Chain transfer to solvent in two-state anionic polymerization, 1. Fast exchange between propagating species

A theoretical consideration of molecular weights and molecular weight distribution (MWD) of polymers formed in anionic polymerization proceeding via active centres of two different types under conditions of chain transfer to solvent with a fast exchange between propagating species is presented. Analytical expressions for number-and weight-average degrees of polymerization are obtained. Expressions for P_n and P_w are shown to be the same as in a one-centre process with the apparent intensity of chain transfer proportional to the weight fraction of the polymer formed via “transferring” centres. The polymers formed possess a moderately wide unimodal MWD. The dependence of the polydispersity index on the effective intensity of chain transfer goes through a maximum; for M₀/I₀ = 10³ the maximum value of P_w /P_n is ca. 4,6. The method is suggested for the estimation of the relative reactivity in chain propagation of two active centres from the dependence of molecular weight on initiator mixture composition. The effects of association of active centres on the average molecular weights are analyzed. The case when one of the centres is dormant is also considered.     

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.     

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.     

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     

Aromatic poly(amic acids): Fundamental structural studies

Aromatic poly(amic acids) derived from pyromellitic dianhydride and 4,4′,-diaminodiphenyl ether were characterized by dilute solution techniques. Number-average molecular weights M?_n of 13 samples ranged from 13,000 to 55,000 (DP 31–131). Weight-average molecular weights M?_w of 21 samples ranged from 9,900 to 266,000. The ratio M?_w/M?_n was between 2.2 and 4.8. Heterogeneous polymerization yielded higher molecular weight polymer than homogeneous polymerization. The molecular weight could be varied systematically by control of stoichiometric imbalance. Use of very pure monomers and solvent gave polymers of relatively high number-average molecular weight (～50, 000) and the most probable molecular weight distribution M?_w/M?_n = 2. Impure monomers and/or solvent resulted in lower number-average molecular weight (M?_n ? 20,000–30,000) and wider distributions (M?_w/M?_n = 3–5). The Mark-Houwink relation obtained was [η] = 1.85 × 10^?4M?_w^0.80 The exponent is characteristic of moderately extended solvated coils. The unperturbed chain dimensions (r₀² /M)^1/2 were 0.848 A., and the steric factor σ was 1.24 which is close to the limiting value of unity for an equivalent chain with free internal rotations. The sedimentation constant–molecular weight relation was S₀ = 2.70 × 10^?2M?_w^0.39. This exponent is consistent with the Mark-Houwink exponent.     

Tensile strength of highly oriented polyethylene. II. Effect of molecular weight distribution

The tensile strength of oriented polyethylene filaments is discussed in relation to molecular weight. Short-term tensile properties at room temperature were obtained in our laboratory and from the literature for polymer samples covering the molecular weight (M _w) range from 54 × 10³ to 4 × 10⁶, and polydispersities ranging from 1.1 to 15.6, oriented by solid-state extrusion, melt spinning/drawing, solution spinning/drawing, and “surface growth.” It was found that both the molecular weight and its distribution markedly affected tensile strength. The breaking stress σ of highly oriented fibers varied with molecular weight roughly as σ ∝, M^0.4, at constant M _w/M _n over the entire range studied. Reduction of polydispersity from 8 to 1.1 by an increase of M _n with M _w approximately constant at 10⁵ increased tensile strength of oriented polyethylene filaments by a factor of nearly 2.     

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.     

Controlled cationic polymerization of styrene using AlCl3OBu2 as a coinitiator: Toward high molecular weight polystyrenes at elevated temperatures

The controlled cationic polymerization of styrene using CumOH/AlCl₃OBu₂/Py initiating system in a mixture CH₂Cl₂/n‐hexane 60/40 v/v at ?40 and ?60 °C is reported. The number‐average molecular weights of the obtained polystyrenes increased with increasing monomer conversion (up to M_n = 85,000 g mol^?1) although experimental values of M_n were higher than the theoretical ones at the beginning of the reaction that was ascribed to slow exchange between reversible‐terminated and propagating species. The molecular weight distribution became narrower through the reaction and leveled of at the value of M_w/M_n = 1.8–2.0. A kinetic investigation revealed that the rate of polymerization was first‐order in AlCl₃OBu₂ concentration meaning that monomeric counteranion (AlCl₃OH^? or AlCl) involved in the initiation and propagation steps of the reaction. It was also found that the rate of polymerization decreased with lowering temperature, which could be attributed to a decrease in concentration of free Lewis acid (AlCl₃), the true coinitiator of polymerization, because of an increase in the tightness of its complex with dibutyl ether. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3736–3743, 2010     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Titanium complexes of dialkanolamine ligands as initiators for living ring‐opening polymerization of ε‐caprolactone

The titanium complexes with one ( 1a , 1b , 1c ) and two ( 2a , 2b ) dialkanolamine ligands were used as initiators in the ring‐opening polymerization (ROP) of ε‐caprolactone. Titanocanes 1a and 1b initiated living ROP of ε‐caprolactone affording polymers whose number‐average molecular weights (M_n) increased in direct proportion to monomer conversion (M_n ≤ 30,000 g mol^?1) in agreement with calculated values, and were inversely proportional to initiator concentration, while the molecular weight distribution stayed narrow throughout the polymerization (M_w/M_n ≤ 1.2 up to 80% monomer conversion). ¹H‐NMR and MALDI‐TOF‐MS studies of the obtained poly(ε‐caprolactone)s revealed the presence of an isopropoxy group originated from the initiator at the polymer termini, indicating that the polymerization takes place exclusively at the Ti–OⁱPr bond of the catalyst. The higher molecular weight polymers (M_n ≤ 70,000 g mol^?1) with reasonable MWD (M_w/M_n ≤ 1.6) were synthesized by living ROP of ε‐caprolactone using spirobititanocanes ( 2a , 2b ) and titanocane 1c as initiators. The latter catalysts, according MALDI‐TOF‐MS data, afford poly(ε‐caprolactone)s with almost equal content of α,ω‐dihydroxyl‐ and α‐hydroxyl‐ω(carboxylic acid)‐terminated chains arising due to monomer insertion into “Ti–O” bond of dialkanolamine ligand and from initiation via traces of water, respectively. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1230–1240, 2010     

Control of the molecular weight of hyperbranched polyglycerols

Hyperbranched polyglycerols exceeding M_n > 15,000 g/mol (DP_n > 270) have been prepared, using a modified version of the synthetic protocol reported earlier. In the optimized process polydispersities recorded by SEC remained narrow, with M_w/M_n < 1.7 over a large molecular weight range. The drastic increase of viscositity in the course of the reaction, was found to be responsible for the increased fraction of cycles (MALDI‐TOF MS) at high molecular weights.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

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.     

Ruthenium‐catalyzed fast living radical polymerization of methyl methacrylate: The R?Cl/Ru(Ind)Cl(PPh3)2/n‐Bu2NH initiating system

A fast living radical polymerization of methyl methacrylate (MMA) proceeded with the (MMA)₂? Cl/Ru(Ind)Cl(PPh₃)₂ initiating system in the presence of n‐Bu₂NH as an additive [where (MMA)₂? Cl is dimethyl 2‐chloro‐2,4,4‐trimethyl glutarate]. The polymerization reached 94% conversion in 5 h to give polymers with controlled number‐average molecular weights (M_n's) in direct proportion to the monomer conversion and narrow molecular weight distributions [MWDs; weight‐average molecular weight/number‐average molecular weight (M_w/M_n) ≤ 1.2]. A poly(methyl methacrylate) with a high molecular weight (M_n ～ 10⁵) and narrow MWD (M_w/M_n ≤ 1.2) was obtained with the system within 10 h. A similarly fast but slightly slower living radical polymerization was possible with n‐Bu₃N, whereas n‐BuNH₂ resulted in a very fast (93% conversion in 2.5 h) and uncontrolled polymerization. These added amines increased the catalytic activity through some interaction such as coordination to the ruthenium center. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 617–623, 2002; DOI 10.1002/pola.10148     

Well‐defined amphiphilic polymethylene‐b‐poly(acrylic acid) diblock copolymers: New synthetic strategy and their self‐assembly

Well‐defined amphiphilic polymethylene‐b‐poly (acrylicacid) diblock copolymers have been synthesized via a new strategy combining polyhomologation and atom transfer radical polymerization (ATRP). Hydroxyl‐terminated polymethylenes (PM‐OH) with different molecular weights and narrow molecular weight distribution are obtained through the polyhomologation of dimethylsulfoxonium methylides following quantitative oxidation via trimethylamine‐N‐oxide dihydrate. Subsequently, polymethylene‐based macroinitiators (PM‐MIs M_n = 1,300 g mol^?1 [M_w/M_n = 1.11] and M_n = 3,300 g mol^?1 [M_w/M_n = 1.04]) are synthesized by transformation of terminal hydroxyl group of PM‐OH to α‐haloester in ～100% conversion. ATRPs of tert‐butyl acrylate (t‐BuA) are then carried out using PM‐MIs as initiator to construct PM‐b‐P(t‐BuA) diblock copolymers with controllable molecular weight (M_n = 8,800–15,800 g mol^?1 M_w/M_n = 1.04–1.09) and different weight ratio of PM/P(t‐BuA) segment (1:1.7–1:11.2). The amphiphilic PM‐b‐PAA diblock copolymers are finally prepared by hydrolysis of PM‐b‐P(t‐BuA) copolymers and their self‐assembly behavior in water is preliminarily investigated via the determination of critical micelle concentrations, dynamic light scattering, and transmission electron microscope (TEM). © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Viscosity–molecular weight relationship for fractionated poly(ethylene terephthalate)

Poly(ethylene terephthalate) was separated into 12 fractions of equal size by a stepwise increase in the amount of solvent in the two-phase liquid fractionation system of phenol-tetrachloroethane (PTCE) (1:1) and n-heptane. Various molecular weight parameters of the fractions were measured by osmotic pressure and gel-permeation chromatography. Intrinsic viscosity-molecular weight plots were made for three different solvents at 25°C. Mark-Houwink constants for viscosity-average molecular weight were measured and gave values of K of 2.50, 2.37, and 2.25 × 10^?4 dl/g and values of a of 0.73 for 1:1 PTCE, 3:2 PTCE, and o-chlorophenol, respectively. A comparison with the literature values for this polyester was made, and application of the Mark-Houwink equation to the determination of number-average (M _n) and weight-average (M _w) molecular weight of whole polymers is considered.     

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     

Some applications of gel-permeation chromatography in investigations of structure and the solution properties of radical-initiated poly(vinyl chloride)

The applicability of the published universal calibration parameters for gel-permeation chromatography on polystyrene standards and poly(vinyl chloride) samples with a defined structure has been compared. It was shown experimentally that of several theoretically possible molecular weight averages attributed to the elution volume at the position of the peak maximum, the root mean-square average molecular weight M _Rms = (M _wM _n)^0.5 shows the best accordance. The molecular weights obtained by gel-permeation chromatography were compared with those determined by viscometry, osmometry, and the light-scattering method. The reproducibility of gel-permeation chromatography measurements is 3%, and the average variance of the results as compared with results obtained by the above methods is about 8%. It was also found that the gel-permeation chromatography does not involve any anomalies interfering with results obtained by other methods.     

Polymerization of 1-octene and determination of markhouwink constants of poly(1-octene)

The polymerization of 1-octene initiated by methylalumoxane（MAO）-activated Ni（Ⅱ）-based-α-diimine complexes[（2,6-i-Pr）₂C₆H₃-DAB（An）]NiBr₂ was investigated.Using this catalyst,poly（1-octene）s with molecular weight between 100×10³ and 400×10³ and polydispersity（M_w/M_n） between 1.3 and 1.5 were synthesized successfully by varying reaction time at room temperature.The poly（1-octene）s were amorphous polymers and could be well soluble in tetrahydrofuran（THF）.After fractional precipitation,poly（1-octene）s with narrow molecular weight distributions（M_w/M_n≤1.12） were obtained.Their weight-average molecular weights were measured by gel permeation chromatography（GPC） in conjunction with online model BI-MwA multiangle laser light scattering（MALLS）,and their intrinsic viscosities were measured by Maron’s single-point method.The k and a values in Mark-Houwink equation[η]= KM^αin THF at 40℃were 0.089 mL/g and 0.61 respectively.     

Intrinsic viscosity–molecular weight relationship for chitosan

The intrinsic viscosity–molecular weight relationship for chitosan was determined in 0.25 M acetic acid/0.25M sodium acetate. Chitosan samples with a degree of acetylation (DA) between 20 and 26% were prepared from shrimp‐shell chitosan by acid hydrolysis (HCl) and oxidative fragmentation (NaNO₂). Absolute molecular weights were measured by light scattering and membrane osmometry. Size exclusion chromatography (SEC) was used to determine average molecular weights (M_n, M_v, and M_w) and polydispersity. The following Mark–Houwink–Sakurada equation (MHS) is proposed for chitosan of M_w in the range of 35–2220 kDa: The value of the MHS exponent a suggests that chitosan behaves as a flexible chain in this solvent. Examination of MHS constants obtained in this work and those available in the literature with other solvents indicates that a and K are inversely related and that they are influenced by DA, and pH and ionic strength of the solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2591–2598, 2000