Estimation of molecular weight distribution parameters for free-radical polymerization

A method is described which allows the precise estimation of molecular weight distribution parameters p and A which pertain to free-radical polymerizations. Thus, expressions are developed which allow the estimation of (1 ? p) by means of a programmable calculator using molecular weight distribution data derived from GPC. Values of A may subsequently be calculated by means of a plot of one of the expressions given. Values of (1 ? p) and A obtained in this paper were checked using theoretical values as well as by a comparison between calculated and observed values. The agreement between calculated and theoretical or experimental values indicates that the method presented for the estimation of (1 ? p) and A is both reliable and relatively rapid. Previously reported methods for the estimation of (1 ? p) and A have involved curve-fitting trial calculations as well as more precise interpolation procedures. However, the latter are based on single-peak maximum values.     

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.     

Electrospray mass spectrometry for characterizing polyglycerols and the effects of adduct ion and cone voltage

Polyglycerol intermediates have been characterized by liquid chromatography-mass spectrometry (LC-MS) with electrospray ionization (ESI). Linear and cyclic components from n=2–23 in a sample of decaglycerol, for example, have been resolved in the second dimension or mass axis. Molecular weight (MW) distributions for tri-, hexa-, and decaglycerol products have been analyzed as a function of cone voltage and adduct ion (H⁺, Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, and NH₄ ⁺). A different combination is required to obtain a reliable MW distribution for each polyglycerol intermediate. The best distribution obtained by ESI/MS is determined by comparing the calculated hydroxyl number and cyclic content to that obtained by wet chemistry and gas chromatography, respectively. Once ESI/MS conditions are established, the distribution can be used, for the first time in polyglycerol analysis, to calculate important parameters such as number average MW, weight average MW, polydispersity, % cyclics, hydroxyl number, wt% above n=6, etc.     

Dynamic light‐scattering characterization of the molecular weight distribution of unfractionated polyimide

Using a developed laser light‐scattering (LLS) procedure, we accomplished the characterization of an unfractionated polyimide (UPI) in CHCl₃ at 25°C. The Laplace inversion of precisely measured intensity–intensity time correlation function from dynamic LLS leads us first to an estimate of the characteristic line‐width distribution G(Γ), and then to the translational diffusion coefficient distribution G(D). By using a previously established calibration of D (cm²/s) = 3.53 × 10^?4 M^?0.579, we were able to convert G(D) into a molecular weight distribution. The weight‐average molecular weight M_w, calculated from the molecular weight distribution, agrees well with that directly measured in static LLS. Our results indicate that both the calibration and LLS procedure used in this study are ready to be applied as a routine method for the characterization of the molecular weight distribution of polyimide. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1670–1674, 2001     

Fluorescence excitation spectroscopy of polystyrene near the critical concentration c*

The critical concentration c* was measured using both fluorescence excitation spectroscopy and light scattering for four narrow molecular weight distribution samples of polystyrene (MW = 225,000–1,500,000) in bicyclo[4.4.0]decane (decahydronaphthalene, decalin) at 20 and 30°C. A discontinuity in the corrected intensity of a band in the excitation spectrum (assigned to the dimmer complex) as a function of concentration allowed determination of the critical concentration, c*, from the excitation spectra. The c* resulting from fluorescence and light scattering were identical within experimental error and were comparable to c* values calculated from literature methods. Fluorescence excitation spectroscopy should be a convenient method for determining c* for aromatic polymers. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 360–364, 2007     

A study on the optical properties of three‐armed polystyrene and poly(styrene‐b‐isobutyl methacrylate)

Atom transfer radical polymerization (ATRP) of three‐armed polystyrene[PS] and poly(styrene‐b‐isobutyl methacrylate)[PS‐b‐PiBμMA] were accomplished using an initiator with tri‐active C‐Br end group function and cuprous (I) bromide/2,2′‐bipyridyne catalytic system. The characterization obtained by FT‐IR, ¹H‐NMR, and GPC techniques. The average molecular weight and polydispersity of PS and PS‐b‐PiBμMA were determined as 19,800, 29,300 and as 1.37 and 1.15, respectively, which indicates that the constant concentration of growing chains are present throughout the polymerization. The refractive index and extinction coefficient of the samples were determined in the visible range as a function of wavelength. The refractive index dispersion curves of the thin films were fitted by the Cauchy‐Sellmeier model. The width of localized states (E_u) values changed inversely with optical band gaps (E_g) of the films. While the calculated E_u values of films for initiator, PS and PS‐b‐PiBμMA were determined as 2.72, 2.98, and 2.94 eV, the E_g values were determined as 3.43; 3.11, and 3.16 eV, respectively. The dispersion parameters of thin films were determined. These parameters changed in the investigated wavelength ranges. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Fiber reinforced polypropylene: Influence of iPP molecular weight on morphology,crystallization, and thermal and mechanical properties

The influence of molecular weight and its distribution on the nucleation density, crystallization, thermal and mechanical behavior of isotactic polypropylene based composites has been investigated. The composites were prepared by compression molding. The ability of carbon and Kevlar fibers to nucleate the polypropylene has been studied during isothermal and nonisothermal crystallization, by optical microscopy and differential scanning calorimetry (DSC), as function of crystallization temperature T_c and iPP molecular weight. Two extreme crystallization conditions were tested: quenching and slow crystallization to obtain crystals and amorphous phases of different structure. The ability of fibers to enhance mechanical properties in polypropylene based composites was examined by tensile tests at room temperature. It was found that nucleation density, crystallization parameters, and the results of tensile tests strongly depend on the molecular weight M w of iPP, molecular weight distribution, and thermal history of polypropylene. The numerical values of the nucleation density have been found to strongly depend on the nature of fiber. In fact, Kevlar fiber has shown a better nucleating ability than carbon fiber. The results of tensile tests have been related to the sample morphology. The analysis of fractured specimens also provided useful information about fiber-matrix adhesion.     

Phase equilibria in SBR/polybutadiene elastomer blends: Application of Flory–Huggins theory

Blends of anionically-polymerized polybutadiene (BR) and styrene–butadiene copolymer (SBR) must be treated as mixtures of terpolymers and tetrapolymers, due to the presence of three different BR isomers: cis-1,4, trans-1,4, and vinyl-1,2. Moreover, in the absence of specific interactions or chemical reactions that strongly influence miscibility, structural characteristics of the component polymers, such as BR isomer content, SBR styrene content, monomer sequence distribution, molecular weight, and molecular weight distribution, are expected to have an increased role in determining the blend miscibility characteristics. Small angle neutron scattering (SANS) studies of SBR/BR blends have resulted in the computation of the monomer–monomer segmental interaction energetics via a Flory–Huggins treatment. This allows quantitative prediction of miscibility behavior as a function of polymer structure. We have used the Flory–Huggins chi parameters, describing the styrene/cis-1,4, styrene/trans-1,4, and cis-1,4/trans-1,4 segmental interactions, to identify certain blend combinations expected to exhibit phase transitions in an experimentally accessible temperature range. The appropriate polymers were synthesized, solution blended, and the blends analyzed via optical microscopy and thermal analysis. Our results show that the blend behavior, observed experimentally, is consistent with the calculated cloud point curves. © 1994 John Wiley & Sons, Inc.     

Log‐normal distribution for a description of the molecular weight distribution of N‐acetylated chitosans depolymerized with hydrolytic enzyme

N‐acetylated chitosans (NACs) with different degrees of N‐acetylation (DAs) were enzymatically depolymerized at pH 5.1 and 40 °C, and the molecular weight distributions (MWDs) of the depolymerized NACs were then measured by size exclusion chromatography and were fitted by the log‐normal distribution function with two distribution parameters, β and M₀. We discuss also the time‐evolution of the distribution parameters derived from the experimentally obtained MWD as well as the effects of experimental conditions, such as DA and initial NAC concentration (S₀), on the distribution parameters. Copyright © 2003 Society of Chemical Industry     

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.     

Statistical moments of elution bands and their application in gel permeation chromatography of polydisperse macromolecules

Equations have been derived that relate the statistical moments of uncorrected and spreading-corrected chromatograms for a general form of the spreading function in gel permeation chromatography of polydisperse macromolecules. The first moment (centroid) of the chromatogram is shown to be directly given by the centroid, In M^*, of a suitably defined molecular weight distribution function of the polydisperse sample, regardless of the position of the calibration dependence, provided it is linear. Both the molecular weight M^* associated with the centroid of the chromatogram and its second central moment (variance) are but little sensitive to the shape of sample molecular weight distribution and can be easily calculated from the polydispersity index M_w/M_n, at least for polymers of a not excessively broad distribution. The derived relations are shown to find application in the calibration of GPC columns by means of characterized, polydisperse standards and in the separation of independent contributions to peak width which originate in sample polydispersity and in band broadening processes in the column. Improved column- and packing performance criteria are also proposed.     

Estimation of molecular weight distribution of poly(vinylpyrrolidone) from diaphragm-cell diffusion measurements

Viscometry, gel permeation chromatography (GPC) and diffusion measurements on three samples of poly(vinylpyrrolidone) (PVP) were made. The diffusion measurements were carried out by means of a Stokes cell. An equation with five parameters was derived, linking the difference in PVP amount between the two compartments of the cell to the time of the experiment: three parameters are related to the diffusional behavior of the macromolecules and the other two define the molecular weight distribution (the Tung expression has been chosen). A least-squares procedure allowed us to obtain the five parameters and the calculated weight average molecular weights agree with the ones evaluated by viscometry and GPC. The ratio M _w/M _n (heterogeneity of the polymer) calculated from the parameter z of the Tung expression is very different from the one obtained from GPC.     

Dynamic light-scattering characterization of the molecular weight distribution of a broadly distributed phenolphthalein poly(aryl ether ketone)

Using a recently developed laser light-scattering (LLS) procedure, we accomplished the characterization of a broadly distributed unfractionated phenolphthalein poly(aryl ether ketone) (PEK-C) in CHCl₃ at 25°C. The laplace inversion of precisely measured intensityintensity time correlation function from dynamic LLS leads us first to an estimate of the characteristic line-width distribution G(T) and then to the translational diffusion coefficient distribution G(D). By using a previously established calibration of D (cm²/s) = 2.37 ×10⁻⁴M^−0.57, we were able to convert G(D) into a differential weight distribution f_w(M). The weight-average molecular weight M_w calculated from f_w(M) agrees well with that directly measured in static LLS. Our results indicate that both the calibration and LLS procedure used in this study are ready to be applied as a routine method for the characterization of the molecular weight distribution of PEK-C. © 1996 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.     

The structural,morphological and thermal properties of grafted pH-sensitive interpenetrating highly porous polymeric composites of sodium alginate/acrylic acid copolymers for controlled delivery of diclofenac potassium

In present investigation new formulations of Sodium Alginate/Acrylic acid hydrogels with high porous structure were synthesized by free radical polymerization technique for the controlled drug delivery of analgesic agent to colon. Many structural parameters like molecular weight between crosslinks (M_c), crosslink density (M_r), volume interaction parameter (v_2,s), Flory Huggins water interaction parameter and diffusion coefficient (Q) were calculated. Water uptake studies was conducted in different USP phosphate buffer solutions. All samples showed higher swelling ratio with increasing pH values because of ionization of carboxylic groups at higher pH values. Porosity and gel fraction of all the samples were calculated. New selected samples were loaded with the model drug (diclofenac potassium).The amount of drug loaded and released was determined and it was found that all the samples showed higher release of drug at higher pH values. Release of diclofenac potassium was found to be dependent on the ratio of sodium alginate/acrylic acid, EGDMA and pH of the medium. Experimental data was fitted to various model equations and corresponding parameters were calculated to study the release mechanism. The Structural, Morphological and Thermal Properties of interpenetrating hydrogels were studied by FTIR, XRD, DSC, and SEM.     

The influence of molecular weight distribution on melt viscosity,melt elasticity,processing behavior and properties of polystyrene

The influence of molecular weight and molecular weight distribution on the melt rheological behavior of two polystrenes of approximately the same weight average molecular weight, but of widely different molecular weight distribution, was determined. Then, using a series of capillaries with different length-to-diameter ratios in an Instron Capillary Rheometer, the entrance correction methods of E. B. Bagley and the relationships of W. Philippoff and F. H. Gaskins, the recoverable shear strain (S_R) in the melt at the capillary wall for these mono- and polydisperse polystyrenes was determined. Shear modulus (G) and normal stress (P_N) were calculated using the relationships: G = τ_RC/S_R and P_N = 2τ_RC S_R, where τ_RC is the corrected shear stress at the capillary wall. These are compared to values obtained using a Weissenberg Rheogonimeter. These two polystyrenes were also injection molded into an ASTM specimen mold over a wide range of stock temperature, using a 12 OZ . in-line reciprocating screw injection press, and evaluated for mechanical property values. The effects of the elasticity parameters (S_R G & P_N) and their magnitude on the rheology, processability and mechanical properties of these polystyrenes are discussed.     

The numerical evaluation of parameters in distribution functions of polymers from their molecular weight distributions

It has been shown that the parameters in the log-normal (LN) and generalized exponential (Gex) distributions can be evaluated if molecular weight ratios H and H_z, or their equivalents, are known for a linear, unimodal homopolymer. It is suggested that better checks of observed and calculated values of M_z can be obtained for such polymers as are characterized by m ≤ 0.15, by treating them as Gex rather than LN distributions.     

Prediction of linear viscoelastic response for entangled polyolefin melts from molecular weight distribution

The linear viscoelastic properties of polymer melts depend strongly and systematically on the molecular weight distribution. A molecular theory relating dynamic modulus and molecular weight distribution for linear polymers, developed and confirmed earlier with data for three other polymer species, is applied here to commercial samples of isotactic polypropylene and high density polyethylene. Experimental master curves are compared with predictions based on only the fundamental rheological parameters of the species and molecular weight distributions as obtained by the methods of size exclusion chromatography. Agreement is fairly good for the two polypropylene samples, about the same as had been found earlier for the other species, but it is highly variable for the ten polyethylene samples. We attribute this variability to differences among high density polyethylenes in the frequency, length, and type of long-chain branching. However, we could find surprisingly little supporting evidence for this from such supposed signatures of long branches in polyethylene as the flow activation energy E_a. Measured values of E_a agreed well with the literature results for linear polyethylene; none showed the elevation in E_a that would be expected for polyethylene with long branches.     

Thermal degradation kinetics of rigid polyurethane foams blown with water

The thermal decomposition behavior of rigid polyurethane foams blown with water was studied by dynamic thermogravimetric analysis (TGA) in both nitrogen and air atmosphere at several heating rates ranging from room temperature to 800°C. The kinetic parameters, such as activation energy (E), degradation order (n), and pre‐exponential factor (A) were calculated by three single heating rate techniques of Friedman, Chang, and Coats–Redfern, respectively. Compared with the decomposition process in nitrogen, the decomposition of foams in air exhibits two distinct weight loss stages. The decomposition in nitrogen has the same mechanism as the first stage weight loss in air, but the second decomposition stage in air appears to be dominated by the thermo‐oxidative degradation. The heating rates have insignificant effect on the kinetic parameters except that the kinetic parameters at 5°C/min have higher values in nitrogen and lower values in air, indicating different degradation kinetics in nitrogen and air. The kinetic parameters of foam samples blown with different water level in formulation decline firstly and then increase when water level increases from 3.0 to 7.0 pph. According to the prediction for lifetime and half‐life time of foams, water‐blown rigid foams have excellent thermostability, when used as insulation materials below 100°C. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:4149–4156, 2006     

Dielectric relaxation and thermodynamic properties of polyvinylpyrrolidone using time domain reflectometry

Temperature‐dependent values of dielectric permittivity ε′ and dielectric loss ε″ of polyvinylpyrrolidone (PVP, commercialized as PVP K‐60) solution of average molecular weight 160 000 g mol^?1 were measured. The measurements were carried out in the frequency range 10 MHz to 20 GHz using time domain reflectometry at temperatures from 25 to 0 °C. The dielectric spectra can be described by the Davidson‐Cole model. Dielectric parameters such as the static dielectric constant ε₀, the high frequency limiting dielectric constant ε_∞, the relaxation time τ₀ and the distribution parameter β and thermodynamic parameters such as the free energy of activation ΔF_τ, the enthalpy of activation ΔH_τ and the entropy of activation ΔS_τ were determined. The average free energy of activation was found to be in the range 12.55–14.65 KJ mol^?1 and the enthalpy of activation was found to be 6.86 KJ mol^?1. Entropies of activation were found to be positive at all the measured temperature values and these large positive values of entropies reveal a less ordered structure of the PVP solution. The Kirkwood correlation factor g and the dipole moment µ were also determined for PVP solution. The results were compared with the results of the PVP‐water system studied previously. Copyright © 2011 Society of Chemical Industry