4,7-Di(thiophen-2-yl)benzothiadiazole (DTBT) has been used to construct a number of donor-acceptor low band gap polymers for bulk heterojunction (BHJ) photovoltaics with high efficiency numbers. Its strong tendency to pi-stack often leads to polymers with low molecular weight and poor solubility, which could potentially be alleviated by anchoring solubilizing chains onto the DTBT unit. A systematic study of the effect of positioning alkyl chains on DTBT on properties of polymers was implemented by investigating a small library of structurally related polymers with identical Conjugated backbone. This series of donor-acceptor polymers employed a common donor unit, benzo[2,1-b:3,4-b']dithiophene (BDT). and modified DTBT as the acceptor unit. Three variations of modified DTBT units Were prepared with alkyl side chains at (a) the 5- and 6-positions of 2,1,3-benzothiadiazole (DTsolBT), (b) 3-positions of the flanking thienyl groups (3DTBT), and (c) 4-positions (4DTBT), in addition to the unmodified DTBT. Contrary to results from previous studies, optical and electrochemical studies disclosed almost identical band gap and energy levels between PBDT-4DTBT and PBDT-DTBT. These results indicated that anchoring solubilizing alkyl chains on the 4-positions of DTBT only introduced a minimum steric hindrance within BDT-DTBT maintaining the extended conjugation of the fundamental structural unit (BDT-DTBT). More importantly, the additional high molecular weight and excellent solubility of PBDT-4DTBT led to a more uniform mixture with PCBM, with better control on the film morphology. All these features of PBDT-4DTBT led to a significantly improved efficiency of related BHJ solar cells (up to 2.2% has beep, observed), triple the efficiency obtained from BHJ devices fabricated from the "conventional" PBDT-DTBT (0.72%). Our discovery reinforced the importance of high molecular weight and good solubility of donor polymers for BHJ solar cells, in addition to a low band gap and a low HOMO energy level, in order to further enhance the device efficiencies.