Single- and binary-phase nano-particle infiltrated electrodes (SIE and BIE) have been actively studied experimentally. To properly understand the experimental results and the benefits of SIE and BIE designs, new models for electrical conductivities of BIE and TPB lengths of SIE and BIE are proposed here. The models agree with experiments on the variation of conductivity with LSM loading. SIE and BIE may provide adequate electronic conductivity at low loading of conducting material. The theoretical effective properties are further used in multi-physics modeling and the obtained I-V curves also agree with the experiments. Quantitative comparisons of the ionic conductivities of SIE, BIE and conventional composite electrode (CE) are made. BIE possesses the longest TPB length and SIE may also yield a TPB length that is one order of magnitude larger than that of CE. The new theory allows for in-depth analysis and design optimization of BIE and SIE for improved performance. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.