Evaluation of the relaxation modules from the response to a constant rate of strain followed by a constant strain

The stress response σ(t) to a constant rate of strain $ \dot \varepsilon $ ε during the period 0 < t ≤ t^* and to the constant strain ε^* $ ( = \dot \varepsilon t*) $ thereafter is considered in terms of the Boltzmann superposition principle. When t ≤ t^*, the data directly give the constant-rate modulus F (t) ≡ σ(t)/ε(t), which can be converted straightforwardly into the relaxation modulus E(t). Results from illustrative calculations show that a reduction in the relaxation rate effects a decrease in [σ(t^*)/ε^*]/E(t^*) and also in the time at which [σ(t)/ε^*]/E(t) becomes essentially unity. To evaluate E(t) at t > t^*, F(t) is first obtained from σ(t) and F(t ? t^*) by using a derived equation similar to that presented by Meissner. Thereafter, F(t) is transformed into E(t). For illustration, E(t) for a rubbery solid is evaluated over some 2.5 decades of time from its response to a strain rate of 0.25 min^?1 for 0.40 min and thereafter to the attained strain of 0.10 for 5.4 min.     

A Comparative Study on the Thermodynamics of Halogen Bonding of Group 10 Pincer Fluoride Complexes

The thermodynamics of halogen bonding of a series of isostructural Group 10 metal pincer fluoride complexes of the type [(3,5-R₂-^tBuPOCOP^tBu)MF] (3,5-R₂-^tBuPOCOP^tBu=κ³-C₆HR₂-2,6-(OPtBu₂)₂ with R=H, tBu, COOMe; M=Ni, Pd, Pt) and iodopentafluorobenzene was investigated. Based on NMR experiments at different temperatures, all complexes 1-tBu (R=tBu, M=Ni), 2-H (R=H, M=Pd), 2-tBu (R=tBu, M=Pd), 2-COOMe (R=COOMe, M=Pd) and 3-tBu (R=tBu, M=Pt) form strong halogen bonds with Pd complexes showing significantly stronger binding to iodopentafluorobenzene. Structural and computational analysis of a model adduct of complex 2-tBu with 1,4-diiodotetrafluorobenzene as well as of structures of iodopentafluorobenzene in toluene solution shows that formation of a type I contact occurs.     

Microcalorimetric study on expression of foreign genes in Bacillus thuringiensis

The thermogenic curves of the aerobic metabolism of the three strains of Bacillus thuringiensis B.t. A, B.t. B and B.t. C have been determined by using an LKB-2277 BioActivity Monitor. B.t. A was the host bacterium without foreign gene. B.t. B and B.t. C were constructed by transforming different foreign genes into the host B.t. A, respectively. B.t. B expressed erythromycin resistant gene, while B.t. C expressed both erythromycin resistant gene and tyrosinase gene. The heat flow rate of these strains is B.t. A> B.t. B >B.t. C. These results indicated that there is obvious interrelation between expression of foreign genes and heat flow rate of B.t. strains. This revised version was published online in August 2006 with corrections to the Cover Date.     

Limitations in the analysis of ac impedance data with poorly separated faradaic and diffusional processes

The kinetics of charge transfer across liquid-liquid interfaces is frequently analysed in terms of the Randles equivalent circuit. For this circuit, two time constants, t_f and t_d, can be defined for the faradaic and diffusional components respectively. Conventional methods of analysing impedance/admittance data will give valid estimates for the kinetic parameters only when t_f < t_d. Non-linear regression is capable of extracting valid estimates of the kinetic parameters for t_f 30t_d. Liquid-liquid systems appear to have t_f t_d. The difficulties in extracting kinetic parameters from such data will also apply to other transient techniques.     

Pivaloylmetals (tBu‐COM: M=Li,MgX, K) as Equilibrium Components

Short‐lived pivaloylmetals, (H₃C)₃C‐COM, were established as the reactive intermediates arising through thermal heterolytic expulsion of O=CtBu₂ from the overcrowded metal alkoxides tBuC(=O)‐C(‐OM)tBu₂ (M=MgX, Li, K). In all three cases, this fission step is counteracted by a faster return process, as shown through the trapping of tBu‐COM by O=C(tBu)‐C(CD₃)₃ with formation of the deuterated starting alkoxides. If generated in the absence of trapping agents, all three tBu‐COM species “dimerize” to give the enediolates MO‐C(tBu)=C(tBu)‐OM along with O=CtBu₂ (2 equiv). A common‐component rate depression by surplus O=CtBu₂ proves the existence of some free tBu‐COM (separated from O=CtBu₂); but companion intermediates with the traits of an undissociated complex such as tBu‐COM & O=CtBu₂ had to be postulated. The slow fission step generating tBu‐COMgX in THF levels the overall rates of dimerization, ketone addition, and deuterium incorporation. Formed by much faster fission steps, both tBu‐COLi and tBu‐COK add very rapidly to ketones and dimerize somewhat slower (but still fairly fast, as shown through trapping of the emerging O=CtBu₂ by H₃CLi or PhCH₂K, respectively). At first sight surprisingly, the rapid fission, return, and dimerization steps combine to very slow overall decay rates of the precursor Li and K alkoxides in the absence of trapping agents: A detailed study revealed that the fast fission step, generating tBu‐COLi in THF, is followed by a kinetic partitioning that is heavily biased toward return and against the product‐forming dimerization. Both tBu‐COLi and tBu‐COK form tBu‐CH=O with HN(SiMe₃)₃, but only tBu‐COK is basic enough for being protonated by the precursor acyloin tBuC(=O)‐C(‐OH)tBu₂.     

Tetrahydropyridines and furans from the reaction of 4-t-butylpyridine 1-oxide with t-butyl and 1-adamantyl mercaptan

The reaction of 4-t-butylpyridine 1-oxide (1) with t-butyl or 1-adamantyl mercaptan in acetic anhydride yielded the expected 2- and 3-alkylthio-4-t-butylpyridines and 1-acetyl-2,6-bis-(alkylthio)-3-acetoxy-4-t-butyl- and the unexpected 1-acetyl-2-acetoxy-3,6-bis(alkylthio-4-t-butyl-1,2,3,6-tetrahydropyridines. The addition of t-butyl mercaptan to a solution of 1 in acetic anhydride containing triethylamine produced the expected 1-acetyl-2-t-dmtylthio-3-acetoxy-4-t-butyl-6-hydroxy-1,2,3,4-tetrahydropyridine ( 6a ) and the unexpected 1-acetyl-2,6-bis(hydroxy)-3-t-butylthio-4-t-butyl-1,2,3,6-tetrahydropyridine. Mild alkaline hydrolysis of 6a yielded predominantly 2-[(acetamido) (t-butylthio)methyl]-3-t-butyl-5-hydroxy-2,5-dihydrofuran. The latter was converted by very mild acidic reagents to the corresponding furan and with 2,4-dinitrophenylhydrazine and sulfuric acid furnished 3-t-butylfurfural 2,4-dinitrophenyl-hydrazone.     

Synthesis of a Molecule with Five Different Adjacent Pnictogens

The first molecular compound with all five pnictogens was obtained by a multi-step reaction. Lithiation of the (bisamido)diazadiarsetidine (tBuNAs)₂(tBuNH)₂ in aliphatic solvents leads to the dimeric metallated species [(tBuNAs)₂(tBuNLi)₂]₂ ( 1₂ ). Upon reactions with AsCl₃, SbCl₃ and BiCl₃ the polycyclic compounds [(tBuNAs)₂(tBuN)₂]PnCl (Pn=As ( 2 ), Sb ( 3 ), Bi ( 4 )) can be obtained. Conversion of 2 – 4 with [tBu₂SbP(tBu)Li(OEt₂)]₂ leads to the remarkable interpnictogens [(tBuNAs)₂(tBuN)₂]PnP(tBu)SbtBu₂ (Pn=As ( 5 ), Sb ( 6 ), Bi ( 7 )), whereby 7 is the first example of a molecule containing all five Group 15 elements. The compound with adjacent AsNBiPSb-chains is surprisingly stable and does not show high sensibility against light as the labile Bi−P bond might suggest.     

The Reactions of Carbon Monoxide with Silyl and Silenyl Lithium – Synthesis and Isolation of the First Stable Tetra‐Silyl Di‐Ketyl Biradical and 1‐Silaallenolate Lithium

Reactions of carbon monoxide (CO) with tBu₂MeSiLi and (E)‐(tBu₂MeSi)(tBuMe₂Si)C=Si(SiMetBu₂)Li?2 THF ( 4 ) were studied both experimentally and computationally. Reaction of tBu₂MeSiLi with CO in hexane yields the first stable tetra‐silyl di‐ketyl biradical [(tBu₂MeSi)₂COLi]^.₂ ( 3 ). Reaction of 4 with CO yields selectively and quantitatively the first reported 1‐silaallenolate, (tBu₂MeSi)(tBuMe₂Si)C=C=Si(SiMetBu₂)OLi?THF ( 5 ). Both 3 and 5 were characterized by X‐ray crystallography and biradical 3 also by EPR spectroscopy. Silaallenolate 5 reacts with Me₃SiCl to produce siloxy substituted 1‐silaallene (tBu₂MeSi)(tBuMe₂Si)C=C=Si(SiMetBu₂)OSiMe₃. The reaction of 4 with CO provides a new route to 1‐silaallenes. The mechanisms of the reactions of tBuMe₂SiLi and of 4 with CO were studied by DFT calculations.     

Synthesis and Structures of New Oxidation/ Cycloaddition Products of λ3‐Cyclodiphosphazanes

Reaction of the cyclodiphosphazane [(OC₄H₈N)P(μ‐N‐t‐Bu)₂P(HN‐t‐Bu)] ( 1 ) with an equimolar quantity of diisopropyl azodicarboxylate afforded the phosphinimine product [(OC₄H₈N)P(μ‐N‐t‐Bu)₂P=N‐t‐Bu)(N(CO₂ ‐i‐Pr)NHCO₂‐i‐Pr] ( 6 ) having a P^III‐N‐P^V skeleton. Similar products [(t‐BuNH)P(μ‐N‐t‐Bu)₂P=N‐t‐Bu)(N(CO₂Et)NHCO₂Et] ( 7 ) and [(CO₂‐i‐Pr)HNN(CO₂‐i‐Pr)](t‐BuN=P(μ‐N‐t‐Bu)₂POCH₂CMe₂CH₂O[P(μ‐N‐t‐Bu)₂P=N‐t‐Bu)(N(CO₂‐i‐Pr)NH(CO₂‐i‐Pr)] ( 8 ) were spectroscopically characterized in the reaction of [(t‐BuNH)P‐N‐t‐Bu]₂ ( 2 ) and [(t‐BuNH)P(μ‐N‐t‐Bu)₂POCH₂CMe₂CH₂OP(μ‐N‐t‐Bu)₂P(NH‐t‐Bu)] ( 3 ) with diethyl‐ and diisopropyl azodicarboxylate, respectively. By contrast, the reaction of [(μ‐t‐BuN)P]₂[O‐6‐t‐Bu‐4‐Me‐C₆H₂]₂CH₂ ( 4 ) and [(C₅H₁₀N)P‐μ‐N‐t‐Bu]₂ ( 5 ) with diisopropyl azodicarboxylate afforded the mono‐ and bis‐oxidized compounds [(O)P(μ‐N‐t‐Bu)₂P][O‐6‐t‐Bu‐4‐Me‐C₆H₂]₂CH₂ ( 9 ) and [(C₅H₁₀N)(O)P‐μ‐N‐t‐Bu]₂ ( 10 ), respectively. Oxidative addition of o‐chloranil to 7 and its DIAD analogue [(t‐BuNH)P(μ‐N‐t‐Bu)₂P=N‐t‐Bu)(N(CO₂‐i‐Pr)NHCO₂‐i‐Pr] ( 11 ) afforded [(C₆Cl₄‐1, 2‐O₂)(t‐BuNH)P(μ‐N‐t‐Bu)₂P=N‐t‐Bu)(N(CO₂R)NHCO₂R] [R = Et ( 12 ) and i‐Pr ( 13 )] containing tetra‐ and pentacoordinate P^V atoms in the cyclodiphosphazane ring. The structures of 6 , 9 , 12 and 13 have been confirmed by X‐ray structure determination. For comparison, the X‐ray structure of the double cycloaddition product [(C₆Cl₄‐1, 2‐O₂)(t‐BuNH)PN‐t‐Bu]₂ ( 14 ), obtained from the reaction of 2 with two mole equivalents of o‐chloranil is also reported.     

Approximate relations among compliance functions of linear viscoelasticity for amorphous polymers

In the glass–rubber transition region of viscoelastic behavior of amorphous polymers, it is found that is a good first approximation. Here J(t) is the value of the shear creep compliance at time t and J″(1/t) is the value of the shear loss compliance at an angular frequency of 1/t. Previous approximations related the creep compliance to the storage compliance. When J(t) is proportional to t^m, where m is a positive constant, J″(1/t) is within 30% of J(t) for m > 0.6. Over the entire range, is a better approximation than either of the other two. The relaxation modulus G(t) is hardly ever a good approximation for the loss modulus G″(1/t).     

The chain conformations of a polyether based on bis(4-hydroxyphenoxy)-p-xylylene and 1,11-dibromoundecane (HPX-c11) in its mesophase states,derived from 13C NMR

A thermotropic main-chain polyether based on bis(4-hydroxyphenoxy)-p-xylylene and 1,11-dibromoundecane has been studied by variable-temperature solid-state ¹³C NMR. Between isotropization and glass transition temperatures, the material can be identified to be semicrystalline, consisting of two conformationally and motionally distinguishable phases. The more mobile component is liquid-like and thus, can be attributed to an amorphous phase. In the more rigid component, the molecules have a conformationally disordered methylene sequence. In the low-temperature ordered phase approximately ? of the carbon-carbon bonds are trans (t). Starting from the bond between the oxygen and the first methylene carbon, the bond conformations are: d? t? d? t? t? t? t? t? t? d? t? d, where d stands for disordered (i.e., it represents the common dynamic interchange between gauche and trans with an overall gauche content of perhaps 40%). The motion of the αα′-diphenoxy-p-xylylene unit consists mainly of 180° ring-flips, which cause no entropy increase relative to ordered phenylene groups in a crystal, but significantly changes the ¹³C NMR spectra. The central p-xylylene ring starts its flipping motion at a lower temperature than the two phenoxy rings. The high-temperature mesophase contains a methylene sequence of the bond conformations: d? t? d? d? d? t? t? d? d? d? t? d. Thus, the difference between the low-temperature and high-temperature mesophases consists of different degrees of conformational disorder. Thermal analysis seems to indicate that additional mesophases may be possible. © 1994 John Wiley & Sons, Inc.     

Beiträge zur Chemie des Phosphors. 152. Funktionalisierte Cyclotriphosphane des Typs (t-BuP)2PX (X = K,SiMe3, SnMe3, Cl,Br, PCl2, P(t-Bu)Cl,P(t-Bu)I)

Contributions to the Chemistry of Phosphorus. 152. Functionalized Cyclotriphosphanes of the Type (t-BuP)₂PX (X = K, SiMe₃, SnMe₃, Cl, Br, PCl₂, P(t-Bu)Cl, P(t-Bu)I) Functionalized cyclotriphosphanes of the type (t-BuP)₂PX with electropositive or electronegative substituents X have been prepared on various synthetic routes: KP(t-BuP)₂ ( 1 ) can be obtained in 50–55 per cent purity by reacting (t-BuP)₄ or (t-BuP)₃ with potassium. Reaction of 1 with Me₃SiCl or Me₃SnCl leads to the cyclotriphosphanes (t-BuP)₂PSiMe₃ ( 2 ) and (t-BuP)₂PSnMe₃ ( 3 ), respectively; the cyclocondensation of Cl(t-Bu)P? P(t-Bu)Cl with P(SnMe₃)₃, however, is more convenient for the preparation of 3 . In a similar way the halogenated compounds (t-BuP)₂PCl ( 4 ) and (t-BuP)₂PBr ( 5 ) can be obtained from Me₃Sn(t-Bu)P? P(t-Bu)SnMe₃ ( 6 ) and PX₃ (X = Cl, Br). The phosphino-substituted cyclotriphosphanes (t-BuP)₂P? PCl₂ ( 7 ), (t-BuP)₂P? P(t-Bu)Cl ( 8 ), and (t-BuP)₂P? P(t-Bu)I ( 9 ) are accessible by the reaction of 3 with PCl₃ and t-BuPX₂ (X = Cl, I), respectively. 2–9 could be obtained free from phosphorus-containing by-products and were ³¹P-NMR spectroscopically characterized as compounds with a cyclic P₃ skeleton.     

The theory of phase transition kinetics with growth site impingement. II. Heterogeneous nucleation

The kinetics of phase transformation are treated for heterogeneous nucleation, where all nuclei are simultaneously initiated, and where initiation follows first-order kinetcs. The phase transformation curves are sigmoid. For simultaneous initiation in two dimensions, a(t)/(1 ? a(t)) ∝ t². For first-order initiation, we have, approximately, a(t)/(1 ? a(t)) ∝ t^2.85, and v(t)/(1 ? v(t)) ∝ t^3.74.     

On the (im)possibility of evaluating correct individual rate constants of chain propagation kp and chain termination kt by combining kp2/kt and kp/kt data for chain‐length dependent termination

On the basis of simulated data two ways of evaluating individual rate constants by combining k_p²/k_t and k_p /k_t (k_p , k_t = rate constants of chain propagation and termination, respectively) were checked considering the chain‐length dependence of k_t. The first way tried to make use of the fact that pseudostationary polymerization yields data for k_p²/k_t as well as for k_p /k_t referring to the very same experiment, in the second way k_p²/k_t (from steady state experiments) and k_p/k_t data referring to the same mean length of the terminating radical chains were compared. In the first case no meaningful data at all could be obtained because different averages of k_t are operative in the expressions for k_p /k_t and k_p²/k_t. In spite of the comparatively small difference between these two averages (≈15% only) this makes the method collapse. The second way, which can be regarded as an intelligent modification of the “classical” method of determining individual rate constants, at least succeeded in reproducing the correct order of magnitude of the individual rate constants. However, although stationary and pseudostationary experiments independently could be shown to return the same k_t for the same average chain‐length of terminating radicals within extremely narrow limits no reasonable chain‐length dependence of k_t could be derived in this way. The reason is an extreme sensitivity of the pair of equations for k_p/k_t and k_p²/k_t towards small errors and inconsistencies which renders the method unsuccessful even for the high quality simulation data and most probably makes it even collapse for real data. This casts a characteristic light on the unsatisfactory situation with respect to individual rate constants determined in the classical way, regardless of a chain‐length dependence of termination. As a consequence, all efforts of establishing the chain‐length dependence of k_t are recommended to avoid this way and should rather resort to methods based on inserting a directly determined k_p into the equations characteristic of k_p²/k_t or k_p/k_t, properly considering the chain‐length dependent character of k_t.     

The Iminoborane tBuB≡NtBu as a Dipolarphile in (2+3) Cycloadditions

The iminoborane tBuB≡NtBu and the diazomethane tBuCH=N₂ give the (2+3) cycloadduct [—HC(tBu)—N=N—N(tBu)=B(tBu)—] in a 1:1 reaction and the seven‐membered ring [—C(tBu)=N—NH—N(tBu)=B(tBu)—N(tBu)=B(tBu)—] in a 2:1 reaction. The (2+3) cycloadduct decomposes above 0 °C to give the seven‐membered ring, N₂, and HC(tBu)=N—N=CH(tBu) in the ratio 2:1:1. The borane tBuB≡NtBu and organic azides R″N₃ yield the (2+3) cycloadducts [—R″N—N=N—N(tBu)=B(tBu)—] (R″ = Me, Et, Pr, Bu, iBu, sBu, C₅H₁₁, c‐C₅H₉, c‐C₆H₁₁, Bzl, EtOOC).     

Asymmetric cyclopolymerization of N‐tert‐butyl‐N‐allylacrylamide in the presence of β‐cyclodextrin

The radical polymerization of N‐tert‐butyl‐N‐allylacrylamide (t‐BAA) was carried out in a dimethyl sulfoxide/H₂O mixture in the presence of β‐cyclodextrin (β‐CD). The polymerization proceeded with the complete cyclization of the t‐BAA unit and yielded optically active poly(t‐BAA). The IR spectrum of the obtained polymer showed that the cyclic structure in the polymer was a five‐membered ring. The optical activity of poly(t‐BAA) increased with an increasing molar ratio of β‐CD to the t‐BAA monomer. The interaction of β‐CD with t‐BAA was confirmed by ¹H NMR and ¹³C NMR analyses of the polymerization system. It is suggested that interaction of the t‐BAA monomer with the hydrophobic cavity of β‐CD plays an important role in the asymmetric cyclopolymerization of t‐BAA. The radical copolymerization of t‐BAA with styrene (St), methyl methacrylate, ethyl methacrylate, or benzyl methacrylate (BMA) also produced optically active copolymers with a cyclic structure from the t‐BAA unit. St and BMA carrying a phenyl group were predicted to compete with t‐BAA for interaction with β‐CD in the copolymerization system. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2098–2105, 2000     

Vapour phase alkylation of ethylbenzene with t -butyl alcohol over mesoporous Al-MCM-41 molecular sieves

The alkylation of ethylbenzene witht-butyl alcohol was studied over Al-MCM-41 (Si/Al = 50 and 90) and Al, Mg-MCM-41 (Si/(Al+Mg) = 50) in the vapour phase from 200 to 400°C. The products werep-t-butylethylbenzene (p-t-BEB),p-t- butylvinylbenzene (p-t-BVB) andm-t-butylethylbenzene (m-t-BEB). Ethylbenzene conversion decreased with increase in temperature and increase in the ethylbenzene content of the feed. The reaction between the freely diffusing ethylbenzene in the channel and thet-butyl cations remaining as charge compensating ions yieldedp-t- BEB.p-t-BVB, an unexpected product in this investigation, was produced by dehydrogenation ofp-t-BEB over alumina particles present in the channels of the molecular sieves. Adsorption of ethylbenzene on Br?nsted acid sites and its subsequent reaction with very closely adsorbedt-butyl cations proved to be necessary to obtainm-t-BEB. Thoughm-t-BEB was obtained, the correspondingm-t-butylvinylbenzene was not observed in this study. Study of time durations indicated rapid and slow catalyst deactivation at lower and higher streams respectively.     

Kinetics of oxidation of adenosine by t-butoxyl radical: Protection and repair by caffeic acid

The kinetics of oxidation of adenosine and caffeic acid by t-BuO^• has been studied by the photolysis of t-BuOOH in the presence of t-BuOH. The rates and the quantum yields (φ) of oxidation of caffeic acid by t-BuO^• radicals have been determined in the absence and presence of varying concentrations of adenosine. An increase in the concentration of adenosine has been found to decrease the rate of oxidation of caffeic acid suggesting that adenosine and caffeic acid compete for t-BuO^• radicals. From competition kinetics, the rate constant of t-BuO^•–caffeic acid reaction has been calculated to be 8.15 × 10⁸ dm³ mol⁻¹ s⁻¹. The results of experimentally determined quantum yield (φ_exptl) values of oxidation of caffeic acid and the quantum yield values calculated (φ_cal) by assuming that caffeic acid reacts only with t-BuO^• radicals suggest that caffeic acid not only protects adenosine from t-BuO^• radicals but also repairs adenosine radicals formed by the reaction of t-BuO^• radicals. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 515–521, 2005     

Thermally reversible polymer systems by cyclopentadienylation. I. A model for termination by cyclopentadienylation of olefin polymerization

The reaction between tert-butylchloride (t-BuCl) and dimethylcyclopentadienylaluminum (Me₂AlCPD) was studied as a model for initiation by the tert-butyl cation (t-Bu^⊕) and termination by cyclopentadienylation by the Me₂Al(CPD)Cl^? counteranion of isobutylene polymerization. All reaction products formed in this model system have been identified and quantitatively determined. A comprehensive scheme that indicates pathways to these products was developed (scheme III). It is proposed that the predominant product, tert-butylcyclopentadiene (t-BuCPD), arises in the collapse of the t-Bu^⊕-Me₂Al(CPD)Cl^? ion pair, mainly by CPD^? transfer to the tert-butyl cation. The minor products are neopentane (t-BuMe) and isobutylene (i-C₄H₈), which are probably formed, respectively, by Me^? transfer to and proton loss from the t-butyl cation. Cyclopentadienylation selectivity increases by lowering the temperature and extrapolation of results suggests 100% cyclopentadienylation at ?55°C. The t-BuCl/Me₂AlCPD ratio strongly influences the overall reaction pathway. The reaction is first order in t-BuCl with ΔE_a of ca. 7 kcal/mole (1,2-dichloroethane or chlorobenzene solvents, +24 to ?29°C). Indirect evidence indicates that the kinetic product of cyclopentadienylation is 5-t-BuCPD and that this isomer cannot be tert-butylated; that is, the initiation of 5-t-BuCPD polymerization by t-Bu^⊕ is sterically unfavorable. Detailed analysis of the chemistry and kinetics of the t-BuCl/Me₂AlCPD model system holds important clues to the controlled polymerization of olefins leading to macromolecules with cyclopentadiene (CPD) termini.     

Linearization of second-order reaction data

Reaction data described by the second-order growth function A(t) = A_∞(αt) (1 + αt)^?1, where A_∞ is the ultimate value of the product concentration A(t), can be linearized by plotting a suitable function F(t) against the time (t). The slope of the straight line obtained is (2α), where α is the product of the rate constant (k₂) and the initial concentration of either reactant, with the result that k₂ can be determined without knowledge of A?. Optimal determination of the parameter α requires that data taking be limited to the interval 0 ≤ t ≤ T, where (αT) is approximately 4.0. Numerical data derived from an experiment on the exchange of lead by zinc ions in the enzyme carbonic anhydrase are analyzed to illustrate the method. The effects of small errors in the initial concentrations and of small deviations from second-order kinetics are briefly discussed.