Pectin is a major component of the primary plant cell wall and is known to play an important role in many physiological processes. It also has has many uses in the food and biomedical industries as it is abundant, mechanochemically versatile and non-toxic. However, the relationship between its chemistry and mechanical properties is not fully understood. In this thesis, pectin in vitro and the pectin-rich outer cells of Arabidopsis seedlings are studied using an AFM methodology adapted from the animal rheology literature. The effects of the degree of methylation, and degree of blockiness on the viscoelastic properties of pectin are explored. Elastic and viscous properties of pectin are found to be negatively correlated with its degree of methylesterification, whilst elastic properties are positively correlated with its degree of blockiness. Mixed gels, composed of pectin with differing degrees of methylesterification are also investigated and their parameters are found to scale in accordance with their volume fraction. In vivo mechanical properties observed in the Arabidopsis hypocotyl are harder to disentangle, but a number of interesting differences between transverse and axial cell walls are observed. A modelling approach is taken, and although a model based on exponentially decaying terms is found to be adequate for the two material types studied, a fractional viscoelastic model is found to be far superior for pectin in vitro.

Fractional viscoelasticity is the use of fractional differential equations for the modelling of viscoelastic phenomena. In addition to its aforementioned use for pectin, its utility is evidenced here by re-analysis of data gathered from the biomechanical literature. In spite of the apparently simple qualitative behaviours they exhibit, there are a number of unique challenges associated with the selection and fitting of fractional viscoelastic models due to their mathematical complexity. This complexity may, in part, explain why fractional viscoelasticity has seen limited use thus far, even though it captures many of the qualitative behaviours commonly observed in biomaterials. This observation led to the development of an open-source rheology analysis software package, RHEOS, which has many of the common fractional and non-fractional viscoelastic models built-in. The architecture, features and implementation specifics of RHEOS are discussed.