Context : Trans-Neptunian objects ( TNOs ) contain the most primitive and thermally least-processed materials from the early accretional phase of the solar system . They allow us to study interrelations between various classes of small bodies , their origin and evolution . Aims : We exploit the use of polarimetric techniques as a remote-sensing tool to characterize the surface of TNOs . Methods : Using FORS1 of the ESO VLT , we have obtained linear-polarization measurements in the Bessell R filter for five TNOs at different values of their phase angle ( i.e. , the angle between the Sun , the object , and the Earth ) . Due to the large distance of the targets ( \ga 30 AU ) , the observed range of phase angles is limited to about 0 \degr - 2 \degr . Results : We have analyzed our new observations of five TNOs , and those of another four TNOs obtained in previous works , and discovered that there exist two classes of objects that exhibit different polarimetric behaviour . Objects with a diameter > 1000 km , such as , e.g. , Pluto and Eris , show a small polarization in the scattering plane ( \sim 0.5 % ) which slowly changes in the observed phase angle range . In smaller objects such as , e.g. , Ixion and Varuna , linear polarization changes rapidly with the phase angle , and reaches \sim 1 % ( in the scattering plane ) at phase angle 1° . The larger objects have a higher albedo than the smaller ones , and have the capability of retaining volatiles such as CO , N _ { 2 } and CH _ { 4 } . Both of these facts can be linked to their different polarimetric behaviour compared to smaller objects . Conclusions : In spite of the very limited range of observable phase angles , ground-based polarimetric observations are a powerful tool to identify different properties of the surfaces of TNOs . We suggest that a single polarimetric observation at phase angle \sim 1 \degr allows one to determine whether the target albedo is low or high .