Graphene has unique physical and chemical properties, making it appealing for a number of applications in optoelectronics, sensing, photonics, composites, and smart coatings, just to cite a few. These require the development of production processes that are inexpensive and up-scalable. These criteria are met in liquid-phase exfoliation (LPE), a technique that can be enhanced when specific organic molecules are used. Here we report the exfoliation of graphite in N-methyl-2-pyrrolidinone, in the presence of heneicosane linear alkanes terminated with different head groups. These molecules act as stabilizing agents during exfoliation. The efficiency of the exfoliation in terms of the concentration of exfoliated single- and few-layer graphene flakes depends on the functional head group determining the strength of the molecular dimerization through dipole-dipole interactions. A thermodynamic analysis is carried out to interpret the impact of the termination group of the alkyl chain on the exfoliation yield. This combines molecular dynamics and molecular mechanics to rationalize the role of functionalized alkanes in the dispersion and stabilization process, which is ultimately attributed to a synergistic effect of the interactions between the molecules, graphene, and the solvent.