Edward F. Casassa

On the length and molecular weight of tropocollagen from calf skin

Abstract Calf skin tropocollagen has been investigated by a variety of techniques: light scattering, velocity and equilibrium sedimentation, viscometry, flow birefringence, optical rotation, and electron microscopy. Some discrepancies among molecular weights and lengths obtained by other workers from various measurements and preparations are confirmed. From a critical assessment of the data, it is concluded that the molecular weight is at most about 310,000. The best estimate of the length of the rod-like macromolecule appears to be 2800 A although values from electron microscopy are about 15% smaller.

Errata: Statistical Thermodynamics of Polymer Solutions. I. Theory of the Second Virial Coefficient for a Homogeneous Solute

An approximate theory of the second virial coefficient A2 for a system of identical random flight polymer chains of n steps, of average length b, is developed on the basis of a treatment by Zimm in power series form which, though formally exact, is not rapidly enough convergent to be practically useful. By introducing, as an approximation, a spherically symmetrical distribution of the chain segments of two interacting molecules averaged relative to the locus of an initial intersegmental contact, it becomes possible to sum the series, the terms of which relate to molecular configurations with progressively greater numbers of simultaneous contacts. The result, a double integral, is evaluated numerically; but the simple relation A2=const[1−exp(1.42ψ)]/1.42ψ, in which ψ=4βn1/2(3/2πb2)3/2 and β is the mutually excluded volume for a pair of segments, differs from the integral by less than one percent for all positive values of the parameter ψ. The analytical form of this equation is justified in terms of the th...

Statistical Thermodynamics of Polymer Solutions. II. Excluded Volume Effect and Second Virial Coefficient

A recently published theory of the second virial coefficient in polymer solutions is modified to take account of the fact that in a good solvent the mean dimensions of two interacting linear molecules are increased beyond random‐flight size through both intermolecular and intramolecular mutual volume exclusion among chain segments. Since the model for a bimolecular cluster bears a formal resemblance to a cruciform branched chain, a method for calculating the dimensions of such polymers can be applied to the two‐molecule problem. This treatment improves the agreement of calculated virial coefficients with experiment as compared with the simpler assumption, made in the original formulation of the theory, that each molecule of an interacting pair is expanded independently in consequence of intramolecular interactions alone.

THE TEMPERATURE DEPENDENCE OF THE DIELECTRIC CONSTANTS OF ALKANOLS

Abstract The dielectric constants of methanol, ethanol, n-propanol, n-butanol, and n-pentanol measured between 0 and 50°C are reported. The data were obtained from low-frequency measurements, using a transformer ratio-arm bridge and a fully shielded and guarded three-terminal capacitance cell. Our results agree closely with recently published functions obtained by fitting the most precise data from the literature, and at least in the case of pentanol may afford even better accuracy.

Gel Permeation Chromatography and Thermodynamic Equilibrium

Abstract Although gel permeation chromatography is firmly established as a technique for investigating heterogeneity in synthetic polymers, the character of the chromatographic process-whether it is dominated by diffusion, by flow effects, or by an equilibrium partitioning of polymer between the mobile phase and the micropores in the column packing-is still disputed. General chromatographic theory supports the idea that under ordinary experimental conditions the equilibrium distribution of a solute determines the position of its elution peak in the chromatogram. Statistical mechanical calculations of distribution coefficients for linear and branched polymer chains and idealized pores of simple geometry lead to predictions in good accord with some experimental findings.

Effect of heterogeneity in molecular weight on the second virial coefficient of polymers in good solvents

Abstract Recent theoretical treatments of the second virial coefficient A2 for chain polymers in good solvents lead to rather complicated results, which because of mathematical difficulties have not so far been extended to the general case of solutes heterogeneous in molecular weight. Expressions in simple analytical form can be obtained, however, if three simple assumptions are made: for homogeneous polymers, A2 varies as a power of molecular weight; interactions between two unlike solute species are given by the relation for rigid spheres of the equivalent radii determined by A2 in the homogeneous cases; in heterogeneous polymers the dispersion of molecular weight is described by a Schulz distribution function or a sum of several such functions. For one special case, a solution of two polymer fractions differing only in molecular weight, results are in qualitative accord with both prior theory and experiment in indicating the existence of conditions under which A2 passes through a maximum as a function of the relative proportions of the two components in the solute. It is also predicted that A2 is increased by heterogeneity in comparison with the value for a sharp fraction of molecular weight corresponding to the appropriate average weight of the heterogeneous polymer.

On the determination of thermodynamic interactions in solutions of mixtures of two polymer fractions

Abstract For the second virial coefficient of a solution of two sharp polymer fractions in a good solvent to pass through a maximum as a function of solute composition, it is necessary that the coefficient for interaction of unlike species be greater than either coefficient for interaction of like species. The three interaction coefficients can be calculated from measurements on three different compositions, but data of the highest precision are needed. The use of results covering the entire composition range to determine these quantities, i.e. the use of all the data to obtain the best parameters in the analytical form required thermodynamically for the composition dependence of the virial cofficient of the solution —is a more reliable means of establishing the occurrence of a maximum than is the completely empirical determination of its presence. This analysis confirms the reality of the maxima reported for two systems of mixed fractions, identical except for molecular weight, and in a third shows an apparent instance to be questionable, although the presence of the maximum is required, according to a theory of Flory and Krigbaum, in all three cases.

Calculation of the unperturbed dimensions of polymers via an equation derived from the combination of the two-parameters theory with the blob theory

Abstract A combination of two equations for the viscometric expansion factor, derived from the two-parameters theory and the blob theory, leads to an equation that permits the calculation of the unperturbed dimensions parameter Kϑ of a polymer from the values of the parameters K and a of the Mark-Houwink-Sakurada equation. The method is especially useful in the high molecular weight region in which the Stockmayer-Fixman-Burchard equation is not valid.

Statistical Thermodynamics of Polymer Solutions. VII. The Triple‐Contact Contribution to Pairwise Interactions of Linear Chains Differing in Molecular Weight

The influence on the osmotic second virial coefficient of configurations with three contacts between pairs of chain segments has been calculated, in part analytically and in part numerically, for a bimolecular cluster of linear polymer chains chemically alike but unequal in degree of polymerization. All classes of contributing chain configurations are included—those with three intermolecular contacts, and those with two intermolecular contacts and one intramolecular contact. The new calculations indicate the need for minor quantitative revision of results published earlier for the special case of triple‐contact interactions between two identical chains.

A light-scattering study of the effect of calcium chloride on the molecular weight of busycon hemocyanin

Solutions of Busycon canaliculatum have been studied by light scattering. In 0.05 M Trizma buffer +0.1 M NaCl at pH 7.0 at 14 degrees, the weight-average molecular weight is 8.9 X 10(6). In the presence of added CaCl2 (0.02 M), the molecular weight of the protein increases to 10.7 X 10(6), and the second virial coefficient is reduced. At pH 9.95, the molecular weights with and without 0.02 M CaCl2, are 3.7 X 10(6) and 1.3 X 10(6), respectively; and the effect of Ca++ in reducing the second virial coefficient is much greater than at pH 7.0. These results can be understood on the basis that at pH 7.0, ca++ increases the association of hemocyanin, by binding and intermolecular linkage through the carboxyl groups of protein side chains. At pH 9.95, amino groups are deprotonated and therefore also become available for Ca++ binding. The relative effect of Ca++ in enhancing the association of hemocyanin therefore becomes greater at the higher pH.