Prediction of second virial coefficients from intrinsic viscosities

One of the most readily available characteristics of a polymer sample is its intrinsic viscosity in a particular solvent. This datum can often be estimated reasonably from a single relative viscosity measurement. A number of theories permit the calculation of the second virial coefficient of a polymer/solvent mixture given the intrinsic viscosity and polymer molecular weight. The intrinsic viscosity of the polymer under theta conditions is also needed, but this can be estimated, if necessary, from the molecular weight. This article compares the efficiencies of various alternative models for the prediction of second virial coefficients of a series of polymers and solvents. The most effective technique for this purpose first calculates the concentration-dependent equivalent hydrodynamic volume of a solvated polymer coil. This value is used with a primitive statistical mechanical theory for virial coefficients of hard-sphere suspensions to calculate the osmotic pressure or turbidity of the polymer solution. These simulated experimental values are fitted with a least-squares line as in the real experiment, and the second virial coefficient is derived from the slope. The computations are relatively simple; the average deviation between observed and predicted virial coefficient was less than 16% for a variety of polymer types, molecular weights, and solvents.     

Molecular weight distribution and rheological properties of polyisobutylene solutions

The molecular weight distribution of a series of polyisobutylenes was determined using osmotic pressure measurements, gel permeation chromatography, and intrinsic viscosity. All of the polymers except for one, a blend of the highest and lowest molecular weight constituents, had similar moderate molecular weight distributions. The “extended chain length” method of calibrating the gel permeation chromatograph for polyisobutylenes was found to be effective. Steady state and transient shear stresses and normal stresses were measured on 5% decalin solutions of these polymers. The zero shear viscosity increased with the 3.3 power of molecular weight, and the zero shear normal stress coefficient (σ₁₁ ? σ₂₂)/Γ² varied with the 7.5 power. Relative elastic memory as measured by (σ₁₁ ? σ₂₂)/σ₁₂ or stress relaxation increased with increasing molecular weight (and at constant number- or weight-average molecular weight) with breadth of distribution. Stress overshoot also correlated with this tendency.     

Correlating mooney viscosity to average molecular weight

Copolymers of styrene and butadiene of the same chemical conposition, but widely different molecular weight distributions, were characterized by gel permeation chromatography. A very good correlation was obtained between the logarithm of the Mooney viscosity and the logarithm of the geometric mean of the number- and weight-average molecular weights. Instead of this molecular weight average, one can equally well use the very convenient “Av log M,” which is a weight-average molecular weight, using a logarithmic molecular weight scale. This correlation makes it possible to predict the Mooney viscosity from GPC data with a precision of about 15% (± one standard deviation), independent of the molecular weight distribution of the polymer. The obtained correlation was much better than with either weight-average molecular weight or viscosity-average molecular weight with α = 0.67.     

Relation between intrinsic viscosity and molecular weight

The connection between intrinsic viscosity and number-average and weight-average molecular weight has been revealed by calculations from distribution curves. Log-normal distributions, and moderate variations thereon, were chosen as typical for polystyrene and other thermoplastics. Intrinsic viscosity and number-average molecular weight are unlikely to be related because of the highly disturbing effect of small variations in molecular weight distribution. Conversely, intrinsic viscosity is a good practical measure of weight-average molecular weight up to a ratio of 10 for weight-to-number average.     

An improved block osmometer used to determine the molecular weight distribution of commercial poly(vinyl chloride)

Commercial PVC was fractionated into five fractions by the incremental addition of a nonsolvent to the polymer solution. The number-average molecular weights of the original sample and fractions were determined by osmometry. The weight-average molecular weights of the sample and fractions were also determined by means of viscosity measurements and by the application of a Mark-Houwink type of equation. From a knowledge of the polydispersity of each fraction and the assumption that the number distribution of molecular weights was Gaussian, the molecular weight distribution for the composite sample was determined. The block osmometer used incorporated most of the features found useful in earlier work to facilitate rapid and reliable osmotic pressure measurements. In addition, microvolume-regulating valves were utilized in the capillary tube lines to permit an independent precise positioning of the interface level in either capillary.     

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.     

Branching and molecular weight distribution of polyethylene SRM 1476

A method of determining the distribution of branching in a polymer is developed employing limiting viscosity numbers (intrinsic viscosity), gel permeation chromatography (GPC), and absolute molecular weight determinations of fractions of the whole polymer. A molecular weight calibration of the GPC column set is first determined empolying these fractions. From the limiting viscosity number measurements of these fractions and their molecular weight distribution determined from the GPC chromatogram, the viscosity–molecular weight relationship is determined by a nonlinear least-squares fitting procedure. For the same molecular weight, the limiting viscosity number of the branched polymer is less than the limiting viscosity number of the linear polymer. From the ratio of the two, the number of branches per unit molecular weight of the branched polymer is calculated. The method was applied to SRM 1476, the standard reference branched polyethylene issued by the National Bureau of Standards. The branching density for the constituents of SRM 1476 rise from zero at molecular weights less than 10,000 to about 6 to 8×10^?5 at molecular weights of 50,000 and above. The branching of SRM 1476 was also determined by the method of Drott and Mendelson, giving a result in fair agreement with the above method.     

Viscosity and molecular weight distribution of ultrahigh molecular weight polyethylene using a high temperature low shear rate rotational viscometer

To obtain accurate measurements of the limiting viscosity number (LVN) or the intrinsic viscosity [η] of solutions of ultrahigh molecular weight polyethylene (UHMWPE), a low shear floating-rotor viscometer of the Zimm-Crothers type was constructed to measure viscosities at elevated temperatures (135°C) and near zero shear rate. The zero shear rate measurements for UHMWPE whole polymer and UHMWPE fractionated by hydrodynamic crystallization were compared with viscosity measurements at moderate and high shear rates (up to 2000 _s^?1) carried out in a capillary viscometer. The limiting viscosity number of UHMWPE decreases, as expected, with shear rate. The higher shear rate data could not be extrapolated to yield the correct zero-shear rate viscosities. Fractionation of UHMWPE gave 10 fractions ranging in LVN from 9 to 50 dL/g. A tentative integral molecular weight distribution for the whole polymer was calculated on the basis of the Mark-Houwink equation, but because it had been previously established only for lower molecular weight polyethylenes, it may not be accurate. A correlation was found between the LVNs for the fractions in the two types of viscometers.     

Molecular weight of polymers. Errors involved in osmotic and viscometric measurements

The errors associated with the determinations of number average molecular weights through osmotic measurements and intrinsic viscosities through viscometric measurements are calculated by statistical computing. They are compared with the results previously obtained by means of graphical extrapolations, showing the advantages of the proposed method.     

壳聚糖相对分子质量的测定方法

讨论了利用HPLC、特性黏度、动态黏度3种方法的关联来推导测定壳聚糖相对分子质量的简便方法。对6种壳聚糖样品,采用HPLC凝胶系统测定相对分子质量,利用乌氏黏度计一点法测定特性黏度,得出MHS方程为[η] = 3.72 × 10^－5M_w^1.37。同时还建立了10 mg/mL壳聚糖溶液降解过程中相对分子质量和动态黏度之间的关系。     

Linear low density polyethylenes and their blends: Part 1. Molecular characterization

Ten commercial linear low-density polyethylenes (LLDPE) were characterized by solution viscosity, size exclusion chromatography, SEC, and ¹³C nuclear magnetic resonance. The resins were copolymers of ethylene with butene, hexene, or octene. They were prepared in gas phase (with narrow or very broad molecular weight distribution), or in solution. The macromolecules were found to be linear. For all but the very broad molecular weight distribution resins the average comonomer sequence length was found to be 1; in the other case diad formation was observed. The weight average molecular weights calculated from SEC, and intrinsic viscosities agreed quite well. Mechanical degradation of LLDPE was observed during the solution viscosity measurements.     

A gel permeation chromatography calibration method for a broad molecular weight distribution polymer

A novel, precise, and simple method is described for developing a GPC calibration curve for a polymer where only broad molecular weight distribution samples are available. The method demands a GPC calibration curve for another polymer (e.g., polystyrene) and measurement of the intrinsic viscosity and an average molecular weight for each of several samples of the broad molecular weight distribution polymer in addition to GPC measurements on those samples. Results of applying the procedure to poly(n-lauryl methacrylate) are presented.     

Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Intrinsic viscosity dependence on polymer molecular weight and fluid temperature

Experimental solution intrinsic viscosity responses to temperature and polymer molecular weight variations were used to test the modeling capability of a simplified intrinsic viscosity equation. The multiple linear equation contains three parameters that are related to the thermodynamic properties of a polymer solution. Simple linear regression was used to produce an intrinsic viscosity equation containing unique fitted parameters for each of three solutions. These parameters describe the polymer coil size at unperturbed conditions and the polymer coil expansion capabilities of the solvent as a function of fluid temperature and molecular weight. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2831–2835, 2003     

Compatibility analysis of pectin at different esterification degree from intrinsic viscosity data of diluted ternary solutions

This paper aims to set-up a compatibility criterion for couple of pectins at different degree of methoxylation (DM) based on specific viscosity data, slightly modifying a criterion already proposed in the field of synthetic polymers. Four different commercial pectins were preliminarily characterised by using dilute solution viscosity measurements and molecular weight was calculated from intrinsic viscosity data. Four ternary dilute solutions of pectin at different DM, were also investigated and two compatibility criteria, based on viscosity data, were applied. Data revealed that positive molecular interactions take place when pectins in solution have a different DM (i.e. HM/LM mixtures), whilst an incompatible behaviour was found for similar pectin in solution (i.e. both HM or LM). In addition, in the case of incompatible pairs of pectin, also the apparent average molecular weight of mixed pectin, obtained by measurements carried out on ternary solutions, showed an increase with respect to the additive mixing rule, owing to repulsive forces. On the contrary, owing to attractive forces in case of compatible pectin pairs, the apparent molecular weight is lower than the calculated average.     

Physical-chemical studies of polyhexene-1. Some dilute solution properties

This work is a study of some dilute solution properties of polyhexene-1. Results with the following experimental measurements are reported: osmotic pressure, phase equilibrium, viscosity, light scattering, molecular weight, molecular weight distribution, and degree of chain extension. Three good solvents were used, cyclohexane, tetrahydrofuran, and toluene, and one poor solvent, phenetole, in order to obtain theta conditions. The properties of polyhexene-1 are compared with those of other α-olefin polymers reported in the literature.     

Synthesis and characterization of low relative molecular weight trans‐1,4‐poly(isoprene)

Low relative molecular weight trans‐1,4‐polyisoprene oligomers were synthesized successfully by bulk precipitation and solution polymerization with supported titanium catalyst using hydrogen as relative molecular weight modifier. The effects of polymerization conditions on intrinsic viscosity ([η]), catalyst efficiency (CE) and structure of polymer were studied. Increasing the hydrogen pressure resulted in the decrease of [η] of the polymer. With the increasing of hydrogen pressure and reaction temperature, CE decreased but still maintained above 2500 g polymer/g Ti. The percentage composition of (trans‐1, 4‐unit) in the polymer was over 90% in all results. The crystallinity of polymer was about 50–60% with T_m being about 60°C. The relative molecular weight distribution index (MWD) was quite difference according to the polymerization method. While number average molecular weight (M_n) exceeded 860, polymer turned from viscous materials to fragile wax materials, and then to toughness materials at 1800. Dynamic property testing showed that the additional of this oligomer could increase the wet‐skid resistance of the rubber. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

氯化聚丙烯甲苯溶液的特性黏数及其黏均分子量

分别用乌氏黏度计和旋转黏度计测定了氯化聚丙烯甲苯溶液的特性黏数和黏度,把特性黏数和黏度进行关联,发现ηsp/C与浓度C(ml/g)的关系用多项式ηsp/C=[η]+k1[η]2C+k2[η]2C2拟合,可以得到很好的结果。并且用特性黏数和Mark-Houwink方程求出了不同氯化聚丙烯(CPP)的黏均分子量。     

Influence of number average molecular weight on the properties of 3D printed precursor ceramics

A deliberately selected end-capping agent was introduced into the precursor to form a low number average molecular weight precursor and meet the need for liquid crystal display (LCD) 3D printing. The influence of number average molecular weight on the photocuring properties of precursor and the physical properties of pyrolysis samples were studied in detail for the first time. The results proved that a relatively low number average molecular weight precursors had low ceramic yields after pyrolysis. As the number average molecular weight of the precursor decreased, the photocuring ability of the precursor photosensitive resin increased. With the decrease in the number average molecular weight of the precursor in the precursor photosensitive resin, the ceramic yield of 3D printed PDCs decreased from 58.4% to 30.2%, and the linear shrinkage increased from 27.2% to 40.3%. The bending strength of the LCD 3D printed specimen reached 61.5 ± 3.7 MPa. The low cost of precursor synthesis and equipment in this study points the way for the preparation of precursor non-oxide ceramic composites and can be conducive to the development and application of LCD 3D printing precursor ceramics.     

Molecular heterogeneity characterization in polyglycols

This paper deals with polydispersity coefficient characterization in poly(propylene glycols) (PPG 425, 750, 1025, 1200, and 2025) and poly(ethylene glycols) (PEG 200, 600, and 1000). The methods used involved ratio of 50% solution to intrinsic viscosity and ratio of weight-average to number-average molecular weight, as determined by gel permeation chromatography, light-scattering photometry, and vapor pressure osmometry. The methods used assigned the same value to this coefficient. Polydispersity in polyglycols, which have low molecular weights (≤2200) and narrow distributions (≤1.1), may thus be determined from viscosity measurements.