Hydrophobically modified polyelectrolytes I. Dilute solution properties of fluorocarbon-containing poly (acrylic acid)

Dilute solution viscosity of fluorocarbon‐containing hydrophobically modified poly (acrylic add) was measured in aqueous solutions of various NaCl concentrations. The intrinsic viscosity ([η]) and Huggins coefficient (k_H) were evaluated using Huggins equations. It is found that, at low Nacl concentration, the modified polymers exhibit values of intrinsic viscosity ([η]) and Huggins coefficient (k_H) similar to those of unmodified polymers. For both of the modified and unmodified polymers, the intrinsic viscosity decreases with increase of NaCl concentration, while the Huggins coefficient increases upon addition of NaCl. But the variation of [η] and k_H is more significant for the modified polymers, which reflects the enhanced intra‐ and intermolecular hydrophobic association at higher Nacl concentration.     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Concentration Effects in Sec for Polymer/Polymer/Solvent Systems

Abstract

A model quantitatively describing the experimental shifts in elution volumes of polymeric solute A in the presence of another polymer B is developed. The concentration-dependent shrinkage of A coils has been evaluated from the intrinsic viscosity displayed by polymer A in the ternary solution formed by itself at c_A concentration + polymer B at c_B concentration + solvent. Resulting concentration effects depend on both polymer concentrations (c_A and c_B), on the intrinsic viscosities of both polymers in the solvent (|η|A and |η|B), on the Huggins' coefficients k_A and k_B, and on the quadratic concentration coefficients in the polynomial expansion of ηsp/c, namely k^′ _A and k^′ _B. Predicted elution volumes are compared with experimental ones for two different types of literature systems: those studying polymer A elution at diverse c_A concentrations in eluents consisting of mixtures of polymer B + solvent and those in which polymer A + polymer B mixtures are injected at once in the pure solvent used as eluent. In order to eliminate experimental uncertainties about k_i and k^′ _i (i=A, B) values, applied k^′ _i values were those obtained from the empirical correlation k^′ _i + 0.122 = k_i ² whereas k_i ones were obtained from Imai's equation.     

Streaming birefringence. VII. Influence of the intermolecular hydrodynamic interaction on the viscosity and streaming birefringence of polymer solutions

The cavity model used in the theory of dielectrics was applied to hydrodynamics to calculate the force exerted by a system of soft dumbbells on a reference dumbbell in a hydrodynamic field. The influence of this force on the viscosity and flow birefringence and its dependence on both the concentration and velocity gradient were calculated. The system of equations has a real solution only for values of β = M[η]η₀γ/RT which are smaller than a critical value rapidly decreasing with increasing concentration. At zero concentration the results obtained agree with the theory of a single isolated dumbbell model. The calculated Huggins constant is k′ = 0.4. The extinction angle is connected with the relative viscosity very nearly as derived from experiments. However, the theory fails at higher concentrations and gradients yielding an increase in viscosity with the gradient and infinite zero-shear viscosity for the concentration c = 2.5/[η].     

Rheological properties of wheat gliadins in aqueous propanol

Rheological properties of wheat gliadins in 50%(V/V) aqueous propanol were carried out as a function of gliadin concentration c and temperature.The solutions at 20 g L 1 to 200 g L 1 behave as Newtonian fluids with an flow activation energy of 23.5 27.3 kJ mol 1.Intrinsic viscosity [η] and Huggins constant k H are determined according to Huggins plot at c ≤ 120 g L 1.The results reveal that gliadins are not spherical shaped and the molecular size tends to increase with temperature due to improved solvation.     

Evaluation of Huggins' Constant,Kraemer's Constant and Viscosity Concentration Coefficient of Polymer Dextran in Urea,Glycine and Glucose

Abstract

Reduced viscosity (η_sp/c) and Inherent viscosity (In η_rel/c) of dilute solution of water soluble polysaccharide polymer “Dextran” has been calculated by measuring the flow time of the polymer solution in solvents like 6(M) Urea, 2(M) Glycine and 50% Glucosc at three different temperatures ? 25°C, 30°C and 35°C. From extrapolation of curve (η_sp/c) versus (c) and (In η_rel/c) versus (c), thermo viscosity parameters like Huggins' constant (k′_H) Kraemer's constant (k″_H) and viscosity concentration coefficient (a ₂) have been estimated which enable us to know the fate of the polymer molecules in these solvents.     

Self-diffusion and electron spin exchange of hydrophobic probes in dilute solution

Electron spin exchange rate constants have been measured by ESR spectroscopy for a nitroxide spin probe in a number of solvents, including water. The apparent collision rate constants (k _c ^′ ) calculated from the spin exchange rate constants showed marked deviations from the Smoluchowsky equation (k _c ^′ η=const), which were greatest in solvents of lowest viscosity. These effects are attributed to inefficiency of the spin exchange process. Self-diffusion coefficients (D) were measured for diamagnetic analogs of the nitroxide spin probe in similar solvent systems by pulsed field gradient NMR spectroscopy. TheD values gave reasonable agreement when corrected for viscosity (Dη=const). Collision rate constants calculated fromD were in good agreement with those measured by ESR in solvents of high viscosity. Thek _c ^′ value for the spin probe in water was significantly lower than that in isoviscous organic solvents. This effect is discussed in terms of a hydrophobic hydration shell for the spin probe which acts as an additional barrier to collision.     

New insights in the properties of cellulose in phosphoric acid: viscometric study

Measurements of viscosity were carried out using several solutions of cellulose in different concentrations of phosphoric acid at different temperatures. The intrinsic viscosity [η]₀, a measure for the size of a single chain and the Huggins constant k_H, a measure for the interaction between chains were derived.     

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).     

Variation of polymer chain dimensions with temperature below the theta point

The temperature dependence of the intrinsic viscosity [η] for the system polystyrene-cyclohexane in the interval ?20 < (T ? ψ) ≤ 0 near the ideal temperature ψ has been investigated. The observed diminution in size of the molecular coil with decreasing temperature is attributable to attractive net polymer-solvent interactions, denoted by negative values for the excluded volume parameter z. The data thus comprise an interesting selection for comparison with the predictions of various excluded volume theories. Among the approximate, closed-form expressions the functional relationship of Flory (x⁵ ? α³ ～ z) appears to describe best the variation of [η] with temperature in the region examined. The behavior of the Huggins constant k′ derived from the intrinsic viscosity plots is also examined, in accordance with the Peterson-Fixman model, suitably extended to the temperature region below ψ.     

Thermal Back‐Isomerization of Spirocyclic Naphtho‐oxazine and Phenanthro‐oxazine Derivatives in Alcohols,Nitriles, and Poly(alkyl methacrylates)

The thermal back‐isomerization of spiro[indole‐naphtho‐oxazine] 1 and spiro[indole‐phenanthro‐oxazine] 2 was studied in a series of primary alcohols, nitriles, and poly(methylmethacrylate), poly(ethylmethacrylate), and poly(isobutyl methacrylate) films by laser‐flash photolysis in the temperature range of 0 – 70°. The decay is monoexponential in fluid solution, but deviates strongly from this behavior in polymeric environments even above the glass transition temperature of the polymers (Tg). In liquids, a very small solvent effect is observed on the isomerization rate constants (k_iso) for 1 , which is attributed mostly to the solvent viscosity η. The values of k_iso for 2 show influence of solvent viscosity and polarity, which were studied by application of a semiempirical relationship that accounts for non‐Markovian processes. The decay kinetics in polymers was described by a Gaussian distribution of the activation energy and by a kinetic model that takes into account the simultaneous relaxation of the probe and the environment. For 1 and 2 , the rate constant at the center of the Gaussian distribution is very similar to the first‐order rate constant in nonpolar solvents. The Gaussian width of the distribution (σ) decreases with temperature and is very similar in all polymers under Tg, and, above Tg, σ decreases more abruptly. We make comparisons of the parameters derived from analysis of both 1 and 2 in polymers, as well as of their behaviors in solution and in polymers.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Proposed GPC and intrinsic viscosity analyses of randomly crosslinked polymers having primary distributions of the schulz-zimm form

A mathematical treatment is presented for the gel-permeation chromatographic and intrinsic viscosity behavior of randomly crosslinked polymers having primary molecular weight distributions of the Schulz-Zimm form. Kimura's serial solution of the integro-differential equation derived by Saito for randomly crosslinked polymers is employed for the distribution function. The intrinsic viscosity of a molecule containing i crosslinks is assumed related to that of a linear molecule of the same number of units through [η]_br/ = g_i^½[η]_l where g_i = (R_br²)_i/R_l² = {[1 + (i/6)]^½ + (4i/3π)}^?½. R_brand R_l denoting the root-mean-square radii of gyration of branched and linear chains of the same mass. It is also assumed that GPC elution is controlled by the hydrodynamic volumes of the molecules. Representative calculation results are displayed for polymers with a narrow primary distribution and the “most probable” primary distribution. Results for the latter polymers are compared with those previously obtained by a somewhat different mathematical approach.     

Effect of viscosity on termination rate constant in radical polymerization at low conversion

By using the expression, k_t = A₁D_s for the chain termination rate constant (where A₁ is a constant and D_s is the diffusion constant of radical chain end), a familiar chain termination rate constant, k_t = A₂/η_s (where A₂ is a constant and η_s is solvent viscosity) was examined with variation of conversion x. It was found that the proportionality of chain termination rate constant and solution viscosity is a valid relation at conversion 0 but is approximate at conversion x_c ≥ x > 0. Here x_c denotes a critical conversion under the average distance around spherical polymers formed in polymerization solution is zero. At conversions above x_c, the inverse relation between chain termination rate constant and solution viscosity is not correct.     

Mark-Houwink relations for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene

The parameters in the Mark-Houwink relationship, [η] = K′M?_v^a, for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene at 130°C have been estimated. They were found by measuring the limiting viscosity numbers of a series of fractions with molecular weights ranging from less than 10,000 to almost 700,000. The results are for 1-chloronaphthalene, [η] =0.0555 M?_v^0.684 (with a standard error of 0.0064 in K′ and 0.010 in a) and for 1,2,4-trichlorobenzene, [η] = 0.0392M?_v^0.725 (with a standard error of 0.00703 in K′ and 0.015 in a), where [η] is expressed in ml/g. The unperturbed end-to-end distance calculated from the viscosity-molecular weight data agrees with the theoretically expected value.     

Effect of the solvent upon the diffusion coefficient of polydisperse polystyrene and styrene-acrylonitrile copolymer in dilute solution

A laser homodyne spectrometer was used to obtain translational diffusion coefficients for dilute polystyrene and styrene-acrylonitrile copolymer solutions at room temperature. Data were obtained in the concentration range from 0.01 to 2.0 g polymer per 100 cm³ solution for polystyrene in benzene and in decalin; and for copolymer in dimethyl formamide, in methyl ethyl ketone, and in benzene. The samples were polydisperse polystyrenes of weight average molecular weights between 80,000 and 350,000 and polydisperse copolymers of weight average molecular weights between 200,000 and 800,000. The SAN copolymers were random copolymer samples containing 24% by weight acrylonitrile. For each of the systems investigated the concentration dependence of the diffusion coefficient was linear over the concentration range studied, and was expressed as D(c) = D₀(1+k_Dc). Values of D₀ could be explained with a modified Kirkwood-Riseman expression. Values of the parameter k_D obtained from the slopes could be interpreted using the two-parameter theory approach as suggested by Vrentas and Duda. The value of k_D is positive for high-molecular-weight polymers and negative for low-molecular-weight polymers. For a particular polymer, the molecular weight at which k_D changes sign is greater for poor solvents than for good solvents. Observed values of D₀ were 1 × 10^?7 to 7 × 10^?7 cm²/sec.     

Conformational Relaxation of p‐Phenylenevinylene Trimers in Solution Studied by Picosecond Time‐Resolved Fluorescence

Two p‐phenylenevinylene (PV) trimers, containing 3′‐methylbutyloxyl (in MBOPV3) and 2′‐ethylhexyloxyl (in EHOPV3) side chains, are used as model compounds of PV‐based conjugated polymers (PPV) with the purpose of clarifying the origin of fast (picosecond time) components observed in the fluorescence decays of poly[2‐methoxy‐5‐(2′‐ethylhexyloxy)‐p‐phenylenevinylene] (MEH‐PPV). The fluorescence decays of MBOPV3 and EHOPV3 reveal the presence of similar fast components, which are assigned to excited‐state conformational relaxation of the initial population of non‐planar trimer conformers to lower‐energy, more planar conformers. The rate constant of conformational relaxation k_CR is dependent on solvent viscosity and temperature, according to the empirical relationship k_CR=aη_o^?α?exp(?αE_η/RT), where aη_o^?α is the frequency factor, η_o is the pre‐exponential coefficient of viscosity, E_η is the activation energy of viscous flow. The empirical parameter α, relating the solvent microscopic friction involved in the conformational change to the macroscopic solvent friction (α=1), depends on the side chain. The fast component in the fluorescence decays of MEH‐PPV polymers (PPVs), is assigned to resonance energy transfer from short to longer polymer segments. The present results call for revising this assignment/interpretation to account for the occurrence of conformational relaxation, concurrently with energy transfer, in PPVs.     

Characterization of a single sample of an unknown polymer by size exclusion chromatography

The relationship between viscosity constants, k', a and K_η from the equations of Huggins and Mark-Kuhn-Houwink has been considered. It is shown, theoretically, that the sum of k' and a must be constant for all flexible-chain macromolecules irrespective of the solvent used. On this basis, a combination of chromatography and viscometry measurements can be used to characterize a new species. The method has been applied to the new polymer, poly[methyl(pyridin-3-yl) siloxane] ( 1 ) where no suitable calibration standards are available. The value of a, k', and K_η for 1 has been calculated. The calculated constants enabled an estimation of different average molecular weights (M_nM_wM_z) and polydispersity (M_w/M_n) from a minimum of experimental data. The new method is general and can be applied to any homogeneous linear flexible-chain nondraining macromolecule.     

Dilute solutions of poly(vinyl alcohol) derived from vinyl trifluoroacetate

The dilute-solution behavior of poly(vinyl alcohol) (PVA_VTFA), derived from vinyl trifluoroacetate, in water-dimethylsulfoxide (DMSO) mixtures was investigated. With solvent mixtures ranging from 10 to 20 vol % DMSO, the relation between the reduced viscosity η_sp/C and the polymer concentration C was linear for polymer concentrations above 0.2 g/dL, whereas in solutions in mixed solvents of other compositions the dependence was linear for polymer concentrations above 0.1 g/dL. The relation between the intrinsic viscosity [η] obtained for aqueous solutions of PVA_VTFA and the molecular weight M estimated from viscosity measurements in solutions of poly(vinyl acetate) (PVA_VTFA), obtained by acetylation of PVA_VTFA, was given by [η] = 7.34 × 10^?4 M^0.63. The value of [η] was greatest for the solvent mixture with 10 vol % DMSO and smallest for about 50 vol % DMSO, and Huggins constants k were smallest and greatest for these two cases, respectively. The turbidity of the solutions of low-molecular-weight PVA_VTFA, was higher than that of high-molecular-weight PVA_VTFA up to 30 vol % DMSO, and the reverse relation held for 40-70 vol % DMSO.     

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.