Properties of cellulose acetate in solution. I. Light scattering,osmometry, and viscometry on dilute solutions

Light-scattering, osmotic pressure, and viscometric studies on fractions of cellulose acetate (degree of substitution 2.45) in three solvents are described. The data yield the dependence of the mean-square radius of gyration 〈s²〉, the second virial coefficient Γ₂, and the intrinsic viscosity [η] on molecular weight M and temperature. The results are interpreted to show that excluded volume effects on 〈s²〉 are negligible, even though Γ₂ is large and dΓ₂/dT is positive. The large experimental value of d In [η]/d In M is interpreted in terms of partial draining effects. Data on 〈s₂〉 and [η] for other cellulose esters in the literature are similarly interpreted. Significant aggregation found in solutions of cellulose acetate in many solvents is discussed.     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Configurational-conformational statistics of stereoirregular polystyrene

The dependence of the configurational-conformational characteristics, such as the mean-square end-to-end distance, the mean-square radius of gyration, and the temperature coefficient of the stereoirregular polystyrene chains on the fraction of meso dyads, P_m was investigated, using the periodic condition method. The calculation shows that polystyrene has the most compact chain when P_m = 0.7, and the temperature coefficient of the characteristic ratio of the mean-square end-to-end distance reaches the minimum, −0.89 × 10⁻³ K⁻¹, at P_m = 0.5. The theoretical result of the mean-square radius of gyration for atactic polystyrene, 〈S²〉^1/2 = 0.2245 M^0.5106 shows good agreement with the experimental measurement in both bulk amorphous state and θ-solvent.     

Solution properties and chain conformation characteristics of cellulose tricarbanilate

Fractions of two cellulose tricarbanilate samples were characterized by light-scattering (weight-average molecular weight, second virial coefficient, mean-square radius of gyration), gel permeation chromatography (polydispersity index), and viscometry (intrinsic viscosity) in tetrahydrofuran and acetone. The intrinsic viscosity data were analyzed in terms of the theory developed for the continuous wormlike cylinder model, and the chain parameters (Kuhn statistical segment length λ^?1, chain diameter d, and shift factor M_L) were evaluated. The molecular-weight dependence of the mean-square radius of gyration in tetrahydrofuran was calculated for the Kratky—Porod chain model and compared with the experimental results. Data on the intrinsic viscosity and radii of gyration for other solvents at temperatures from 0 to 100°C were analyzed in the same way, and the effects of solvent and temperature on the statistical segment length were evaluated. Polymer—solvent interaction parameters were estimated from the second virial coefficients.     

Temperature dependence of unperturbed dimensions for stereoirregular 1,4-polybutadiene and poly(α-methylstyrene)

The temperature coefficient of chain dimensions, d ln〈r²〉₀/dT, was determined for stereoirregular 1,4-polybutadiene and poly(α-methylstyrene) via dilute solution viscometry. The 1,4-polybutadiene was examined in oligomeric 1,4-polybutadiene (an athermal solvent), and poly(α-methylstyrene) was evaluated under near-theta conditions using 1-chloro-n-alkanes as solvents. Both approaches minimize the potential for influence by specific solvent effects. The resulting temperature coefficients, ?0.1₀ × 10^?3 deg^?1 for 1,4-polybutadiene and ?0.3₀ × 10^?3 deg^?1 for poly(α-methylstyrene) are in excellent agreement with rotational isomeric state calculations.     

Unperturbed chain dimensions of isotactic polypropylene in theta solvents

The unperturbed mean-square end-to-end distance 〈R₀²〉 and its temperature variation d In 〈R₀²〉/dT for isotactic polypropylene have been estimated from intrinsic viscosity data in three theta solvents, i.e., diphenyl, diphenyl ether, and dibenzyl ether, measured at their θ temperatures as determined by precipitation temperature measurements. The characteristic ratios, 〈R₀²〉/nl², where n is the number of bonds of length l in the main chain, evaluated by assuming Φ = 2.87 × 10²¹, are 5.80 in diphenyl (at θ = 125.1°C.), 5.41 in diphenyl ether (at θ = 142.8°C.), and 4.56 in dibenzyl ether (at θ = 183.2°C.). These values lead to the temperature coefficient d In 〈R₀²〉/dT = ?4.09 × 10^?3 deg.^?1 Results are compared with the data previously reported on polyethylene.     

Solution properties of poly(methacrylamide)

Poly(methacrylamide) samples obtained by radical polymerization were fractionated by isothermal precipitation (formamide-methanol). Molecular weights were determined by light scattering and the Archibald approach-to-equilibrium method (in 0.4 M aqueous magnesium perchlorate), and the [η] M correlation was constructed. The characteristic ratio (C₁ = 6.1). Its temperature coefficient (dln C₁ dT ? 0) and the interaction parameters of the polymer in aqueous solutions of urea (2–8 M) and magnesium perchlorate (0.4–1.2 M) at 10–50°C were determined using analysis of the viscometric data ([η], dln [η]/dT). The data thus obtained are used to discuss the behaviour of the polymer in water.     

Hydrodynamic interaction effects on intrinsic viscosity of perturbed chains: Experimental results for polystyrene

Experimental measurements of intrinsic viscosity and radii of gyration of monodisperse samples of polystyrene of molecular weights 2.33 X 10⁵, 4.11 X 10⁵, 6.70 X 10⁵, and 2.3 X 10⁶ dissolved in the homologous series of 1-chloroparaffins from butane to undecane are reported. The dependence of the viscosity expansion coefficient α_η on the expansion factor α_s for the radius of gyration is discussed in the light of the results obtained by an expansion of the Fixman theory for perturbed chains to include partial draining. These results give support to the finite chain effect on the hydrodynamics of expanded coils in the usual range of molecular weight. The exponent a in the relation α³_η = α^a_s depends on molecular weight and agrees with recent nondraining theoretical calculation for exceedingly high polymers.     

Studies of micro-brownian motion of a polymer chain by the fluorescence polarization method. I. Fluorescent conjugates of polyacrylamide

Polyacrylamide having a fluorescent residue at the chain end was prepared by polymerization of acrylamide in the presence of a fluorescent dye. The segmental motion of the chain end in dilute solution was studied by the fluorescence polarization method on the fluorescent polyacrylamide conjugates thus obtained. The linear relation between 1/p and T/η₀ held for every sample studied in aqueous media, where p is the degree of polarization of the fluorescence, T is the absolute temperature, and η₀ is the viscosity of the medium. The mean relaxation time 〈ρ〉 of the conjugate was evaluated from these data as a function of the molecular weight of the conjugate. The value of 〈ρ〉 increased slightly with molecular weight, varying from 3.3 × 10^?9 to 7 × 10^?9 sec. The absolute values of 〈ρ〉 and its molecular weight dependence suggest that 〈ρ〉 represents the mean rotational relaxation time for the cooperative motion of about ten monomeric units at the chain end. The effect of the mean extension of polymer chain on the segmental motion was found to be negligible.     

Hydrodynamic properties and statistical coil dimensions of poly(o-chlorostyrene)

The theta temperature for the system poly(o-chlorostyrene)-methyl ethyl ketone has been determined as 24·5°. The samples used in the determination were prepared by radical polymerization. The dependence of intrinsic viscosity on molecular weight has been measured in methyl ethyl ketone at 24·5° and found to be $\text{η}{}_{\mathrm{\theta }}\text{= 4·68 × 10}{}^{\mathrm{?4}}\text{M}{}_{\mathrm{<mtext>w</mtext>}}{}^{\mathrm{<mtext>M1</mtext><mtext>2</mtext>}}$. The ratio 〈s₌²〉/M was found, by light scattering, to be 5·60 × 10^?18 cm². Analysis of the solution properties indicates that the Kurata-Yamakawa theory is valid in the vicinity of the Flory temperature (UCST).     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Electrode kinetic studies of single electron charge transfer redox couples using the faradaic rectification method

Three single electron charge transfer redox reactions have been studied using the faradaic rectification method. The kinetic parameters obtained for the ferricyanide-ferrocyanide redox couple are α=0.49, k_a⁰=12×10^?2 cm s^?1; for the chromic-chromous system α=0.47, k_a⁰=2×10^?3 cm s^?1 and for the titanic-titanous reaction α=0.49 and k_a^o=6×10^?4 cm s^?1 at 27°C.     

Heat of immersion of iron(III) oxides in water at 25°C

The heat of immersion in water was measured at 25°C for three iron(III) oxides using a twin-type microcalorimeter. One of the samples was commercial α-Fe₂O₃ (sample C) and the other two (samples M and F) were prepared by calcining magnetite and iron(III) hydroxide in air at various temperatures, T_p, from 300 to 700°C. The samples were evacuated at outgassing temperature, T_o, between room temperature and 500°C at a pressure of 1 × 10^?2?2.7 × 10^?2N m^?2 for 6 h. The heat of immersion, h_i(J m^?2), of samples C and M increased with an increase in T_o and showed the maximum h_i at T_o =400°C, while sample F did not show the maximum up to T_o =500°C. The systematic correlation was not observed between h_i and T_p of sample F. The heat of reproduction of the surface hydroxyl group on sample F was approximately estimated as 6.6 × 10⁴ J mole^?1 H₂O.     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

Influence of excluded volume on the conformational property of tail-like chain on the simple cubic lattice

The influence of excluded volume on the conformational property of linear tail-like chain with one end attached to a flat surface is investigated by means of dynamic Monte Carlo method. Conformational properties such as mean-square end-to-end distance 〈R²〉, mean-square radius of gyration 〈S²〉 and mean asphericity parameter 〈A〉 are calculated for random walking (RW) and self-avoiding walking (SAW) tail-like chains on the simple cubic lattice. We find that the EV has nearly the same effect on 〈R²〉 as on 〈S²〉: (1) 〈R²〉_SAW/〈R²〉_RW≈〈S²〉_SAW/〈S²〉_RW∝n^0.204±0.05, where n is the chain length, and (2) the limiting value of 〈R²〉/〈S²〉≈7.7 for both chains. The distribution P(R) of the SAW tail-like chain can be expressed as a R⁴ correction of that of the RW one. We find that the value 〈A〉 of the SAW tail-like chain is bigger than that of the RW tail-like chain for all chain lengths, and the limiting values are 0.446±0.006 and 0.403±0.005 respectively.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Moderately concentrated solutions of polystyrene. I. Viscosity as a function of concentration,temperature, and molecular weight

Data on the viscosity η of moderately concentrated solutions of polystyrene are reported. Several solvents were investigated, including cyclopentane solutions over a temperature span between θ_U = 19.5°C and θ_L = 154.5°C. The data were analyzed in terms of a relation giving η as a function of αφM, where α_φ is the expansion factor for the chain dimensions in a solution with volume fraction φ of polymer with molecular weight M. It is shown that values of α_φ so determined decrease as ? lnα_φ/? lnφ = (1 ? 2μ)/6μ for φ greater than φ^* = 0.2M/s³ for moderately concentrated solutions, where s is the root-mean-square radius of gyration and μ = ? ln[η]/? lnM with [η] the intrinsic viscosity.     

Mean-square radius of gyration of polysiloxanes

The mean-square radius of gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S²〉 on the molecular weight follows the general formula 〈S²〉 = aM^b with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean-square radius of gyration given in this paper with that reported by Flory shows that the difference is obvious for low-molecular-weight polymer and it gradually declines with increasing degree of polymerization.