Abstract : Context. Physical characterization of trans-Neptunian objects, a primitive population of the outer solar system, may provide constraints on their formation and evolution. Aims. The goal of this work is to characterize a set of 15 scattered disk (SDOs) and detached objects, in terms of their size, albedo, and thermal properties. Methods. Thermal flux measurements obtained with the Herschel-PACS instrument at 70, 100 and 160 mu m, and whenever applicable, with Spitzer-MIPS at 24 and 70 mu m, are modeled with radiometric techniques, in order to derive the objects' individual size, albedo and when possible beaming factor. Error bars are obtained from a Monte-Carlo approach. We look for correlations between these and other physical and orbital parameters. Results. Diameters obtained for our sample range from 100 to 2400 km, and the geometric albedos (in V band) vary from 3.8% to 84.5%. The unweighted mean V geometric albedo for the whole sample is 11.2% (excluding Eris); 6.9% for the SDOs, and 17.0% for the detached objects (excluding Eris). We obtain new bulk densities for three binary systems: Ceto/Phorcys, Typhon/Echidna and Eris/Dysnomia. Apart from correlations clearly due to observational bias, we find significant correlations between albedo and diameter (more reflective objects being bigger), and between albedo, diameter and perihelion distance (brighter and bigger objects having larger perihelia). We discuss possible explanations for these correlations.