Water uptake in free films and coatings using the Brasher and Kingsbury equation: a possible explanation of the different values obtained by electrochemical Impedance spectroscopy and gravimetry

Determination of water uptake in organic coatings deposited on 2024 aluminium alloy: Comparison between impedance measurements and gravimetry

“…The swelling of the coating was not considered in the present work. Even the highest swelling values reported by other authors [36] would not cause an error higher than 5% in the determination of the dielectric constant. Under the assumption of a linear propagation of errors following Eq.…”

“…A modified formula proposed by Sykes [35], who removed a possibly unjustified approximation from Brasher and Kingsbury calculation, leads to even stronger overestimations. Vosgien Lacombe et al [36] have recently shown that the BK formula yields water uptake values in agreement with gravimetry if coating swelling is taken into account. These authors have suggested that unjustified assumption of negligible swelling probably explains reported water uptake values calculated according to the BK formula that were larger or much larger than those determined by gravimetry.…”

Graphene-Based Reinforcing Filler for Double-Layer Acrylic Coatings

“…Thus, the values of C shown in Table 4 were employed in the calculation of the water uptake level φ, according to the formula defined by Brasher and Kingsbury in 1954 [ 76 , 77 ]: φ = K(log C t /C 0 )/(logε w ), where C t and C 0 represent the capacitance at an instant t and the capacitance of the “dry” coating at the beginning of the test (time = 0 h), respectively, while ε w is the water dielectric constant. K is a parameter that consider the possible volume increase of the coating, but it is usually taken equal to 1.…”

Dielectric analysis of water uptake in polymer coating using spatially defined Fick's law and mixing rule

“…However, conventional gravimetry and dielectric analyses, including associated modeling as well as their correlations, are usually conducted considering global measurements. This therefore yields, in addition to some quantitative inconsistencies between the two approaches ( [29,30]), to perfectible results in terms of coating structural state assessment. More precisely, the typically considered laws, namely Fick's second law of diffusion ( [31,32]), double Fick's law or Langmuirtype law ( [16,33,34,35]) for gravimetric approach, completed by Brasher and Kingsbury method for the link with dielectric aspects ( [36]) -whose origin lies in permittivity approximation in a complex medium ( [37]) -, usually consider the material as a whole, and only relates the global time-domain evolution (i.e., not assessing the water penetration spatial profile, which can however be of significant importance for monitoring and prognosis purposes).…”