An empirical model relating the molecular weight distribution of high-density polyethylene to the shear dependence of the steady shear melt viscosity

An empirical model has been developed to relate molecular weight distribution to the shear dependence of the steady shear viscosity in high-density polyethylene melts. It uses a molecular weight, M_c, which partitions molecular weights into two classes; those below M_c contribute to the viscosity as they do at zero shear, and those above M_c contribute to the viscosity as though they were of molecular weight M_c at zero shear. Each individual molecular weight species contributes on the basis of its weight fraction. M_c is proposed to be a unique function of the shear rate. Using this method of treating the molecular weight distribution, and the zero shear relation for relating η0 to molecular weight, the calculated steady shear viscosities at various shear rates for polyethylene samples of widely varying polydispersities agree well with experimental results. The model makes no judgment on the existence or importance of entanglements in non-Newtonian behavior since it has no specific parameters involving an entanglement concept. Use of the model suggests that for the samples studied, only the upper portion of the molecular weight distribution contributes toward the experimentally observed decrease of steady shear viscosity with shear rate for shear rates of up to 10,000 sec^?1. The lower molecular weight species are assumed to behave in a Newtonian manner.     

Calibration of size-exclusion chromatography columns with polydisperse polymer standards. II. Applications

New methods for calibrating SEC columns by means of polydisperse polymer samples with known M_n and M_w have been tested with computer-generated chromatograms and with experimental data of high-performance SEC. Calculations with the artificial chromatograms show that accurate calibration dependences can be recovered even when polymers with broad and/or bimodal molecular weight distributions are used as standards. Polystyrene calibration calculated by the proposed method from chromatograms of five polydisperse polystyrenes follows closely the curve obtained in a conventional manner from nine narrow polystyrene standards. The dependence log M vs. ν for PMMA determined from chromatograms of six PMMA samples with moderately broad molecular weight distributions agrees well with the curve obtained by shifting the dependence for polystyrene using the universal calibration concept. The new method is particularly useful when SEC columns are to be calibrated for dextrans in water, where only a few standards having a rather broad molecular weight distribution are available, and can considerably improve the accuracy of molecular weight determination by SEC.     

Molecular weight distribution of commercial PVC

The molecular weight distribution (MWD) of commercial suspension grade poly(vinyl chloride) (PVC) resins with K values from 50 to 93 and mass grade PVC resins with K values from 58 to 68 has been determined by size exclusion chromatography (SEC), using literature Mark‐Houwink coefficients. The MWD is characterized by the number average molecular weight (M_n), the weight average molecular weight (M_w) and the polydispersity (M_w/M_n). Our results for M_w are consistent with recently published data, but we find different results for M_n and consequently for M_w/M_n. The polydispersity of PVC increases with increasing K value. This effect can be explained by two mechanisms. The first mechanism is a reduced terminating reaction rate between two growing polymer chains (disproportionation) at higher molecular weight owing to the reduced mobility of the polymer chains. The second mechanism is long‐chain branching of molecules with high molecular weight which lets the molecules grow at two ends. For two examples graphs of the measured MWD are compared with the theoretically expected MWD.     

Estimation of molecular weight averages from intrinsic viscosity

The weight-average molecular weight is estimated by an extrapolation technique based on a linear relation between the viscosity-average molecular weight M_v and a Mark–Houwink–Sakurada constant. This method may also be used to assess the unperturbed dimensions of polymers. If the M_v data are known with high accuracy, then the straight line may be stretched to reach the number-average molecular weight confidently. The slope of the linear plot is associated with the molecular weight distribution and as such can be utilized to compute the polydispersity index.     

Effect of sonolysis on kinetics and physicochemical properties of treated chitosan

Low molecular weight chitosan with weight‐average molecular weight from 161 to 22,000Da were obtained by sonolysis. Optimal conditions for sonolysis were described. The influence of sonolysis condition and the molecular parameters of initial chitosan on the degradation rate and degradation rate constant were investigated in detail. Weight‐average molecular weight (M_w) and molecular weight dispersion (M_w/M_n) of samples were measured by gel permeation chromatography. The structure of degraded chitosan were characterized by Fourier transform infrared, X‐ray diffraction, and electrospray ionization mass spectrometry. For a given sonolysis time, the decrease in molecular weight has been found to be greatest at lowest reaction temperature and lowest chitosan concentration. Molecular weight of samples decreased exponentially with increasing sonication time at early stages. The action mode of ultrasound on the splitting of molecular chain of chitosan has been discussed. The degree of deacetylation of the main hydrolysis products almost unchanged compared with the initial chitosan. The decrease of molecular weight led to transformation of crystal structure but the chemical structures of residues were not modified. Ultrasonic treatment on chitosan is an alternative, safe method to prepare chitosan having different molecular weights, which are more suitable for biomedical and food applications. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Polyether polyols as GPC calibration standards for determination of molecular weight distribution of polyether polyols

Average molecular weights (M_n, M_w and M_p) are important characteristics of oligomers and polymers, and therefore there is a need to have a precise and reliable determination method. A gel permeation chromatography (GPC) coupled with a single refractive index detector was used to determine the molecular weight distributions of commercial polyether polyols calibrated against a series of polyether polyols with known molecular weights and low polydispersity. Results of these GPC analyses were compared to the ones calibrated against the commercially available polystyrene (PS) standards. The number‐average molecular weights (M_n) obtained with GPC using polyether polyols calibration were closer to the theoretical values than the M_n obtained using PS as calibration standards. Hence, these GPC analyses using polyether polyols as calibration standards can provide reliable determination of molecular weight distribution of polyether polyols and can be potentially applied to natural oil‐based polyols, including palm oil‐based polyols. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42698.     

Molecular weight and solution viscosity characterization of PVC

As a means of developing the most accurate possible Mark-Houwink relationship possible for PVC, the literature Mark-Houwink coefficients for the weight average molecular weight (M_W) of PVC in THF are plotted and the derived “grand average” Mark-Houwink relationship (K = 15.56 × 10^?3 ml/g, a = 0.7690) is shown. High pressure-size exclusion chromatography (HP-SEC) data from two independent laboratories was used along with the “grand average” Mark-Houwink coefficients to calculate absolute number of average molecular weight (M_N) and weight average molecular weight values for PVC. An easy-to-use table has been developed to detail the relationships between M_N, M_W, K value, and inherent viscosity (I. V.).     

Low-angle laser light scattering–aqueous size exclusion chromatography of polysaccharides: Molecular weight distribution and polymer branching determination

A low-angle laser light scattering detector (LALLS) used with size exclusion chromatography (SEC/LALLS) has been applied for the determination of molecular weight, molecular weight distribution (MWD), and degree of branching of polysaccharides in 0.5N NaOH aqueous solution. Data from both detectors [differential refractive index (DRI) and LALLS] are used to calculate the absolute molecular weight at each point in a sample chromatogram. The correct average molecular weight and MWD can be obtained without calibration methods used in conventional SEC. As a consequence of this technique, Mark—Houwink coefficients can be predicted from a single broad-distribution, homopolymer without recourse to time-consuming fractionation methods. Moreover, the hydrodynamic volume separation mechanism of SEC can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper, SEC/LALLS has been employed to obtain data about the branching parameters g_v and g_M for samples of amylose, amylopectin, starch, and glycogen. For three homopolymers (amylose, amylopectin, and glycogen), branching frequency (as measured by chemical means), and the branching parameters (g_v and g_M) are inversely related. This trend is consistent with theoretical predictions. For starch, a nonhomogeneous branching distribution is observed as a function of molecular weight.     

Determination of number-average and weight-average molecular weights of polymer sample from diffusion and sedimentation velocity measurements in theta solvent

Several methods to determine number-average molecular weight M_n and weight-average molecular weight M_w, of a polymer sample are proposed from diffusion and sedimentation velocity measurements at the θ point. According to these methods, M_n and M_w are determined from the diffusion constant vs. molecular weight relationship, and also from the equations of Svedberg and Flory–Mandelkern, using the 2nd-order and the –2nd-order diffusion constants. These methods have been applied to four samples of polydisperse polystyrene in the θ solvent, cyclohexane at 35°C. It was experimentally ascertained that M_n and M_w of each sample determined by the present methods were in good agreement with the results of column fractionation, light scattering, and calculated values from molecular weight distribution curve within experimental errors. It is concluded that the present methods are useful for determining M_n and M_w, since the reliabilities of M_n and M_w values, which are fundamental quantities of polymer characterization, can be raised by comparing the experimental data observed by conventional methods such as osmotic pressure, light scattering, and the Archibald method with those observed by the present methods.     

Characterization of a nylon 6/poly(methyl acrylate) copolymer produced by radiation grafting

Acrylic acid has been grafted onto nylon 6 by the mutual γ-irradiation technique. Methods are described for removing poly(acrylic acid) homopolymer and ungrfted nylon, the latter involving intermediate conversion to the calcium ionomer. The pure graft copolymer in its methylated form, viz., nylon 6/poly(methyl acrylate), NY/PMA, was characterized by light scattering in mixed solvents to yield the true molecular weight (3.2 × 10⁶) as well as the molecular weights M_PMA(domain) and M_NY(domain) of the PMA and NY portions, respectively. The molecular weight M_PMA of the grafts was measured after hydrolysis of the backbone, and the molecular weight M_NY of the backbone was determined via a previously devised indirect procedure. Comparisons of M_PMA(domain) with M_PMA and of M_NY(domain) with M_NY gave ? 7 nylon chains and ? 17 poly(methyl acrylate) chains per copolymer molecule. Chain transfer and bimolecular terminatin during grafting are proposed as probable contributory factors to the branched structure of the copolymer.     

Polydiallylorthophthalate resist for electron-beam lithography

Polydiallylorthophthalate, PDOP, of low molecular weight and low molecular weight dispersivity has been prepared and investigated as a negative resist for electron-beam, X-ray and ultraviolet lithographies. The resist polymers were prepared by a conventional fractional precipitation method. It has been found that a high resolution pattern is obtained by using a molecular weight of 1 × 10⁴ and an M_w/M_n < 2. This gives a good solubility difference between the exposed and unexposed portions in the developer. Resolution is less than 1 μm without any scum. Sensitivity for 15 kV electron bourns is 4 × 10⁶C/cm²; and for X-rays (Al Kα) it is 100 mJ/cm². Sensitivity for UV is 10 times that of poly(methyl methacrylate), and resistance for C₃F₈ dry etching is comparable to AZ-1350J.     

Molecular Weight Determination of Palm Olein Polyols by Gel Permeation Chromatography Using Polyether Polyols Calibration

Natural oil polyols have been intensively developed and successfully used for the production of various polymers, notably polyurethanes. The need to access the average molecular weight (MW) and the MW distribution (MWD) has led to the efforts to have a precise and reliable determination method. A series of commercial polyether polyols, with well‐defined MW, was used as a gel permeation chromatography (GPC) calibration standard to determine the MW of palm olein polyols. This GPC analysis was compared to the one calibrated against the commercially available polystyrene (PS) standards and to the number‐average molecular weight (M_n) obtained via vapor pressure osmometry (VPO) technique. For example, the M_n obtained for palm olein polyol E‐135 calibrated against polyether polyols was 2,537 Da, which was closer to the M_n via VPO (1,618 Da), than the M_n obtained using PS as calibration standards (3,836 Da). Hence, this GPC analysis using polyether polyols as calibration standards can offer reassured determination of MWD of palm olein polyols.     

The Effect of Uncertainties in the Kuhn-Mark-Houwink-Sakurada Constants on the Quantitative Analysis by Gel Permeation Chromatography

The effect of uncertainties in Kuhn-Mark-Houwink-Sakurada (KMHS) constants on weight average and number average molecular weights and molecular weight distributions of some poly(ethyl methacrylate) samples have been investigated. Parameters were computed by the Weiss and Cohn-Ginsberg method. Whereas errors introduced in M_w, M_n and HI values due to uncertainty in the K value are insignificant, uncertainties in the KMHS exponent present a serious problem. Deviations of ± 3% around a particular a value cause a ± 20% error in M_w and ± 15% error in M_n, values. The effect of deviations in the KMHS exponent on the HI values is dependent on the polydisperity of the sample investigated.     

Rheological properties of polypropylenes with different molecular weight distribution characteristics

Relationships between the rheological properties and the molecular weight distribution of two polypropylene series with different molecular weight distribution characteristics were studied. The end correction coefficient in capillary flow is determined by the molecular weight M_w and the molecular weight distribution M_w/M_n, and is higher as both characteristic values are larger. The die swell ratio at a constant shear rate depends on M_w, M_w/M_n, and M_z/M_w, and is higher as the three characteristic values are larger. The critical shear rate at which a melt fracture begins to occurs depends on the molecular weight M_w and the molecular weight distribution M_z/M_w, and is proportional to M_z/M_w² in a log–log plot. The critical shear stress does not depend on the molecular weight, and is higher as M_z/M_w is higher. The zero‐shear viscosity is determined by a molecular weight of slightly higher order than M_w, and the characteristic relaxation time is determined by M_z. The storage modulus at a constant loss modulus scarcely depends on the molecular weight, and is higher as the molecular weight distribution M_w/M_n is higher. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2128–2141, 2002     

Controlled antibody release from a matrix of poly(ethylene-co-vinyl acetate) fractionated with a supercritical fluid

A new method is presented for controlling the rate of antibody (Ab) release from an inert matrix composed of poly(ethylene-co-vinyl acetate) (EVAc), a biocompatible polymer that is frequently used to achieve controlled release. Using supercritical propane, a parent EVAc sample (M_n = 70 kDa, M_w/M_n = 2.4) was separated into narrow fractions with a range of molecular weights (8.7 < M_n < 165 kDa, 1.4 < M_w/M_n < 1.7). Solid particles of Ab were dispersed in matrices composed of different polymer fractions and the rate of Ab release into buffered saline was measured. The rate of Ab release from the EVAc matrix depended on molecular weight: > 90% of the incorporated Ab was released from low molecular weight fractions (M_n < 40 kDa) during the first 5 days of release, while < 10% was released from the high molecular weight fraction (M_n > 160 kDa) during 14 days of release. No significant differences in polymer composition, glass-transition temperature, or crystallinity were identified in the different molecular weight fractions of EVAc. Mechanical properties of the polymer did depend on the molecular weight distribution, and correlated directly with Ab release rates. Because it permits rapid and reproducible fractionation of polymers, supercritical fluid extraction can be used to modify the performance of polymeric biomaterials. © 1993 John Wiley & Sons, Inc.     

Flexibility of epoxy coatings. Part 2: The relationship with the degree of cure

The flexibility of epoxy coating films, crosslinked by a phenolic resin, has been evaluated. The network structures of these films were estimated by the method proposed in the companion paper. The coating films with a higher molecular weight of network chain, M_c, showed more flexibility. This was achieved by the use of an epoxy resin with higher molecular weight or an epoxy resin with a lower content of lower molecular weight components and by control of cure.     

Synthesis of Hyperbranched Polyglycerol in a Continuous Flow Microreactor

Hyperbranched polymers have been synthesized in a microreactor for the first time, employing the known ring‐opening multibranching polymerization of glycidol. Microreactors are well‐known to be beneficial for highly exothermic reactions because of their capability to enhance mass and heat transfer due to short diffusion pathways and large interfacial areas per volume. The characteristics of the microstructured reaction system were utilized to engineer a continuous flow process for the preparation of well‐defined hyperbranched polyglycerols with molecular weights up to 1,000 g/mol. Increased flow rates, as well as the use of highly polar solvents, led to the partial formation of very narrowly distributed (M_w/M_n = 1.05–1.15) high molecular weight fractions (M_n up to 150,000 g/mol). NMR‐ and MALDI‐ToF spectra confirmed incorporation of the multifunctional initiator core into the hyperbranched polymer structure.     

Estimation of Mw from dilute solution viscosity

The viscosity-average molecular weight, M_v, of a polymer is given operationally through its limiting viscosity number [η] and the Mark-Houwink equation [η] = KM_v^α, where K and α are empirical constants. If [η] is measured under different conditions, α and M_v will vary for the same sample. M_v^α is the α-order moment about the origin of the differential weight distribution of the polymer. Practically, the results of a series of M_v measurements on the same polymer are equivalent to a cluster of fractional moments of the weight distribution, with orders between 0.55 and 0.80. It is shown that the first moment of this distribution, M_w, may be estimated reliably by a straightline plot of M_v against α-extrapolated to α equals 1. This simple expedient is effective although there are probably no molecular weight distributions in which the relation is strictly linear and there are no mathematical distributions for which the αth root of the αth moment is a linear function of α for all α. The deviation from linearity is small enough, however, that the real curve can be represented by a straight line over a short range of α. Thus, M_w can be measured accurately, but M_n, M_z, or the breadth of the distribution is not accessible by this method. Experimental and literature examples show that the precision of M_w estimated by this method compares well with that of primary methods for measuring this molecular weight average. If a linear relationship is observed with reliable α values, this appears to be a sufficient condition for estimation of a valid M_w.     

Variation of periodic crazing based on polymer blends of an ultra‐high and a low molecular weight poly(methyl methacrylate)

Periodic crazes are caused in a polymer film by the unique mechanical method using bending. Generation of a craze depends on entanglements of the molecular chains of a polymer. Therefore, control of composite morphology of periodic crazes was attempted by varying the entanglements of molecular chains. An effective entanglement network became sparse by polymer blends of an ultra‐high molecular weight polymethylmethacrylate (PMMA) and a low molecular weight PMMA. Consequently, the composite morphology of periodic crazes caused in the blend film varied. In other words, the periodic craze can be used for the evaluation of the effective entanglements. In addition, it was figured out that PMMA of which the number‐average molecular weight (M_n) is less than twice of the effective entanglement molecular weight (M_e^*) works as a plasticizer in the blend film. And also, it was revealed that the mechanical properties of the blend film decreased dramatically at M_n ≒ 6M_e^*. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44332.     

Molecular weight distribution in disulfide polymers

The published data on molecular weight distribution in polysulfide are rather contradictory and cannot be correlated with the concept of the existence of thiol–disulfide interchange in these polymers. In the present work the viscosity and molecular weights of liquid thiokols have been investigated (the number-average molecular weight by iodometric titration and by ebulliometry and the weight-average molecular weight by the light-scattering method). When measuring the light scattering in Thiokol Solutions a considerable depolarization of the scattered light was observed. This fact must be taken into account in the molecular weight determination. It has been established that in polydisulfides with thiol endgroups thiol–disulfide interchange reactions take place not only during the synthesis, but also in the polymer itself (in bulk). These reactions lead to the formation of polymers with an equilibrium molecular weight distribution. A relation of log η = f(M _w)^½ has been found that can be used in determining the weight-average molecular weight of liquid Thiokols.