COMPARISON OF THE MAXIMUM-ENTROPY AND ADDITIVE POTENTIAL METHODS FOR OBTAINING ROTATIONAL POTENTIALS FROM THE NMR-SPECTRA OF SAMPLES DISSOLVED IN LIQUID-CRYSTALLINE SOLVENTS - THE CASE OF 4-NITRO-1-(BETA,BETA,BETA-TRIFLUOROETHOXY)BENZENE

The maximum entropy (ME) and additive potential (AP) methods of determining the angular distribution functions, p(omega,chi), from the partially-averaged dipolar couplings obtained from the NMR spectra of liquid crystalline samples are compared. Here omega represents the orientation of the mesophase director in a molecular frame, and chi represents bond rotational motion. It is emphasized that these two methods are fundamentally different. Thus, the model-independent ME analysis can determine only p(LC(omega,chi) and p(LC(chi), which are dependent on the potential of mean torque, U(ext)(omega,chi), and the subscript LC denotes that these distributions are for the liquid-crystalline phase. The AP method, which is model-dependent, can also determine p(LC)(omega,chi) and p(LC)(chi) but in addition yields p(iso)(chi), the distribution of the internal angular coordinate in an isotropic phase, which depends on U(int)(chi), an effective, mean conformational energy. The advantages of applying both the ME and AP methods to analyzing the same set of dipolar couplings is illustrated by the case of 4-nitro-1-(beta,beta,beta-trifluoroethoxy)-benzene dissolved in two nematic solvents. The ME analysis reveals that motion about the ring-O and O-C(H-2) bonds is cooperative, which was then used to guide the choice for the form of U(int)(chi) in the treatment of the same data by the AP method.