So, dipole-dipole interaction exists between two polar molecules? A polar molecule consists of two ions and different charges (one is higher)?
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Atoms in polar molecules do not necessarily have to have ionic bond - it can be covalent. It happens because different atoms have different electronegativity - some want electrons more than others. In water oxygen is more electronegative than hydrogen, therefore it pulls the electrons closer to itself and makes the water molecule polar. Thus water has partially negative and partially positive sides which could make dipole-dipole interaction with other molecules.
See this video on intermolecular forces.

Mithoron
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Stanislav Bashkyrtsev
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