Chenxi Liang

When considering the interaction between atoms and molecules, then always the forces of attraction compete with the forces of repulsion. This can be seen on the curve of the potential energy of the system versus distance. A compromise of these forces leads to a minimum of the energy of the system or to a gain in the energy of the molecule in comparison with its constituent atoms. Usually these forces are short-range (as you write in nm).

In the vicinity of phase transitions, strong fluctuations of the extensive quantities of the entire system are observed. The so-called parameter of order changes. In its meaning, the order parameter is a macroscopic quantity associated with the collective (cooperative) properties of the molecules that make up the medium. it changes in space and time on scales exceeding the size of molecules. In your case, ether molecules, since phase transition occurs in one molecule of your polymer. Therefore, your fluctuations in distance are approximately equal to the size of a macromolecule.

Thank you for your explaination, Prof. Yuri Mirgorod . I understand huge changes will happen in the vicinity of phase transitions.

In my case, 5μm polymer particles are synthesized via precipitation and then centrifugation. Then I redisperse these particles in solvent (organic ester). I use optical tweezers to measure the force between two individual particle versus distance. When particles come close near 1μm, a strong repulsive force is detected, which can be classified as long-range force. No phase separation occurs during the process.

Chenxi Liang

You are working with particles of soft matter. When you centrifugally precipitate polymer from water, you create pressure and a phase transition occurs. For example, a polymer moves from a spiral into a coil. Some of the water does not disappear. She stays. Then you disperse such particles in the ether. You bring hydrophilic particles together in a hydrophobic ether. They will repel,since the force of their attraction is less than the force of repulsion. The hydrophilic particle does not like the hydrophobic ester. If it is a polyelectrolyte, then the effect may be related to quantum phenomena. If you do not want to disclose, then read my preprints.

I additionally replied to a personal letter Chenxi Liang

not sure of your system, do you speak of only 5 µm polystyrene particles in an organic ester or do you have in addition a dissolved polymer with molecular mass of 5000?

It seems that, as expected, your PS particles are swollen in the organic solvent and you squeeze the swollen layers against each others.

Titus Sobisch thank you for your idea. In my case, only 5 µm polystyrene particles in an organic ester.

Swollen particles should be visible via optical microscope. I see only 5 µm particles, however, the repulsion force shows when center-to-center distance is 8 µm.