Detection of low levels of long‐chain branching in polydisperse polyethylene materials

Creep experiments have been applied to probe the zero‐shear viscosity, η₀, of polyethylene chains directly and precisely in a constant‐stress rheometer at 190°C. Such experiments, when combined with precise measurements of the weight‐average molecular weight, M_w, calibrated relative to linear chains of high‐density polyethylene, are shown to provide a very sensitive approach to detect low levels (0.005 branches per 1000 carbons) of long‐chain branching (LCB). This detection limit is shown to be insensitive to whether the molecular weight distribution (MWD) breadth, M_w/M_n, rises from about two to ten. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

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.     

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.     

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.     

Influence of poly(arylether sulfone) molecular weight distribution on measures of global thermal stability

The dependence of the thermal stability of high-performance poly(arylether sulfones) (PAES) on the initial molecular weight distribution and backbone structure was assessed experimentally and through computer simulation. Reaction of PAES polymers resulted in the formation of an insoluble gel fraction and significant changes in weight and number average molecular weights of the sol fraction. A PAES with alternating ether and sulfone linkages formed a larger fraction of gel at a given reaction time than a PAES with the hydroquinone moiety. For a given chemical composition, more rapid molecular weight changes and gel fraction formation were observed for the polymer with the higher value of the initial weight average molecular weight. The growth of molecular weight was also faster for the polymer with the broader initial distribution. The simultaneous increase in M_w and decrease in M_n suggested the occurrence of two types of overall reactions: scission and addition. Simulation of these reactions using Monte Carlo kinetics allowed estimation of the range of probability for bond scission, R, of 0.5 < R < 0.8 capable of accounting for the observed experimental behavior. The dependence of the simulated molecular weight changes on the initial molecular weight distribution agreed qualitatively with the experimental trends. © 1995 John Wiley & Sons, Inc.     

Experimental investigation of flow induced molecular weight fractionation during extrusion of HDPE polymer melts

In this work, two different HDPEs with virtually identical number, M_n, and weight, M_w, average molecular weights were investigated from rheological as well as die drool phenomenon point of view. It has been revealed that long-chain branching, low polymer melt elasticity and shear viscosity significantly reduce die drool phenomenon at the die exit region. It has been concluded that die drool phenomenon of HDPE polymer melts can be explained by the flow induced molecular weight fractionation.     

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     

Relationship between the structure and mechanical properties of polypropylene: Effects of the molecular weight and shear‐induced structure

A series of homopolymer polypropylenes (PPs), within a weight‐average molecular weight (M_w) range of 100–1600 kg/mol, were manufactured as dumbbell microspecimens. The effects of the molecular weight and shear‐induced crystallization on the mechanical properties and morphology were studied to gain a better understanding of the structure–property relationship. The results showed that the crystallinity decreased from 50 to 41% and the lamellar thickness increased as M_w increased. Tensile tests demonstrated that the stiffness and especially the tensile strength rose to extremely high values (Young's modulus = 2400 N/mm², stress at 30% strain = 120 N/mm²). Furthermore, the strain hardening effect was strongly affected by the lamellar thickness and highly oriented superstructures. Dynamic mechanical analysis demonstrated that the mobility of the molecular chains depended on M_w and on the lamellar thickness. In addition, the viscoelastic properties of unannealed and annealed samples indicated further the existence of shish‐kebab structures caused by shear‐induced crystallization during injection molding. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 519–533, 2007     

Mark–Houwink equation and GPC calibration for linear short-chain branched polyolefines,including polypropylene and ethylene–propylene copolymers

The reduction in molecular dimensions due to the presence of short side chains in otherwise linear polyolefins can very simply by calculated by assuming that the configuration of the main chain is not influenced by the side chains. This enables us to express the intrinsic viscosity–molar mass relationship as a function of the mass fraction of side chains (S): [η] = (1 ? S)^α+1K_PEM_ν^α and, with use of the universal calibration principle, to convert the GPC calibration for purely linear polymers samples into the calibration for short-chain branched polymers: M^* = (1 ? S)M. Experimental data from literature on short-chain branched poly-ethylenes, and our own data on ethylene–propylene copolymers are used to verify the above assumption. It appears that the experimentally found relations between [η], M_w and M^*_w (GPC) within the usual accuracy justify this approach.     

Statistics of star-shaped molecules III. Stars with branched nuclei

Number and weight average molecular weights and scattering behaviour of star molecules with extended branched nuclei are calculated by application of cascade theory. The nuclei considered arise from random polycondensation of monomers of the A₃ or of the A—B/C type. Nuclei of the first type are characterised by very large molecular polydispersities (M_w/M_n α M_w), while nuclei of the second type have less broad molecular weight distributions (M_w/M_n α M_n). The rays of the stars are assumed to be either monodisperse or to obey the Schulz—Flory “most probable” length distribution. Analytic expressions are given for M_w, M_n, 〈S²〉_z and the particle scattering factor P_z(h) which was averaged over the ensemble. The results are compared with stars of spherical and uniform nuclei whose molecular weights and mean square radii of gyration equal M_wN and 〈S²〉_zN from the other two types of nuclei. In the limit of very large ray lengths the scattering behaviour is determined solely by the number of branches z. At shorter chain length of the rays structure and polydispersity of the nuclei have marked influence. This influence is still easily noticed from the angular dependence of scattered light at chain lengths where no differences in the 〈S²〉_z versus M_w plot are detectable. The mean square radius of gyration depends only weakly on the number of rays and eventually becomes independent of it if z 15. In that limit 〈S²〉_z depends virtually on the length of the rays alone and its distribution. Stars whose rays have a most probable length distribution exhibit 〈S²〉_z values twice as large as stars with monodisperse rays. A procedure is suggested and discussed for the determination of the number and length of the rays if the scattering behaviour of the isolated nucleus and the isolated linear chains is known.     

Effects of the composition and molecular weight of maleimide polymers on the dispersibility of carbon nanotubes in chloroform

We synthesized maleimide polymers (MIPs) as effective carbon nanotube (CNT) dispersants for stable CNT-dispersed solutions. The MIPs were random copolymers which consist of N-phenyl maleimide (PhMI) units that imparted strong physical adsorption to the CNT surfaces and methyl methacrylate units; we evaluated the effects of the PhMI content and molecular weight in the MIPs on the dispersibility of the CNTs in chloroform. Increasing the PhMI content in the MIPs increased the grafting amount (GA) (g m⁻²) of MIPs on the CNT surfaces and led to a large increase of CNT dispersion. In particular, when single-walled carbon nanotubes (SWCNTs) were used, MIPs having 100 mol% PhMI units (MIP100s) were imperative for a drastic increase in the GA value. Increasing the weight average molecular weight (M_w) of the MIPs resulted in no significant effect on CNT dispersibility; however, the particularly low M_w (?10,000) of the MIPs dramatically improved CNT dispersion. Therefore, MIP100s with particularly low M_w’s were extremely effective for dispersing various CNTs with different diameters. In the case of SWCNTs, much more effective exfoliation of SWCNT bundles was achieved by MIP100s with particularly low M_w’s than MIP100s with higher M_w’s.     

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.     

Compatibilization of recycled poly(ethylene terephthalate) and polypropylene blends: Effect of polypropylene molecular weight on homogeneity and compatibility

The effectiveness of compatibilizers in enhancing the dispersion of polypropylene (PP) at various molecular weights in recycled polyethylene terephthalate (RPET) was elucidated. The idea of incorporating PP of different molecular weights evolved from the intention of simultaneously recycling the PET bottles together with the PP‐based bottle caps, which are often of low molecular weight (M_w). Three grades of PP with known molecular weights were blended with RPET at various loadings of compatibilizers. Morphological analyses suggest that the dispersion of the PP particles was more homogeneous, and the average particle size was smaller when low M_w PP was incorporated. This indicates that the interaction between the compatibilizer and PP particles was more intense with the presence of a large number but shorter PP molecular chains. Moreover, specimens containing low M_w PP were found to remain homogeneous regardless of compatibilizer and PP content in the RPET/PP blends. The homogeneity of the blends significantly affected their mechanical performance as well. Higher stiffness, yield strength, deformability, and toughness were observed when low M_w PP was incorporated, regardless of PP and compatibilizer loadings. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Extending the continuum of molecular weight distributions based on the generalized exponential (Gex) distributions

Literature data on the average molecular weights M_n, M_W, M_z, and/or M_v for several polymers indicated that they fell outside the continuum originally proposed to model molecular weight distribution (MWD), where the log-normal (LN) distribution, or positively valued Gex parameters m and k, define the continuum. Following the papers of Kubin, it is possible to embrace these polymers in an extended continuum by including these parameters, both negatively valued, in it. To the extent that m ≥ ?1 and k < ?5, the extended continuum models average molecular weights through M_z+2. The correspondence of Gex models of MWD of a polymer obtained from data on its M_n, M_w, and M_z with that obtained from data on its M_n, M_v, and M_w is indicated, using published data. The numerical value of the m parameter in a Gex model is of use in polymerization kinetics; when m values are obtained for each analysis from multiple analyses upon a given polymer, their consistency indicates the concordance of the three average molecular weights from each test run. The Gex parameters based upon M_n, M_w, and M_v or M_z can be used to estimate values for higher average molecular weights of linear, unimodal homopolymers. This is of use in interpreting rheological data on such polymers.     

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.).     

Effects of molecular weight and molecular weight distribution on creep properties of polypropylene homopolymer

The molecular weights of the industrial-grade isotactic polypropylene (i-PP) homopolymers samples were determined by the melt-state rheological method and effects of molecular weight and molecular weight distribution on solid and melt state creep properties were investigated in detail. The melt-state creep test results showed that the creep resistance of the samples increased by M_w due to the increased chain entanglements, while variations in the polydispersity index (PDI) values did not cause a considerable change in the creep strain values. Moreover, the solid-state creep test results showed that creep strain values increased by M_w and PDI due to the decreasing amount of crystalline structure in the polymer. The results also showed that the amount of crystalline segment was more effective than chain entanglements that were caused by long polymer chains on the creep resistance of the polymers. Modeling the solid-state viscoelastic structure of the samples by the Burger model revealed that the weight of the viscous strain in the total creep strain increased with M_w and PDI, which meant that the differences in the creep strain values of the samples would be more pronounced at extended periods of time.     

Molecular weights of natural rubbers from selected temperate zone plants

Molecular weights and molecular weight distributions are compared by gel permeation chromatography for rubbers from 33 north temperate zone plants, guayule, and Hevea. Rubbers isolated from all the northern plants had much lower weight-average molecular weight (M _w) values (9.72 × 10⁴–4.95 × 10⁵) than milled Hevea (1.31 × 10⁶) or guayule (1.28 × 10⁶) rubber. Pycnanthemum incanum, Lamiastrum galeobdolon, Monarda fistulosa, and Vernonia fasciculata produced potentially useful natural rubbers having M _w values above 4 × 10⁵ and polydispersity factors of 3.1–4.5.     

Molecular weight development in emulsion copolymerization of n‐butyl acrylate and styrene

The seeded emulsion copolymerization of n‐butyl acrylate and styrene in a weight ratio of 50/50 was investigated. The effect of the type of process (batch vs. semicontinuous) and the amounts of initiator and emulsifier charged into the reactor on the time evolution of the fractional conversion, number of polymer particles, and weight‐average molecular weight (M_w) was analyzed. It was found that the M_w depends to a slight extent on the type of process and the emulsifier concentration and to a larger extent on the initiator concentration. The molecular weight distributions (MWDs) and the gel content of the final latexes were also analyzed. In the absence of chain transfer agents (CTAs), the fraction of gel was higher in the semicontinuous processes. It was also found that the gel content increased with increasing initiator concentration in the recipe. The addition of 1 wt % CTA avoided gel formation and led to an important reduction of the M_w. Nevertheless, the MWDs presented a shoulder or even a second peak at high molecular weights that was due to reactions of chain transfer to the polymer. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1918–1926, 2003     

Bulk polymerization of styrene in presence of polybutadiene: Calculation of molecular macrostructure

In our previous publication the detailed molecular macrostructure generated in a solution polymerization of styrene (St) in the presence of polybutadiene (PB) at 60°C, was theoretically calculated. In this work, an extended kinetic mechanism that incorporates monomer thermal initiation, chain transfer to the rubber, chain transfer to the monomer, and the gel effect is proposed, with the aim of simulating a bulk high-impact polystyrene (HIPS) process. The mathematical model enables the calculation of the bivariate weight chainlength distributions (WCLDs) for the total copolymer and for each of the generated copolymer topologies and the univariate WCLDs for the free polystyrene (PS), the residual PB, and the crosslinked PB topologies. These last topologies are characterized by the number of initial PB chains per molecule; copolymer topologies are characterized by the number of PS and PB chains per molecule. The model was validated with published literature data and with new pilot plant experiments that emulate an industrial HIPS process. The literature data correspond to a dilute solution polymerization at a constant low temperature with chemical initiation and a bulk polymerization at a constant high temperature with thermal initiation. The new experiments consider different combinations of prepolymerization temperature, initiator concentration, and solvent concentration. One of the main conclusions is that most of the initial PB is transformed into copolymer. For example, for a prepolymerization temperature of 120°C with addition of initiator, the experimental measurements indicate that the final total rubber mass is approximately three times higher than the initial PB. Also, according to the model predictions, the final weight fractions are: free PS, 0.778; graft copolymer, 0.220; initial PB, 0.0015; and purely crosslinked PB, 0.0005. The final graft copolymer exhibits the following characteristics: average molecular weights, M _n,C = 492,000 and M _w,C = 976,000; average weight fraction of St, 0.722; and average number of PS and PB branches per molecule, 5.19 and 1.13, respectively. © 1996 John Wiley & Sons, Inc.     

Determination of the absolute molecular weight of a styrene–butyl acrylate emulsion copolymer by low-angle laser light scattering (LALLS) and GPC/LALLS

The application of low-angle laser light scattering (LALLS) and combined GPC/LALLS for the measurement of absolute molecular weight distribution of a styrene–butylacrylate (30/70) emulsion copolymer is discussed. From the static light scattering measurements in four different solvents, i.e., toluene, tetrahydrofuran (THF), methyl ethyl ketone (MEK), and dimethylformamide (DMF), the true weight average molecular weight (M _w) and heterogeneity parameters are determined. The apparent M _w obtained from the static measurement in THF was in good agreement with the M _w determined from the multiple solvent analysis, suggesting the validity of using THF as the mobile phase in the combined GPC/LALLS analysis.