Number-average molecular weight by size exclusion chromatography

It is now theoretically possible to obtain absolute accurate values of number-average molecular weight of complex polymers (e.g., branched polymers or copolymers) using size exclusion chromatography (SEC) with only a detector that measures the difference between the eluting polymer solution viscosity and the viscosity of the pure mobile phase (a differential viscometer [DV] detector). However, both precision and accuracy of these “DV M?_n” values are of concern. In this work, the precision of NBS 706 polystyrene was found to be two to three times worse for the DV M?_n than for the conventionally calculated M?_n. Also, regarding accuracy, the DV M?_n values were affected by the location of the universal calibration curve along the retention volume axis (a problem intimately associated with the problem of specifying the correct interdetector volume), the sensitivity of the DV detector to low molecular weights present in the sample, and axial dispersion. Each of these sources of error are examined in turn and two methods of calculating M?_n values are proposed. © 1994 John Wiley & Sons, Inc.     

Deformation behavior of polystyrene as a function of molecular weight parameters

The mechanical deformation of polystyrene as it relates to molecular weight parameters was investigated. Mechanical testing consisted of uniaxial tension and compression experiments on a variety of polystyrenes. Such quantities as modulus, proportional limit, and various yield stress measurements were determined on polystyrene samples of controlled number-average molecular weight and molecular weight distribution. A basic tool for the mechanical behavior analysis was the use of a power law equation σ = K?ⁿ to examine the initial nonlinear region of each experimentally determined stress–strain curve. Correlations between mechanical deformation and molecular weight parameters were determined using statistical linear regression analysis. It was generally found for uniaxial tension that mechanical parameters in or near the elastic region were independent of M?_n and MWD, while at larger strains correlations were found. For uniaxial compression, stress maxima and the strain where this occurred increased with increasing MWD. Otherwise, mechanical parameter changes in uniaxial compression did not occur with changing M?_n and MWD. Finally, a direct comparison of tension versus compression showed only the initial moduli to be the same. All other mechanical parameters showed significantly differing values, indicating different deformation mechanisms operating in tension verus compression. The analysis of this behavior from both a mechanics and molecular weight viewpoint provides some insight about glassy polymer deformation processes on the microscopic level.     

Entanglement network model relating tensile impact strength and the ductile-brittle transition to molecular structure in amorphous polymers

A model is presented to account for the large variations in tensile and tensile impact strength of amorphous polymers from a consideration of an idealized entanglement network. The material strength under tensile impact conditions is shown to be predictable and to increase with the “fineness” of the entanglement network; a higher entanglement density leading to more molecular chains supporting the stress. The entanglement density is, in turn, shown to increase with number-average molecular weight and the quotient of the length to the molecular weight of the chemical repeat unit (empirically found to be related to the critical enganglement molecular weight). Ductile behavior is demonstrated to occur under tensile impact conditions when the material strength σ_B exceeds the yield stress σ_y and brittle behavior when σ_y > σ_B. It is further demonstrated that the large variation in tensile impact strength among the amorphous polymers studied can be adequately accounted for in terms of the large and predictable variation in σ_B; the larger σ_B is relative to σ_y, the more the polymer can draw (absorbing energy in the process) until σ_B is reached. Surprisingly, the predictions of strength for high-molecular-weight polycrystalline materials also gave good agreement with experimental data.     

Calibration of thermal field-flow fractionation using broad molecular weight standards

Thermal field-flow fractionation (ThFFF) is a new elution-based separation method for determining molecular weight distributions of polymers. Calibration can be achieved using monodisperse standards of the specific polymer of interest. In order to expand the range of polymer types for which absolute molecular weight data can be obtained using ThFFF a calibration procedure has been developed and tested which uses only broad molecular weight polymer samples. The method requires two polydisperse molecular weight standards of the required polymer whose average molecular weight (normally M?_w) is measured by an independent method (e.g. light scattering). From the average molecular weight data and the ThFFF elution pattern (fractogram) the required calibration constants can be calculated. The method has been tested using the polystyrene-tetrahydrofuran system and gave satisfactory results when checked against a series of monodisperse polystyrene standards. This calibration approach should expand the applicability of ThFFF to include a wide range of polymer types.     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.     

The effect of molecular weight on fatigue crack propagation in nylon 66 and polyacetal

The influence of molecular weight on fatigue and fracture behavior in nylon 66 (N66) and polyacetal (PA) is examined. Fatigue crack propagation (FCP) resistance and apparent fracture toughness (K_cf) in these two semicrystalline polymers increase with increasing molecular weight in a manner consistent with that reported for another semicrystalline polymer (HDPE) as well as for several amorphous polymers. The improved FCP resistance with increasing molecular weight is attributed to the development of a molecular entanglement network that more effectively resists cyclic-load-induced breakdown. A type of discontinous crack growth is identified in PA at 100Hz and in N66 (2.6% H₂O) at 50 Hz and compared with that observed in amorphous polymers.     

Control of molecular weight distribution and tensile strength in a free radical styrene polymerization process

A new method is presented for modeling and controlling polymer molecular weight distribution (MWD) and tensile strength in a batch suspension polymerization of styrene. The molecular weight distribution is modeled by computing the weight fraction of the polymer in different chain length intervals. Tensile strength is then related to the modeled molecular weight distribution using a correlation available in the literature and based on the concept of a threshold molecular weight. This method enables the design of operating conditions for a batch suspension polymerization reactor, which will theoretically yield amorphous polystyrene with a desired tensile strength. Two numerical examples are presented to illustrate the feasibility of the proposed method. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1017–1026, 1998     

Preparation of ultrahigh molecular weight polyacrylonitrile and its terpolymers

The synthesis of high molecular weight (in excess of 10⁶ million Daltons) poly(acrylonitrile) and poly(acrylonitrile-co-methylacrylate-co-itaconic acid) is described. An inverse emulsion polymerization formulation with AIBN as the initiator was used. However, polymer precipitation occurred early in the polymerization. In each case, the molecular weight distribution was surprisingly narrow (M?_w/M?_n ～ 1.5). Conversion vs. time plots with monomers containing the inhibitor had the “S” shape typical of emulsion polymerizations. The terpolymer composition and molecular weight were quite uniform throughout the polymerization. With inhibitor-free monomers, the initial molecular weights were very high (～ 3 × 10⁶ Daltons), but gelation occurred at ca. 50% conversion. There was an inverse relationship between the monomer inhibitor content and the polymer molecular weight. It is suggested that the growing polymer radicals are occluded in the precipitated polymer particles and are terminated by inhibitor diffusing into the particles, accounting for the narrow molecular weight distribution. © 1995 John Wiley & Sons, Inc.     

Influence of temperature,molecular weight,and molecular weight dispersity on the surface tension of PS,PP, and PE. I. Experimental

In this work, the influence of temperature, molecular weight (M?_n), and molecular weight dispersity (MWD) on the surface tension of polystyrene (PS) was evaluated using the pendant drop method. The influence of temperature on the surface tension of isotatic polypropylene (i‐PP) and of linear low‐density polyethylene (LLDPE) was also studied here. It was shown that surface tension decreases linearly with increasing temperature for all the polymers studied. The temperature coefficient ?dγ/dT (where γ is the surface tension, and T, the temperature) was shown to decrease with increasing molecular weight and to increase with increasing MWD. The surface tension of PS increased when the molecular weight was varied from 3400 to 41,200 g/mol. When the molecular weight of PS was further increased, the surface tension was shown to level off. The surface tension was shown to decrease with increasing molecular weight distribution. Contact angles formed by drops of diiomethane and water on films of PS with different molecular weights were measured at 20°C. The surface energies of those polymers were then evaluated using the values of the different pairs of contact angles obtained here using two different models: the harmonic mean equation and the geometric mean equation. It was shown that the values of the surface energy obtained are slightly less than are the ones extrapolated from surface‐tension measurements in the rubbery state. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1907–1920, 2001     

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     

Control of molecular orientation

I. Amorphous polymers . The mechanical performance of a glassy amorphous polymer is strongly dependent upon molecular orientation. The pattern of molecular orientation is governed by the kinematics (and temperature) of mechanical forming operations. Three types of controllable orientation are: (a) uniaxial, (b) biaxial, and (c) “crossed.” The optimum pattern of orientation in a part is one which is appropriate for the mechanical stresses encountered in service. For a fiber subjected to tensile and bending loads, uniaxial orientation is appropriate. A shell structure, subjected to multiaxial stresses, requires either biaxial or crossed orientation for maximum performance. As a rule, the maximum achievable multidirectional strength in such a structure is less than the maximum strength of a uniaxially oriented fiber. II. Crystalline polymers . Oriented crystalline polymer structures can be created in two distinct ways. An isotropic polycrystalline polymer can be deformed below the melting point, with extensive reorganization of the crystal morphology, or an oriented amorphous melt can undergo crystallization to yield oriented crystalline polymer. Performance of an oriented semicrystalline polymer depends upon orientation of the amorphous portion as well as orientation of the crystallites. As with amorphous polymers, orientation can be uniaxial, biaxial, or crossed. “Orientation” usually denotes c-axis orientation only, but drawing followed by rolling can result in double orientation—orientation of a-axis, b-axis, and c-axis.     

Low molecular weight block copolymers as plasticizers for polystyrene

Polystyrene‐b‐alkyl, polystyrene‐b‐polybutadiene‐b‐polystyrene, and polystyrene‐b‐poly(propylene glycol)monotridecyl ether were synthesized using macro initiators and atom transfer radical polymerization or by esterifications of homopolymers. The aim was a maximum molecular weight of 4 kg/mol and minimum polystyrene content of 50 w/w %, which by us is predicted as the limits for solubility of polystyrene‐b‐alkyl in polystyrene. DSC showed polystyrene was plasticized, as seen by a reduction in glass transition temperature, by block copolymers consisting of a polystyrene block with molecular weight of approximately 1 kg/mol and an alkyl block with a molecular weight of approximately of 0.3 kg/mol. The efficiency of the block copolymers as plasticizers increases with decreasing molecular weight and polystyrene content. In addition, polystyrene‐b‐alkyl is found to be an efficient plasticizer also for polystyrene‐b‐polyisoprene‐b‐polystyrene (SIS) block copolymers. The end use properties of SIS plasticized with polystyrene‐b‐alkyl, measured as tensile strength, is higher than for SIS plasticized with dioctyl adipate. The polystyrene‐b‐polybutadiene‐b‐polystyrene and polystyrene‐b‐poly(propylene glycol)monotridecyl ether series were only partially soluble in polystyrene and insoluble in the polystyrene phase of SIS. For the lowest molecular weight samples, this leads to measurable plasticization of polystyrene but no plasticization of SIS. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 981–991, 2005     

Liquid-liquid equilibria in polymer blends–molecular weight effects

Flory's equation-of-state theory has been successfully used by several scientists to predict the qualitative nature of the liquid-liquid phase equilibria in polymer blends. This theory in its most simple form requires characteristic PVT parameters for each component plus an interaction energy parameter for the mixture. The melt titration technique was used to measure the miscibility of a series of polystyrene fractions (Mw = 4000 to 1,800,000) in low density polyethylene. Because the PVT properties of both of these polymers are well known, the experimental results could be compared with the predicted equilibrium compositions from Flory's equation-of-state theory using the interaction energy as an adjustable parameter. This comparison led to the conclusion that the interaction energy parameter may have some molecular weight dependence.     

A conducting composite of polypyrrole with ultrahigh molecular weight polyethylene foam

Through a chemical polymerization of pyrrole inside ultrahigh molecular weight polyethylene (UHMWPE) foam, a conducting polymer composite was obtained. To produce conductive polymer foams, successive imbibiting of reactives, FeCl₃ and pyrrole in tetrahydrofuran solutions, were carried out. The conductive polymeric materials were characterized by FTIR, DSC, and SEM. Mechanical property measurements were carried out on the films prepared by the compression molding of the conductive foam polymers. These films showed rather high tensile strength compared to pure UHMWPE. Conductivity determined by a two‐probe technique showed that it increased with the pyrrole content in the UHMWPE foam matrix. The compression molding, however, resulted in a considerable reduction in the conductivities. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 1843–1850, 1999     

Effect of molecular weight and polymer concentration on the triple temperature/pH/ionic strength-sensitive behavior of poly(2-(dimethylamino)ethyl methacrylate)

Poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) samples were synthesized via aqueous atom transfer radical polymerization with DP_n of 35, 151, 390, and 546 and dispersity of 1.13, 1.17, 1.20, and 1.18, respectively. All samples were exposed to temperature and pH variations at different concentration of polymer and salt (NaCl). Results indicated that cloud point (T_cl) can be controlled by changing DP_n, polymer concentration, and ionic strength of solution. According to results, T_cl of the PDMAEMA chains shifted to lower temperatures with increasing solution pH at all molecular weight ranges due to deprotonation of tertiary amine groups in polymer structure. However, higher molecular weight polymers were more sensitive to pH variation especially in alkaline media. Also, higher polymer concentration acted as driving force to decrease cloud point of samples and formation of aggregates that was more predominant for higher molecular weights at alkaline media. T_cl of PDMAEMA chains decreased with increasing ionic strength even at low pH values for low molecular weight polymers.     

Dependence of intrinsic viscosity and molecular size on molecular weight of partially hydrolyzed polyacrylamide

As a typical water-soluble polymer, ultra-high molecular weight (UHMW) partially hydrolyzed polyacrylamide (HPAM) has been widely used in various industries as thickeners or rheology modifiers. However, precise determination of its critical physical parameters such as molecular weight, radius of gyration (R_g) and hydrodynamic radius (R_h) were less documented due to their high viscosity in aqueous solution. In this work, the molecular structure of five UHMW-HPAM samples with different MW was elucidated by ¹H and ¹³C NMR spectroscopy, and their solution properties were characterized by both static and dynamic light scattering. It is found that all the second virial coefficient (A₂) values are positive and approaching zero, indicating of a good solvent of 0.5 M NaCl for UHMW-HPAM. The weight-average molecular weight (M_w) dependence of molecular size and intrinsic viscosity [η] for these series of HPAM polymers with MW ranging from 4.81 to 15.4 × 10⁶ g·mol⁻¹ can be correlated as R_g = 3.52 × 10⁻²M_w^0.51, R_h = 1.97 × 10⁻²M_w^0.51, and [η] = 6.98 × 10⁻⁴ M_w^0.91, respectively. These results are helpful in understanding the relationship between molecular weight and coil size of HPAM polymers in solution, and offer references for quick estimation of molecular weight and screening of commercial UHMW-HPAM polymers for specific end-users.     

Humid aging of plastics: Effect of molecular weight on mechanical properties and fracture morphology of polycarbonate

Polycarbonate tensile bars were aged up to 18 months at 0%, 75%, and 100% relative humidity and temperatures of 65–93°C. In the humid aged samples hydrolysis caused progressive reductions in molecular weight. Below a critical molecular weight (M _w = 33,800, M _n = 14,300) tensile strength dropped off rapidly. A transition from ductile to brittle failure was also observed at that point. Extrapolations indicate that the ductile–brittle transition at 38°C will be reached after 5 years at 100% relative humidity for the polycarbonate studied. Elongation was affected even in the early stages of hydrolysis. This suggests that whenever the degradation mechanism is a molecular weight reduction, toughness will be affected before the strength properties are lost. Mechanical properties are affected by annealing and antiplasticization which reduce localized stresses and increase short-range order. The brittle fracture surfaces of polycarbonate consist of four distinct regions. The size of the regions and the prominence of the features changed as the molecular weight decreased.     

Size-exclusion chromatography with two-angle laser light-scattering (SEC-TALLS) of high molecular weight and branched polymers

The accuracy and precision of results obtained from light-scattering detection at two angles (TALLS) for size-exclusion chromatography (SEC) are examined for linear narrow molecular weight distribution polystyrenes between 1,290,000 and 20,000,000 MW and for branched polyesters. The ratio of light-scattering intensities at 15° and 90° is used to calculate weight-average molecular weight, M?_w, and an average root-mean-square radius, r?_gu, equivalent to the z-average radius. A shape for the polymer molecule is assumed and an analytical relationship for the particle-scattering function is required. It is shown that analysis of the data using the particle-scattering function for a random coil is valid for both high molecular weight, linear polystyrenes and long-chain branched polyesters. The radius, r?_gu, is determined with high precision by using the ratio of light-scattering signals, which is insensitive to errors in sample concentration and changes in the eluent flow rate. The correct average radius for the whole polymer is obtained despite using low-efficiency, large-particle diameter SEC columns; however, axial dispersion significantly affects molecular weights and radii calculated at each retention volume that can limit the utility of plots used to deduce polymer conformation. © 1995 John Wiley & Sons, Inc.