Aims. We propose a new description of astronomical dust emission in the spectral region from the far-infrared to millimeter wavelengths. Methods. Unlike previous classical models, this description explicitly incorporates the effect of the disordered internal structure of amorphous dust grains. Our model is based on results from solid state physics used to interpret laboratory data. The model takes into account the effect of absorption by disordered charge distribution, as well as the effect of absorption by localized two level systems. Results. We review constraints on the various free parameters of the model from theory and laboratory experimental data. We show that, for realistic values of the free parameters, the shape of the emission spectrum will exhibit very broad structures whose shape will change in a non trivial way with the temperature of dust grains. The spectral shape also depends upon the parameters describing the internal structure of the grains. This opens new perspectives for identifying the nature of astronomical dust from the observed shape of the FIR/mm emission spectrum. A companion paper will provide an explicit comparison of the model with astronomical data.

Aims. In a previous paper we proposed a new model for the emission by amorphous astronomical dust grains, based on solid-state physics. The model uses a description of the disordered charge distribution (DCD) combined with the presence of two-level systems (TLS) defects in the amorphous solid composing the grains. The goal of this paper is to compare this new model to astronomical observations of different Galactic environments in the far-infrared/submillimeter, in order to derive a set of canonical model parameters to be used as a Galactic reference to be compared to in future Galactic and extragalactic studies. Methods. We compare the TLS model with existing astronomical data. We consider the average emission spectrum at high latitudes in our Galaxy as measured with FIRAS and WMAP, as well as the emission from Galactic compact sources observed with the Archeops balloon experiment, for which an inverse relationship between the dust temperature and the emissivity spectral index has been shown. Results. We show that, unlike models previously proposed that often invoke two dust components at different temperatures, the TLS model successfully reproduces both the shape of the Galactic spectral energy distribution and its evolution with temperature as observed in the Archeops data. The best TLS model parameters indicate a charge coherence length of 13 nm and other model parameters in broad agreement with expectations from laboratory studies of dust analogs. We conclude that the millimeter excess emission, which is often attributed to the presence of very cold dust in the diffuse ISM, is very likely caused solely by TLS emission in disordered amorphous dust grains. We discuss the implications of the new model, in terms of mass determinations from millimeter continuum observations and the expected variations in the emissivity spectral index with wavelength and dust temperature. The implications for analyzing the Herschel and Planck satellite data are discussed.