Chemo-mechanical ageing of paper: effect of acidity, moisture and micro-structural features

Abstract

A multi-scale modeling framework is proposed for the prediction of the chemo-mechanical degradation of paper, with the particular aim of uncovering the key factors affecting the degradation process. Paper is represented as a two-dimensional, periodic repetition of a fibrous network unit cell, where the fibers are characterized by a moisture-dependent chemo-hygro-mechanical constitutive behavior. The degradation of paper occurs primarily as a result of the hydrolysis of cellulose, which causes a reduction of the degree of polymerization and a consequent decrease of the effective mechanical properties, ultimately leading to fiber embrittlement and a loss of material integrity. The interplay between the acidity of the paper, the ambient environmental conditions, and its chemo-mechanical degradation behaviour is a complex process. In the model, these interactions are accounted for by determining the coupled temporal evolution of the degree of polymerization, the acidity of the paper, and the moisture content, from which the time-dependent tensile strength of the paper is calculated. The internal stresses developing in the fibrous network under a change in moisture content lead to brittle fiber fracture once they reach the fiber tensile strength. The successive breakage of individual fibers results in damage development in the fibrous network, altering its effective constitutive properties. The temporal evolution of the effective hygro-mechanical properties of the fibrous network is calculated by employing asymptotic homogenization. For obtaining accurate model input, the strength and stiffness properties of individual fibers and the degree of polymerization of paper samples are measured at different ageing times by carrying out dedicated experiments. Subsequently, a series of numerical simulations is performed to analyze the chemo-mechanical degradation process of paper, highlighting the influence of the time-evolving acidity and moisture content. The numerical study further considers the effects of micro-structural features (i.e., the anisotropy of the fibrous network orientation and the fiber longitudinal elastic modulus) on the macroscopic degradation response of paper. The results of this work may help conservators of cultural heritage institutions determining optimal environmental conditions to limit or delay the time-dependent degradation of valuable historical paper artefacts.