One-point method for determination of number-average molecular weight

The following well-known equation permits the ready determination of M _n from a single osmotic pressure measurement at a known concentration, if the second virial coefficient is previously given: On this basis, the one-point method was investigated to determine the number-average molecular weight. It was found that this method was applicable to commercial polymers. However, in this application, the dependence of Γ₂ on molecular weight distribution has to be kept in mind.     

A one-point intrinsic viscosity method for polyethylene and polypropylene

A statistical analysis of dilute solution viscosity data for a wide range of polyethylene and polypropylene samples in Decalin at 135°C has shown that the Martin equation fits the experimental data better than the Huggins equation at higher values of [η]c. A grand average k of 0.139 is applicable to both polymers. Based upon this, tables have been calculated permitting the ready determination of [η] from a single relative viscosity measurement at a known concentration. The Martin equation has been put into a universal form, permitting [η] to be calculated from a measured η_sp if k and c are known. Graphs relating η_sp to [η] are included for use of the Martin equation over wide ranges of both k and c. It was found that the Solomon and Ciuta equation fits the experimental polyethylene and polypropylene data, and the reasons for this are discussed.     

The relation between melt flow properties and molecular weight of polyethylene

The non-Newtonian behavior of commercial linear polyethylene samples and their fractions were studied at 190°C. The viscosity η versus shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} curves of whole polymers could be superimposed onto a single master curve despite the variations of their molecular weights and molecular weight distributions. For fractions, however, the same master curve was inapplicable, and the sensitivity of the viscosity to shear rate was found to be greater than those of the whole polymers. The zero-shear viscosities η₀ of fractions were related to the 3.42 power of the weight-average molecular weight M_u as follows: For whole polymers, the zero-shear viscosities were found to be considerably higher at the same M_w and markedly lower at the same z-average molecular weight M_z than those of the fractions. Thus, it was concluded that η₀ corresponds to an average of molecular weight between M_w and M_z. It was found that the molecular relaxation time τ is proportional to M_z^5.3 for whole polymers and to η₀M_w for fractions. Using these relations it was possible to relate the flow ratio, the ratio of flow rates at two different shear stresses, with the molecular weight distribution.     

Studies on determination of molecular weight for ultrahigh molecular weight partially hydrolyzed polyacrylamide

The molecular weight characterization of partially hydrolyzed polyacrylamide (HPAM) for enhanced oil recovery use is rather difficult because of its ultrahigh molecular weight copolymer and polyelectrolyte behaviors in solution. In this work the effects of aqueous NaCl solution concentration and degree of hydrolysis of polymer on molecular dimension were studied. A simple and precise method for determining molecular weight of HPAM is presented. The molecular weight of HPAM with any degree of hydrolysis can be calculated from the [η]−M_w equation of unhydrolyzed PAM in an H₂O system by measuring , of HPAM obtained in aqueous NaCl solutions by extrapolating salt concentration to infinity. Because the values of of HPAM of different degrees of hydrolysis are all equal to the corresponding [η] value of the unhydrolyzed PAM of the same degree of polymerization, the molecular weight of HPAM of any degree of hydrolysis can thus be calculated from the [η] − M_w equation for PAM homopolymer. © 1996 John Wiley & Sons, Inc.     

Criteria to predict the embrittlement of polycarbonate

A direct correlation is found between the time evolution of the yield stress in unnotched tensile bars and that of the impact energy measured using notched tensile bars. In both cases a master curve can be constructed with an Arrhenius type of shift function, using the same activation energy. Combining these experimental findings with numerical simulations lead to a maximum hydrostatic stress as a criterion to predict the onset of failure, . Where aging kinetics is not dependent on the polymer’s molecular weight, embrittlement is, and for higher molecular weights a higher is found. Moreover, for high polymers we observe a more stable craze extension and crack propagation after cavitation, causing the computed impact energies to underestimate the experimental ones for all but the lowest molecular weight polymers. Because the maximum in hydrostatic stress under the notch, σ^h, increases with the polymer’s age, defined by the value of the state parameter S_a, and given the proportionality between S_a and the yield stress, σ_y, an alternative failure criterion is proposed which is a molecular weight dependent critical value of the evolving yield stress, σ_y,c. It predicts a product’s increased sensitivity to damage under the influence of progressive aging as enhanced by temperature.     

Stress relaxation behaviour of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

The stress relaxation behaviour of liquid crystal-forming ethyl celllulose (EC) solutions in m-cresol was determined by means of a cone-plate type viscometer at 30°C. The effect of molecular weight (MW) on the behaviour was also determined. The relaxation behaviour could be fitted with the following equation: where σ_i and σ_f are steady-state shear stresses at shear rate $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, σ(t) is time- dependent stress, A₁ and A₂ are constants, τ₁ and τ₂ are relaxation times, t is time, and t_c is a characteristic time. When log σ* was plotted against time, one straight line was obtained for isotropic solutions, whereas anisotropic solutions yielded two straight lines. This suggests that the liquid crystalline solutions have two separate relaxation processes: Process 1 has a relatively short relaxation time, and process 2 has a long one. The parameters τ₁, τ₂, and A₂ were greatly dependent on polymer concentration, combination of $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, and MW, whereas A₁ was independent thereof and was close to unity. The process 1 was supposed to be valid for individual molecules, and process 2 for liquid crystalline domains or randomly aggregated or entangled molecules.     

A model relating the elastic properties of high-density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady-shear melt viscosity of high-density polyethylene to the molecular weight distribution is applied toward predicting the steady-shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ_m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ_c, the maximum relaxation time allowed at ${\rm \dot \gamma }$. Equations relating molecular weight and relaxation time to the steady-shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady-shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone-and-plate viscometer. The assumed proportionality constant between τ_c and 1/${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ_m = 1.4 × 10^?19 (M)^3.33. Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.     

Melting Properties of Syndiotactic Polystyrenes and Effect of Hydrogen on Molecular Weight Distribution

Summary: The melting properties of syndiotactic polystyrenes are significantly affected by the structural molecular properties of the polymers. The most important influences on the melting behavior are stereoregularity, molecular weight and molecular weight distribution of the polymers. The melting temperature is increased by an enhanced syndiotacticity at sufficiently high molecular weights and at narrow molecular weight distributions. The degree of syndiotacticity obtained primarily depends on the kind and structure of the cyclopentadienyl ligand of the transition metal catalyst, whereas the effect of the other ancillary ligands on stereoregularity is negligible at the same cyclopentadienyl ligand. At narrow molecular weight distributions with below 2.8 and at constant stereoregularities, the molecular weight has a remarkable effect on the melting behavior at weight‐average molecular weights lower than about 80 000 g · mol^?1, resulting in a significant decrease of the melting temperature until below 230 °C. The presence of hydrogen during polymerization leads to a significant shift to lower molecular weights at comparably small amounts of hydrogen, but results in the occurrence of an additional peak in the molecular weight distribution at larger hydrogen concentrations giving evidence for the formation of a second active polymerization site producing lower molecular weight polymers. At constant stereoregularity, the broadening of the molecular weight distribution leads to decreased melting temperatures and to improved flow properties of the syndiotactic polystyrenes with increasing shear rates at moderate molecular weight distributions.

Detailed molecular weight distributions of syndiotactic polystyrenes in dependence on the hydrogen concentration.     

The molecular weight average obtained by combining quasielastic light-scattering and intrinsic viscosity measurements

For “monodisperse”, randomly coiled macromolecules, we find that the molecular weight, intrinsic viscosity, and diffusion coefficient are accurately related by This equation holds for denatured proteins in 6M GuHCl(aq) as well as for narrow polystyrene fractions in tetrahydrofuran. For a Schulz distribution of molecular weights, the weight measured from combining diffusion and viscosity data is closely approximated by These equations are verified with measurements of wide molecular distributions of polystyrene in toluene and data from the literature. These relations provide a rapid, nondestructive method to determine a well-specified molecular weight average of small quantities of polymers in a wide diversity of solvents using quasielastic light scattering techniques to evaluate polymer diffusion coefficients.     

Struktur und eigenschaften von ABS-polymeren II.. Grenzviskositäts-molekulargewichtsbeziehungen für azeotrope styrol/acrylnitril-copolymerisate

Limiting viscosity numbers of azeotropic copolymers of styrene and acrylonitrile were measured in dimethylformamide (DMF) and in methyl ethyl ketone (MEK). Their weight average molecular weights (10⁴ g/mole ? M_w ? 10⁶ g/mole) were determined by light scattering. The viscosity – molecular weight relationships obtained, are for DMF and for MEK The number average molecular weights were determined by osmotic pressure measurements, and now molecular weight heterogenities were calculated. The homogenity in composition was investigated by light scattering measurements in different solvents. In addition the viscosity-molecular weight relationship for polystyrene in DMF was determined and compared with the relationship for the azeotropic poly (styrene-co-acrylonitriles) and for polyacrylonitrile: On account of the results a possibility is shown for calculating molecular weights of poly (styrene-co-acrylonitrile) of any composition from limiting viscosity numbers and the acrylonitrile contents.     

Electrospinning of linear homopolymers of poly(methyl methacrylate): exploring relationships between fiber formation, viscosity, molecular weight and concentration in a good solvent

A series of seven linear homopolymers of poly(methylmethacrylate) ranging from 12,470 to 365,700 g/mol M_w, were utilized to further explore scaling relationships between viscosity and concentration in a good solvent at 25 °C and to investigate the impact of these relationships on fiber formation during electrospinning. For each of the polymers investigated, chain dimensions (hydrodynamic radius and radius of gyration) were measured by dynamic light scattering to determine the critical chain overlap concentration, c^*. The experimentally determined c^*, was found to be in good agreement with the theoretically determined value that was calculated by the criteria c^*∼1/[η], where the intrinsic viscosity was estimated from the Mark-Houwink parameters, K and a (at 25 °C in dimethyl formamide) obtained from the literature. The plot of the zero shear viscosity vs. c/c^* distinctly separated into different solution regimes, viz. dilute (c/c^*<1), semidilute unentangled (1<c/c^*<3) and semidilute entangled (c/c^*>3). The crossover between semidilute unentangled and semidilute entangled regimes in the present investigation occurred at c/c^*∼3, which, therefore, marked the onset of the critical chain entanglement concentration, c_e, according to the procedure utilized by Colby and co-workers [Colby RH, Rubinstein M, Daoud M. J de Phys II 1994;4(8):1299-310. [52]]. Electrospinning of all solutions was carried out at identical conditions to ascertain the effects of solution concentration, molecular weight, molecular weight distribution and viscosity on fiber formation and morphological features of the electrospun material. Only polymer droplets were observed to form from electrospinning of solutions in the dilute concentration regime due to insufficient chain overlap. As the concentration was increased, droplets and beaded fibers were observed in the semidilute unentangled regime; and beaded as well as uniform fibers were observed in the semidilute entangled regime. Uniform fiber formation was observed at c/c^*∼6 for all the narrow MWD polymers (M_w of 12,470-205,800 g/mol) but for the relatively broad MWD polymers (M_w of 34,070 and 95,800 g/mol), uniform fibers were not formed until higher concentrations, c/c^*∼10, were utilized. Dependence of fiber diameter on concentration and viscosity was also determined, viz. fiber dia∼(c/c^*)^3.1 and respectively. These scaling relationships were in general agreement with that observed by Mckee et al. [McKee MG, Wilkes GL, Colby RH, Long TE. Macromolecules 2004;37(5):1760-67. [33]].     

A kinetic model of persulfate–bisulfite-initiated acrylonitrile polymerization

The molecular weight distribution has been derived for a homopolymer polymerized in a continuous-feed reactor under homogeneous conditions. The derived equations are then compared with data obtained on polymers of acrylonitrile–co(vinyl acetate) prepared under heterogeneous conditions with the potassium peroxydisulfate–sodium bisulfite–iron redox system. The termination reaction is assumed to be effected completely by recombination of active radicals with no disproportionation. The only transfer reaction considered is the transfer-to-activator reaction The transfer and termination reactions produce polymers with different acid groups as endgroups. Each molecule, on the average, contains one sulfonate group, whereas the concentration of sulfate groups depends upon the extent of the transfer-to-activator reaction. The basic dye acceptance of the polymer depends on the number of acid groups in the polymer and hence on the activator and catalyst concentrations. Analysis of the basic dye acceptance and conversion data at a variety of catalyst and activator concentrations yields the following parameters at 50°C: k_p/k = 1.01 (1./mole sec)^1/2, k_tr/k_p = 0.2063, and k₁ [see eq. (1)] = 50.7 l./mole sec. Owing to the heterogeneous nature of the polymerization, the weight-average molecular weight of the polymer depends only on the activator concentration and the conversion and not directly on the catalyst concentration as predicted.     

Eine η-c-M-beziehung für polymerlösungen

A simple equation is developed for the dependence of the viscosity upon molecular weight and concentration of polymer solutions. The validity of such a simple equation is given if the plot of log η_sp = f (log (c · [η])) is a straight curve for all viscosity values. This is demonstrated for aqueous polyacrylamide solutions. The covered region is M = 12300-6900 000 (g/mol) and concentrations c = 0,1?5 (g/100cm³). The established η-M-c-relationship is:      

Relationships between surface wettability and glass temperatures of high polymers

The adhesion between a polymer and a solid substrate may be considered to be one type of complex liquid-solid interaction. Relationships between surface wettability and bulk properties of liquidlike polymers are discussed. A new and direct empirical relationship between the glass temperature (T_g) and critical surface tension of a polymer (γ_c) is established: where n = degree of freedom, defined by Hayes, V_m = molar volume, and Φ = interaction parameter, or the ratio between reversible work of adhesion and geometrical mean of the work of cohesion. The effect of polarity and hydrogen bonding on this relationship is also discussed. The calculated γ_c's are much closer to the observed values than those calculated on the basis of parachor. With this new wettability relationship the wettability of polymers, especially of those forming no hydrogen bonds, can be related to thermal, rheological, mechanical, and relaxational properties.     

Shear rate dependence of the viscosity of cellulose nitrate solutions in the dilute concentration regime revisited

A detailed rheological study of cellulose nitrate in ethylacetate had been carried out in the dilute concentration (c) regime, covering a degree of polymerization (DP) range between 300 < DP_η < 7000 and shear rates ($ \dot \gamma $) between 100 s^?1 < $ \dot \gamma $ < 2000 s^?1. The results show a strong dependence of the transition Newtonian to non-Newtonian behavior on the three variables $ \dot \gamma $, DP, and c, similar to that found recently on solutions of synthetic polymers. Emphasis has been put on the critical concentrations corresponding to the standard shear rate 1000 s^?1 to correspond to the standard conditions ($ \dot \gamma $ ? 1000 s^?1; 0.3 < [η] · c < 0.6; DS = 2.90 ± 0.02) proposed for the determination of the intrinsic viscosity [η] of cellulose nitrates. It is shown that solutions with concentrations adjusted according to the above given conditions still exhibit Newtonian behavior, up to the highest range of DP. It follows, therefore, that applying the standard conditions, an extrapolation to $ \dot \gamma $ = 0 as has been proposed often for the intrinsic viscosity determination of cellulose nitrate is not advisable and results in considerable error. Considering the relationship between [η] and DP, the present results indicate that the decrease of the exponent ( a ) from a = 1.0 to a = 0.76, taking place above a DP ? 1000, is not a consequence of the applied shear rate but rather of the molecular properties of the solutes themselves.     

Determination of carboxyl endgroups and comonomers in poly(ethylene terephthalate) with hydrazine

On complete hydrazinolysis of poly(ethylene terephthalate), terephthalomonohydrazide is formed from carboxyl-end terephthaloyl residues in a quantity equivalent to the content of carboxyl endgroups in the polymer. The compound is separated from the reaction mixture by ion exchange and determined photometrically [epsiv;₂₄₀ in 0.1 N HCl = 16,700 (1000 cm²/mole)]. A COOH determination carried out in this way is endgroup specific and, unlike titration, is not subject to interference by ionogenic fiber additives. Aromatic comonomers with acidic substituents (e.g., 5-sulfoisophthalic acid) in chemically modified, cationically dyeable poly(ethylene terephthalate) are determined simultaneously with the carboxyl endgroups by the same analytical method. In this case, the terephthalamonohydrazide and 5-sulfoisophthalodihydrazide are separated by ion exchange, and the difference in their spectral behavior is used for quantitative determination with the aid of a two-component analysis: where c₁c₂ = concentration of terephthalomonohydrazide and 5-sulfoisophthalodihydrazide, respectively; and D₂₄₀ D₂₁₂ = optical density at 240 and 212 nm, respectively. The content of carboxyl endgroups in polyether esters poly(p-(2-ethyleneoxy)-benzoate), is determined on the basis of the p-(β-hydroxyethoxy)benzoic acid [epsiv;₂₅₈ in 0.1 N HCl = 16,100 (1000 cm²/mole)] liberated from carboxyl-end monomer units by hydrazinolysis. For copolyether esters with p-(β-hydroxyethoxy)benzoic acid as a comonomer, the contents of carboxyl-end terephthalic acid and p-(β-hydroxyethoxy)benzoic acid are determined simultaneously with the acid of a spectrophotometric twocomponent analysis: where c₂, c₂ = concentration of terephthalomonohydrazide and p-(β-hydroxyethoxy)-benzoic acid, respectively; and D₂₄₀, D₂₅₈ = optical density at 240 and 258 nm, respectively.     

Hydrolysis of 1,4-cyclohexanedimethanol-based copolyester

The solid state hydrolysis of a copolyester based on a mixture of 1,4-cyclohexanedimethanol and ethylene glycol condensed with terephthalic acid was studied at 100°C and 57 to 96 kPa water vapor partial pressure (55% to 95% relative humidity). The equilibrium water sorption in weight percent (C_∞) was found to be where P is the water vapor partial pressure in kPa. For specimens 0.32-cm thick, it took about 24 h to reach 0.9C_∞. The intrinsic viscosity (IV) was measured and used to calculate the relative change in molecular weight (M?_w) from the relationship IV ∝? (M?_w)^0.7. The decrease in molecular weight was linear with time, and the rate of decrease was found to be proportional to C_∞; the empirical correlation is where the rate constant, k, is in day^?1. A decrease of 50% in M?_w was observed after 22 days at 95% relative humidity.     

A three-parameter equation for molecular weight distribution of low-density polyethylene

A new three-parameter distribution function is proposed which fits best the experimental molecular weight distribution curves of branched lowdensity polyethylenes. The data were interpreted from GPC measurements, and a special computer program was utilized in order to derive the best values of the empirical constants a, b, and c.