G. C. Berry

Thermodynamic and Conformational Properties of Polystyrene. I. Light‐Scattering Studies on Dilute Solutions of Linear Polystyrenes

The results of an extensive study of some dilute solution properties of a series of linear, homogeneous (anionically prepared) polystyrenes (4.8<10−4M<440) over a wide temperature interval (10°<T<110°C) in decalin and toluene are described. The data are used to obtain detailed comparisons among the second virial coefficient A2, the mean‐square molecular radius 〈s2〉, the molecular weight M, and the temperature. The empirical correlations thus obtained are compared to theoretical predictions. In particular, it is found that A2M½(〈s2〉/M)0−32 and α2=〈s2〉/〈s2〉0 are each single‐valued functions of the interaction parameter z=B(〈s2〉0/M)0−32M½, when B is assumed to have the temperature dependence B=B0[1—(Θ/T)]. Certain theoretical predictions for the dependence of A2M½/α3 on z/α3 are found to adequately describe the form of the observed behavior and can be used as the basis for a satisfactory empirical relation. The observed dependence of α2 on z is satisfactorily predicted by recent calculations of Flory and Fis...

Thermodynamic and Conformational Properties of Polystyrene. II. Intrinsic Viscosity Studies on Dilute Solutions of Linear Polystyrenes

The results of an extensive study of the intrinsic viscosity [η] of a series of linear, homogeneous (anionically prepared) polystyrenes (1.9 ∼106. Above this molecular weight the dependence of [η]/[η]0 on z is satisfactorily predicted by recent calculations of Fixman; [η]/[η]0 is not linear in z contrary to other recent suggestions. The failure of the data on lower molecular weight polymers to be a single‐valued function of z is discussed in terms of partial draining effects.

Rheo‐optical studies on aligned nematic solutions of a rodlike polymer

Rheo‐optical studies on shear deformation of well‐aligned nematic solutions of the rodlike poly (1,4‐phenylene‐2,6‐benzobisthiazole), PBT, are reported. Conoscopic microscopy was used to follow the director during shear, and during relaxation on cessation of flow. The results show that the molecules are not homogeneously aligned in shearing flow. Rather, various complex director field distortions may occur, depending on the relative orientation of the initial director to the flow direction. The results are compared quantitatively with predictions based on the Ericksen–Leslie constitutive equation for nematic fluids.

Branched Polymers. III. Dimensions of Chains with Small Excluded Volume

Mean‐square radii 〈s2〉 for various branched molecules are calculated taking into account the initial effect of segment excluded volume β. Explicit expressions are given for the coefficient of the linear term in the series development of 〈s2〉 in powers of z=(3/2πb2)32n12β, for certain idealized regular star and regular comb structures containing n segments, each of length b. Numerical values of the coefficient, derived primarily through computer calculations, are tabulated as functions of pertinent structural parameters. It is found that at given molecular weight the coil dimensions of star molecules with excluded volume are initially augmented by increase in the number of branches; for comb structures the relationship of size to number of branches and branch‐to‐backbone length ratio is more complex. For both classes of branched molecules the theoretical quantities evaluated find direct application in analyses of dilute solution data obtained on polymer—solvent systems.

Solution and bulk properties of branched polyvinyl acetates IV—Melt viscosity☆

Abstract The melt viscosities of some randomly branched and some comb shaped branched polyvinyl acetate fractions were compared to the viscosities of linear polymer over a range of molecular weights. The melt viscosity of the branched polymer was usually higher than that of linear polymer of the same weight average molecular weight. The extent of this increase was related to the molecular weight of the branches but no correlation could be found which included the number of branches per molecule. This unusual behaviour is believed to be due to the fact that the length of the branches in the polymers of this study was above the critical chain length for polyvinyl acetate which made it possible for the branches to be engaged in intermolecular chain entanglements.

Rheological Properties of Nematic Solutions of Rodlike Polymers

Abstract The rheological properties of nematic solutions of rodlike polymers are discussed. Comparisons are made with the behavior of isotropic solution of rodlike polymers as well as that of small molecule nematogens. Evaluation of the Frank elastic constants and the Leslie-Ericksen viscosity coefficients by light scattering methods is discussed, along with theoretical prediction of the latter of rodlike systems. The nature of shear deformation over a wide range of shear rates is discussed in terms of possible flow instabilities revealed by rheological and rheo-optical observations.

Solution and bulk properties of branched polyvinyl acetates part III—Intrinsic viscosity and light scattering measurements

Abstract Light scattering and intrinsic viscosity measurements have been made on three different series of vinyl acetate polymers, one linear and two branched. One of the branched series was obtained by fractionation of a high conversion polymer, the other by a graft polymerization under conditions that allowed structural characterization of the resultant comb-shaped polymers. These data show that the ratio of the mean-square radii of gyration of branched and linear polymers of the same molecular weight is greater in good solvents than the ratio calculated tl eoretically for a theta solvent. The ratio of the second virial coefficients of the comb-shaped branched and linear polymers of the same molecular weight is equal within experimental error to the ratio of the intrinsic viscosities. The ratio of the intrinsic viscosities of branched and linear polymers is greater in a good solvent than in a theta solvent, in support of inferences from the behavior of the radius of gyration. A theoretical expression for the ratio of the intrinsic viscosities in a poor solvent is obeyed more nearly in a good solvent than in a theta solvent.

On the use of stretched-exponential functions for both linear viscoelastic creep and stress relaxation

The use of the stretched-exponential function to represent both the relaxation function g(t)=(G(t)-G∞)/(G0-G∞) and the retardation function r(t) = (J∞+t/η-J(t))/(J∞-J0) of linear viscoelasticity for a given material is investigated. That is, if g(t) is given by exp (−(t/τ)β), can r(t) be represented as exp (−(t/λ)µ) for a linear viscoelastic fluid or solid? Here J(t) is the creep compliance, G(t) is the shear modulus, η is the viscosity (η−1 is finite for a fluid and zero for a solid), G∞ is the equilibrium modulus Ge for a solid or zero for a fluid, J∞ is 1/Ge for a solid or the steady-state recoverable compliance for a fluid, G0= 1/J0 is the instantaneous modulus, and t is the time. It is concluded that g(t) and r(t) cannot both exactly by stretched-exponential functions for a given material. Nevertheless, it is found that both g(t) and r(t) can be approximately represented by stretched-exponential functions for the special case of a fluid with exponents β=µ in the range 0.5 to 0.6, with the correspondence being very close with β=µ=0.5 and λ=2τ. Otherwise, the functions g(t) and r(t) differ, with the deviation being marked for solids. The possible application of a stretched-exponential to represent r(t) for a critical gel is discussed.

Solution and bulk properties of branched polyvinyl acetates part II—Synthesis of some branched polyvinyl acetates

Abstract A series of comb-shaped branched polyvinyl acetates has been prepared by a graft polymerization technique. Branches of a specified average chain length have been grafted to a linear backbone polymer with a narrow molecular weight distribution. The branched polymers have a molecular weight distribution whose breadth is very close to the linear fraction used for the backbone chain. The number average molecular weight of the branches has been varied from 18 000 to 106 000. The molecular weight of the linear backbone polymers is of the order of one million.

Crossover behavior in the viscosity of semiflexible polymers: Solutions of sodium hyaluronate as a function of concentration, molecular weight, and temperature

Viscometric data on moderately concentrated solutions of the semiflexible macromolecule sodium hyaluronate over a range of molecular weight M and solute concentration c in aqueous 0.1M NaCl are analyzed using a generalized expression for the viscosity of isotropic polymers and their solutions. Owing to its semiflexible nature, the effects of excluded volume interactions are effectively screened for sodium hyaluronate under the conditions studied, and intramolecular hydrodynamic interactions are largely screened, even at infinite dilution. The consequences of this for scaling of the viscosity relative of solutions of sodium hyaluronate with the parameters c[η] and cM is discussed. The dependence of the viscosity on cM is in accord with the generalized relation, and leads to an estimate for the persistence length in reasonable accord with that found by light scattering measurements on dilute solutions. The temperature dependence of the viscosity suggests that the dependence of the persistence length on temp...