The
spatial dimensions and the stiffness (characteristic ratio, C
∞) of polymer chains are intimately related
to key macroscopic properties such as the plateau modulus and the
melt viscosity. Furthermore, these molecular features are very important
in the selection and design of copolymer species used in directed
self-assembly lithographic processes. We have developed a general
methodology for predicting the chain dimensions of any polymer chain
in the unperturbed state starting from its detailed atomistic structure.
The methodology is based on performing Metropolis Monte Carlo (MC)
simulation, leading to equilibration of the conformational distribution
of a single unperturbed polymer chain, subject only to local interactions
along its backbone. To define what constitutes local interactions,
the maximal topological distance of repeat units between which nonbonded
forces are active is varied systematically, until a maximum in stiffness
is achieved. Our methodology was validated by comparing the predicted
characteristic ratios for a series of polymers against the corresponding
values estimated from MC simulations of the same polymers in the melt
state based on the same force field. Furthermore, we have predicted
the characteristic ratios for three polymers used in directed self-assembly
lithographic processes and shown that they are in good agreement with
reported experimental values.