Isometric and isotensional force-length profiles in polymethylene chains

The force-length curves and related thermodynamic quantities of single polymethylene (PM) chains in the high-force region were calculated by the statistical mechanics. Two statistical mechanics ensembles (isometric and isotensional) were used to represent the chain stretching under the conditions, respectively, of the fixed length L or of the fixed force F in single-chain experiments by AFM and related techniques. The input deformation potentials of highly extended conformations of PM chains were obtained from the molecular-mechanics calculations. Variations of the energy, entropy, and Helmholtz energy with the end-to-end length L of chains were computed under the condition of fixed length. The ensuing isometric profile of the mean force < F >(L) is non-monotonic, featuring a sawtooth-like pattern of ascending peaks. In contrast, the mechanical equation tinder isotensional conditions, given by the variation of the mean length < L >(F), shows a conventional monotonous shape with a distinct plateau region at low temperatures. The considerable difference in the shapes of < F >(L) and < L >(F) curves arises from the large fluctuations of mean values due to the small number of conformers present in molecules at high strains. The computed data should be relevant to the AFM stretching experiments on short polyethylenes or on other soft matter materials involving linear paraffinic chains. It is argued that the dual character of elastic response described by the conjugated force profiles is a universal feature of mechanochemistry of chain molecules whenever the chain length discontinuously increases at a transition.