types of laser radiation, we assume that the best conductivity areas in all cases are non-porous external layers with thickness in the range 0.5-1 \(\upmu\)m. The formed contacts between crystallites and their large size values indicate the better conductivity of pore-free external layers in comparison with porous zones. In contrast, in porous zones, silver crystallites are connected in agglomerates with conductive contacts inside, between which there are many submicron pores, potentially reducing conductivity. Particularly this occurs in porous zones of samples sintered by pulsed laser radiation (Figure 5,e). Assuming that the specific conductivities in the porous and pore-free zones of the sample are significantly different and homogeneous, the average specific conductivity for the entire sample is expressed by the following equation:  
\[\sigma=\frac{\left(S_{np}\sigma_{np}+S_{p}\sigma_{p}\right)}{S_{0}}, \tag{1}\]  
where S\({}_{\text{np}}\), S\({}_{\text{p}}\), S\({}_{0}\)--the cross-sectional areas for the pore-free and porous zones and the cross-section for the whole line, respectively, \(\sigma_{\text{np}}\), \(\sigma_{\text{p}}\)--unknown specific conductivities for the pore-free and porous zones, respectively. So, while sintering by pulsed radiation with wavelengths 527 and 1054 nm in optimal regimes, the maximum achieved values of the average specific conductivity are less than the specific conductivity of bulk silver by 66 and 30 times, respectively. Since the cross-sectional area of the pore-free layers S\({}_{\text{np}}\) in the experiments is approximately 10% of the cross-sectional area for the entire line fracture S\({}_{0}\), the local specific conductivities for these layers \(\sigma_{np}\) according to (1) may approach  
Figure 6: Characteristic images for silver lines sintered by laser radiation on polyamide substrates: (**a,b**) The general view obtained by optical microscope; (**c,d**) SEM images of line surface. Sintering was done by pulsed laser radiation with wavelengths (**a,c**) 527 and (**b,d**) 1054 nm in optimal regimes. to values, around 6.6 and 3 times less than for bulk silver if the conductivities in the porous zones are greatly less and may be neglected. In similar experiments with CW laser radiation the average conductivity of the samples was found to be 7 and 2 times larger than the specific conductivity of bulk silver for wavelengths 527 and 980 nm, respectively. In these samples, the cross-sectional area of the non-porous layers is approximately 16% of the cross-sectional area for the entire line fracture. Based on the high values of the lines average conductivity and Equation (1), we may conclude that in both cases the specific conductivity of pore-free layers approach the specific conductivity of bulk silver. With longwave CW laser sintering, an additional significant contribution to the conductivity is made due to the porous microstructure. The microstructure of surface pore-free layers with well-formed inter-granular boundaries (Figure 5f,h) indicates their high conductivity. Despite the many submicron pores in the inner cross-sectional area of the sample sintered by CW radiation with a wavelength 980 nm (Figure 5i), well-formed inter-crystalline contacts providing significant conductivity are observed. In contrast, for a sample sintered by CW radiation with a wavelength 527 nm (Figure 5g), the inner porous cross-sectional area of the sample is characterized by poorly formed contacts between crystallites, which cannot provide significant conductivity. The interaction of laser radiation with the sample surface is characterized by scattering and absorption processes on NP agglomerates [24]. Considering the agglomerate array consisting of individual NPs [31], a Rayleigh scattering model may be applied to each NP [32; 33; 34]. It explains the significant back propagation of radiation.