Robert Simha

On a General Relation Involving the Glass Temperature and Coefficients of Expansion of Polymers

Treating the glass temperature TG of polymers as an iso‐free volume state allows one to derive the result (αL—αG). TG=K1, a constant; or the approximate result αLTG=K2, another constant. The αs are the coefficients of cubical expansion for 100% amorphous polymer above and below TG. K1 is 0.113 for a wide variety of polymers differing in cohesive energy density, chain stiffness, and geometry. We thus have a general criterion for TG. K2 is 0.164. This latter relation combined with the principle of corresponding states, results in an expression for Tg as a function of cohesive energy density and chain rigidity. The polyalkyl methacrylates which have side‐chain transitions below TG follow the first equation if αG is replaced by αG′, the expansion coefficient below the side‐chain transition. Polymer‐solvent systems are similar to the polyalkylmethacrylates. Two additional products, αL·TM and ΔCP·TG, where TM is the melting point of the polymer and ΔCP is the jump in specific heat at TG, are approximately cons...

The characterization of amino acid sequences in proteins by statistical methods

Abstract Three different but related comprehensive statistical analyses of amino acid sequences in proteins are described. The goal in each case is to search for evidence of significant sequence structure in individual proteins relative to a purely random arrangement of the amino acid residues and to attempt to relate any significant structure uncovered to the secondary and/or tertiary configuration of the protein. In the first of these analyses, which is reviewed briefly in an appendix, amino acids are divided into subgroups according to a variety of side chain physical properties (e.g. polarity, hydrophobicity). Deviations from randomness are expressed in terms of correlation indices ϱ ij ( c ) which are composition normalized doublet frequencies. Here i and j denote membership in a particular group for the physical property chosen and c denotes the “lag”, that is the number of residues along the chain separating the doublet. The other more refined analyses are described in some detail. For both of these each amino acid in a given protein is replaced by its appropriate value on a continuous physical property scale. Six such scales are employed: bulkiness, polarity, R F , p I , p K 1 and hydrophobicity. The resulting amino acid index sequences are treated as discrete series and are analyzed first by means of serial correlation methods and subsequently by employing spectral analysis techniques. Periodicities exhibited in these series are evaluated statistically and speculations are made concerning the connection between such structure and protein configuration. Although more than forty individual proteins whose primary sequences are known have been analyzed by these methods, results for the cytochrome c series, the hemoglobins and lysozyme are emphasized in the present paper. In the case of the cytochrome c family of proteins several relationships between primary sequence structure and “evolutionary order” are discussed. In addition, the results of several homogeneity studies are described in which the sequence structure of various portions of a given protein chain are compared.

A Treatment of the Viscosity of Concentrated Suspensions

In current theories of the concentration dependence the solute molecules are treated as point centers of disturbance. The finite size that produces a shielding of two interacting particles in the presence of intervening ones reduces the interaction calculated in the point approximation and thus reduces the discrepancy between experiment and theory. An approximate treatment for a spherical solute based on the cage model, and hence more adequate at high concentrations, is presented. It operates with a spherical enclosure around a central particle. The position of this shell reflects the relative extent to which particles beyond nearest neighbors can hydrodynamically interact with the central molecule. Thus, a parameter f appears in the theory which increases slowly with concentration and approaches a limit corresponding to the coincidence of the shell with the wall of the nearest neighbor cage at high concentrations. In the framework of the present theory, f must be regarded as a semiempirical quantity. The...

Theory of Depolymerization of Long Chain Molecules

A theory of depolymerization of long chain molecules is developed on a statistical basis. It is assumed that all bonds connecting monomeric elements in the system have the same probability of being broken regardless of their position in a given polymer and regardless of the size of the polymer in which they are found. Expressions are derived for the distribution of molecular sizes in the depolymerized system as a function of the initial chain length and the average number of bonds split per molecule. Also, relationships are established between the average molecular weight of the degraded product and the average number of bonds split per molecule. Experiments on the acetolytic degradation of cellulose acetate are briefly discussed.

Statistical Mechanics of Flexible High Polymers at Surfaces

The isotherm corresponding to monolayer adsorption and the equation of state of a monolayer at a liquid interface are derived. As previously, we replace the number of segments per chain actually deposited, by an average value, which is proportional to t½ (t total number of segments) and depends on chain flexibility. This introduces a considerable simplification. However, a previous overcounting of configurations on the surface is eliminated. This affects primarily the results at low surface coverage and leads to the anticipated limiting laws. The isotherms differ considerably, although not as much as for rigid macromolecules of equal chain length, from the Langmuir type. The change in surface tension in solution as a function of bulk concentration, molecular weight, and solvent power is calculated.

Multiple transitions in polyalkyl methacrylates

A series of polyalkyl methacrylates, two hydroxylated methacrylates, polymethoxy ethyl methacrylate, and polymethyl acrylate have been studied by linear expansion and torsion‐pendulum measurements, in the temperature range from −180°C to just above the respective glass transition temperatures. The length‐temperature data (L‐T) were analyzed by a least‐squares differentiation procedure, based on moving arcs, to give directly the thermal expansion coefficients as a function of temperature. The L‐T measurements suggest the existence of two Tgg transitions (Tg−100<Tgg<Tg) in the polymers with the more flexible side chains, and one transition for polymers with bulky side groups. There is also evidence of a third Tgg transition at about −120° to −90°C, which may be associated with adsorbed water molecules. In similar fashion to that of Tg, the location of the Tgg transitions decreases upon increasing the length of the n‐alkyl side chain. The hydroxylated polymers have higher Tgs than the corresponding alkyl sa...

Compression of Flexible Chain Molecules in Solution

The compression of coiling molecules in good solvents at finite concentrations has been previously treated. However, the expressions were evaluated earlier by means of an expansion in the effective pressure acting on a coil. They are now presented in a form appropriate to include the range of reduced concentrations c/c0≥1. As an example volume ratios for polystyrene solutions in toluene are computed. They depend only slightly on molecular weight and amount to a reduction of about 30% in the most probable encompassed volume, at c/c0=1.

Monolayers of Linear Macromolecules

A model is proposed for monolayers composed of linear macromolecules, particularly at an oil/water interface. If the polymer at the interface is sufficiently flexible, the layer will consist of anchored portions connected by bridges of segments lying out of the plane in which the anchored segments are deposited. An equation of state for the monolayer is derived and its limiting form is compared with those due to Singer and Bull. The limiting form of our equation of state seems to be in satisfactory agreement with some published experimental data. These results suggest the possibility of obtaining rough indications of the shape and mean dimensions of the macromolecule at the interface from film studies at both the air/water and oil/water interface. Finally the application of this model to explain the apparent dissociation of protein monolayers is indicated.

Equation of State of Polymer Liquids and Glasses at Elevated Pressures

By a combination of experimental isotherms and making use of theoretical results, we establish the validity of the theorem of corresponding states for chain liquids and derive an explicit expression for the reduced pressure—volume—temperature surface encompassing oligomer and high‐polymer liquids. For this purpose empirical Tait isotherms are employed with one adjustable parameter only, by showing that they describe experimental data for high‐polymer liquids also. One observes furthermore that the Tait relation remains valid below the glass transition temperature with only one of the parameters changing its functional dependence on temperature in the transition. We are able to conclude that a reduced equation of state describes the isotherms of polymer glasses with the same reducing parameters which characterize the liquid. This permits appropriate predictions at elevated pressure from volume—temperature studies of the glass at atmospheric pressure, combined with equation of state results of the liquid po...

High‐Speed Computations in the Kinetics of Free‐Radical Degradation. I. Random Initiation

The theory of free‐radical degradation leads to large sets of difference‐differential equations for the reacting species, which can be solved analytically for practical purposes only in the extremes of preponderant chain depropagation and random or terminal scission, respectively. Moreover, the equations are linearized by neglecting the variation of the steady‐state radical concentration with degree of volatilization. Numerical solutions of the linearized set were obtained on the SEAC and the resulting zeroth and first moments of the distribution tabulated for the case of random initiation. Thus the rate of volatilization and the number‐average degree of polymerization can be computed as functions of conversion. Initially monodisperse systems and a maximum chain length of 400 C atoms, which determines the size of the set, were assumed. In addition to the latter there are three parameters, viz., the average ``zip length, (1/e—1), a transfer constant, σ, and the maximum size of vaporizing chain fragments....