Polyoxymethylene dimethyl ethers (PODEn, CH3O(CH2O)(n)CH3, where n >= 1) are ideal diesel fuel additives. Among the PODEn compounds, PODE3-5 have the best properties as diesel additives. A theoretical analysis of the molecular size distribution of PODEn synthesized from dimethoxymethane (DMM) and paraformaldehyde (PF) was performed based on a sequential reaction mechanism. The molecular size distribution model follows the Schulz-Flory distribution, and showed a good prediction ability at different reaction temperatures (T) and DMM/CH2O mole ratios (M), which verified the sequential reaction mechanism during the formation of PODEn. The product distribution was optimized using the molecular size distribution model and response surface methodology (RSM). At optimum operating conditions of T = 105 degrees C and M = 1.1, the conversion of formaldehyde X-CH2O has a high value of 92.4%, and the fraction of PODE3-5 in the PODEn mixture is 33.2 wt%, while the fractions of PODEn>5 and PODE2 are 9.4 wt% and 24.3 wt%, respectively. (C) 2014 Elsevier B.V. All rights reserved.