Intermolecular forces are fundamental to the separation of compounds via TLC. We have three components at play here, the stationary phase, the mobile phase, and the sample. The balance between the interactions of these components causes separation.
The stationary phase consists of a 3D silica gel network of repeating silicon oxygen chains, with OH groups creating a polar surface, as shown in figure 1.
This interacts with the sample, which is often a mixture of compounds with differing polarities. Compounds with polar functional groups will have a stronger interaction with the TLC plate than non-polar compounds. As they will interact with the surface via a range of intermolecular forces including, dipole-dipole interactions, hydrogen bonding (functional group dependant), and Van der Waals forces. Whereas, non-polar compounds will only interact via weak van der waals forces. Polar compounds will be adsorbed more strongly onto the TLC plate and will not move as far, creating a separation.
The final component in this interaction puzzle is the mobile phase, this is the one you have the most control over. The choice of mobile phase will be dependent on the samples you are separating. The solvent itself has an affinity for the mobile phase, and the samples are essentially competing with the binding sites of the plate with the solvent. The mobile phase pushes the samples up the plate. If the solvent has too weak an interaction with the mobile phase, the samples will remain at the baseline. Whereas, if it has too strong an interaction, it will displace the samples all the way up the top of the plate. The balance of the interaction is finding a solvent with a similar affinity to the stationary phase than the samples, causing different compounds to move at different rates.