Intrinsic viscosities of four homopolymers and one copolymer in nonpolar solvents. II. Effect of solvent steric hindrance

Intrinsic viscosities at 25°C of an ethylene-propylene copolymer containing 81% ethylene (81% E) of polypentenamer (PPmer), polyisobutylene (PIB), polypentene-1 (PP-1), and polydimethylsiloxane (PDMS) have been measured in n-C₉ and three branched nonanes and n-C₇ and five branched heptanes. The effect of the solvent steric hindrance on the free energy, i.e., on the χ parameter was investigated. The highly sterically hindered, cruciform molecules 3,3-dimethylpentane and 3,3-diethylpentane are the best solvents for four of the five polymers. The enhancement of solvent quality due to the steric hindrance diminishes when the polymer free volume increases. The difference in [η] between 2,4-dimethylpentane and 2,3-dimethylpentane is ?50%, ?35%, ?2% for PPmer, PIB, PDMS, and can be correlated to a measure of the polymer free volume, i.e., the lower critical solubility temperature. The χ, χH, and χS are calculated from [η] using the Stockmayer-Fixman relation and from h, the heat of mixing at infinite dilution of the polymer, obtained previously. With each polymer, a good correlation is found between h and [η] obtained with the six heptanes and four nonanes. The correlation points to the same effect being at the origin of χH and χS but of different magnitude. In cases showing the steric hindrance effect, a negative contribution occurs in h (or χH) which is larger in magnitude than the corresponding negative entropic contribution leaving a net negative effect in χ itself. Probably due to their very compact shape and fewer degrees of freedom, the cruciform solvents lose less entropy than the chain solvents in mixing.     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

Reactions of coordinated molecules: XLIX. Carboncarbond bond formation between the donor atoms of adjacent acyl and alkenyl ligands

When the ferraenolate anion, (η-C₅H₅)(CO)₂FeC(O)CH₂⁻, is treated sequentially with methyllithium/TMEDA and benzoyl chloride, the known η³-allyl complex, (η-C₅H₅)(OC)Fe{η³-CH₂C[OC(O)Ph]C[OC(O)Ph](CH₃}, is isolated in 36% yield. When the neutral alkenyl complexes, (η-C₅H₅)(CO)₂Fe[C(Me)CH₂] and (η-C₅H₅)(OC)₂Fe{C(OMe)CH₂], were treated sequentially with methyllithium and benzoyl chloride, the η³-allyl complexes, (η-C₅H₅)(OC)Fe{η³-CH₂C(Me)C[OC(O)Ph](Me) and (η-C₅H₅)(OC)Fe{η³-CH₂C(OMe)C[OC(O)Ph](Me) are isolated in 8 and 11% yield, respectively. These η³-allyl ligands are presumably formed via CC coupling of the donor atoms of the formal acyl and alkenyl ligands in the intermediate complexes.     

Novel polyisobutylene/poly(dimethylsiloxane) bicomponent networks. I. Synthesis and characterization

The synthesis of novel polyisobutylene (PIB)/poly(dimethylsiloxane) (PDMS) bicomponent networks is described. The synthesis strategy (see Figure 1) was to prepare well-defined and -characterized allyl-tritelechelic polyisobutylenes [ϕ(PIB—C—C=C)₃] and SiH-ditelechelic poly(dimethylsiloxanes) (HSi–PDMS–SiH) and then crosslink these moieties by hydrosilation. The ϕ(PIB—C—C=C)₃ was prepared by living isobutylene polymerization followed by end-quenching with allyltrimethylsilane, whereas the HSi–PDMS–SiH was obtained by equilibrium polymerization of octamethylcyclotetrasiloxane and tetramethyldisiloxane. The detailed structures of the starting polymers were characterized by GPC and ¹H-NMR spectroscopy. A series of PIB/PDMS bicomponent networks of varying compositions and average molecular weights between crosslinks (M _c) of ∼ 20,000 g/mol were assembled. Optimum crosslinking conditions were defined in terms of H₂PtCl₆ catalyst concentration, nature of solvent, time, temperature, and stoichiometry of ∼ CH₂CH=CH₂/∼SiH groups, allowing for the convenient synthesis of well-defined model bicomponent networks. Swelling studies and elemental analysis confirm the correctness of the synthetic strategy. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1891–1899, 1998     

Determination of Polymer Compatibility by Viscometric Measurements on Ternary Solutions of the Two Polymers

Results on the intrinsic viscosity [η] are reported for the system solvent(1)/polymer(2)/polymer(3) in which the solvent was benzene, polymer(2) was polystyrene (PS), and polymer(3) was poly(dimethylsiloxane) PDMS. The values of [η] were then used to determine the likely compatibility of polymer blends of PS and PDMS. Initial focus was on the traditional interaction parameter b ₂₃ ⁽¹⁾ used by several authors to predict compatibilities, it but depends on the molar mass, weight fractions, and concentrations of each polymer. A new interaction parameter b ₂₃ ⁽²⁾ that is independent of polymer(3) concentration and molar mass was evaluated for determinations of polymer compatibility.     

Synthesis and solution properties of linear,four-branched,and six-branched star polyisoprenes

A number of linear, four- and six-branched regular star polyisoprenes were synthesized by anionic polymerization techniques in benzene using lithium as the counterion and polyfunctional silicon chloride compounds as the coupling agents. Light-scattering measurements in dioxane were performed in order to establish Θ solvent conditions. Determinations of the radius of gyration of the polymers of different structure indicate that g = 〈S²〉_0,br/〈S²〉_0,lin agree closely with random flight calculations for the ratios. Intrinsic viscosities determined in a Θ solvent establish g′ = [η]_br/[η]_lin to be 0.77₃ and 0.62₅ for the four- and six-branched polyisoprenes, respectively. In a good solvent g′ values are slightly lower. These values are compared with theoretical estimates. Viscosities of 19.29% (w/w) solutions of the polyisoprenes in n-decane at 25°C are correlated with the intrinsic viscosities of the polymers under Θ conditions.     

Organometallic polymers I. Solution polymerization of α-ferrocenylmethylcarbonium fluoborate

The self-condensation of α-ferrocenylmethylcarbonium ion in nitroethane yielded polymers of M_n up to 20,000. The change of [η] and M_n with the reaction time indicated that the process consisted of a rapid primary growth stage, an induction period, a second growth stage, and a crosslinking stage. The [η]–M_n correlation for a series of polymeric fractions in the M_n = 0.1–7.2 × 10⁴ range points to a highly branched structure.     

Thermochemistry of bis-arene- and arenetricarbonyl-chromium compounds containing hexamethylbenzene, 1,3,5-trimethylbenzene and naphthalene.

Microcalorimetric measurements at elevated temperatures of the heats of thermal decomposition and iodination have led to values of the standard enthalpies of formation of the following crystalline compounds (values given in kJ mol^?1) at 298K: [Cr(η⁶-1,3,5-C₆H₃(CH₃)₃)₂] = (63±12); [Cr(η⁶-C₆(CH₃)₆)₂] : -(88±12); [Cr(1,2,3,4,4a,8a-η-C₁₀H₈)₂] = (407±11); [Cr(CO)₃(1,2,3,4,4a,8a-η-C₁₀H₈)] = -(258±8). Separate measurements by the vacuum sublimation microcalorimetric technique gave the following values for the enthalpy of sublimation at 298K (kJ mol^?1) : [Cr(η⁶-1,3,5-C₆H₃(CH₃)₃)₂] = (104±1); [Cr(η⁶-C₆(CH₃)₆)₂] = (119±4); [Cr(CO)₃(1,2,3,4,4a,8a-η-C₁₀H₈)] = (107±3). From these and other data, the bond enthalpy contributions of the metal-ligand bonds in the gaseous metal complexes were evaluated as follows: [(η₆-C₆(CH₃)₆)-Cr] (155±7); [(η⁶-C₆H₃(CH₃)₃)-Cr] (151±6); [(1,2,3,4,4a, 8a-η-C₁₀H₈)-Cr](145±6) kJ mol^?1]The question of the transferability of the enthalpy contributions of chromium—ligand bonds between organochronium complexes is discussed with aid of information from structural and spectroscopic investigation. The limitations of the procedure are defined.The thermodynamic data are used to discuss various substitution, redistribution and exchange reaction of Cr(η-arene)₂ and [Cr(CO)₃(η-arene)] compounds.     

Ligand exchange reactions of fac -(dihapto-[60]fullerene) (dihapto-1,2- bis -(diphenylphosphino)ethane tricarbonyl chromium(0)

The complex fac-(η²-C₆₀)(η²-dppe)Cr(CO)₃ (dppe?=?1,2-bis(diphenylphosphino)ethane and C₆₀?=?[60]fullerene) reacts with piperidine (pip) to produce fac-(η²-C₆₀)(η¹-pip)₂Cr(CO)₃. The reactions are first order with respect to [?fac-(η²-C₆₀)(η²-dppe)Cr(CO)₃] under flooding conditions where [pip]???[?fac-(η²-C₆₀)(η²-dppe)Cr(CO)₃]. The pseudo-first order rate constant values (k _obsd) are [pip]-dependent. Curved (upward) plots of k _obsd versus [pip] and linear plots of k _obsd versus [pip]² indicate that the piperidine-assisted dppe displacement from fac-(η²-C₆₀) (η²-dppe)Cr(CO)₃ is second order with respect to [pip]. The proposed mechanism involves a [60]fullerene-stabilized intermediate.     

Synthesis of polyisobutylene with arylamino terminal group by combination of cationic polymerization with alkylation

The controlled cationic polymerization of isobutylene (IB) initiated by H₂O as initiator and TiCl₄ as coinitiator was carried out in n‐Hexane/CH₂Cl₂ (60/40, v/v) mixture at −40 °C in the presence of N,N‐dimethylacetamide (DMA). Polyisobutylene (PIB) with nearly theoretical molecular weight (M_n = 1.0 × 10⁴ g/mol), polydispersity (M_w/M_n) of 1.5 and high content (87.3%) of reactive end groups (tert‐Chlorine and α‐double bond) was obtained. The Friedel‐Crafts alkylation of triphenylamine (TPA) with the above reactive PIB was further conducted at different reactions, such as [TPA]/[PIB], solvent polarity, alkylation temperature, and time. The resultant PIBs with arylamino terminal group were characterized by ¹H NMR, UV, and GPC with RI/UV dual detectors. The experimental results indicate that alkylation efficiency (A_eff) increased with increases in [TPA]/[PIB], reaction temperature, and reaction time and with a decrease in solvent polarity. The alkylation efficiency could reach 81.0% at 60/40(v/v) mixture of n‐Hex/CH₂Cl₂ with [TPA]/[PIB] of 4.49 at 50 °C for 54 h. Interestingly, the synthesis of PIB with arylamino terminal group could also be achieved in one pot by combination of the cationic polymerization of IB initiated by H₂O/TiCl₄/DMA system with the successive alkylation by further introduction of TPA. Mono‐, di‐ or tri‐alkylation occurred experimentally with different molar ratio of [TPA]/[PIB]. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 936–946, 2008     

The reactions of [Fe2(η-C5H5)2(CO)4−n(CNMe)n] (n = 0–4) complexes with halogens and mercury(II) salts

Halogens, X₂, and HgY₂ (X = Cl, Br, I; Y = X, F, NO₃, BF₄) cleave the metalmetal bonds in [Fe₂(η-C₅H₅)₂(CO)_4−n(CNMe)_n] complexes (n = 0–4). Typically, e.g., when n = 2, X₂ electrophiles give [Fe(η-C₅H₅)(CO)(CNMe)X] (a) and [Fe(η-C₅H₅)(CO)(CNMe)₂]X (b) in relative yields which depend on X, the reaction solvent and n, but HgY₂ give equimolar amounts of [Fe(η-C₅H₅)(CNMe)₂Y] (c and [Fe(η-C₅H₅)(CO)₂HgY] only. Hg(CN)₂ reacts more slowly than other HgY₂, and [Hg(PPh₃)₂I₂] does not react at all. It is suggested that the reactions which give rise to products of type (a), (b) or (c) are all two-electron oxidation which proceed by way of adducts containing μ-CA → X₂ or μ-CA → HgX₂ groups (Ca = CO or CNMe). One of these adducts has been isolated, namely [Fe₂(η-C₅H₅)₂(CNMe)₂{μ-CN(Me)HgCl₂}₂] · CHCl₃.     

Ring-Opening Polymerisation of Low-Strain Nickelocenophanes: Synthesis and Magnetic Properties of Polynickelocenes with Carbon and Silicon Main Chain Spacers

Polymetallocenes based on ferrocene, and to a lesser extent cobaltocene, have been well-studied, whereas analogous systems based on nickelocene are virtually unexplored. It has been previously shown that poly(nickelocenylpropylene) [Ni(η⁵-C₅H₄)₂(CH₂)₃]_n is formed as a mixture of cyclic ( 6 _x ) and linear ( 7 ) components by the reversible ring-opening polymerisation (ROP) of tricarba[3]nickelocenophane [Ni(η⁵-C₅H₄)₂(CH₂)₃] ( 5 ). Herein the generality of this approach to main-chain polynickelocenes is demonstrated and the ROP of tetracarba[4]nickelocenophane [Ni(η⁵-C₅H₄)₂(CH₂)₄] ( 8 ), and disila[2]nickelocenophane [Ni(η⁵-C₅H₄)₂(SiMe₂)₂] ( 12 ) is described, to yield predominantly insoluble homopolymers poly(nickelocenylbutylene) [Ni(η⁵-C₅H₄)₂(CH₂)₄]_n ( 13 ) and poly(tetramethyldisilylnickelocene) [Ni(η⁵-C₅H₄)₂(SiMe₂)₂]_n ( 14 ), respectively. The ROP of 8 and 12 was also found to be reversible at elevated temperature. To access soluble high molar mass materials, copolymerisations of 5 , 8 , and 12 were performed. Superconducting quantum interference device (SQUID) magnetometry measurements of 13 and 14 indicated that these homopolymers behave as simple paramagnets at temperatures greater than 50 K, with significant antiferromagnetic coupling that is notably larger in carbon-bridged 6 _x /7 and 13 compared to the disilyl-bridged 14 . However, the behaviour of these polynickelocenes deviates substantially from the Curie–Weiss law at low temperatures due to considerable zero-field splitting.     

Cu(I), Ag(I) complexes containing (η 5-cyclopentadienyl) [η 5-1-(diphenylphosphino) cyclopentadienyl] cobaltocenium

{Cu₄Br₅[(η ⁵-C₅H₄PPh₂)(η ⁵-C₅H₅)Co]₄}[PF₆]₃, [(η ⁵-C₅H₄PPh₂)(η ⁵-C₅H₅)Co]⁺ = ((η ⁵-cyclopentadienyl)[η ⁵-1-(diphenylphosphino) cyclopentadienyl] cobaltocenium) and {Ag(NO₃)(CH₃COCH₃)[(η ⁵-C₅H₄PPh₂)(η ⁵-C₅H₅)Co]} _n [PF₆] _n have been synthesized and characterized by elemental analyses, infrared spectroscopy, X-ray diffraction techniques, and by cyclic voltammetry. {Cu₄Br₅[(η ⁵-C₅H₄PPh₂)(η ⁵-C₅H₅)Co]₄}[PF₆]₃ contains four coplanar copper atoms bridged by four μ-Br and one central μ ₄-Br occupying the apex of a square pyramid, and {Ag(NO₃)(CH₃COCH₃)[(η ⁵-C₅H₄PPh₂)(η ⁵-C₅H₅)Co]} _n [PF₆] _n affording a 1-D coordination zigzag polymer.     

Anionic polymerization of caprolactam. XLIII. Relationship between osmometric molecular weight,viscosity, and endgroups of a polymer

For unfractionated anionic polymers, the following relationship between the osmometric molecular weight and intrinsic viscosity is valid: M?_n = 13200[η]^1.115 (cresol), or M?_n = 13000[η]^1.021 (93.8% H₂SO₄). A comparison of the osmometric and viscometric data with the number of endgroups of a polymer confirmed the finding that under certain conditions, moderately branched molecules can be formed; the above parameters depend on the type of the activator used.     

Synthesis and characterization of ring polybutadienes

It has been shown that butadiene initiated with potassium naphthalene in the mixture THF-n-hexane polymerizes conveniently rapidly. The active center is sufficiently stable below 0°C to produce narrow molecular weight linear polybutadiene. The two-ended living polymer has also served to prepare ring polybutadienes. The analysis of the ring polymers by a high-resolution set of SEC columns proved superior to the conventional method for the determination of the linear content in rings and in synthetic mixtures of rings and linear polymers. Dilute solution characterization of the linear and ring polymers shows that g_r′ = [η]/_r[η]_l is less than 0.66 in a good solvent.     

Disproportionation reactions between alkyl and fluoroalkyl radicals. VI. Difluoromethyl and n-propyl radicals

Cross-disproportionation to combination ratios for CF₂H and n-C₃H₇ radicals have been determined (the hydrogen acceptor radical is given first) to be Δ(n-C₃H₇, CF₂H) = 0.30 ± 0.01 and Δ(CF₂H, n-C₃H₇) = 0.057 ± 0.006.     

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

Alkynyl Ti-M complexes based on M(CO)4 and MO2 building blocks (M = Mo, W)

The synthesis and properties of heterobimetallic Ti-M complexes of type {[[Ti](μ-η¹:η²-CCSiMe₃)][M(μ-η¹:η²-CCSiMe₃)(CO)₄]} (M = Mo: 5, [Ti] = (η⁵-C₅H₅)₂Ti; 6, [Ti] = (η⁵-C₅H₄SiMe₃)₂Ti; M = W: 7, [Ti] = (η⁵-C₅H₅)₂Ti; 8, [Ti] = (η⁵-C₅H₄SiMe₃)₂Ti) and {[Ti](μ-η¹:η²-CCSiMe₃)₂}MO₂ (M = Mo: 13, [Ti] = (η⁵-C₅H₅)₂Ti; 14, [Ti] = (η⁵-C₅H₄SiMe₃)₂Ti). M = W: 15, [Ti] = (η⁵-C₅H₅)₂Ti; 16, [Ti] = (η⁵-C₅H₄SiMe₃)₂Ti) are reported. Compounds 5-8 were accessible by treatment of [Ti](CCSiMe₃)₂ (1, [Ti] = (η⁵-C₅H₅)₂Ti; 2, [Ti] = (η⁵-C₅H₄SiMe₃)₂Ti) with [M(CO)₅(thf)] (3, M = Mo; 4, M = W) or [M(CO)₄(nbd)] (9, M = Mo; 10, M = W; nbd = bicyclo[2.2.1]hepta-2,5-diene), while 13-16 could be obtained either by the subsequent reaction of 1 and 2 with [M(CO)₃(MeCN)₃] (11, M = Mo; 12, M = W) and oxygen, or directly by oxidation of 5-8 with air. A mechanism for the formation of 5-8 is postulated based on the in-situ generation of [Ti](CCSiMe₃)((η²-CCSiMe₃)M(CO)₅), {[Ti](μ-η¹:η²-CCSiMe₃)₂}-M(CO)₄, and [Ti](μ-η¹:η²-CCSiMe₃)((μ-CCSiMe₃)M(CO)₄) as a result of the chelating effect exerted by the bis(alkynyl) titanocene fragment and the steric constraints imposed by the M(CO)₄ entity.The molecular structure of 5 in the solid state were determined by single crystal X-ray diffraction analysis. In doubly alkynyl-bridged 5 the alkynides are bridging the metals Ti and Mo as a σ-donor to one metal and as a π-donor to the other with the [Ti](CCSiMe₃)₂Mo core being planar.     

Synthesis of hetero-binuclear derivatives of the tetrathiolato complexes [Mo(η-C5H5CH2SR)2)], R = Prn and Ph,with platinum,palladium, and rhodium

The compound Mo(η-C₅H₄(CH₂)₂SPrⁿ)₂(SPrⁿ)₂ acts as a bidentate ligand giving the heteronuclear bi-metallic compounds [Mo(η-C₅H₄CH₂CH₂SPrⁿ)₂-(SPrⁿ)₂(PtCl₂)],[Mo(η-C₅H₄CH₂CH₂SPrⁿ)₂(SPrⁿ)₂(PdCl₂)₂], [Mo(η-C₅C₄CH₂CH₂SPrⁿ)₂(SPrⁿ)₂(RhCl₃)₂], [Mo(η-C₅H₄CH₂CH2SPrⁿ)₂(μ-SPrⁿ)₂Rh(dppe)]BF₄, [Mo(η-C₅H₄CH₂CH₂SPrⁿ)₂(μ-SPrⁿ)₂(COD)Rh]Cl, [Mo(η-C₅H₄CH₂CH₂SPrⁿ)₂-(μ-SPrⁿ)₂Pt(PPh₃)₂](PF₆)₂, and the compound [Mo(η-C₅H₄(CH₂)₂-μ-SPh)₂Cl₂Rh(COD)]Cl bonds via the ring-sulphur substituents giving [Mo(η-C₅H₄(CH₂)₂-μ-SPh)₂-Cl₂Rh(COD)]Cl.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.