The interaction between lignin and cellulose is essential to the structural integrity of plant cell walls, and these strong interactions are key to biomass recalcitrance. Previous studies have indicated that the hydrophobic face of cellulose is the primary face of interaction between cellulose and lignin. However, due to the structural inhomogeneity of lignin and the small lengthscales that would need to be probed, the relative binding affinities for lignin to different cellulose faces has not been previously determined. Through the creation of idealized infinite cellulose faces for the (200), (110), (1-10) and, (010) planes, we determine through computation the relative binding affinities for selected lignin compounds to these different faces of cellulose. The preference for individual lignin monomers to bind to hydrophobic faces of cellulose is found to be remarkably weak. We develop a mathematical model to determine the structural features of lignin have the strongest relationship with the computed binding affinities for large lignin polymers.