Liquid chromatography at the critical condition (LCCC) method has been proposed as an attractive method to characterize individual blocks in block copolymers because it can make one block chromatographically "invisible" at the critical condition of its corresponding homopolymer. However, observable dependence of retention time on the "invisible" block length was reported in LCCC experimental studies of diblock copolymer [Macromolecules 2001;34:2353-2358; Anal Chem 2001;73:3884-3889.]. In this study, we re-examined the validity of the LCCC method for AB, BAB and ABA block copolymers by the lattice Monte Carlo simulation method with using random walk (RW) and self-avoiding walk chain (SAW) models. In the current study, the A block is set in the size exclusion mode and is chromatographically "visible". The interaction between the B type monomer and the column surface are varied to identify the critical condition of B block in the block copolymer. Our simulation results establish that individual block, i.e. B block in the current work, from the block copolymer has its own critical condition for the first time. However, it was also found that the critical condition of B block might be different from the critical condition of B homopolymer. The critical condition of B block in the AB diblock is exactly equal to the critical condition of B homopolymer only when the chain is modeled by RW model. However, deviations of the critical condition of B block away from that of the B homopolymer are observed for AB copolymer using SAW model, and also for BAB and ABA copolymers whether the chain is modeled by RW or SAW models. Moreover, under the critical condition of B homopolymer, no dependence of the partition coefficient on the "invisible" B block length was observed for the AB and BAB copolymers when the copolymer chains were modeled by RW model. Distinct dependence of the partition coefficient of these two types' copolymers on the B block length was found when the chain was modeled by SAW model. For the ABA triblock copolymer, slight dependence of the partition coefficient on B block length was observed even for the RW model while this dependence became much stronger when the chain was modeled by SAW model. Moreover, it was also found that the partition coefficient of ABA copolymer is much smaller than those of AB and BAB copolymers under the critical condition of B homopolymer because of the chain architecture effect. The current study confirms that the block in the block copolymer is hard to be made completely chromatographically "invisible" because the intrinsic nature of the excluded volume interaction existed in real polymer system. (C) 2013 Elsevier Ltd. All rights reserved.