Unperturbed dimensions and the theta temperature of dextran in aqueous solutions

Intrinsic viscosity measurements were carried out on dextran samples (of different molecular weights) in aqueous solutions at 25, 28, 31, 34, 37, 40, and 43°C. The extrapolation methods were used for the data; they gave unperturbed dimensions, K₀, of the chain. The unperturbed root‐mean‐square end‐to‐end distance 〈r²〉[STACK]^1/2₀[ENDSTACK] calculated for the polymer samples in water indicate that the polymer coils are slightly contracted in this solvent as the temperature is increased. The long‐range interaction parameter, B, was also determined. In aqueous dextran solutions, this showed a significant decrease in the long‐range interactions between 25 and 43°C. The values of Θ = 317.82 and 316.57 K were obtained from the temperature dependence of the interaction parameter B in the Kurata–Stockmayer–Fixman and Berry equations. Calculated values were interpreted mainly on the basis of hydrogen‐bond formation between polymer segments and dextran–water molecules in solution. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 871–876, 1999     

Solution thermodynamics of poly(ethylene glycol)/water systems

The unperturbed molecular dimensions of poly(ethylene glycol) (PEG) samples (of different molecular weights) have been evaluated in aqueous solutions from viscosity measurements at 25, 30, 35, and 40°C. The unperturbed dimension, K_θ, has been determined from extrapolation methods, i.e., Kurata–Stockmayer–Fixman (KSF), Inagaki–Suzuki–Kurata (ISK), and Berry equations. The hydrodynamic expansion factor, α_η, as well as the unperturbed root‐mean‐square end‐to‐end distance, 〈r²〉, found for the system indicated that the polymer coils contract as the temperature is raised from 25 to 40°C. The long‐range interaction (excluded volume) parameter, B, was also evaluated and a significant decrease was found for the PEG/water system between 25 and 40°C. The theta temperatures, θ, were obtained from the temperature dependence of (1/2 ? χ) and the second virial coefficient was detected in the temperature interval of 25–40°C for the system and quite a good agreement with the calculated values evaluated via extrapolation and interpolation methods was observed. The thermodynamic interaction parameter χ was evaluated through the sum of the individual values of enthalpy and entropy dilution parameters, χ_H and χ_S, for PEG samples. All the unperturbed molecular dimensions of PEG/water system were calculated and compared according to M _w and M _n values of PEG samples. Calculated values were interpreted mainly on the basis of hydrogen‐bond formation between polymer segments and PEG‐water molecules in solution. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 203–216, 2006     

Unperturbed molecular dimensions and the theta temperature of dextran in dimethylsulfoxide (DMSO) solutions

Summary The unperturbed molecular dimensions of dextran samples have been determined in dimethylsulfoxide (DMSO) solutions from intrinsic viscosity measurements at different temperatures. The unperturbed dimension parameter, K_o, has been calculated from extrapolation methods.The unperturbed root-mean-square end-to-end distance, <r²>_o ^1/2, found for the polymer samples in DMSO solutions, indicate that the polymer coils are contracted. This distance varies from 3.25 × 10⁻⁷ cm to 2.94 × 10⁻⁷ cm for the sample T 40 and from 8.28 × 10⁻⁷ cm to 7.48 × 10⁻⁷ cm for the sample T 500, in the chosen solvent as the temperature is raised from 25°C to 45°C. In the system of dextran/DMSO, the long-range interaction parameter, B, was also determined and a significant decrease is observed between 25°–45°C. The theta temperatures, Θ, were obtained as Θ= 327.25 K, Θ= 327.41 K and Θ= 323.38 K from the temperature dependence of the interaction parameter in Kurata-Stockmayer-Fixman, Berry and Inagaki-Suzuki-Kurata equations, respectively. Received: 19 January 1998/Revised version: 9 June 1998/Accepted: 10 June 1998     

Hydrodynamic characteristics of aqueous poly(N-vinyl-2-pyrrolidone) solutions in the presence of denaturing agents

The aqueous solution properties of poly(N-vinyl-2-pyrrolidone) (PVP)-denaturing agents (i.e., thiourea, guanidinium chloride, and carbonate) were studied by viscosity measurements. The polymer dimensions were calculated at 25°C and at previously determined theta temperatures. The unperturbed dimension parameter, K₀, hydrodynamic expansion factor, α_η, and unperturbed root-mean-square end-to-end distance, , have been evaluated. Viscosimetrically determined characterisics (e.g., intrinsic viscosity, Huggins constants) and the high values of α_η and can be explained by the interaction between the polymer and denaturing agents. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1615–1618, 1998     

The unperturbed molecular dimensions of poly(ethylene oxide) in aqueous solutions from intrinsic viscosity measurements and the evaluation of the theta temperature

Intrinsic viscosity measurements were carried out on five well characterized fractions of poly(ethylene oxide) in aqueous solutions at 24.9°, 34.9°, and 45.5°C. The Stockmayer-Fixman extrapolation was applied to the data: it yields the unperturbed dimensions K₀ of the chain. The unperturbed root-mean-square end-to-end distance $\text{〈}\text{R}\text{?}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_0$ calculated for the polymer fractions in water indicate that the polymer molecules are expanded in this solvent as the temperature is raised. The temperature coefficient of unperturbed dimension, $\text{d In}\text{〈}\text{R}\text{?}{}^2\text{〉}{}_0\text{d}\text{t}\text{= 0.024}\text{K}{}^{\mathrm{?1}}$, calculated for poly(ethylene oxide) in water using the present data is about 100 times higher than the literature values of 0.23 (±0.02) × 10^?3 K^?1 and 0.2 (±0.2) × 10^?3 K^?1, respectively, obtained from force-temperature (‘thermoelastic’) measurements on elongated networks of the polymer in the amorphouse state and form viscosity measurements on this polymer in benzene. A value of θ=108.3°C was obtained from the temperature dependence of the interaction parameter B in the Stockmayer-Fixman equation.     

Viscosity Behaviour of Dilute and Moderately Concentrated Solutions. 1. Poly(vinylpyrrolidone) in 2-propanol

Abstract

The zero-shear viscosity of dilute to moderately concentrated poly(vinylpyrrolidone) solutions in 2-propanol were measured at different temperatures in the newtonian flow range. The viscosity data were analyzed in terms of Martin's and Fedor's equations. The viscosity-concentration data were generalized in terms of reduced variables. The relation between the K_M parameter for the rheological interaction and some characteristics of polymer solutions such as the flexibility of the PVP chain is discussed. The temperature dependence of viscosities was expressed by the Arrhenius-Frenkel-Eyring equation and the activation energy of viscous flow of polymer solutions (ΔGv) was calculated. It was shown that ΔGv increases with concentration and it is independent of the temperature.     

Huggins' constant and unperturbed parameter of dilute polymer solutions

A novel method developed to evaluate the unperturbed parameter K_θ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, k_Hθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κ_Hθ. All calculations were done by the linear least-squares method. The K_θ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on K_θ can be obtained for polystyrene and poly(vinyl acetate).     

Influence of external environments on fracture toughness of epoxy resin

Crack propagation in an epoxy resin in the presence of organic solvents was investigated. Fracture toughness (K_IC, a critical stress intensity factor) of the epoxy resin in various external environments was measured using a double cantilever beam specimen. Fracture toughness for initiation (K_ICi) of the resin in the presence of organic solvents was larger than that in the absence of solvents, and the epoxy resin showed a minimum value of K_ICi in the presence of the organic solvent whose solubility parameter was about 11 (cal/cm³)^1/2. This was due to large plastic deformation at a crack tip and the yield strength was lowered by exposure to organic solvents. The former increases K_IC, while the latter decreases K_IC. Fracture surfaces of the resin fractured in solvents suggest that a crack grew slightly when accompanied by a large plastic deformation, and then propagated at high speed.     

Some properties of low molecular weight polybutadiene and polytetrahydrofuran

The proposition, that low molecular weight polymer fractions in good solvents behave as if they were under ? conditions, has been examined experimentally. Series of monodisperse hydroxy-terminated polytetrahydrofuran (PTHF), 82% 1,4-polybutadiene (PBD), and 30% 1,4-PBD were prepared, and values of M?_n obtained by vapor-pressure osmometry and endgroup analysis. The Mark–Houwink viscosity parameters K and ν were determined in a number of solvents. The general conclusion is that the proposition is invalid for these systems notwithstanding the fact that ν = 0.50 for one of them [82% 1,4-PBD in methyl ethyl ketone (MEK) at 25°C]. For this particular case, the following evidence suggests that these are actually ? conditions so that the apparent fulfilment of the proposition is fortuitous. (1) Cloud-point precipitation yields ? = 26 ± 3°C in MEK. (2) The value of K is close to that of K_? found elsewhere for PBD in a different solvent at a similar temperature. (3) Application of the Kurata-Stockmayer iterative procedure for estimating K_? from data in good and bad solvents yields a reasonably small discrepancy (10%) between the K_? values from data in toluene and MEK at 25°C for this polymer and only a 3% difference in the unperturbed dimensions (〈r₀²〉/M)^1/2 derived from them. Measured melting points T_m of PTHF (M?_n = 1000–13000), plotted as a function of chain length Z, viz., 1/T_m = 1/T_m0 + 2R/ZΔH_f, yield 43 ± 3°C and 1.6 kcal/submole, respectively, for the limiting melting point T_m0 and the heat of fusion ΔH_f. The former is in good agreement with the value obtained dilatometrically for high molecular weight polymer, while the latter indicates a degree of crystallinity of ca. 54%.     

The temperature dependence of the doolittle equation parameter for polymer liquids

The Doolittle equation parameter for polymer liquids is a function of temperature. Its dependence on temperature can be expressed by a quadratic equation. The constants in the equation are determined for four vinyl-type polymer liquids: polystyrene (PS), poly(vinyl acetate) (PVAc), polydimethylsiloxane (PDMS), and polyisobutylene (PIB). It was found that the Doolittle parameter decreases with increasing temperature. Equations are presented for the pressure and temperature coefficients of viscosity, isoviscous temperature coefficient of volume, and the constant K_m in the Miller equation. Comparisons of the predictions of the equations, with those in the literature, are favorable. © 1993 John Wiley & Sons, Inc.     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002     

Rheological properties of concentrated polymer solution: Polybutadiene in good and θ solvents

The zero shear viscosity, η° of three polybutadiene samples having different molecular weights over a wide range of concentration (1.0–35.0% polymer) in good and θ solvents has been studied. Superposition of viscosity data has been made to give a single composite curve for each solvent by shifting them vertically by a factor (M°/M)^3.4, where M° represents the molecular weight of the reference sample. The shift factor is found to be proportional to M^3.4 in the region of higher concentration, which indicates that the 3.4-power law is valid for the data of polybutadiene. The double-logarithmic plots of relative viscosity η°_r as a function of c⁵M^3.4 yielded a single composite curve approximating a straight line with slope of unity at the higher values of the variables. The results indicate that over a considerable range of the variables (molecular weight and concentration) at a constant temperature, the relative viscosity is a single function of c⁵M^3.4. The results for double-logarithmic plots of zero shear specific viscosity η°_csp as a function of concentration confirmed those observed in polycholoroprene samples studied earlier that the η0_sp values in θ solvents at higher concentration region are found to be higher than those found in good solvents, whereas in the moderately concentrated region the values are just opposite in θ and good solvents. The viscosity crossover in θ solvents is not as sharp as is found in case of polychloroprene samples and that crossover, too, has taken place in the range of concentration of 11.7–31.6% polymer, which is comparatively higher than that of polychloroprene samples (6.06–21.0% polymer). The results indicate some relation between viscosity crossover and polymer polarity, supporting the idea of enhanced intermolecular association in poor solvents. To correlatethe viscosity data obtained in good and poor solvents, two methods, one given by Graessley and the other given by Dreval and coworkers involving the correlating variable c[η], were considered. The plots of relative viscosity η°, versus the correlating variable c[η] in benzene (good solvent) yielded one curve, but in the case of θ solvents (dioxane and isobutyl acetate), the same plots yielded three separate curves instead of a single curve, which is rather unusual. The appropriate correction on the correlating variable for chain contraction in the concentrated region in a good solvent moved the data to a common curve, especially in lower concentration region, but at the higher concentration region a slight overestimation of data seems to have been effected. On the other hand, the plots of log η as a function of correlating variable c[η] yielded a single curve for three samples in the good solvent benzene, but in poor solvents (diozane and isobutyl acetate) the same plots yielded three separate curves for three samples instead of a single curve, the reason for which is not known at present. However, the normalization of the correlating variable c[η] with Martin constant K_M reduced all experimental data of the polymer samples to a common curve. The correlation of the viscosity data by either of the two methods seems to be possible in the case of the nonpolar flexible polymer, polybutadiene.     

Properties of aqueous salt solutions of poly(vinylpyrrolidone). II. Polymer dimensions and thermodynamic quantities

The unperturbed dimensions and thermodynamic parameters of poly(vinylpyrrolidone) (PVP) have been studied in aqueous salt solutions, e.g. phosphates, mono- and dihydrogen phosphates, carbonates, sulphates of sodium and potassium. Values of K₀ ( = [η]_ΘM^-1/2, where [η]_Θ is intrinsic viscosity at the theta temperature and M is molecular weight) with M_w = 78 000 g mol^-1 were found to range from 4·63×10^-4 to 5·56×10^-4 dl g^-1, and root-mean-square end-to-end distances, 〈r²〉₀^1/2, ranging from 1·61×10^-6 to 1·68×10^-6cm were evaluated. Values of the characteristic ratio, C_n, the steric parameter, σ, and the enthalpy and the entropy of dilution parameters, χ_H and χ_S, have also been calculated, and the interaction parameter was found to be χ-0·5<-0·001 for aqueous salt solutions of PVP. ©1997 SCI     

Phase equilibria of modified ethylene glycol–maleic anhydride–phtalic anhydride polyester resins

This paper describes the influence of a termination of ended carboxyl groups of ethylene glycol–maleic anhydride–phtalic anhydride polyesters with cyclohexanole on a position of phase interface of the unsaturated polyester–styrene system. At given temperatures, optimal molecular weights were determined for the achievement of maximal miscibility of this polymer with styrene. Simultaneously, a model implicit equation was proposed, which is based on the assumption that the dependence of the interaction parameter χ on number-average molecular weights is similar to that dependence of the interaction parameter χ on temperature. Solution of these implicit equation are isotherms in the phase diagram M _n??₂?T_{cloude point}.     

Solution properties of polyacrylic esters. II. Evaluation of unperturbed dimensions

According to existing well-known theories unperturbed dimensions can be calculated from light scattering and viscosity measurements. The statistical segment A_m proposed by Kuhn is a good measure for the flexibility of an unperturbed polymer coil. With the data reported in part I of the dependence of the radius of gyration and the Staudinger index, respectively, on the molecular weight, A_m was calculated for nine polyacrylic esters and poly(acrylic acid). Poly(acrylic acid) with A_m = 13,6 Å has the highest flexibility. The stiffness of the polymer chain is increased with growing C-number of the alcohol. Branching in the alcohol further increases the stiffness of the polymer chain.     

Hydrodynamic properties of poly-1, 2,5-trimethyl- and 2,5-dimethyl-4-ethynilpyperidol-4 hydrochlorides in solution

Poly-1,2,5-trimethyl- and 2,5-dimethyl-4-vinylethynyl-pyperidol-4 hydrochlorides with strong polyelectrolyte properties have been investigated in water-salt and water-alcohol mixtures. The parameters K_η and a, K_s and b in the Mark-Houwink equation, the unpertubed dimensions K_o and flexibility factor of polymer chain σ were determined in these solvents. We also studied the influence of ionic strength, the values of counterion charges and temperature on the size of polyelectrolyte molecules. The formation of interchain ‘bridges’ in the case of multivalent anions were found, resulting in a strong decrease of the chain dimensions. The addition of organic solvent gives a 2–3-fold in intrinsic viscosity, whereas the conformational parameters change little.     

Unperturbed dimensions and intrinsic viscosity-molecular weight relationship of copolyesters poly(ethylene terephthalate-co-ethylene isophthalate)

The relationship [η] = KM^a and unperturbed dimensions of the copolyesters poly(ethylene terephthalate-co-ethylene isophthalate) with 7.5% and 25% isophthalic structures in the main chain were determined. The experimental data proved the influence of the amount of isophthalic structures upon the values of K and a from the relation between intrinsic viscosity and molecular weight and on the values for unperturbed dimensions.     

Viscosity Behaviour of Poly(N-vinyl-2-pyrrolidone) in a Water/VOSO4 Binary Mixture: Preferential Interactions

Poly(N-vinyl-2-pyrrolidone) (PVP) [2]/water [1]/VOSO₄ [3] ternary system interactions have been studied by viscometric and densitometric techniques. Preferential water absorption inside the macromolecular coil and preferential salt interaction with the polymer external domain were observed. The unperturbed dimensions of the macromolecule increased with the salt concentration up to 75mM VOSO₄, a point where the intrinsic viscosity was also a maximum and a conformational transition could be produced. The polymer– solvent interaction became worse with salt concentration and VOSO₄ behaved as a salting-in agent for the polymer, the binary solvent mixture being thermodynamically unfavourable. © of SCI.     

Solubility profiles of poly(ethylene glycol)/solvent systems. II. comparison of thermodynamic parameters from viscosity measurements

Solution thermodynamics of PEG samples in aqueous and nonaqueous (methanol, chloroform, tetrahydrofuran, and dimethylsulfoxide) solutions have been investigated by viscometric studies at 25, 30, 35, and 40°C. The hydrodynamic expansion factor, a_h, and the unperturbed root mean square end‐to‐end distance, , found for the system indicated that the polymer coils contract as the temperature is raised. The long‐range interaction parameter, B, was also evaluated and a significant decrease with increasing temperature was observed. The theta temperatures, θ, obtained from the temperature dependence of (1/2 ? χ) and the second virial coefficient, A₂, are quite good in agreement with the calculated values evaluated via extrapolation and interpolation methods. The thermodynamic interaction parameter, χ, was evaluated through the sum of the individual values of enthalpy and entropy dilution parameters for PEG samples. The restrictions applying to the establishment of concentration regimes, short‐range, and long‐range interactions are discussed. A parallelism is found between solubility profiles obtained by solution viscometry and solubility parameter approaches for PEG/solvent systems. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Concentration dependence on viscosity of oligourethane diols

To obtain viscosity suitable for application, relatively low molecular weight polymers, i.e., oligomers, are used in the formulation of high solids coatings. To support this requirement, the concentration dependence of the viscosity of synthesized oligourethane diols in different solvents was analyzed using Erickson's models. By regression analysis, it was found that the correlation coefficients are fairly good and the plots of the residuals are more random. The weight intrinsic viscosity, [η_o], composed of the oligomer component, O_5[η]o, and the oligomer-solvent interaction component, I_[η]o, was calculated from the intercept of the plot of 1/ln η_r vs. 1/o₀. The parameter I_[η]o, related to the solvent molar volume and the distance between the oligomer and solvent partial cohesion parameter coordinates, indicates the degree of interaction between the oligomer and solvent. The partial cohesion parameters of the oligomers obtained by the group-contribution method were used for calculating the interaction component of oligourethane diols. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1343–1351, 1997