Polyisocyanates, long studied as theoretical models for wormlike chains in dilute solution and liquid crystals, differ from their biological helical analogs in the absence of a pre-determined helical sense. These polymers have an unusual sensitivity to chiral effects that arises from a structure in which alternating right- and left-handed long helical blocks are separated by infrequent and mobile helical reversals. Statistical thermodynamic methods yield an exact description of the polymer and the cooperative nature of its chiral properties. Minute energies that favor one of the helical senses drive easily measurable conformational changes, even though such energies may be extremely difficult to calculate from structural theory. In addition, the chiral nature of the polymer can be used to test theoretical ideas concerned with cholesteric liquid crystals, one of which solves the problem of assigning the helical sense.

The evaluation of the configurational partition function of a polypeptide molecule, with the internal rotation angles as variables, leads to an improved treatment of the phenomenon of helix-coil transition in polypeptide molecules. The conditional probabilities of occurrence of helical and coiled states of the peptide units are obtained in the form of a 3×3 matrix. The order of this matrix is the lowest possible for the model employed, and is derived by a logical procedure which serves to eliminate redundancies in the enumeration of states. The eigenvalues of this matrix yield the various molecular averages as functions of the degree of polymerization, temperature, and molecular constants. Explicit formulas are given for the degree of intramolecular hydrogen bonding, average number of helical sequences, and the distribution of their lengths, as well as the number average and the weight average of these lengths.

Cooperative phenomena, described by one-dimensional statistical physical methods, are observed between the enantiomeric characteristics of monomeric materials and the polymers they produce. The effect of minute energies associated with this amplified chirality, although currently not interpretable, can be easily measured. Nonlinear relationships between enantiomeric excess or enantiomeric content and polymer properties may offer the possibility of developing chiral catalysts and chiral chromatographic materials in which the burden of large enantiomeric excess or content may be considerably alleviated. New approaches to information and sensor technology may become possible.

No abstract

SynopsisData on the decrease of the DNA melting temperature T , with the salt concentration i M are report,ed and discussed. The electrost.atic free energy change in the helix-coil transition, AF,, is related to the potential, $, which represents the electrostatic repulsion between the phosplmte charges; $ is calculated as a function of M and of the dist,ances bet,ween the charges of the two strands. The Debye-Huckel approximation is shown to overest,imate $. I t is suggested that the high local concentration of the counterione in the immediate vicinity of the fixed charges screen these charges from interacting with other fixed charges, to the extent, that the system behaves as if the fixed ions carry :L redriced charge. The notioii of a redriced charge represents in a single parameter the deviation of the 1)ehye-Hiickel approximation from the true potential. A plot, of T , versris AHu is Calculated from the slope and Our calculations support t,he hypothesis that the change of T , with salt concentration is due to changes in the screened iriteractioris between the fixed phosphate charges. In analyzing the results of these caldations, we are able on the one hand t,o indicate some of the limitations of the theoretical model and, on the other hand, draw some conchisions about the order of magnitude of the nonelectrostat,ic interaction energy of format,ion of the double helix. ~~ -~~ gives a straight line as predict,ed. erit with experimentally determined vahies.

An inductive method for a systematic selection of energy functions of interatomic interactions in large families of molecules is suggested and is applied to the family of cycloalkane and n-alkane molecules. Equilibrium conformations, vibrational frequencies, and excess enthalpies, including strain energies and vibrational enthalpies, are all derived from the same set of energy functions. The energy-function parameters are optimized by a least-squares algorithm to give the best possible agreement with a large amount and variety of observed data. Analytical derivatives of the various calculated quantities with respect to the energy parameters help to facilitate the computational procedures. The resulting agreement with experiment is used as a measure of success of the energy functions with optimized parameters, referred to as "consistent force field" (CFF). Different CFF's are compared and selected according to their relative success. Energy functions commonly used in conformational analysis are examined in preliminary consistent-forcefield calculations and are found inadequate. Considerable imporvement is obtained when Coulomb interactions between residual atomic charges are included, and when interactions between atoms bonded to a common atom are represented by a Urey-Bradley-type force field, while Lennard-Jones potentials are used for nonbonded interactions between atoms separated by more than one atom. Vibrational frequencies as well as vibrational molecular enthalpies are derived for all cycloalkanes C, through CIS. The spectroscopic force constants are derived from the CFF as functions of molecular conformations. Agreement with available spectroscopic assignments of frequencies is reasonably good. A few improvements are suggested for cyclopentane assignments. The path and moment of inertia of pseudorotation in cyclopentane are calculated. Cyclodecane frequency assignments, based on the derived conformational C2h symmetry, are suggested for the first time. Calculated excess enthalpies of C~lO and medium cydoalkanes agree well with observed values. Contributions of vibration-translation-rotation are shown to amount to a significant part of the excess enthalpy.

The self-diffusion of ions in a polyelectrolyte solution is investigated both with respect to the average time an ion is associated with a particular polyelectrolyte molecule and with respect to the effect of the electrostatic field of the macro-ions on the macroscopic self-diffusion constant. The results on the macroscopic self-diffusion constant are shown to be generally compatible with experiments on self-diffusion of counterions in polyelectrolyte solutions. On the other hand, the study of the time of association of a counterion with a particular macro-ion yields results which cannot be reconciled with the common interpretation of transference experiments on the same solutions.

No abstract