The solution phase characterization of poly(ferrocenyldimethylsilane)s by small‐angle neutron scattering

A series of monodisperse (M_w/M_n < 1.1) poly(ferrocenyldimethylsilane)s was prepared with number‐averaged degrees of polymerization, 〈z〉_n, of 9, 33, 206, and 506 ( 2 – 5 , respectively), as determined by gel permeation chromatography (GPC). The polymers were studied by small‐angle neutron scattering (SANS) in solution with the aim of obtaining the radius of gyration, R_g, the weight‐averaged molecular weight, M_w, and the polydispersity index, M_w/M_n. Data were collected over the range 0.008 < Q/Å^?1 < 0.5 and for a series of concentrations (weight fraction, w = 0.0063, 0.0125, 0.025, and 0.05). The scattered intensity, I(Q), was fitted to a model based on a Schultz–Zimm distribution of isolated chains with excluded volume. A comparison of the molecular weight and size data determined by GPC and SANS indicated an acceptable agreement between the values for R_g, M_w and M_w/M_n. The results of this study demonstrate the potential utility of SANS to fully characterize metallopolymers, and other polymer systems where traditional methods cannot be applied. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4011–4020     

Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [?]M, averaged across a chromatogram was found to become KM^a+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KM_n ^a+1 where M_n is the number average molecular weight.

Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KM_n ^a+1, KM_w ^a+1, and [η]M_w were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]M_n was displaced from the polystyrene universal calibration plot by factor which equaled M_w/M_n. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).     

SYNTHESIS OF POLYPROPYLENE-POLY(METH)ACRYLATE BLOCK COPOLYMERS USING METALLOCENE CATALYZED PROCESSES AND SUBSEQUENT ATOM TRANSFER RADICAL POLYMERIZATION

ABSTRACT

The synthesis of block copolymers containing low molar mass polypropylene and poly(meth)acrylates is reported. Vinyl-terminated polypropylene (M_n SEC=3,100; M_w/M_n=1.45) was used to prepare a macroinitiator for atom transfer radical polymerization (ATRP) via hydrosilation with 1-(2-bromoisobutyryloxy)propyl-tetramethyldisiloxane. Polar segments were then incorporated to polypropylene by chain extension using either methyl methacrylate, or n-butyl acrylate. While blocking efficiency was limited in this system, well-defined PP-b-PMMA (M_n=22,220; M_w/M_n=1.14) was obtained by extraction of unreacted polypropylene with diethyl ether.     

Gel permeation chromatography: Examination of column efficiency

Gel permeation chromatographic (GPC) separations have been performed with several commercially available column packing materials. The results have been analyzed in the conventional manner to obtain the ratio of weight average to number-average molecular weight, M_w/M_n, for solutes with narrow molecular weight distribution. Various other parameters proposed to measure the efficiency of GPC columns have been evaluated and compared. It is proposed that the experimentally determined value of M_w/M_n for a series of different molecular weight samples with similar, narrow distribution for a given set of columns is a convenient parameter for comparing column efficiency in GPC. This parameter may be calculated from a single chromatogram unlike resolution, R, resolution index, RI, or specific resolution, RS, which require a pair of chromatograms. Results from the M_w/M_n method are usually in agreement with those from the R, RI, and RS calculations but one exception has been found. The number of theoretical plates calculated from the elution of a small molecule or from the polymer peak bears little relation to efficiencies predicted from the proposed M_w/M_n method or from R, RI, or RS.     

Ring-Opening Polymerization of Cyclic Monomers with Aluminum Triflate

A green method for the controlled synthesis of aliphatic polymers is presented. The ring-opening polymerizations of cyclic monomers including several lactones, such as caprolactone (CL) or pentadecalactone (PDL), and cyclic anhydride monomers, such as succinic anhydride (SUC) and tetrahydrofuran (THF), catalyzed by a series of metal triflates (trifluoromethanesulfonate) were studied. Aluminum triflate was found to be an advantageous candidate to catalyze the ring-opening polymerization of cyclic monomers. The details of the ring-opening polymerization of CL catalyzed by aluminum triflate were studied. The maximum number average molecular weight (M_n), polydispersity (M_w/M_n) and yield of the obtained poly(-caprolactone) (PCL) at 60 °C for 6 hours were 18,400, 1.94 and 89 wt%, respectively. Those of poly(pentadecalactone) (PPDL) at 100 °C for 6 hours were 12,400, 2.24 and 49 wt%, respectively. The M_n, M_w/M_n and yield of the obtained poly(butylene succinate) (PBS) from SUC and THF at 100 °C for 48 hours were 4,900, 2.03 and 84 wt%, respectively. Furthermore, the mechanism of the polymerization was discussed based on the relationship between the conversion of CL and time. The molecular weight buildup of PCL was linear with a conversion in 50 min before the conversion reached 100 % and with M_w/M_n stabilized at about 1.5. The M_w/M_n of PCL then gradually increased. From these data, a living polymerization with a small transesterification was suggested from the PCL polymerization by aluminum triflate.     

Model Development in Thermal Styrene Polymerization

Summary: The thermal polymerization of styrene is usually modeled by relying on a reaction scheme and a set of equations that were developed more than three decades ago by Hui and Hamielec. Many detailed models of styrene polymerization are available in the open literature and they are mostly based on the work of Hui and Hamielec, which nearly makes this the standard to follow in explaining the behavior of polystyrene reactors. The model of Hui and Hamielec does a very nice job of describing monomer conversion data but discrepancies are seen between observed and predicted values of number and weight average molecular weights, M_n and M_w. Discrepancies in number average molecular weight seem to be the result of random noise. Discrepancies in weight average molecular weight grow as the polymerization temperature decreases and some of the trends observed in the residuals over the entire temperature range cannot be attributed to random noise. Hui and Hamielec attributed the observed deficiencies to a standard deviation of ±10% in their GPC measurements. A new data set with an experimental error of 2% for average molecular weights is presented. The set contains measured values of M_n, M_w and M_z, so the polymerization scheme has been extended to include third order moments. The data set also includes the effect of ethylbenzene as a chain transfer agent. We present the results of comparing model predictions to our measurements and the adjustments made in the original set of kinetic parameters published by Hui and Hamielec.     

Emulsion polymerization of vinyl acetate using iodine‐transfer and RAFT radical polymerizations

This study deals with control of the molecular weight and molecular weight distribution of poly(vinyl acetate) by iodine‐transfer radical polymerization and reversible addition‐fragmentation transfer (RAFT) emulsion polymerizations as the first example. Emulsion polymerization using ethyl iodoacetate as the chain transfer agent more closely approximated the theoretical molecular weights than did the free radical polymerization. Although ¹H NMR spectra indicated that the peaks of α‐ and ω‐terminal groups were observed, the molecular weight distributions show a relatively broad range (M_w/M_n = 2.2–4.0). On the other hand, RAFT polymerizations revealed that the dithiocarbamate 7 is an excellent candidate to control the polymer molecular weight (M_n = 9.1 × 10³, M_w/M_n = 1.48), more so than xanthate 1 (M_n = 10.0 × 10³, M_w/M_n = 1.89) under same condition, with accompanied stable emulsions produced. In the M_n versus conversion plot, M_n increased linearly as a function of conversion. We also performed seed‐emulsion polymerization using poly(nonamethylene L ‐tartrate) as the chiral polyester seed to fabricate emulsions with core‐shell structures. The control of polymer molecular weight and emulsion stability, as well as stereoregularity, is also discussed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Influences of molecular weight and crystalline structure on fracture behavior of controlled-rheology-polypropylene prepared by reactive extrusion

The molecular weight of ethylene-block-co-polypropylene (co-PP) was adjusted by reactive extrusion with the incorporation of dicumyl peroxide (DCP), and the effect of molecular weight on the crystallization behavior, crystal morphology, and fracture behavior was investigated. It was found that, with increasing DCP content, the molecular weight (MW) decreased and the polydispersity (M_w/M_n) slightly decreased. After modification, the number of spherulites with obscure boundaries increased, and the size of the spherulites was more even due to increasing amount of grafting and micro-cross-linking structures, generated in co-PP degradation, which were acting as nucleating agents. Evaluated by essential work of fracture method, the specific essential work of fracture, w_e, was found to be strongly dependent on the molecular weight, especially, on the number average molecular weight (M_n) linearly, while the specific non-essential work of fracture, βw_p, was enhanced with decreasing z-average molecular weight (M_z), probably owing to the reduction of ultra-high molecular weight component in degraded co-PP.     

Effect of polycondensation methods on molecular weight distribution of nylon 610

Polycondensation methods greatly influence the molecular weight distribution of poly(hexamethylene sebacamide) (nylon 610) as determined by gel permeation chromatography (GPC). The ratio of weight average molecular weight to number average molecular weight (M_w/M_n) was used as a measure for estimating the molecular weight distribution. The M_w/M_n ratios of nylon 610 obtained from melt, solid phase, and high temperature polycondensation methods were 2 to 3.5, which were expected values for the most probable distribution. However, those for polymers obtained from the direct polycondensation in the presence of triphenylphosphine, interfacial polycondensation and low temperature polycondensation using an acid chloride varied over a wide range from 3.5 to 8.5. The effect of the kind of organic solvents in the interfacial method on the M_w/M_n ratios was especially large, and the molecular weight distribution could be controlled to some extent by selecting an appropriate solvent.     

Ultrasonic Solution Degradations of Poly(Alkyl Methacrylates)

Ultrasonic (70 W, 20 kHz) solution (2%) degradations of poly(alkyl methacrylates) have been carried out in toluene at 27°C and in tetrahydrofuran (THF) at -20°C. M_w and M_n of all polymers (before and after sonification) were computed from GPC. Irrespective of the alkyl substituent, M_w decreased rapidly at first and then slowly approached limiting values. All M_w/M_n ratios were in the vicinity of 1.5 at the limiting chain lengths. For identical M_n, the rate constants k were (4.2 ± 2.0) × 10^?6 min^?1 in toluene at 27°C and (5.4 ± 2.0) × 10^?6 min^?1 in THF at -20°C. For poly(isopropyl methacrylate) and poly(octadecyl methacrylate) with higher, but identical, M_n,0, k values were higher ((9.0 ± 1.0) × 10^?6 min^?1 at 27°C and (18.0 ± 1.5) × 10^?6 min^?1 at -20°C). This suggests that M_n,0 and not the bulk size of the alkyl substituents is the factor that determines the rate of degradation. Lowering of the temperature accelerates degradation due primarily to lower chain mobility of poly-(alkyl methacrylates) and enhanced cavitation. The average number of chain scissions ([(M_n)₀/(M_n)_t] - 1) calculated from component degradation data are much higher than those obtained with overall M_n,t values.     

Effects of radiation and chain ends on fatigue behaviour of polystyrene

Fatigue lifetimes, under a given alternating stress amplitude, have been determined for a series of linear and branched polystyrenes. The branched polymers were obtained by a crosslinking reaction using γ-irradiation from a Co⁶⁰ source. By control of irradiation time, a series of branched samples of progressively increasing weight average molecular weight ($\text{M}$_w), with little change in number average molecular weight ($\text{M}$_n, were obtained. From comparison of fatigue data for these irradiated and branched samples with fatigue data obtained on a series of linear polystyrenes of increasing molecular weight, it may by concluded that appreciable increases in fatigue endurance can be achieved by increase in $\text{M}$_n and reduction in chain end density. For the irradiated samples, whether irradiated in air or in vacuum, fatigue lifetimes were comparable to or less than lifetimes to fracture for the unirradiated polymer, even though significant increases in $\text{M}$_w had occurred. It is suggested that the improved fatigue performance with increase of $\text{M}$_n is a consequence of increased craze stability resulting from the greater degree of chain entanglement and the smaller proportion of chain end defects.     

Reaction parameters in the RAFT mediated dispersion polymerization of styrene

Monodisperse polystyrene (PS) particles were prepared by a living radical dispersion polymerization with a reversible addition‐fragmentation chain transfer (RAFT) agent in an ethanol medium. In the presence of RAFT agent, the effects of various reaction parameters on the characteristics of PS particles were systematically investigated. When no RAFT agent was involved, the number‐average molecular weight (M_n) of the PS particles increased from 17,800 to 30,000 g/mol, but the weight‐average diameter (D_w) decreased from 2.54 to 2.06 μm with the increase of poly(N‐vinylpyrrolidone) content from 4.0 to 16.0 wt %. No correlation between the M_n and the coefficient of variation (CV) was observed. However, when the RAFT concentration varied from 0 to 2.0 wt %, all of the conversion, M_n, D_w, CV, and polydispersity index (M_w/M_n) decreased. This indicates that the RAFT agent alters the inverse behavior between the molecular weight (MW) and particle size shown in the conventional dispersion polymerization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 872–885, 2008     

Comments on the Numerical Treatment of CPC Data

Abstract

The magnitude of the errors introduced in the calculated molecular mass averages is discussed in the case of gel permeation chromatography (CPC). It was shown, that neglecting the undetectable parts at both tails of a chromatogram where the intensity of the curve is very small, results in serious errors. For chromatograms with Gaussian shapes it was found, that if the molecular mass limits of the calculations were set at ±35 (S is the standard deviation of the curve) the numerically calculated M_n and M_m values deviated by 1 to 10% from the theoretical ones. The errors increased with increasing polydispersity and decreased as the number of data points increased. However, there was no significant difference in the results if the number of data points was greater than 20.     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

New Interpretations: Molecular Weight Averages for a Polymer

The statement is often made in the polymer literature, without proof, that M _z ≤ M _w ≤ M _n, where M _z, M _w, and M _n are the z-, z weight-, and number-average molecular weights respectively. Four proofs of a generalization of these inequalities are given. It is shown that a higher-order molecular weight average is larger than a lower-order one, regardless of the form of the molecular weight distributions, except for the case when all the molecules have the same molecular weight. A brief discussion of the viscosity-average molecular weight is also included.     

Maximum tensile properties of oriented polyethylene,achieved by uniaxial drawing of solution‐grown crystal mats: Effects of molecular weight and molecular weight distribution

The effects of molecular weight (MW) and MW distribution on the maximum tensile properties of polyethylene (PE), achieved by the uniaxial drawing of solution‐grown crystal (SGC) mats, were studied. The linear‐PE samples used had wide ranges of weight‐average (M_w = 1.5–65 × 10⁵) and number‐average MWs (M_n = 2.0–100 × 10⁴), and MW distribution (M_w/M_n = 2.3–14). The SGC mats of these samples were drawn by a two‐stage draw technique, which consists of a first‐stage solid‐state coextrusion followed by a second‐stage tensile drawing, under controlled conditions. The optimum temperature for the second‐stage draw and the resulting maximum‐achieved total draw ratio (DR_t) increased with the MW. For a given PE, both the tensile modulus and strength increased steadily with the DR_t and reached constant values that are characteristic for the sample MW. The tensile modulus at a given DR_t was not significantly affected by the MW in the lower DR_t range (DR_t < 50). However, both the maximum achieved tensile modulus (80–225 GPa) and strength (1.0–5.6 GPa), as well as those at higher DR_ts > 50, were significantly higher for a higher MW. Although the maximum modulus reached 225 ± 5 for M_n ≥ 4 × 10⁵, the maximum strength continued to increase with M_n even for M_n > 4 × 10⁵, showing that strength is more strongly dependent on the M_n, even at higher M_n. Furthermore, it was found that each of the maximum tensile modulus and strength achieved could be expressed by a unique function of the M_n, independently of the wide variations of the sample MW and MW distribution. These results provide an experimental evidence that the M_n has a crucial effect on the tensile properties of extremely drawn and chain‐extended PE fibers, because the structural continuity along the fiber axis increases with the chain length, and hence with the M_n. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 153–161, 2006     

Copolymerization of norbornene with ω‐alkenylaluminum as a precursor comonomer for introduction of carbonyl moieties

Norbornene copolymers functionalized with methyl ester group or carboxy group are facilely synthesized by the copolymerization of norbornene and 7‐octenyldiisobutylaluminum (ODIBA) with ansa‐dimethylsilylene(fluorenyl)(t‐butylamido)dimethyltitanium ( 1 ) activated by Ph₃CB(C₆F₅)₄, and the sequential CO₂/methanolysis reactions or CO₂/hydrolysis reactions, respectively. The methanolysis and the hydrolysis are simply switched by engaging acidic methanol or acidic aqueous acetone as the quenching/washing solution, respectively. Meanwhile, the increase of ODIBA in the copolymerization abruptly decreases the yield and number–average molecular weight (M_n) of the product. However, the addition of triisobutylaluminum (8 mM) and the use of excess Ph₃CB(C₆F₅)₄ (twofold of 0.4 mM of 1 ) significantly increase the yield, accompanying the increase in the M_n and the narrowing of the molecular weight distribution (M_w/M_n), especially in the case of the use of excess Ph₃CB(C₆F₅)₄. The yield (g polymer/g monomers), M_n, and M_w/M_n reach up to 0.82, 341,000, and 1.46, respectively, at a copolymerization condition. The carboxy groups in the norbornene copolymers are controlled in the range of 0–1.8 mol % in high polymer yields with high M_n and narrow M_w/M_n accompanied by the decrease in the contact angle with water from 104° to 89°. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5085–5090     

Characterization of a single sample of an unknown polymer by size exclusion chromatography

The relationship between viscosity constants, k', a and K_η from the equations of Huggins and Mark-Kuhn-Houwink has been considered. It is shown, theoretically, that the sum of k' and a must be constant for all flexible-chain macromolecules irrespective of the solvent used. On this basis, a combination of chromatography and viscometry measurements can be used to characterize a new species. The method has been applied to the new polymer, poly[methyl(pyridin-3-yl) siloxane] ( 1 ) where no suitable calibration standards are available. The value of a, k', and K_η for 1 has been calculated. The calculated constants enabled an estimation of different average molecular weights (M_nM_wM_z) and polydispersity (M_w/M_n) from a minimum of experimental data. The new method is general and can be applied to any homogeneous linear flexible-chain nondraining macromolecule.     

Quantification of uncertainties involved in the conformational study of polymers by light scattering

Gel permeation chromatography (GPC) combined with a multi-angle light scattering (MALS) is a very powerful characterization technique because it provides both absolute molecular weight (M_w) and the radius of gyration (R_g) throughout the separated slices obtained by GPC. This combination of M_w and R_g, can be used to obtain information about the conformation of polymer chains in solutions and the branching of molecules. Due to the interesting properties obtained for polymers, it is essential to quantify the effect of different error sources in light scattering measurements as well as in the data treatment that highly affect the accuracy of obtained molar mass and radius of gyration. Usually, the results obtained for M_w and R_g in this analysis are dispersed for determined ranges of retention time and to have both reliable R_g and M_w for calculation, only high confidence data points have to be chosen. This range is arbitrarily chosen by the user for the data observation.In this work a new method of calculation to obtain R_g and M_w by means of GPC–MALS technique has been developed. As a first point, a data analysis procedure was set in order to describe both R_g and M_w vs. retention time and to determine the range where experimental data are confident. Several aspects in the data analysis have been studied. The polynomial fit function, the influence of the concentration of the sample, the reproducibility of the experiments and the conformational scaling law have been investigated by statistic technique in order to quantify the uncertainties involved.     

Living ring‐opening polymerization based on neighboring group participation

Cationic ring‐opening polymerization of a five‐membered cyclic dithiocarbonate having benzoxymethyl group; 5‐benzoxymethyl‐1,3‐oxathiolane‐2‐thione, was carried out with TfOH or TfOMe as an initiator in PhCl at rt – 60 °C. The molecular weight distribution (M_w/M_n) of the polymer obtained with TfOMe was very narrow even at 60 °C (M_w/M_n 1.14), and the Mn value of the polymers estimated by GPC was in good agreement with the molecular weight determined from ¹H‐NMR. The living nature of the polymerization was confirmed by the conversion dependence of the Mn (M_w/M_n) and the correlation of the experimental and theoretical M_n (M_w/M_n) values.