Solution characterization of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A series of four well‐defined poly(ferrocenyldimethylsilane) (PFS) samples spanning a molecular weight range of approximately 10,000–100,000 g mol⁻¹ was synthesized by the living anionic polymerization of dimethyl[1]silaferrocenophane initiated with n‐BuLi. The polymers possessed narrow polydispersities and were used to characterize the solution behavior of PFS in tetrahydrofuran (THF). The weight‐average molecular weights (M_w ) of the polymers were determined by low‐angle laser light scattering (LALLS), conventional gel permeation chromatography (GPC), and GPC equipped with a triple detector (refractive index, light scattering, and viscosity). The molecular weight calculated by conventional GPC, with polystyrene standards, underestimated the true value in comparison with LALLS and GPC with the triple detection system. The Mark–Houwink parameter a for PFS in THF was 0.62 (k = 2.5 × 10⁻⁴), which is indicative of fairly marginal polymer–solvent interactions. The scaling exponent between the radius of gyration and M_w was 0.54, also consistent with marginal polymer–solvent interactions for PFS in THF. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3032–3041, 2000     

Light-scattering characterization of poly(ethylene terephthalate)

By using a closed-circuit filtration system, we have succeeded in clarifying poly(ethylene terephthalate) (PET) dissolved in hexafluoroisopropanol (HFIP). Such static properties as the radius of gyration R_g, the weight-average molecular weight M_w, and the second virial coefficient A₂ and such dynamic properties as the translational diffusion coefficient D, or its equivalent hydrodynamic radius R_h, and the second (diffusion) virial coefficient k_d were determined for several PET samples of different molecular weights by using light-scattering intensity and linewidth measurements. An empirical relation between D_o (or R_h) and M_w was established: R_h = (1.77±0.15)X10^?2 M with R_h and M_w expressed in units of nanometers and grams per mole, respectively. The empirical exponent α_D(ca. 0.58±0.01) is in good agreement with the less precisely determined intrinsic viscosity/molecular weight exponent α_η (ca. 0.71±0.02). Several intensity correlation functions were measured very precisely using long accumulation times. A Laplace inversion was performed using the singular-value decomposition technique. The approximate molecular weight distribution (MWD) determined by light-scattering spectroscopy was in reasonable agreement with a completely independent determination of MWD using gel permeation chromatography (GPC). It was interesting to note, though not surprising, that GPC showed emphasis on lower-molecular-weight fractions, while light-scattering emphasized higher-molecular-weight fractions. The agreement further strengthens some complementary aspects of the two techniques.     

Scalings of fluorine‐containing polyimides in cyclopentanone

Eight 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride‐4,4′‐diamino‐3,3′‐dimethylbiphenyl (6FDA‐OTOL) fractions and seven 2,2′‐bis[4‐(3,4‐dicarboxyphenoxy) phenyl] propane dianhydride‐4,4′‐diamino‐3,3′‐dimethylbiphenyl (BISADA‐OTOL) fractions in cyclopentanone at 30 °C were characterized by a combination of viscometry and static and dynamic laser light scattering (LLS). In static LLS, the angular dependence of the absolute scattered intensity led to the weight‐average molar mass (M_w), the z‐average root mean square radius of gyration, and the second virial coefficient. In dynamic LLS, the Laplace inversion of each measured intensity–intensity time correlation function resulted in a corresponding translational diffusion coefficient distribution [G(D)]. The scalings of 〈D〉 (cm²/s) = 8.13 × 10⁻⁵ M_w^−0.47 and [η] (dL/g) = 2.36 × 10⁻³ M_w^0.54 for 6FDA‐OTOL and 〈D〉 (cm²/s) = 3.02 × 10⁻⁴ M_w^−0.60 and [η] (dL/g) = 2.32 × 10⁻³ M_w^0.53 for BISADA‐OTOL were established. With these scalings, we successfully converted each G(D) value into a corresponding molar mass distribution. At 30 °C, cyclopentanone is a good solvent for BISADA‐OTOL but a poor solvent for 6FDA‐OTOL; this can be attributed to an ether linkage in BISADA‐OTOL. Therefore, BISADA‐OTOL has a more extended chain conformation than 6FDA‐OTOL in cyclopentanone. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2077–2080, 2000     

Self‐assembly of N‐carboxyethylchitosan near the isoelectric point

For the first time the possibility to obtain nanostructures by self‐assembly of chitosan polyampholytic derivative was demonstrated. The self‐assembly of N‐carboxyethylchitosan (CECh) took place only near its isoelectric point (pH 5.0–5.6). Out of the pH range 5.0–5.6, CECh aqueous solutions behaved as real solutions. Dynamic light scattering and atomic force microscopy analyses revealed that spherically shaped or rod/worm‐like nanosized assemblies were formed depending on the polymer molar mass, pH value, and polymer concentration. CECh of two different molar masses was studied in concentrations ranging from 0.01 to 0.1 mg/mL. The structures from CECh of weight‐average molar mass (M_w ) 4.5 × 10³ g/mol were spherical regardless the pH and polymer concentration. In contrast, CECh of high molar mass (HMMCECh, M_w = 6.7 × 10⁵ g/mol) formed self‐assemblies with spherical shape only at pH 5.0 and 5.6. At pH 5.2 spherical nanoparticles were obtained only at polymer concentration 0.01 mg/mL. The mean hydrodynamic diameter (D_h) of the obtained nanoparticles was in the range from 30 to 980 nm. On increasing the concentration, aggregation of the nanoparticles appeared, and at HMMCECh concentration 0.1 mg/mL, rod/worm‐like structures were obtained. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6712–6721, 2008     

Conformational changes of a polyelectrolyte in mixtures of water and acetone

Samples of a polyelectrolyte poly(methacryloylethyl trimethylammonium methylsulfate), PMETMMS, with molar masses M_w = 22−25 × 10⁶ were examined with viscosity, static light scattering, and conductivity measurements in a water–acetone solvent. Because acetone is a nonsolvent for this polymer the measurements were performed to determine the influence of the solvent composition, the polymer concentration, and the presence of added ions on the conformation of the polyelectrolyte in mixed solvents. The possible influence of a hydrodynamic field on the polymer conformation was also studied. The viscosity of the polymer solutions as a function of polymer concentration, as well as of the solvent composition, was studied using a broad range of shear rates. When the mass fraction of acetone in the solvent, γ, is below 0.5, the solutions show a usual polyelectrolyte behavior. When γ ≥ 0.80, the polymer adopts a compact conformation. This is observed as a decrease of the radius of gyration, R_g, second virial coefficient, A₂, the viscosity, and also as a change in the conductivity of the solution. The change in the polymer conformation may be induced also by dilution. When 0.60 ≤ γ < 0.80, a gradual decrease in the polymer concentration leads to a sudden decrease of the reduced viscosity, which indicates a decrease in the particle size. The values of M_w measured by static light scattering were constant in all experiments. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1107–1114, 1998     

Synthesis of hyperbranched polymers from vegetable oil based monomers via ozonolysis pathway

In this work, a variety of hyperbranched polymers (HBPs), such as hyperbranched polycarbonates, polyesters, polyurethanes and polyacetals, was successfully synthesized from castor oil and soybean oil based monomers via a A₂ + B₃ polycondensation. First, B₃ monomer triols (TriOL), trialdehydes (TriAD), and tricarboxylic acids (TriAC) were obtained by ozonolysis of castor oil and soybean oil with following reductive or oxidative treatment. Their structures were characterized by ¹H NMR and ATR‐FTIR spectroscopy as well as electrospray ionization‐Time of Flight‐mass spectrometry. These trifunctional B₃ monomers were applied in the preparation of HBPs. The resulting HBPs had number averaged molar mass (M_n) up to 9400 g/mol and weight averaged molar mass (M_w) up to 40,000 g/mol. Through adjusting the initial molar ratio of A₂ to B₃ monomers, hydroxyl terminated (from TriOL monomers) or carboxylic acid (from TriAC monomers) terminated HBPs could be obtained. All the HBPs were characterized by ¹H NMR, size exclusion chromatography, and DSC. These HBPs are potential candidates for the synthesis of cross‐linked polymeric materials or in biomedical applications. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2104–2114     

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     

Synthesis of periodic copolymers via ring‐opening copolymerizations of cyclic anhydrides with tetrahydrofuran using nonafluorobutanesulfonimide as an organic catalyst and subsequent transformation to aliphatic polyesters

To synthesize polyesters and periodic copolymers catalyzed by nonafluorobutanesulfonimide (Nf₂NH), we performed ring‐opening copolymerizations of cyclic anhydrides with tetrahydrofuran (THF) at 50–120 °C. At high temperature (100–120 °C), the cyclic anhydrides, such as succinic anhydride (SAn), glutaric anhydride (GAn), phthalic anhydride (PAn), maleic anhydride (MAn), and citraconic anhydride (CAn), copolymerized with THF via ring‐opening to produce polyesters (M_n = 0.8–6.8 × 10³, M_n/M_w = 2.03–3.51). Ether units were temporarily formed during this copolymerization and subsequently, the ether units were transformed into esters by chain transfer reaction, thus giving the corresponding polyester. On the other hand, at low temperature (25–50 °C), ring‐opening copolymerizations of the cyclic anhydrides with THF produced poly(ester‐ether) (M_n = 3.4–12.1 × 10³, M_w/M_n = 1.44–2.10). NMR and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectra revealed that when toluene (4 M) was used as a solvent, GAn reacted with THF (unit ratio: 1:2) to produce periodic copolymers (M_n = 5.9 × 10³, M_w/M_n = 2.10). We have also performed model reactions to delineate the mechanism by which periodic copolymers containing both ester and ether units were transformed into polyesters by raising the reaction temperature to 120 °C. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Fluorescence recovery after photobleaching measurements of polymers in a surface forces apparatus

The surface forces apparatus has been combined with fluorescence recovery after photobleaching to measure translational diffusion of polymer confined between mica sheets. This article presents findings using polydimethylsiloxane with number‐average molecular weight M_n = 2200 g mol^?1, the chains end‐labeled with soluble fluorescent dye. Melts with thickness 10 nm display a translational diffusion coefficient (D) with a bulk component and a slower component assigned to surface diffusion. Reduction of thickness to 1.8 nm causes mobility to split into two populations—an immobile fraction (immobile on the time scale of 30–60 min) and a mobile fraction who's D slow only weakly with diminishing film thickness. However, when load causes the confining mica sheets to flatten, D of the mobile fraction drops by up to an additional order of magnitude, depending on the local pressure that squeezes on the polymer. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Evaluation of K⊖ from [η]-M-data of binary and ternary polymer systems

Unperturbed dimensions of flexible linear macromolecules can be obtained from [η]-M-data in any solvent, good or poor, single or mixed. Usually K_θ is estimated by a relationship between [η]/M_W^0.5 and M_w^0.5 first proposed by Burchard and by Stockmayer and Fixman. But, it is well-known that the Burchard-Stockmayer-Fixman-plot shows downward curvature, especially for good solvent systems. Various efforts have been made to achieve relations with better linearity. One of the first was the semi-empirical relation between ([η]/M_w^0.5)^0.5 and M_w/[η] by Berry. Predicting a relationship of the excluded volume parameter z to the viscosity expansion factor by α⁵_η instead of α⁵_η Tanaka obtains that ([η]/M_w^0.5)^5/3 is linear in M_w^0.5. By allowing for the dependence of the viscometric interaction parameter B, which is correlated to the second virial coefficient A₂, on molar mass, Gavara, Campos and Figueruelo predict a linear dependence of [η]/M_w^0.5 against A₂.M_w^0.5. It is not our intention here to discuss the validity of these theories, but to compare them with experimental data.     

Synthesis of polycarbosilanes by A2 + Bn (n = 2, 3, and 4) type hydrosilylation reaction and evaluation of their refractive index properties

Polycarbosilanes were synthesized by hydrosilylation reaction of A₂ monomer containing bis Si? H moieties and B_n (n = 2, 3, and 4) monomers containing di‐, tri‐, and tetra‐vinyl groups in the presence of Karstedt's catalyst. The corresponding linear polycarbosilanes (LPC) and hyperbranched polycarbosilanes (HBPC) having M_n 2200–51,500 were obtained in 34–94% yield, without any gel product. The values of refractive index (n_D) of the synthesized LPC and HBPC were in the range from 1.460 to 1.711, and were consistent with the structures of the synthesized products. In the case of HBPC, the values of n_D increased with increase of number‐average molecular weight (M_n), molecular weight distribution (M_w/M_n), and glass transition temperature (T_g), apparently because of increased density due to the presence of microgels, that is, high refractive index hyperbranched carbosilanes could be synthesized by A₂ + B_n (n = 3 and 4) method. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Polydispersity effects in polymer self-diffusion measured by small-angle neutron scattering

The small-angle neutron scattering (SANS) method for measuring the self-diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to M_w/M_n = 1.0?10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient D_e can be obtained from the short time recovery of the SANS intensity. This quantity D_e ≤ 1.3 D(M_w), where D(M_w) is the diffusion coefficient of a monodisperse polymer having molecular weight M = M_w. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 D_e.     

Boron‐functionalized poly(3‐hydroxybutyrate)s from hydroboration of poly(allyl‐β‐hydroxyalkanoate)s: Synthesis and insights into the microstructure

The controlled ring‐opening polymerization of racemic allyl‐β‐butyrolactone (rac‐BL^allyl) in toluene or in bulk, catalyzed by the discrete β‐diiminate zinc amido [(BDI^iPr)Zn(N(SiMe₃)₂)] ( 1 ) or {amino‐methoxy‐bis(phenolate)}yttrium amido [(ONOO^tBu)Y(N(SiHMe₂)₂)(THF)] ( 2 ) complexes, in association with an alcohol, gave poly(β‐hydroxyalkanoate)s (PHAs) with allylic side chains. These PHAs^allyl exhibit either a slightly isotactic‐enriched (P_m = 0.61) or highly syndiotactic‐enriched (P_r = 0.82) backbone structure, respectively, with high molar mass (M _n up to 21,100 g mol^?1) and narrow molar mass distribution values (1.05 < M _w/M _n < 1.28), as evidenced by detailed ¹³C NMR and size exclusion chromatography analyses. Postpolymerization rhodium‐catalyzed hydroboration of the resulting PHAs^allyl with pinacolborane quantitatively afforded the corresponding PHAs^boron. Introduction of boron into the pendant chains did not alter neither the structure of the polymer backbone nor the macromolecular features (M _n, M _w/M _n, and stereoregularity). However, differential scanning calorimetry analyses revealed a significant increase of the glass transition temperature on modifying the allyl for the boron function in these PHAs. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Dynamic and electrophoretic light scattering of poly(dimethyldiallylammonium chloride) in salt-free solutions

Dynamic and electrophoretic light scattering were used to study the diffusion and electrophoretic mobility of poly(dimethyldiallylammonium chloride) as a function of polymer molecular weight in salt-free solutions. Two relaxation modes characterized as fast diffusion (D_f) and slow diffusion (D_s) were obtained from dynamic light scattering. Although the slow diffusion coefficient D_s strongly depends on molecular weight (M_w), the fast diffusion coefficient D_f was found to be independent of M_w over the range in the study. The fast diffusion was considered as the diffusion of a part of the polymer chain; the slow diffusion was interpreted by multichain diffusion. Electrophoretic light scattering results in the salt-free solution show that the electrophoretic mobility of the polymer is independent of M_w. © 1996 John Wiley & Sons, Inc.     

Gel formation with multiple interunit junctions. II—mixture of different functional molecules

Number‐ and weight‐average molecular weight of condensation polymers formed in the mixture of primary molecules carrying different species of functional groups A and B are derived by the cascade theory. These functional groups are allowed to form multiple junctions of arbitrary multiplicity k. From the weight average, the gel point condition is found to be given by 1 ? (f_w ? 1)(μ_A,A ? 1) ? (g_w ? 1)(μ _B,B ? 1) + (f_w ? 1)(g_w ? 1)D_μ = 0, where f_w and g_w are average functionality of the primary molecules, μ _αβ the average multiplicity of β groups in the junctions where a path of an α‐group enters, and D_μ ≡ (μ_A,A ? 1)(μ _B,B ? 1) ? μ _A,Bμ _B,A the multiplicity determinant. Possible applications to thermoreversible gelation are suggested. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2413–2421, 2003     

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     

Diffusion control in radiation graft polymerization with varying dependence of rate on monomer concentration

The quantitative effect of diffusion control on the rate of radiation-initiated graft polymerization has been studied theoretically for systems in which the diffusion-free reaction may show various dependencies of rate on monomer concentration other than the usual first-order dependence. The study is also very general in that it can be applied to systems involving a variety of different modes of initiation and termination. Whether the grafting process is diffusion-free or diffusion-controlled has been analyzed in terms of the interaction of the initiation rate R_i, the propagation and termination rate constants k_p and k_t, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, the diffusivity D of the monomer in the polymer, and the diffusion-free kinetic order of dependence v of the grafting rate on monomer concentration. The dependence of the grafting rate for both the diffusion-free and diffusion-controlled reactions on these parameters is expressed both by mathematical experssions and graphically. Diffusion control is shown to occur at a critical value of the parameter A which is proportional to L(k_pR_i^w/k_t^zD)^1/2M^(ε?1)/2 where w, z, and v have different values depending on the specific modes of initiation, propagation and termination in a particular grafting system. The grafting rate is shown to vary with the value of A according to specific mathematical expressions. In comparing diffusion-free to diffusion-controlled reaction, it is shown that the former is independent of L and D while the latter is directly dependent on L and inversely on D^1/2. Further, the change from diffusion-free to diffusion-controlled reaction involves a change in the dependence of rate on monomer from v-order to [(v ? 1)/2]-order. The nonsteady-state as well as the steady-state reaction rates have been analyzed.     

Living anionic polymerization of ethylphenylketene: A novel approach to well‐defined polyester synthesis

A living polymerization of ethylphenylketene (EPK) was accomplished. When polymerization of EPK was carried out with butyllithium as an initiator in tetrahydrofuran (THF) at −20 °C, EPK was completely consumed within 5 min, and the corresponding polyester with narrow molecular weight distribution (M_w /M_n ∼ 1.1) was obtained almost quantitatively. Kinetic study of the polymerization at −78 °C revealed that conversion of EPK agreed with the first‐order kinetic equation, and that M_n of the polymer increased in virtually direct proportion to the conversion. Along with these results, successful results in postpolymerization at −20 °C strongly supported living mechanism of the present polymerization. Further, lithium alkoxides having a methoxy group, styryl moiety, and nitroxyl radical, also successfully initiated polymerization of EPK to afford the corresponding polymers having functional initiating ends. In the polymerization with varying feed ratio [EPK]₀/[initiator]₀, the linear relationship between the feed ratio and M_n of the obtained polymer was observed, while maintaining narrow M_w /M_n. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1073–1082, 2000     

Controlled ring‐opening polymerization of l‐lactide and ε‐caprolactone catalyzed by aluminum‐based Lewis pairs or Lewis acid alone

Ring‐opening polymerization of cyclic esters was studied using catalysts composed of bulky Lewis acids (LA) and Lewis bases (LB). Controlled polymerization of l ‐lactide (l ‐Lac) was proceeded by Al(C₆F₅)₃·THF in combination with trimesitylphosphine (Mes₃P) or triphenylphosphine (Ph₃P) using BnOH as an initiator to produce poly(l ‐Lac) with narrow molecular weight distribution (MWD; M_w/M_n = 1.1). Both the LA and the LB were indispensable to promote the polymerization. The molecular weights of the resulting poly(l ‐Lac)s were controlled by the feed monomer to initiator ratio. ε‐Caprolactone (CL) was rapidly polymerized by Al(C₆F₅)₃·THF with or without Mes₃P, although the resulting polymer had rather broad MWD (M_w/M_n = 1.7). The CL polymerization by Al(C₆F₅)₃·THF alone at r.t. gave poly(CL) with relatively narrow MWD (M_w/M_n = 1.2). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 297–303     

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.