Relaxation characteristics and intrinsic birefringence and viscosity of polystyrene solutions for a wide range of molecular weights

A comparison is made between measurements on polystyrene solutions and the relaxation characteristics and intrinsic birefringence and viscosity given by the theory for the flexible Gaussian chain of variable number of segments and with internal viscosity and internal hydrodynamic interaction. This is done in order to determine the applicability of the theory to polymers over a wide range of molecular weights, including the low molecular weight range in which there may be conflict with the theoretical assumption of chains having a large number of segments. The longest, terminal relaxation time and the number of chain segments are determined from measurements of the frequency dependence of oscillatory flow birefringence while the intrinsic birefringence and viscosity are determined from steady flow measurements. The range of molecular weights studied is from approximately 900 at 10⁶. It is found that the segment weight is approximately 1000 and the number of segments is in direct proportion to the molecular weight for the range from 1 to 1000 segments. The terminal relaxation time has a molecular weight dependence of the type given by the theory but with better agreement for higher molecular weights. While the measured dependences of the intrinsic viscosity and birefringence are in agreement with theory for molecular weights greater than 5 × 10⁴, they deviate significantly for molecular weights below 1 × 10⁴. The ratio of the intrinsic birefringence to intrinsic viscosity, which in theory is a constant independent of molecular weight, is found to change at the lower molecular weights.     

Hydrodynamic studies on model branched polystyrenes

The measurement of the sedimentation velocity coefficient of narrow distribution linear, four-arm and six-arm star and comb polystyrenes in a theta solvent permits the experimental determination of h, i.e., the ratio of the translational friction coefficients of the branched polymer to that of its linear homolog. A comparison of experimental h/g^1/2 values with theoretical predictions can then be made. It was observed that the equivalent hydrodynamic radii derived from sedimentation and intrinsic viscosity measurements are identical within experimental error.     

Polymer conformation and viscometric behaviour—4. Characterization and conformational studies for poly(dibenzyl itaconate)

Dilute solution properties of poly(dibenzyl itaconate) in various single and binary solvents have been studied by viscosity and gel permeation chromatography measurements. The conformational and thermodynamic parameters and flexibility factor, σ, of this polymer have been determined from intrinsic viscosity, using the semi-empirical Stockmayer and Fixman equation. The results show a variation of σ, calculated on the basis of the unperturbed dimensions under θ condition and in good solvents. The polymer-solvent interactions are discussed in relation to some other polyitaconates and polymethacrylates with the same group in the lateral chain.     

Unperturbed dimensions of poly(2-methyl-6-phenyl-1,4-phenylene oxide) and poly(2,6-diphenyl-1,4-phenylene oxide) chains

The unperturbed chain dimensions of unfractionated poly(2-methyl-6-phenyl-1,4-phenylene oxide) and poly-(2,6-diphenyl-1,4-phenylene oxide) have been measured by combining molecular weight data from light scattering with intrinsic viscosity data in chloroform. The unperturbed chain dimensions of the former polymer were also measured directly by light scattering dissymmetry in a critical consolute solvent mixture (methyl cyclohexane: 1,4-dioxane 50:50 by volume). The results of these measurements and of measurements reported by other investigators are satisfactorily explained by postulating no dimension-expanding prejudice in azimuthal angle in chain conformers of the 2,6-substituted-1,4-phenylene oxide polymers. This corresponds to equal population of the two chain rotation energy minima at azimuthal angles 90° and 270°. Accepting this postulate, one calculates from the observed chain dimensions that the C? O? C bond angle is 118–120° in these aromatic polyethers in solution.     

A Study of the Molecular Weight and Chain Length Distribution of Cyclocopolymers of Divinyl Ether and Maleic Anhydride

Some physical properties of a cyclocopolymer formed by an intra-inter-molecular polymerization mechanism were studied. The cyclic copolymer of divinyl ether and maleic anhydride was chosen for study. Intrinsic viscosities were determined in two solvents. The weight-average molecular weight was determined by light-scattering measurements and the number-average molecular weight was determined by osmometry. Results from a sedimentation velocity pattern indicated that the chain length distribution is much broader than random, which is in agreement with the ratio of the two molecular weight determinations. The polymer was fractionated by precipitation from acetone with hexane as precipitant. Addition of sodium tetraphenyl boron was necessary to obtain separation. Correlation of intrinsic viscosity and weight-average molecular weights was not obtained because of anomalous solubility effects preventing light-scattering determinations.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.     

Hydrodynamic Properties and Unperturbed Dimensions of Polydecahydro- β -naphthyl and Poly- β-naphthyl Methacrylates in Different Solvents

Abstract

Intrinsic viscosity, sedimentation, light-scattering, and osmotic-pressure measurements have been carried out at 25° on dilute solutions of polydecahydro-β -naphthyl meth-acrylate (PDNa) and of poly-β-naphthyl methacrylate (PNa). For both polymers, the degree of polydispersity was around 1.5 and the molecular weight range was large: 10⁵ to 3 × 10⁶. Relations between [η], [S₀], A₂, and molecular weight have been established.

The applicability of the different theories (Stockmayer-Fixman, Kurata-Stockmayer, Fox-Flory, Cowie, Berry, Kamide-Moore) for the determination of the unperturbed dimensions from the viscosity data is discussed; Berry's relation best fits the experimental data.

These dimensions, calculated from the sedimentation data according to the Cowie-Bywater relation, agree with those obtained by viscosity. The flexibility factor is 2.9 for PDNa and 3.1 for PNa. These large values are a consequence of the presence of very bulky groups in the side chain; however, the higher η value for PNa led to the assumption that a specific interaction between the aromatic rings influences the rigidity of the main chain.     

Styrene-methyl acrylate copolymers and acrylate homopolymers in solution

Molecular weight determinations by light scattering and osmometry and intrinsic viscosity measurements were made in various solvents on fractions of styrene–methyl acrylate copolymers with different compositions and on acrylate homopolymers prepared by free-radical reaction. Relations between intrinsic viscosity [η] and molecular weight M thus established are compared with those reported by other authors. 2-Methylcyclohexanol was found to be a theta solvent for the copolymers and both parent homopolymers, and isoamyl acetate was a theta solvent for poly(methyl acrylate). From theta point viscosity data obtained with these solvents, unperturbed chain dimensions were estimated. The results are compared with the unperturbed dimensions estimated from the [η]–M relations obtained in good solvents. On the basis of the experimental data it was found that the unperturbed dimension depends linearly on the copolymer composition, in contrast to the case of styrene–methyl methacrylate copolymers. Composition dependences of the theta temperature and of the parameter describing the long-range interactions between nonadjacent segments in polymer chains were investigated. The result implies that long-range interactions between monomeric units never disappear even when those between the same monomeric units vanish. The Huggins constant for copolymer is discussed in terms of the excluded volume variable.     

Investigation of conformational transition in poly(methylmethacrylate)—III Aromatic esters as solvents

Light scattering and viscosity measurements on fractionated samples of atactic PMMA in methyl and ethyl benzoates show the existence of a conformational transition in the temperature ranges 45–50° and 40–45° respectively. The study of unperturbed dimensions and polymer-solvent interaction parameter shows that the phenomenon affect both inter- and intramolecular interaction. This effect modifies the flexibility of the macromolecular chain and other properties in solution, e.g. intrinsic viscosity.     

Dilute solution behavior of polyelectrolytes. Intrinsic viscosity and light scattering studies

The conformational character of a random copolymer of ethyl acrylate and acrylic acid (mole ratio 3:1) has been examined by intrinsic viscosity and light scattering in organic and in aqueous media. The unperturbed dimensions of this copolymer in its un-ionized state in an organic theta solvent are 1.3 to 1.4 times those obtained for the fully ionized polymer in an aqueous theta solvent. The data also suggest that a change in conformation from a swollen random coil to a compact random coil occurs in aqueous media as a function of ionic strength. These results are interpreted in terms of the hydrophobic interaction of the ester groups on the chain. An application of the wormlike chain model shows that viscosity data can be used to predict the light scattering results well with in experimental error.     

Viscoelastic properties of an isolated polymer chain with arbitrary flexibility,chain length and hydrodynamic interactions from 4‐dimensional Dirac propagator

Kholodenko's theory of semiflexible polymer chains, the conformation and properties of which are obtained from the Dirac propagator, shows applicability to dilute solutions of semiflexible polymers of arbitrary persistence and contour lengths by calculating the static scattering function and the squared end‐to‐end distance of the polymer chain. In the present work, the theory is extended and applied to obtain the intrinsic viscosity with consideration of hydrodynamic interactions. The intrinsic viscosity formula is derived as function of chain length and persistence length. The hydrodynamic interactions are also taken into account following the Kirkwood and Riseman scheme. From this calculation, we obtain the general expression for the intrinsic viscosity and diffusion coefficients covering the whole range of chain flexibilities without confusion with the excluded volume effects. Calculated limiting values of hydrodynamical observables are in complete agreement with those known for random coils and rigid rods.     

Dilute solution properties,chain stiffness,and liquid crystalline properties of cellulose propionate

The solution properties of cellulose derivatives are of interest from both technological and purely scientific aspects. At high concentrations these solutions form liquid crystalline structures. In dilute solution cellulosic chains can be described as semiflexible or wormlike with properties intermediate between random coils and rigid rods. A series of fractions of cellulose propionate have been examined by dilute solution viscometry, static and dynamic light scattering, and polarizing microscopy. Power law exponents are considerably larger than those observed for flexible chains and analysis of the intrinsic viscosity and hydrodynamic radii has yielded chain diameters and Kuhn statistical segment lengths. Corresponding aspect ratios from the hydrodynamic measurements are in good agreement with those obtained from polarizing microscopy, as analyzed in light of Flory's theory. Some aggregation and specific solvent effects have been observed, however separation of these effects has proven to be difficult. Results of these studies are compared to previous work for other cellulose derivatives. ©1995 John Wiley & Sons, Inc.     

Poly(vinyl fluoride) solution characteristics

Nine unfractionated poly(vinyl fluoride) samples were characterized for molecular weight and polydispersity by means of sedimentation velocity, osmometry, and viscosity measurements. Molecular weights were in the range of 143,000–654,000 and M _w/M _n = 2.5–5.6. The Mark-Houwink (M-H) relation was established as [η] = 6.52 × 10^?5 M^0.80. The M-H exponent is at the Flory-Fox upper limit (0.80), as is characteristic of extended, polar polymers, in good solvents. The unperturbed chain dimensions, characteristic ratio and steric factor were derived by the methods of Stockmayer and Fixman and Kurata and Stockmayer. The steric factor is 1.7, which agrees with data reported for other poly(vinyl halides).     

Application of the flory-mandelkern equation to individual unfractionated polymer samples

A method is developed for the application of the Flory-Mandelkern equation to the determination of the weight-average molecular weights of individual, broad, unfractionated polymer samples. The method includes appropriate averaging of the sedimentation constants and of the intrinsic viscosity of an unfractionated polymer sample in a θ solution from the velocity sedimentation data. By means of the method, individual samples of polystyrene, poly(isooctyl methacrylate) and of the copolymer of styrene with 20% isooctyl methacrylate prepared under the same emulsion polymerization conditions from commercial monomers have been investigated. Appropriate θ solvents have been found by the Elias method. Equations for the dependence of the sedimentation constants and of the intrinsic viscosities in the θ solvents on the molecular weights have been established for the polymers without fractionation. Osmometric and light-scattering measurements as well as Archibald experiments have shown that by the proposed method the molecular weight cut-off effect is eliminated in the above equations and in the polydispersity parameter M _w/M _n. Molecular weight distributions have been determined for the polymer samples.     

Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements

Hydrodynamic properties of fibrinogen molecules were theoretically calculated. Their shape was approximated by the bead model, considering the presence of flexible side chains of various length and orientation relative to the main body of the molecule. Using the bead model, and the precise many-multipole method of solving the Stokes equations, the mobility coefficients for the fibrinogen molecule were calculated for arbitrary orientations of the arms whose length was varied between 12 and 18nm. Orientation averaged hydrodynamic radii and intrinsic viscosities were also calculated by considering interactions between the side arms and the core of the fibrinogen molecule. Whereas the hydrodynamic radii changed little with the interaction magnitude, the intrinsic viscosity exhibited considerable variation from 30 to 60 for attractive and repulsive interactions, respectively. These theoretical results were used for the interpretation of experimental data derived from sedimentation and diffusion coefficient measurements as well as dynamic viscosity measurements. Optimum dimensions of the fibrinogen molecule derived in this way were the following: the contour length 84.7nm, the side arm length 18nm, and the total volume 470nm(3), which gives 16% hydration (by volume). Our calculations enabled one to distinguish various conformational states of the fibrinogen molecule, especially the expanded conformation, prevailing for pH<4 and lower ionic strength, characterized by high intrinsic viscosity of 50 and the hydrodynamic radius of 10.6nm. On the other hand, for the physiological condition, that is, pH=7.4 and the ionic strength of 0.15M NaCl, the semi-collapsed conformation dominates. It is characterized by the average angle equal to <φ>=55°, intrinsic viscosity of 35, and the hydrodynamic radius of 10nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be -4kT units, confirming that they are oppositely charged than the central nodule. Results obtained in our work confirm an essential role of the side chains responsible for a highly anisotropic charge distribution in the fibrinogen molecule. These finding can be exploited to explain anomalous adsorption of fibrinogen on various surfaces.     

Size-exclusion liquid chromatography of poly(<Emphasis Type="Italic">N</Emphasis>-vinylformamide)s in aqueous solutions

The exclusion mechanism of the separation of poly(N-vinylformamide) and its derivatives with a cysteamine terminal group in gel permeation chromatography implemented by the suppression of polyelectrolyte swelling and the electroexclusion of macromolecules was established by the transport analytical methods of molecular hydrodynamics (HPLC, velocity sedimentation, and intrinsic viscosity). Based on an analysis of the hydrodynamic characteristics and molecular weights of polymer fractions determined by velocity sedimentation, it was found that the molecular characteristics and polydispersity of the water-soluble poly(N-vinylamide) s of aliphatic carboxylic acids and their derivatives can be calculated with the use of the Benoit universal calibration dependence.     

Depolymerization studies on polyacetaldehyde

Depolymerization of amorphous polyacetaldehyde has been studied by measurements of weight loss versus time for thin films of the polymer in vacuum. Temperatures ranged from 40 to 80°C. The samples were prepared by freezing or melting the monomer in contact with treated glass surfaces. Light scattering, osmometry, and intrinsic viscosity measurements were used to characterize the polymers. Depolymerization rates were between second and third order with respect to the unvolatilized fraction, and the activation energy was 26.3 kcal. Much of the evidence points toward a slow unzipping reaction at the chain ends, but the analysis seems to be complicated by structural variations among the samples.     

Gelation mechanism of ionic polysaccharides

Experimental results obtained by membrane equilibria, osmotic pressure, viscosity and circular dichroism measurements on alginate and pectate solutions in the presence of Ca²⁺ ions are presented. From equilibrium dialysis data both electrostatic and cooperative interactions seem to describe the binding process of Ca²⁺ ions onto polymer chains. An increase of the number-average molecular weight M̄_n for both poly-saccharides with calcium ion concentration is observed. An increase of polymer dimensions can well account for the observed increase of the intrinsic viscosity [η] with bound Ca²⁺ ion concentration at several ionic strengths.     

Unperturbed dimensions of poly(9-vinyladenine)

The effect of base stacking interactions on the conformation of poly(9-vinyladenine) (PVAd) was investigated by osmometry, intrinsic viscosity, and light-scattering measurements. At neutral pH, ideal solution behavior (θ conditions) for this polymer was observed at 26 and 40°C. Intrinsic viscosity measurements revealed a conformational transition on heating from 26 to 40°C, while the ultraviolet absorbance of the solution was insensitive to the change. The transition was accompanied by an inversion in sign of the entropy parameter from negative to positive and an increase in the partial specific volume. At 40°, the variation of intrinsic viscosity with molecular weight corresponded to a random coil conformation, but the characteristic ratio, r?₀²/nl² = 8.6 ± 0.2 indicated that the unperturbed dimensions were smaller than usually observed for comparable vinyl polymers. At 26°, a rare macromolecular phenomenon was found, the intrinsic viscosity–molecular weight relation and the estimated r?₀²/nl² of 6.0–6.8 suggested that the PVAd was in a very highly compacted coil conformation, approaching a semirigid sphere. It is proposed that this effect be named the introversion phenomenon. Unlike polyadenylic acid, whose unperturbed dimensions increase with decreasing temperature due to nearest-neighbor base stacking, the results reported here suggest that both nearest-neighbor and long-range intramolecular base stacking occur in PVAd. The different stereochemical arrangements of bases in PVAd and Poly A are probably responsible for the opposite behavior observed.     

Flow birefringence of short-chain molecules: Cellulose tricarbanilates in benzophenone

Measurements of flow birefringence of cellulose tricarbanilates were carried out on nine fractions (0.27 × 10⁵ < M ≤ 12 × 10⁵) in a temperature range of 55–110°C, with benzophenone as a matching solvent (dn/dc = 0). The ratio of Maxwell constant to intrinsic viscosity, which has been found to be independent of molecular weight for the limiting case of Gaussian molecules, is successfully interpreted as a function of molecular weight in terms of the recent theory of Gotlib and Svetlov (based on the wormlike chain model of Kratky and Porod). From the measurements at 55°C a number of 36.6 monomer units per random link is deduced. This is in accord with results of small-angle x-ray scattering. For the extinction angle curves a clear transition is observed from rodlike to statistical molecules when the molecular weight is increased. At high molecular weights the master curves obtained for anionic polystyrenes and cellulose tricarbanilates coincide. Implications of this observation on the kinetic stiffness of the cellulose tricarbanilate chain are discussed. The intrinsic viscosity-molecular weight relationship is considered. From a comparison with the results of the theory of Eizner and Ptitsyn it is concluded that the cellulose tricarbanilate chain must be highly solvated in benzophenone.