Bimodal molecular weight distributions of a branched condensation polymer

Gel permeation chromatograms of a hindered-phenolic, branched condensation polymer display pronounced bimodality at high conversion. The true molecular weight distributions, obtained by means of a GPC calibration curve based on narrow-distribution fractions, exhibit corresponding anomalous high-molecular-weight “shoulders.” These results are discussed in terms of preferential aggregation and reaction of the higher-molecular-weight species during the polymerization, promoted by intermolecular hydrogen bonding in the apolar reaction medium.     

Ratios of average molecular weights and molecular weight distributions in polymers

If M_min and M_max are lower and upper bounds, respectively, to the molecular weights of different molecular weight species contained in a polymer, the weight-average to number-average molecular weight ratio M _w/M _n cannot exceed (1 + M_max/M_min)²/(4M_max/M_min). The ratio attains this maximum possible value if the masses of the two species with molecular weights M_min and M_max are equal and the masses of all the other species are negligibly small, corresponding to maximum spread in the molecular weight distribution within the specified bounds. Also for a given value of M _w/M _n = α, the M_max cannot be smaller than [2α ? 1 + 2α^1/2(α ? 1)^1/2]M_min. The minimum possible value of M_max/M_min consistent with α given is obtained in the case of maximum spread described above. If only one species is predominant, then both M _w/M _n and M_max/M_min approach unity, as is well known. Similar relations hold for the ratios of higher-order average molecular weights for which the role of the mass fractions is replaced by higher-order distribution functions.     

Electrochemical preparation of polymers with multinodal molecular weight distributions

A direct electrochemical preparation of polybutadiene to a predetermined molecular weight distribution has been achieved. Butadiene is a good model compound, inasmuch as the rate of electrochemical initiation is high relative to the rate of propagation. Rate constants for the temperature interval of interest and for systems of comparable composition were reported and permitted a priori prediction of the weight fractions and the number average molecular weight of each fraction. Polymer was formed by a series of pulses which successively initiated polymerization, permitted growth in the absence of current, and electrochemically terminated polymerization. The polymers produced showed excellent agreement with calculated composition and distribution in the range of molecular weights 10,000 to 50,000.     

Molecular weight distribution in branched polymers

The distribution of molecular weights in realistic free-radical polymerizations with branching was analyzed theoretically. Series solutions were obtained for the fraction of molecules with r repeating units and the number of branch points contained in molecules with r repeating units. Branching by transfer processes was found to increase the proportion of both high and low molecular weight components in the system. The apportioning of branch points among r-mer molecules was shown to be somewhat narrower than a Poisson distribution. The major difference between the calculated distributions and previous model distributions for branched systems was the absence of discontinuities in the moments at all levels of branching.     

Aminosilylene-bridged ansa-zirconocenes for branched polyethylenes with bimodal molecular weight distributions

Reactions of the dilithium salt of aminosilylene-bridged ligands with (Me₂N)₂ZrCl₂(THF)₂ followed by the treatment of Me₃SiCl are found to be an efficient synthetic route to aminosilylene-bridged ansa-zirconocenes, R₂N(Me)Si(η⁵-C₅H₄)₂ZrCl₂ (R = Me (1), Et (2)) and Me₂N(Me)Si(η⁵-C₅H₄)(η⁵-C₅Me₄)ZrCl₂ (3). Crystal structure of 3 determined by X-ray diffraction study reveals the presence of π-bonding interaction between N and Si atoms, which is further supported by DFT calculation results. These complexes are very active (>1 × 10³ Kg/(mol Cat.·atm·h)) for homopolymerization of ethylene in the presence of methylalumoxane (MAO) cocatalyst, generating polyethylenes that contain branches as well as bimodal molecular weight distribution (MWD). Methyl, ethyl, butyl, and other longer branches (n ≥ 6) are observed in the resulting polyethylenes. The polyethylenes from 1, 2 and 3/MAO show a broad MWD range (6.3-42.2, 3.5-4.0 and 2.6-3.4, respectively).     

The true molecular weight distributions of acrylate polymers formed in propagating fronts

We have analyzed fractionated samples of poly(methacrylic acid) produced in a propagating front for the amount of anhydride that formed and determined that a large percentage of acid groups exist as anhydrides (>20%). By analyzing the samples after cleavage, we found that the molecular weight dropped significantly (from M_n = 1.4 × 10⁵ to M_n = 1.0 × 10⁴). We conclude that the high molecular weights observed previously were the result of intermolecular anhydride formation. Poly(butyl acrylate), which cannot form anhydride bonds, produced in fronts had broad (M_w/M_n = 1.7–2.0) but unimodal molecular weight distributions with M_u < 10⁵. The average molecular weight decreased with increasing initiator concentrations. © 1996 John Wiley & Sons, Inc.     

Precise molecular weight distributions of high polymers by semiautomatic solvent extraction

It has been found practical to fractionate relatively monodisperse polystyrenes of molecular weights up to 4 × 10⁶ by using a semiautomatic solvent extraction procedure. The fractionators consist of flow-through mixing chambers provided with settling regions for the removal of finely suspended solid material. Provision is made for accurate control of both temperature and solvent–nonsolvent ratio. Two such apparatus, operated in tandem, were used in the present work; in principle, several more stages could be employed if desired for most polymer systems. Results on polystyrenes prepared in well defined ways appear to be in good agreement with predicted distributions. Applicability to other polymer systems is discussed.     

Calculation of molecular weight distributions for polymers undergoing random crosslinking and scission

A simple, practical calculation procedure has been developed for predicting the changes in molecular weight distribution of a polymer undergoing random crosslinking and/or degradation. Simulations of the random crosslinking and degradation of narrow and broad Poisson-type distributions have been made. The results agree with those calculated from Kimura's analytical solutions to Saito's general equations after a correction has been made for a mathematical error in Kimura's solution. This method can be applied to determining the probabilities of crosslinking and scission for any arbitrary molecular weight distribution expressed in tabular form. The importance of using narrow distribution samples to estimate crosslinking from changes in molecular weight distribution is graphically demonstrated.     

Determination of molecular weight dependences and characterization of molecular weight distributions

Molecular weight dependences of the square of the radius of gyration as well as of the coefficients of diffusion and friction of monodisperse polystyrenes in toluene at 20°C are determined experimentally. For this purpose, the z-averages of these quantities and $\text{M}$_w as determined by light scattering were subjected to the polydispersity correction procedures as described previously. In addition, a method is suggested for the checking of known data with respect to molecular weight distribution, using measured values in conjunction with the polydispersity correction procedures.     

Characterization of polymer molecular weight distributions by ratios of molecular weight averages

The molecular weight (MW) distribution of a polymer is characterized by a hierarchy of average MWs and their appropriate combinations. For example, the ratio of the weight-average to the number-average MW is the most frequently used measure of the polydispersity of a polymer. As is well known the lower bound to this ratio is unity, and it has been shown that the upper bound is (m + 1)²/4m, where m = M_max/M_min is the ratio of the highest to the lowest MW of the MW species present in a given polymer. This upper bound corresponds to an extremely bimodal MW distribution of one half weight fraction with M_min and the other half with M_max. The behavior of the upper bound for two special unimodal distributions is investigated: one is the triangular distribution, the other the quadrilateral. The results suggest that the upper bound for all possible unimodal distributions is considerably less than the corresponding general case, especially for large values of m. For example, the maximum ratios for the quadrilateral distribution and the general upper bound are 1.04 and 1.125 for m = 2; 1.43 and 3.205 for m = 10; 2.56 and 25.5 for m = 100; 3.99 and 250.5 for m = 1000, respectively.     

Synthesis and characterization of high molecular weight branched PBA

We prepared carboxylic acid group terminated linear polybutylene adipate (PBA) by melt polycondensation of adipic acid with 1,4‐butanediol in the presence of titanium(IV) isopropoxide (TIP) as a catalyst. High molecular weight branched PBAs were synthesized through the branching reaction between the carboxylic acid group terminated PBA and branching agent such as glycerol or pentaerythritol in the presence of TIP. The weight‐average molecular weights of the branched PBAs were found to be in the range of about 100,000–240,000 by gel permeation chromatography. Mechanical properties of the linear and branched PBAs were measured on an Instron tensile tester. The moduli of the branched PBAs had lower values of 320–450 MPa than those of the linear PBAs, whereas the elongations at break of the branched PBAs were in the range of 530–590%, which are much greater than the linear PBAs. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2143–2150, 2001     

Effect of interchange reactions on nonequilibrium distributions of condensation polymers and their associated molecular weight averages

Theory is developed to determine the effect of interchange reactions on nonequilibrium distributions of condensation polymers and their associated molecular weight averages. The analysis offers a method for determining the interchange rates of condensation polymers.     

The skewness of polymer molecular weight distributions

A new parameter α₃ for characterization of the skewness of a polymer's molecular weight distribution (MWD) based on the statistics is introduced. For α₃ > 0, the skewness is positive, characterizing the MWD with a tail at higher-MW side. For α₃ = 0, the MWD is symmetric. For α₃ < 0, the skewness is negative, characterizing the MWD with a tail at the lower-MW side. A relationship between α₃ and the first four (from zeroth to third) moments of the MWD is developed which allows calculation of the skewness without detailed calculation of the MWD. An example of polymerization of styrene with n-butyllithium is given to demonstrate the characteristics of α₃.     

The electrochemical preparation of soluble electrically conducting polymers of 3-methoxythiophene with narrow distributions of molecular weight

Solutions of 3-methoxythiophene (MeOT) in dimethylformamide (DMF) were electrolyzed at controlled electrode potentials. The polymerizations were studied under homogeneous conditions in solutions in which the polymer was soluble in the medium, and no coating of the electrodes occurred. The reaction proceeded at high coulombic efficiency and a first order dependence on monomer concentration was observed. The molecular weights of the polymers were determined by gel permeation chromatography. All samples showed a narrow distribution of molecular weights, with M_w/M_n ranging from 1.01 to 1.07. The molecular weight was low (about 3000 Daltons) and did not change in magnitude during the course of the reaction from 10 to 86% conversion, or with change in electrode potential from 1.55 to 1.65 V vs. SCE. The data are interpreted on a model based upon the competitive formation of chemically unreactive bipolarons.     

Flocculation by very high molecular weight polymers

Polymer-induced flocculation in which the size of polymer molecules is much greater than that of colloidal particles is investigated. A dynamic analysis is conducted which takes the transient behaviors of the adsorption of particles to a polymer molecule and the particle-particle interactions into account. We show that the number of particles adsorbed to a polymer molecule follows approximately a binomial distribution. An approximate expression for the degree of flocculation of the system under consideration is presented.     

Microdetermination of molecular weight in high molecular weight polymers soluble in benzene at 37° C

Summary A simplified method has been developed to determine molecular weight by using a constant volume of solvent and using polystyrene as a standard, molecular weights up to 51000 can be obtained with less than 2% error from a graph. If calculated by computer, 5% error is the maximum.

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Zusammenfassung Ein vereinfachtes Verfahren unter Verwendung eines konstanten Lösungsmittelvolumens sowie von Polystrol als Standardsubstanz ermöglicht die Bestimmung von Molekulargewichten bis zu 51 000 mit einer Fehlerbreite von 2% an Hand einer Eichkurve. Bei Berechnung mit einem Computer ist die maximale Fehlerbreite 5%.

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This work was supported by the U. S. Air Force under Contract #F33615-73-C-5013.     

Treatment of high molecular weight wormlike polymers as random coiled polymers

The possibility of treating a wormlike polymer as a random coiled polymer is examined. Taking from the literature intrinsic viscosity data concerning several wormlike polymers, we use two graphical methods which have been proposed for flexible polymers. These methods are only applicable in the region of molecular weights where the wormlike polymer presents a relatively great number of statistical segments. From the values of unperturbed dimensions obtained by the graphical methods, we obtain the statistical segment of wormlike polymers at Θ conditions.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.