Synthesis and characterizations of well‐defined branched polymers with AB2 branches by combination of RAFT polymerization and ROP as well as ATRP

A well‐defined branched copolymer with PLLA‐b‐PS₂ branches was prepared by combination of reversible addition‐fragmentation transfer (RAFT) polymerization, ring‐opening polymerization (ROP), and atom transfer radical polymerization (ATRP). The RAFT copolymerization of methyl acrylate (MA) and hydroxyethyl acrylate (HEA) yielded poly(MA‐co‐HEA), which was used as macro initiator in the successive ROP polymerization of LLA. After divergent reaction of poly(MA‐co‐HEA)‐g‐PLLAOH with divergent agent, the macro initiator, poly(MA‐co‐HEA)‐g‐PLLABr₂ was formed in high conversion. The following ATRP of styrene (St) produced the target polymer, poly(MA‐co‐HEA)‐g‐(PLLA‐b‐PS₂). The structures, molecular weight, and molecular weight distribution of the intermediates and the target polymers obtained from every step were confirmed by their ¹H NMR and GPC measurements. DSC results show one T = 3 °C for the poly(MA‐co‐HEA), T = ?5 °C, T= 122 °C, and T = 157 °C for the branched copolymers (poly(MA‐co‐HEA)‐g‐PLLA), and T = 51 °C, T = 116 °C, and T = 162 °C for poly(MA‐co‐HEA)‐g‐(PLLA‐b‐PS₂). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 549–560, 2006     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.     

Role of anions in the polymerization of 2,5‐dimethoxyaniline in the presence of poly(styrene sulfonic acid)

Poly(2,5‐dimethoxyaniline) (PDMA)–Ag composites were successfully obtained through the oxidative polymerization of 2,5‐dimethoxyaniline in poly(styrene sulfonic acid) with CH₃SO₃Ag and AgNO₃ as oxidants. In situ ultraviolet–visible spectroscopy results showed that the growth rate of PDMA was strongly affected by CH₃SO and NO. The coupling reaction of PDMA and NO was proposed to explain the lower growth rate of PDMA with AgNO₃ as the oxidant in comparison with CH₃SO₃Ag. X‐ray photoelectron spectroscopy and Fourier transform infrared spectroscopy were used to validate the proposed coupling reaction through the monitoring of the side products and oxidized state of PDMA. The results showed that there were more side products and lower oxidized states for the composite structure in the presence of NO than in the presence of CH₃SO, and this agreed with the proposal. Transmission electron microscopy showed that the Ag nanoparticles had almost the same size, regardless of the anions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6624–6632, 2006     

Polymerization of carboxylic ester functionalized norbornenes catalyzed by (η3‐allyl)palladium complexes bearing N‐heterocyclic carbene ligands

An in situ generated cationic allylpalladium complex bearing N‐heterocyclic carbene (NHC) ligands, derived from the reaction of [(η³‐C₃H₅)Pd(NHC)Cl] with AgX (X = BF₄ or SbF₆), is an active catalyst for the addition polymerization of norbornene and norbornene derivatives [5‐norbornene‐2‐carboxylic acid methyl ester ( b ) and 5‐norbornene‐2‐carboxylic acid n‐butyl ester ( c )] with an ester group containing a large portion of endo‐isomers. The catalytic activities, polymer yields, molecular weights, and molecular weight distributions of polynorbornenes were investigated under various reaction conditions: the catalytic activity was highly dependent on the counteranion, the reaction solvent, and the reaction temperature. For b , as the portion of an endo‐isomer increased, the activity of 13 (SbF) was much higher than those of 14 and 15 , and for c (exo/endo = 95:5), the maximum turn over number (TON) was observed with 15 (SbF). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3042–3052, 2007     

Primary radical termination and unimolecular termination in the heterogeneous polymerization of acrylamide initiated by a fluorinated azo‐derivative initiator: A kinetic study

Acrylamide was polymerized in acetonitrile at 82 °C with a perfluorinated azo‐derivative initiator. The polymerization proceeded heterogeneously. Varying amounts of initiator and monomer were used. The activation energy was deduced from three experiments carried out at 59, 71, and 82 °C. The following kinetic law, deviating a great deal from the classical law, was obtained: R ∼ [I₂][M](0.05% < [I₂]_o/[M]_o < 1.00%) and R ∼ [I₂][M](1% < [I₂]_o/[M]_o < 7%). These results can be interpreted in light of the contribution of primary radical termination and the emergence of occlusion. The development of a new kinetic relationship allowed us to confirm the existence of both of these termination reactions. The calculation of the k_prt /k_i · k_p ratio was also achieved. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1834–1843, 2000     

Syndiospecific polymerization of styrene. II. Monocyclopentadienyltributoxy titanium/methylaluminoxane catalyst

Syndiospecific polymerization of styrene was catalyzed by monocyclopentadienyltributoxy titanium/methylaluminoxane [CpTi (OBu)₃/MAO]. The atactic and syndiotactic polystyrenes were separated by extracting the former with refluxing 2-butanone. The activity and syndiospecificity of the catalyst were affected by changes in catalyst concentration and composition, polymerization temperature, and monomer concentration. Extremely high activity of 5 × 10⁷ g PS (mol Ti mol S h)^?1 with 99% yield of the syndiotactic product were achieved. The concentration of active species, [C^*], has been determined by radiolabeling. The amount of the syndiospecific and nonspecific catalytic species, [C] and [C] respectively, correspond to 79 and 13% of the CpTi(OBu)₃. The rate constants of propagation for C and C at 45°C are 10.8 and 2.0 (M s)^?1, respectively, the corresponding rate constants for chain transfer to MAO are 6.2 × 10^?4 and 4.3 × 10^?4s^?1. There was no deactivation of the catalytic species during a batch polymerization. The rate constant of chain transfer with monomer is 6.7 × 10^?2 (M s)^?1; the spontaneous β-hydride transfer rate constant is 4.7 × 10^?2 s^?1. The polymerization activity and stereospecificity of the catalyst are highest at 45°C, both decreasing with either higher or lower temperature. The stereoregular polymer have broad MW distributions, M?_w/M?_n = 2.8–5.7, and up to three crystalline modifications. The T_m of the s-PS polymerized at 0–90°C decreased from 261.8 to 241°C indicating thermally activated monomer insertion errors. The styrene polymerization behaviors were essentially insensitive to the dielectric constant of the medium.     

Novel thermoplastic elastomers. III. Synthesis,characterization, and properties of star‐block copolymers of poly(indene‐b‐isobutylene) arms emanating from cyclosiloxane cores

Novel thermoplastic elastomers (TPEs) consisting of poly(isobutylene‐b‐indene) (PIB‐b‐PInd) arms radiating from hexamethylcyclohexasiloxane (D) cores were prepared, characterized, and their properties investigated. The syntheses of these star‐blocks involved the linking by hydrosilation of PInd‐b‐PIB CH₂ CHCH₂ prearms to D. The prearms were obtained by initiating the living polymerization of Ind by the cumyl chloride (CumCl)/TiCl₄ or cumyl methoxide (CumOMe)/TiCl₄ systems, continuing by the sequential block copolymerization of IB, and concluding the synthesis by end quenching with allyltrimethylsilane (ATMS). Dedicated experiments were carried out to develop conditions for the various synthesis steps. Select mechanical, thermal, and rheological properties of TPE star‐blocks having 5–18 PInd‐b‐PIB arms have been investigated. Because of the high T_g of the glassy PInd segment (T_g,PInd = 170–220°C), these TPEs maintained their strength at higher temperatures than those of similar polystyrene‐based star blocks. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 279–290, 2000     

Depolymerization kinetics of di(4‐tert‐butyl cyclohexyl) itaconate and Mark‐Houwink‐Kuhn‐Sakurada parameters of di(4‐tert‐butyl cyclohexyl) itaconate and di‐n‐butyl itaconate

Multipulse pulsed laser polymerization coupled with size exclusion chromatography (MP‐PLP‐SEC) has been employed to study the depropagation kinetics of the sterically demanding 1,1‐disubstituted monomer di(4‐tert‐butylcyclohexyl) itaconate (DBCHI). The effective rate coefficient of propagation, k, was determined for a solution of monomer in anisole at concentrations, c, 0.72 and 0.88 mol L^?1 in the temperature range 0 ≤ T ≤ 70 °C. The resulting Arrhenius plot (i.e., ln k vs. 1/RT) displayed a subtle curvature in the higher temperature regime and was analyzed in the linear part to yield the activation parameters of the forward reaction. In the temperature region where no depropagation was observed (0 ≤ T ≤ 50 °C), the following Arrhenius parameters for k_p were obtained (DBCHI, E_p = 35.5 ± 1.2 kJ mol^?1, ln A_p = 14.8 ± 0.5 L mol^?1 s^?1). In addition, the k data was analyzed in the depropagatation regime for DBCHI, resulting in estimates for the associated entropy (?ΔS = 150 J mol^?1 K^?1) of polymerization. With decreasing monomer concentration and increasing temperature, it is increasingly more difficult to obtain well structured molecular weight distributions. The Mark Houwink Kuhn Sakurada (MHKS) parameters for di‐n‐butyl itaconate (DBI) and DBCHI were determined using a triple detection GPC system incorporating online viscometry and multi‐angle laser light scattering in THF at 40 °C. The MHKS for poly‐DBI and poly‐DBCHI in the molecular weight range 35–256 kDa and 36.5–250 kDa, respectively, were determined to be K_DBI = 24.9 (10³ mL g^?1), α_DBI = 0.58, K_DBCHI = 12.8 (10³ mL g^?1), and α_DBCHI = 0.63. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1931–1943, 2007     

Non‐transition metal‐catalyzed living radical polymerization of vinyl chloride initiated with iodoform in water at 25 °C

Non‐transition metal‐catalyzed living radical polymerization (LRP) of vinyl chloride (VC) in water at 25–35 °C is reported. This polymerization is initiated with iodoform and catalyzed by Na₂S₂O₄. In water, S₂O dissociates into SO that mediates the initiation and reactivation steps via a single electron transfer (SET) mechanism. The exchange between dormant and active propagating species also includes the degenerative chain transfer to dormant species (DT). In addition, the SO₂ released from SO during the SET process can add reversibly to poly(vinyl chloride) (PVC) radicals and provide additional transient dormant ～SO radicals. This novel LRP proceeds mostly by a combination of competitive SET and DT mechanisms and, therefore, it is called SET‐DTLRP. Telechelic PVC with a number‐average molecular weight (M_n) = 2,000–55,000, containing two active ～CH₂? CHClI chain ends and a higher syndiotacticity than the commercial PVC were obtained by SET‐DTLRP. This PVC is free of structural defects and exhibits a higher thermal stability than commercial PVC. SET‐DTLRP of VC is carried out under reaction conditions related to those used for its commercial free‐radical polymerization. Consequently, SET‐DTLRP is of technological interest both as an alternative commercial method for the production of PVC with superior properties as well as for the synthesis of new PVC‐based architectures. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6267–6282, 2004     

Binding of uranyl ion by poly(ethylenimine) containing a salicylate derivative

Three molecules of 5-(bromoacetyl)salicylate ( 1 ) complexed to uranyl UO ion were crosslinked with branchy poly(ethylenimine) (PEI) in DMSO by alkylation of amino groups of PEI with 1, leading to the formation of UO₂(Sal) PEI. Upon demetalation of UO₂(Sal) PEI with HCl, apo(Sal) PEI was obtained. Based on the pH dependence of log K_f for UO₂(Sal) PEI, it was concluded that each uranyl binding site in UO₂(Sal) PEI or apo(Sal) PEI contains three salicylate moieties. In terms of the equilibrium constant for formation of the uranyl complex, apo(Sal) PEI was found to be comparable to or better than the previously reported effective uranophiles. In terms of the rates for the formation of the uranyl complex, however, apo(Sal) PEI was far superior to those other uranophiles. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2935–2942, 1997     

Preparation and some properties of 2,2,6,6-tetrahydryl-F-heptanedioic acid and its polyester with 1,1,5,5-tetrahydryl-F-1,5-pentanediol

2,2,6,6,-Tetrahydryl-F-heptanedioic acid was prepared by hydrolysis of 1,7-diethoxy-2,6-dihydryl-F-1,6-heptadiene, which was obtained by a copper-induced coupling reaction between 1,3-di-iodo-F-propane and 1-ethoxy-1-fluoro-2-iodethylene. This olefin is obtained almost exclusively as the less thermodynamically stable isomer in the reaction between 1,1-difluoro-2-iodoethylene and soidum ethoxide. Synthesis of the acid via 2,2,6,6,-tetrahydryl-F-heptanedial was unsuccessful, since the latter readily underwent cyclopolymerization. The acid has pK = 2.38 and pK = 3.35, and slowly liberates fluoride ion in aqueous solution. The polyester obtained with 1,1,5,5,-tetrahydryl-F-1,5-pentanediol is highly crystalline with a mp of 79°C and a history-dependent T_g of 6 to 75°C. Polymer with a high amorphous content had a reproducible T_g of ?35°C. The polyester has good solvent resistance to hydrocarbons, and comparable thermal stability to the corresponding polyester prepared from isophthalic acid.     

A chiral polymer‐based turn‐on fluorescent sensor for specific recognition of hydrogen sulfate

A new kind of polymeric chemosensor containing chiral naphthaldimine moiety in the side chain was synthesized by the reversible addition‐fragmentation chain transfer polymerization of N‐{[2‐(4‐vinylbenzyloxy)‐1‐naphthyl]‐methylene}‐(S)‐2‐phenylglycinol (VNP). The resulting polymers (PVNP) showed high selectivity for hydrogen sulfate relative to other anions including F^?, Cl^?, Br^?, H₂PO, CH₃CO, and NO in tetrahydrofuran (THF) solution as judged from UV?vis, fluorescence, and circular dichroism spectrophotometric titrations. Compared with its monomer, the polymer has proven to be more attractive for detection of HSO in terms of sensitivity and reproducibility. Upon addition of the anion it gives remarkable spectral responses concomitant with detectable color change from colorless to pale yellow. Furthermore, the HSO‐induced CD or fluorescence signal can be totally reversed with addition of base and eventually recovered the initial state, leading to a reproducible molecular switch with two distinguished “on” and “off” states. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis and polymerization of racemic and optically active substituted ß-propiolactones. V. α-methyl ß-propiolactone

R(+) and S(?) enantiomers of α-methyl β-propiolactone (MPL) have been synthesized from the corresponding α-methyl β-hydroxymethylpropionates and racemic MPL from methyl methacrylate. The optical purity and absolute configuration of these lactones were determined using ¹H-NMR spectroscopy after complexation with a chiral compound: 2,2,2-trifluoro-1-(9-anthryl)-ethanol. Optical purities of 100% were obtained for both the S(?) ([α₀] = ?10.4°, c = 1.3 g/dL in CHCl₃) and the R(+) ([α₀] = +10.5°, c = 1.0 g/dL in CHCl₃) enantiomers. The corresponding racemic and optically active polylactones [poly(MPL)] were prepared by anionic polymerization, in bulk and in solution, as well as poly(MPL)s of intermediate optical purities. The polymers thus obtained are optically active ([α₀] = 16.2° in CHCl₃ for the optically pure polymer, S configuration) and exhibit significant differences. For example, the racemic poly(MPL) is soluble in several organic solvents such as tetrahydrofuran, benzene, CCl₄, CH₂Cl₂, hexafluoroisopropanol, and CHCl₃, whereas the optically active poly(MPL)s are soluble in CHCl₃ and hexafluoroisopropanol only. Moreover, racemic poly(MPL) is amorphous whereas optically active poly(MPL)s are semicrystalline for optical purities larger than 51%. Melting temperatures and enthalpies of fusion of the semicrystalline polylactones vary with optical purity whereas glass transition temperatures remain invariant for all polymers, at about ?28°C. The poly(MPL) of highest optical purity exhibits a melting temperature of 95°C and an enthalpy of fusion of 61 J/g.     

Visible light induced free radical promoted cationic polymerization using thioxanthone derivatives

The free radical promoted cationic polymerization cyclohexene oxide (CHO), was achieved by visible light irradiation (λ_inc = 430–490 nm) of methylene chloride solutions containing thioxanthone‐fluorene carboxylic acid (TX‐FLCOOH) or thioxanthone‐carbazole (TX‐C) and cationic salts, such as diphenyliodonium hexafluorophosphate (Ph₂I⁺PF) or silver hexafluorophosphate (Ag⁺PF) in the presence of hydrogen donors. A feasible initiation mechanism involves the photogeneration of ketyl radicals by hydrogen abstraction in the first step. Subsequent oxidation of ketyl radicals by the oxidizing salts yields Bronsted acids capable of initiating the polymerization of CHO. In agreement with the proposed mechanism, the polymerization was completely inhibited by 2,2,6,6‐tetramethylpiperidinyl‐1‐oxy and di‐2,6‐di‐tert‐butylpyridine as radical and acid scavengers, respectively. Additionally polymerization efficiency was directly related to the reduction potential of the cationic salts, that is, Ag⁺PF (E = +0.8 V) was found to be more efficient than Ph₂I⁺PF (E = ?0.2 V). In addition to CHO, vinyl monomers such as isobutyl vinyl ether and N‐vinyl carbazole, and a bisepoxide such as 3,4‐epoxycyclohexyl‐3′,4′‐epoxycyclohexene carboxylate, were polymerized in the presence of TX‐FLCOOH or TX‐C and iodonium salt with high efficiency. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Thermal cured epoxy resins using certain calixarenes and their esterified derivatives as curing agents

The acetyl esterified calixarene (CA) derivatives were prepared from calix[4]resorcinarene (CRA), and p‐tert‐butylcalixarene (BCA[n], n = 4, 6, 8), respectively. Using these CA derivatives as curing agents, the thermal curing reactions of two multifunctional epoxy resins (jER 828, 186 g/equiv., and ESCN, 193.7 g/equiv.) were investigated. The temperatures of glass transition (T_g) and decomposition (T) were measured by DSC and TGA, respectively. Based on the yields, T_gs, and T_ds of the thermal cured jER 828 epoxy resin with CRA‐E100, the curing conditions were optimized to be tetrabutylphosphonium bromide (TBPB) as catalyst in NMP at 160 °C for 15 h. Under this curing condition, the cured materials of jER 828 or ESCN using various CA derivatives as curing agents were prepared. Except for BCA4 derivatives, the yields of thermal curing reaction were higher than 90%. T_gs and Ts of the resultant cured materials were in the range of 113–248 °C and 363–404 °C, respectively. These results mean that the cured epoxy resins with excellent T_gs were successfully formed by using CA derivatives as curing agents. It was also found that the T_gs of cured epoxy resins were strongly affected by the degree of esterification of CA derivatives. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1931–1942, 2010     

Kinetics of crosslinking reactions. 2. Reaction rates of intermolecular and intramolecular crosslinkings by using a soluble microgel

Soluble microgels with several pendant vinyl groups were synthesised by radical copolymerization of methyl methacrylate (MMA) with p-divinyl benzene (p-DVB). The competitive reactions of intermolecular and intramolecular crosslinkings of these microgels were carried out at 40°C in the presence of 1-buten-3-ol as a degradative chain transfer agent. The rate constant of intermolecular crosslinking (k) was estimated by GPC (gel permeation chromatography) analysis on the polymer produced from intermolecular propagation between bimolecules. The k depended strongly on the internal structure of microgels. Network formation was discussd inclusive of informations for the rate constant of intramolecular crosslinking (k).     

Novel active ester‐bridged copolynorbornene materials containing terminal functional hydroxyl,amino, methacryloyl,or ammonium groups via ring‐opening metathesis polymerization

Several random and block copolynorbornenes with side chains containing terminal hydroxyl, amino, methacryloyl or ammonium groups were derived from the functional alkyl ester‐containing norbornenes by ring‐opening metathesis polymerization (ROMP). The main chain of ROMP‐type polynorbornene had a more important role for glass‐transition temperature in comparison with vinyl addition polymerization. There is little effect on glass‐transition temperature (about ?39 °C) of polynorbornenes with different length of alkyl side chain. The organosoluble copolynorbornenes with active crosslinkable methylacryloyl side chains derived from functional hydroxyl group were prepared to improve the thermal stability of poly(methyl methacrylate) [decomposition temperature (T_d)^10% = 325 °C in nitrogen] by forming networked AB crosslinked polymer (T = 367 °C in nitrogen). The sizes of nanometer‐scale polymeric micelles of block copolymers having hydrophobic alkyl ester and hydrophilic ammonium groups were measured in the range of 11–25 nm by scanning electron microscopy. These polymeric materials with various functional groups or amphiphilic architectures are accessible by ROMP, whose topology makes them particularly attractive for application potential such as biomedical and photoelectric materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4233–4247, 2005     

Anionic polymerization of N-substituted maleimide. V. A study on the kinetic features of anionic polymerization of N-phenylmaleimide

The kinetic feature of the anionic polymerization of N-PMI was investigated in THF. The polymerization system initiated with lithium tert-butoxide was revealed to be so-called “slow-initiation” system. The rate constant of the initiation reaction, k_i, was obtained to be 4.2 × 10^?3 (L mol^?1 s^?1) at ?72°C. The apparent rate constants of the propagation reaction, k, at ?72°C were individually obtained from each slope of the first-order plots in the later stages of the polymerizations for four different initiator concentrations. Each k is fairly close to that of initiation rate around 10^?3. The propagation reaction was concluded to be dominated by ion-pair mechanism from the analysis of the kinetic data and the results of the addition effects of crown ether and common salt.     

Magnesium chloride-supported high-mileage catalysts for olefin polymerization XI. Determinations of poly(decene-1) molecular weight chain dimension and thermal transitions

Decene-1 was polymerized with the CW catalyst and fractionated by precipitation technique. Light-scattering and viscometric measurements on these fractions established the relationship [η] = 5.19 × 10^?3 M . The unperturbed mean square end-to-end distance is (〈R〉/M)^1/2 = (6.17 ± 0.34) × 10^?9. Light-scattering data is consistent with a relatively stiff molecule with length of L = 1.75 × 10^?5 cm for poly(decene-1) with MW = 397,000. Its mean square radius of gyration 〈R〉 is 2.79 × 10^?11 cm.² The ratio of L²/〈R〉 = 11 is close to the theoretical ratio of 12 for this kind of macromolecule.