Shaul M. Aharoni

Segmental density distribution of linear amorphous polymer molecules

Abstract In light of the inability of the Gaussian segmental distribution with its resultant deep intermolecular entanglements to explain satisfactorily a number of phenomena, a new segmental density model is proposed. This model, a uniform distribution of segmental density through molecular domains, limits intermolecular interactions mostly to the domains surfaces. The model thus predicts that zero shear viscosity and maximum relaxation time follow the same molecular weight dependence, being dependent on M (or N) at low weights and on M3.5 (up to M4.5) at high molecular weights with a smooth transition over a fourfold increase in the molecular weight. The crystallization of crystallizable polymers and the existence of amorphous nodules are explained on the basis of minor ordering within molecular domains and the subsequent agglomeration of the latter to nodules or nuclei in order to minimize their “surface” energy. Experimental data from the literature are shown to agree with the predicted behavior. Oth...

The state of amorphous polymers by small-angle scattering

Abstract In this paper it is clarified that SANS and SANS (small-angle X-ray and neutron scattering, respectively) define two different RGS (radii of gyration). SAXS describes the RG of the volume pervaded by a tagged macromolecule while SAXS determines the RG of a volume defined by density fluctuations. The fact that SAXS is observable is somewhat inconsistent with the extensive intermolecular interpenetrations implicit in the model of Gaussian segmental density distribution. The difference between the RGS observed by SAXS and SANS is quite large and, at least for polystyrene, is maintained over a large molecular weight range. The dependence of the RGS on molecular weight is similar for both SAXS and SANS. Additional information is obtained by studying the effects of molecular weight distribution with SAXS. The consistency of these data with possible models for the amorphous state is discussed.

Rigid backbone polymers. XII. Lyotropic mesomorphicity of semiflexible macromolecules

Abstract It is shown that semiflexible polymers exhibit lyotropic liquid crystallinity once a threshhold solution concentration is surpassed. These polymers, namely polyisocyanides, polyorganophosphazenes, polyacenaphthylene, and cellulose derivatives, are characterized by persistence lengths or characteristic ratios experimentally determined to be intermediate between the very large ones belonging to extended rod polymers and the small ones belonging to flexible coil polymers. At the same time, the coefficient a in the Mark-Houwink equation of these polymers is of a magnitude typical of coiled molecules. Thus the semiflexible polymers adopt the configuration of expanded coils. The ability to pass through an anisotropic state in solution (and in the bulk below the melting point) is shown to be dependent on the ratio of the persistence length to the polymeric chain diameter, a relationship dependent on the flexibility of the chain and originating from Florys theory of semiflexible chain molecules. Except ...

Thermal dilatation of polymers

Abstract The glass-transition temperature, Tg, is the narrow temperature interval (usually approximated by a point) above which long-range mobility of macromolecular segments exists and below which it ceases. For such mobility to be realized two prerequisites are required: (1) a free volume sufficiently large to accomodate the moving segment must exist, or be formed, adjacently to it, and (2) the segment itself must possess sufficiently high thermal energy to overcome the energy barrier confining it to its equilibrium position. The high segmental mobility reflects a relatively low packing density, D, and is reflected in a relatively high coefficient of thermal expansion, α.

Properties of polyamide gels with varying chain stiffness and length synthesized in the swollen state

Abstract Cross-linked networks of rigid, semirigid, and flexible polyamides were polymerized in solution. When transferred to DMAc the volume of the rigid and semirigid networks did not change significantly, but the flexible networks swelled several hundred percent. When gels previously equilibrated in DMAc were immersed in mixtures containing increasing amounts of nonsolvent, they shrank by an amount that depended on chain flexibility: The flexible and semirigid gels shrank to 30% to 40% of their as-synthesized volume, while the rigid gels shrank to only about 60% of their as-synthesized volume. Furthermore, the volume of the rigid gel decreased smoothly with the change in solvent composition. Unlike that of the rigid network, the volumes of the semirigid and flexible gels sharply decreased over a rather narrow range of solvent composition. Semirigid gels prepared at lower polymer concentration shrank over a narrower solvent composition than their counterparts prepared at higher polymer concentration. Al...

Aromatic poly(ester carbonate)/poly-(ethylene terephthalate) alloys

Abstract When mixtures of poly(ester carbonate) (PEC) and poly(ethylene terephthalate) (PET) containing up to two-thirds of the latter are melt extruded, they produce a single-phase amorphous “alloy.” This alloy is characterized by a sharp, single, composition-dependent glass transition temperature, Tg. When annealed below Tg, the alloy remains unaltered, but when annealed above its Tg, the alloy separates into minute pure-PET crystallites and an amorphous PEC/PET phase. The thermal and dynamic mechanical behavior, crystallization kinetics, and SAXS patterns all strongly suggest the PEC-rich alloys to be solid solutions in which the PET molecules are dispersed individually or in small aggregates containing only a few PET molecules each. Calculations of the interaction parameter and assumed interfacial layer thickness tend to support this suggestion. Use of appropriate solvents allows one to selectively dissolve the PEC and recover from the alloys both PET and PEC in the original purity and molecular weigh...

Rigid backbone polymers. XXV. Solvent effects in phase behavior of solutions of cellulose derivatives

Abstract Experimental results for concentrated solutions of nitrocellulose, cellulose triacetate, and cellulose acetate are presented, indicating that the points v2* of onset of anisotropy and v2A of attainment of full anisotropy are dependent on the magnitude and sign of χ12 the polymer-solvent interaction parameter. The smaller is the polymer-solvent interaction parameter χ12 the lower are the concentrations at the points v2* and v2 A.

Segmental distribution in amorphous polymers: Review of light-, neutron-, and x-ray scattering results, stress-optical and dielectric measurements

Abstract Literature data from several disciplines bearing on the shape of macromolecules in the amorphous bulk are reviewed in this report. Such diverse techniques as light scattering, SAXS and SANS, stress-optical determinations, and dielectric measurements combined with Monte Carlo modeling, all point to the possibility that the shape of the molecules is not exactly that of a Gaussian coil but is better described by the macromolecular domain model and is amenable to varying amounts of local order in the amorphous polymer bulk.

Critical exponent equations: Their relation with free volumes at Tg and TR and with the macromolecular domain concept

Abstract Packing density and activation energy considerations reveal that the fractional free volume of a fully amorphous linear polymer at Tg, (FFV)Tg, is about 0.037. Tg is shown to be the temperature at which sufficient free volume and segmental flexibility combine to redistribute the free volume, changing from the uniform distribution below Tg into effective-hole distribution above Tg. The same considerations indicate that at the reference temperature TR, (FFV)TR ≌ 0.113. TR and the exact value of (FFV)TR are determined through a critical exponent equation, with the exponent β = 1/3. It is shown that TR is the temperature at which the number of nearest neighbors of each segment is one less than their number at Tg. TR is the temperature at which the extrapolated mechanical strength is essentially zero, and at which the activation energy for flow asymptotically becomes vanishingly small and temperature-independent. It is further shown that nonpolymeric glass-formers behave in these respects the same as ...

Instantaneous shape and segmental density of flexible macromolecules. II. Observation of individual and aggregate poly-cis-isoprene molecules in polyisobutylene

Abstract A technique is described, leading to dispersions of individual molecules and their aggregates of OsO4-tagged polyisoprene in an untagged matrix of poly-isobutylene. When no demixing takes place, individual molecules have asymmetric shape and segmental density. Integration over all angles and/or over a large population leads to a spherical shape and a bell-shaped Gaussian segmental density. In the incipient stage of phase separation the tagged molecules become spherical and have a monotonic segmental density upon proceeding from the periphery to the center of each macromolecule. Upon further demixing, two gross morphologies become apparent, large spherical aggregates and necklace beads structures, the latter indicating a possible spinodal decomposition mechanism coexisting with others during the phase separation. The thickness of the interfacial layer decreases with the removal of solvent from the system prior to exposure to OsO4 vapors, in good agreement with theoretical expectation. The demixing...