Showing papers in "Macromolecules in 1978"

Statistical Thermodynamics of Polymer Solutions

Abstract: The lattice fluid theory of solutions is used to calculate heats and volumes of mixing, lower critical solution temperatures, and the enthalpic and entropic components of the chemical potential. Results of these calculations are compared with literature data on several polyisobutylene solutions. In most instances the agreement with experiment is favorable and comparable to that obtained with the Flory equation of state theory. Several insights into polymer solution behavior are obtained and include: (1) differences in equation of state properties of the pure components make an unfavorable entropic contribution to the chemical potential that becomes large and dominant as the gas-liquid critical temperature of the solvent is approached; (2) limited miscibility of nonpolar polymer solutions at low and high temperatures is a manifestation of a polymer solution's small combinatorial entropy; and (3) negative heats of mixing in nonpolar polymer solutions are caused by the solvent's tendency to contract when polymer is added. Suggestions on how the theory can be improved are made Freeman and Rowlinson' in 1960 observed that several hydrocarbon polymers dissolved in hydrocarbon solvents phase separated at high temperatures. These nonpolar polymer solutions exhibited what are known as lower critical solution temperatures (LCST), a critical point phenomenon that is relatively rare among low molecular weight solutions. Soon after the discovery of the univ- ersality of LCST behavior in polymer solutions, Flory and co-~orkers~-~ developed a new theory of solutions which incorporated the "equation of state" properties of the pure components. This new theory of solutions, hereafter referred to as the Flory theory, demonstrated that mixture thermodynamic properties depend on the thermodynamic properties of the pure components and that LCST be- havior is related to the dissimilarity of the equation of state of properties of polymer and solvent. Patter~od-~ has also shown that LCST behavior is associated with differences in polymer/solvent properties by using the general cor- responding states theory of Prigogine and collaborators.1° Classical polymer solution theory, i.e., Flory-Huggins theory," which ignores the equation of state properties of the pure components, completely fails to describe the LCST behavior.

Size and Density of Fibrin Fibers from Turbidity

Abstract: In agreement with earlier observations that the angular dependence of light scattering by fibrin gels obeys the theory for light scattering by very long and thin rigid rodlike particles (intensity proportional to the square of half the scattering angle), we find that the turbidity, tau, of the less opaque gels varies as the inverse third power of the wavelength, lambda. Mass-length ratios of the fibers calculated from these two measurements closely agree. For fibrin gels containing fibers with a very high mass-length ratio (of which we had not been able to obtain interpretable scattering data), the turbidity is found not quite to vary as 1/lambda3. For these opaque gels, the fiber diameter is no longer negligible with respect to the wavelength. It is shown how the radius of gyration of the fiber cross section (and therefore the radius of cylindrical fibers) can be obtained from the ratio of slope and intercept of a plot of 1/tau lambda3 vs. 1/lambra2. The square of the radius of the fibers is found to be proportional to the mass-length ratio. The density of the fibers is calculated to be 0.28. This corresponds to a ratio of fiber volume to volume of protein contained in the fiber of 5.0.

Polyelectrolyte Excluded Volume Paradox

Abstract: Straightforward application of the Debye-Huckel screened Coulomb interaction to the excluded volume effect in polyelectrolytes is known to give estimates of the segment-segment excluded volume that may be too large by several orders of magnitude. It is argued that the major defect in this application lies in a conventional assumption of excluded volume theory that does not apply to charge interactions, rather than in the electrostatic potential itself. This assumption is that the cooperative interaction of neighboring segment pairs is unimportant because the interaction is weak. An attempt is made to restore the applicability of this assumption through the choice of a segment that incorporates many monomer units. The segment is modeled as a rod and is required to be longer than the Debye screening length. A numerical value has to be chosen for the linear charge density but not for the contour length of the rod. The present work reproduces the conventional formula for the excluded volume if the charge density is very low, but much smaller values are found for practical applications. An illustrative application is made to poly(acry1ic acid), for which the charge density is chosen to be about twice the structural value for the extended configuration, in agreement with previous work. The Debye-Huckel interaction is found to work quite well.

Influence of Water on Protein Structure. An Analysis of the Preferences of Amino Acid Residues for the Inside or Outside and for Specific Conformations in a Protein Molecule

Abstract: The x-ray structures of 20 proteins have been examined and each of the residues in these proteins was assigned to the inside or outside of the molecules and to a conformational state. The data obtained confirm that polar groups are generally found on the outside of proteins and nonpolar residues are generally found on the inside. Seven of the amino acids (Ala, Arg, Cys, His, Pro, Ser, Tyr) have inside/outside preferences which are not consistent with their usual assignment as either polar or nonpolar residues; explanations are given for these apparent inconsistencies. Of the three types of backbone structure considered here (extended, alpha helix, and nonregular), extended structures have the greatest preference for the inside of proteins, and nonregular structures have the greatest preference for the outside. It is suggested that differences in entropy play an important part in the inside/outside preferences of backbone structures. There are generally significant changes in the conformational preferences of the residues in going from the inside to the outside of proteins; environmental (rather than local) solute-solvent interactions seem to be the predominant cause of these changes in conformational preferences.

The Structure of Rubber Networks with Multifunctional Junctions

Abstract: A number of statistical relationships have been derived for calculating the structure of rubber networks with multifunctional junctions. Some of these quantities appear as parameters in the molecular theory of elastic energy in phantom networks. Others relate to Langley's trapping factor for the entanglement contribution to the modulus, to the maximum extensibility, and to the viscoelastic properties of networks.