In order to understand the nature of the dust that accreted onto chondrules in the nebula and to unravel the conditions of formation of fine grained rims (FGRs), we studied three of the least altered chondrites from different chondrite groups (LL3.00 Semarkona, CO3.0 DOM 08006, CR2.8 QUE 99177) and compared the results with our previous work on the Paris CM chondrite (Zanetta et al., 2021). For each sample, we selected representative rimmed chondrules showing minimal traces of aqueous alteration. We performed high-resolution SEM X-ray chemical mapping to obtain relevant phase abundances and grain size distributions. Four FIB sections were then extracted from each meteorite, two in the rims and two in their adjacent matrix for quantitative TEM analysis. At the microscale, texture, modal abundances and grain size differ depending on the chondrite but also between FGRs and their adjacent matrix. At the nanoscale (i.e. TEM observations), matrices of the four chondrites consist mostly of domains of amorphous silicate associated with Fe-sulfides, Fe-Ni metal, Mg-rich anhydrous silicates and an abundant porosity. The related FGRs in Semarkona (LL) and DOM 08006 (CO) exhibit more compact textures with a lower porosity while FGRs in QUE99177 (CR) are similar to the matrix in terms of porosity. In the three chondrites, FGRs are made of smooth and chemically homogeneous amorphous (or nanocrystalline) silicate with no porosity that encloses domains of porous amorphous silicate bearing Mg-rich anhydrous silicates, Fe-sulfides, Fe-oxides and sometimes metal and Fe-rich olivines. The average compositions in major elements of the amorphous regions are similar for the FGRs and the matrix within a given chondrite (but differ between chondrites). The texture and the chemical homogeneity of the smooth silicate and the fact that it encloses domains of porous amorphous silicate bearing other mineral phases similar to matrix-like material suggests a formation by condensation. Areas that are enclosed in this smooth silicate exhibit Fe-rich olivine formed through Fe interdiffusion that also suggest a thermal modification of the dust accreted to form FGRs. These characteristics indicate a transformation process for the modification of the FGR material similar to the one proposed in our previous work on Paris. We conclude that matrix and FGRs accreted a similar type of dust but FGR material was affected by thermal modification and compaction contemporary with their accretion. For each chondrite, dust accreted onto chondrules under different conditions (dust density, temperature) which led to diverse degrees of compaction/thermal modification of the sub-domains and explain the textural differences observed in FGRs. They accreted on chondrules in a warm environment related to the chondrule formation episode, whereas matrix accreted later in a cooler environment.