Figure 14.

Persistence length of arachidic acid as obtained from statistical thermodynamics (sterically uncorrelated 1D {P(ϕ_l)}) and ensemble averaging (2¹⁰ self-avoiding C₁₉H₃₉COOH chains generated at T = 300, 600, and 900 K). The end-to-end persistence length is the projection of the end-to-end vector in the direction of the first C-C bond. Each C-C bond is the z axis of its own local Cartesian coordinate frame (top). The end-to-end vector is the sum of the individual bond vectors, each of which can be calculated by multiplying its local coordinates by the appropriate power of the coordinate transformation matrix; definition of local coordinate systems for two adjacent C atoms of the backbone is illustrated in the inset (see Text). The end-to-end persistence length of arachidic acid is plotted along with those of infinite linear alkane chains consisting of free and hindered rotors (bottom; see Legend).