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Weaker-Bond Theory

This theory posits that the primary driving force for liquid crystal phase transitions is the preferential alignment of molecules along weaker bonds, leading to self-organization.
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The statement of the theorem

Define the total free energy functional F[r]F[\mathbf{r}] for the system, where r\mathbf{r} represents the molecular configuration. The contribution from weaker bonds, FweakF_{weak}, is modeled by a directional potential VdirV_{dir} acting on the bond vectors rij\mathbf{r}_{ij}. The effective Hamiltonian is then modified such that:\nHeff=Hstandard+∑i<jVdir(rij)⋅cos⁡(θij−θpref)H_{eff} = H_{standard} + \sum_{i<j} V_{dir}(\mathbf{r}_{ij}) \cdot \cos(\theta_{ij} - \theta_{pref})\nwhere θij\theta_{ij} is the angle between the bond rij\mathbf{r}_{ij} and the preferred alignment direction θpref\theta_{pref}, and VdirV_{dir} quantifies the strength of the weaker bond interaction.