Establishment of coverage-mass equation to quantify the corrosion inhomogeneity and examination of medium effects on iron corrosion

Abstract

Metal corrosion is important in the fields of biomedicine as well as construction and transportation etc. While most corrosion occurs inhomogeneously, there is so far no satisfactory parameter to characterize corrosion inhomogeneity. Herein, we employ the Poisson raindrop question to model the corrosion process and derive an equation to relate corrosion coverage and corrosion mass. The resultant equation is named coverage-mass equation, abbreviated as C-M equation. We also suggest corrosion mass at 50% coverage, termed as half-coverage mass M _corro50%, as an inhomogeneity parameter to quantify corrosion inhomogeneity. The equation is confirmed and the half-coverage mass M _corro50% is justified in our experiments of iron corrosion in five aqueous media, normal saline, phosphate-buffered saline, Hank's solution, deionized water and artificial seawater, where the former three ones are biomimetic and very important in studies of biomedical materials. The half-coverage mass M _corro50% is proved to be more comprehensive and mathematically convergent than the traditional pitting factor. Iron corrosion is detected using visual observation, scanning electron microscopy with a build-in energy dispersive spectrometer, inductive coupled plasma emission spectrometry and electrochemical measurements. Both rates and inhomogeneity extents of iron corrosion are compared among the five aqueous media. The factors underlying the medium effects on corrosion rate and inhomogeneity are discussed and interpreted. Corrosion rates of iron in the five media differ about 7-fold, and half-coverage mass values differ about 300 000-fold. The fastest corrosion and the most significant inhomogeneity occur both in biomimetic media, but not the same one. The new equation (C-M equation) and the new quantity (half-coverage mass) are stimulating for dealing with a dynamic and stochastic process with global inhomogeneity including but not limited to metal corrosion. The findings are particularly meaningful for research and development of next-generation biodegradable materials.

Keywords: biodegradable medical device; biodegradable metal; biomaterials; biomimetic media; corrosion inhomogeneity; coverage-mass equation.

Graphical abstract

Figure 1.

Schematic presentation of corrosion inhomogeneity.

Figure 2.

Introduction of Poisson raindrop question to analyze the corrosion process and the derivation of C-M equation to quantify the corrosion inhomogeneity. The corrosion coverage θ is defined as the projected area of all of the corroded units, say, corrosion pits, over the whole projected area.

Figure 3.

Corrosion behavior of iron after immersion in deionized water (DI). (A) Global view of an iron sheet before and after immersion in DI with time increased. (B) SEM images of iron surface after immersion for 4 h and 7 days in DI and the corresponding EDS mapping of the corroded iron. (C) The SEM images of cross-sections of iron after immersed in DI for 4 h and 7 days. A resin was used to seal the corroded surface, and the sealed iron sheet was milled to enable observation of a cross-section.

Figure 4.

Fitting of corrosion data of other four media. (A) Corrosion coverage (θ) and the fitted lines of data with (6) in the indicated four media. Error bars represent SD from independent experiments in each group, and n = 3 for each group. The fitting parameters of k′ and n′ are shown in Supplementary Table S2. (B) Corrosion mass (M_corro) of iron and fitted lines of data with (8) in the indicated four media. The fitting parameters a and b are shown in Supplementary Table S3. (C) Fitting of M_corro versus θ by (9), namely, C-M equation. The fitted parameters of k and n are listed in Supplementary Table S4.

Figure 5.

Corrosion morphology of iron in the other four media. (A) SEM images of iron surfaces after removal of corrosion products. (B) SEM images of cross-sections of iron after immersion for 7 days. The blue arrows point to some typical corrosion products of iron. Two images are shown for each medium, indicative of corrosion inhomogeneity.

Figure 6.

Comparison of the inhomogeneity-relevant parameters among iron corrosion in five media. (A) Corrosion pit depths and pitting factors of iron immersed for 3 and 7 days in different media. The lower picture shows schematically the fluctuation of corrosion pit depths with the examined regions. (B) Half-coverage mass M_corro50% calculated using C-M equation to quantify the corrosion inhomogeneity of iron in the indicated 5 media shown in sequence of increased corrosion inhomogeneity. (C) Corrosion pit density after immersion for 4 h to characterize corrosion inhomogeneity.

Figure 7.

Summary of inhomogeneity parameters and corrosion rates of iron in different media. (A) Experimental data of corrosion rates and calculated M_corro50% in the indicated five media. (B) Comparison of corrosion rates and inhomogeneity extents of iron in the different media. Both the top views and cross-sections are schematically presented. It is worthy of noting that the corrosion rate is strongly dependent of corrosion time, and the description in the lower part is based on 7 days of observation.

Figure 8.

Schematic presentation of iron corrosion in the indicated five typical aqueous media.