Biodegradation of Polyhydroxyalkanoate Films in Natural Environments

Summary: Biodegradation of film specimens from polyhydroxyalkanoates (PHAs) of two types – poly-3-hydroxybutyrate (PHB) and poly-3-hydroxybutyrate-co-3-hydroxyvalerate (PHBV) – was analysed in different environments: tropical sea waters of the South China Sea (Nha Trang, Vietnam) and soils in the environs of Hanoi (Vietnam), Nha Trang (Vietnam) and Krasnoyarsk (Siberia, Russia). In seawater, the mass loss of the specimens of both types was almost equal. However, in tropical soils, PHB degraded quicker than PHBV. In the Siberian soil, the degradation rate of the PHBV was generally higher than that of PHBV. Analysis of molecular mass of PHA specimens showed its decreasing during biodegradation. In the tropical sea conditions, PHA degrading microorganisms were represented by bacteria of Enterobacter, Bacillus and Gracilibacillus genera. Among PHA degrading bacteria, Burkholderia, Alcaligenes, Bacillus, Mycobacterium and Streptomyces genera were identified in Vietnamese soils, and Variovorax, Stenotrophomonas, Acinetobacter, Pseudomonas, Bacillus and Xanthomonas genera in Siberian soils. Micromycetes of Gongronella, Paecilomyces, Penicillium and Trichoderma genera exhibited PHA degrading activity in Vietnamese soils, and Paecilomyces, Penicillium, Acremonium, Verticillium and Zygosporium genera – in Siberian soils.     

Synthesis, π‐Face‐Selective Aggregation,and π‐Face Chiral Recognition of Configurationally Stable C3‐Symmetric Propeller‐Chiral Molecules with a π‐Core

The C₃‐symmetric propeller‐chiral compounds (P,P,P)‐ 1 and (M,M,M)‐ 1 with planar π‐cores perpendicular to the C₃‐axis were synthesized in optically pure states. (P,P,P)‐ 1 possesses two distinguishable propeller‐chiral π‐faces with rims of different heights named the (P/L)‐face and (P/H)‐face. Each face is configurationally stable because of the rigid structure of the helicenes contained in the π‐core. (P,P,P)‐ 1 formed dimeric aggregates in organic solutions as indicated by the results of ¹H NMR, CD, and UV/Vis spectroscopy and vapor pressure osmometry analyses. The (P/L)/(P/L) interactions were observed in the solid state by single‐crystal X‐ray analysis, and they were also predominant over the (P/H)/(P/H) and (P/L)/(P/H) interactions in solution, as indicated by the results of ¹H and 2D NMR spectroscopy analyses. The dimerization constant was obtained for a racemic mixture, which showed that the heterochiral (P,P,P)‐ 1 /(M,M,M)‐ 1 interactions were much weaker than the homochiral (P,P,P)‐ 1 /(P,P,P)‐ 1 interactions. The results indicated that the propeller‐chiral (P/L)‐face interacts with the (P/L)‐face more strongly than with the (P/H)‐face, (M/L)‐face, and (M/H)‐face. The study showed the π‐face‐selective aggregation and π‐face chiral recognition of the configurationally stable propeller‐chiral molecules.     

Light-induced cis/trans isomerization of cis-[Pd(L-S,O)2] and cis-[Pt(L-S,O)2] complexes of chelating N,N-dialkyl-N′-acylthioureas: key to the formation and isolation of trans isomers

Irradiation cis-[M(Lⁿ-S,O)₂] complexes (M = Pt^II, Pd^II) derived from N,N-dialkyl-N′-benzoylthioureas (HLⁿ) with various sources of intense visible polychromatic or monochromatic light with λ < 500 nm leads to light-induced cis?→?trans isomerization in organic solvents. In all cases, white light derived from several sources or monochromatic blue-violet laser 405 nm light, efficiently results in substantial amounts of the trans isomer appearing in solution, as shown by ¹H NMR and/or reversed-phase HPLC separation in dilute solutions at room temperature. The extent and relative rates of cis/trans isomerization induced by in situ laser light (λ = 405 nm) of cis-[Pd(L²-S,O)₂] was directly monitored by ¹H NMR and ¹⁹⁵Pt NMR spectroscopy of selected cis-[Pt(L-S,O)₂] compounds in chloroform-d; both with and without light irradiation allows the δ(¹⁹⁵Pt) chemical shifts cis/trans isomer pairs to be recorded. The cis/trans isomers appear to be in a photo-thermal equilibrium between the thermodynamically favored cis isomer and its trans counterpart. In the dark, the trans isomer reverts back to the cis complex in what is probably a thermal process. The light-induced cis/trans process is the key to preparing and isolating the rare trans complexes which cannot be prepared by conventional synthesis as confirmed by the first example of trans-[Pd(L-S,O)₂] characterized by single-crystal X-ray diffraction, deliberately prepared after photo-induced isomerization in acetonitrile solution.     

Pulsed NMR observation of ultradrawn polypropylene

Proton spin-spin relaxation times have been measured as a function of temperature for ultradrawn polypropylene with draw ratios λ up to 24. The three relaxation times T_2a (the longest), T_2i (intermediate), and T_2c (the shortest), observed for all the samples, have been ascribed to the relaxations of the amorphous, constrained amorphous, and crystalline components, respectively. T_2i and T_2a, which reflect the changes in structure and mobility in the noncrystalline regions, decrease with increasing λ; T_2i becomes saturated at λ > 9, whereas T_2a shows a substantial decrease up to λ = 24. The continued decrease in T_2a indicates that the constraint on the amorphous segments keeps increasing up to the highest λ. The associated mass fractions F_a, F_i, and F_c also change with λ. At λ < 9, the increasc in F_i with increasing λ is accompanied by a decrease in F_a, with F_c remaining unchanged. At higher λ, however, F_a is almost constant, and stepwise rises in F_c at about λ = 12 and 24 are accompanied by corresponding drops in F_i. It seems that, in this high draw ratio range, some of the taut molecules are fully extended and are in sufficiently good lateral register to transform into crystalline bridges. This conjecture is supported by the similarity in the λ dependence of F_c and the mass-fraction crystallinity obtained from the heat of fusion.     

Cationic photopolymerization of 1,3-di(9-carbazolyl)-2-propanol glycidyl ether

An absorbance probe method was used for the investigation of photolysis of cationic photoinitiators. The rates of the photolysis of diphenyliodonium hexafluorophosphate (DPIH), diphenyliodonium tetrafluoroborate (DPIB), di(tert-butylphenyl)iodonium tetrafluoroborate (DTIB), di(tert-butylphenyl)iodonium bromate (DTIBr), triphenylsulfonium hexafluorophosphate (TPS) and cyclopropyldiphenylsulfonium tetrafluoroborate (CPS) were studied in the presence of acid indicator quinaldine red (QR) in acetonitrile. Diphenyliodonium hexafluorophosphate and triphenylsulfonium hexafluorophosphate showed the highest photolysis rate. Photopolymerization of 1,3-di(9-carbazolyl)-2-propanol glycidyl ether (DCPGE) initiated with the iodonium and sulfonium salts in bulk and in solution was studied. It was established that the highest initial rate of polymerization is characteristic of DCPGE photopolymerization initiated with DPIH and TPS in bulk. The oligomers of DCPGE of number average molecular weight ( [`(M<sub>n</sub>)]\overline{M_n} ) ranging from 710 to 1220 were obtained in these reactions in bulk and those with [`(M_n)]\overline{M_n} ranging from 1300 to 1600 were obtained in solution.     

Molecular Recognition of Pyranosides by a Family of Trimeric, 1,1′-Binaphthalene-Derived Cyclophane Receptors

The synthesis and carbohydrate-recognition properties of a new family of optically active cyclophane receptors, 1 – 3 , in which three 1,1′-binaphthalene-2,2′-diol spacers are interconnected by three buta-1,3-diynediyl linkers, are described. The macrocycles all contain highly preorganized cavities lined with six convergent OH groups for H-bonding and complementary in size and shape to monosaccharides. Compounds 1 – 3 differ by the functionality attached to the major groove of the 1,1′-binaphthalene-2,2′-diol spacers. The major grooves of the spacers in 2 are unsubstituted, whereas those in 1 bear benzyloxy (BnO) groups in the 7,7′-positions and those in 3 2-phenylethyl groups in the 6,6′-positions. The preparation of the more planar, D₃-symmetrical receptors (R,R,R)- 1 (Schemes 1 and 2), (S,S,S)- 1 (Scheme 4), (S,S,S)- 2 (Scheme 5), and (S,S,S)- 3 (Scheme 8) involved as key step the Glaser-Hay cyclotrimerization of the corresponding OH-protected 3,3′-diethynyl-1,1′-binaphthalene-2,2′-diol precursors, which yielded tetrameric and pentameric macrocycles in addition to the desired trimeric compounds. The synthesis of the less planar, C₂-symmetrical receptors (R,R,S)- 2 (Scheme 6) and (S,S,R)- 3 (Scheme 9) proceeded via two Glaser-Hay coupling steps. First, two monomeric precursors of identical configuration were oxidatively coupled to give a dimeric intermediate which was then subjected to macrocyclization with a third monomeric 1,1′-binaphthalene precursor of opposite configuration. The 3,3′-dialkynylation of the OH-protected 1,1′-binaphthalene-2,2′-diol precursors for the macrocyclizations was either performed by Stille (Scheme 1) or by Sonogashira (Schemes 4, 5, and 8) cross-coupling reactions. The flat D₃-symmetrical receptors (R,R,R)- 1 and (S,S,S)- 1 formed 1 : 1 cavity inclusion complexes with octyl 1-O-pyranosides in CDCl₃ (300 K) with moderate stability (ΔG⁰ ca. −3 kcal mol⁻¹) as well as moderate diastereo- (Δ(ΔG⁰) up to 0.7 kcal mol⁻¹) and enantioselectivity (Δ(ΔG⁰)=0.4 kcal mol⁻¹) (Table 1). Stoichiometric 1 : 1 complexation by (S,S,S)- 2 and (S,S,S)- 3 could not be investigated by ¹H-NMR binding titrations, due to very strong signal broadening. This broadening of the ¹H-NMR resonances is presumably indicative of higher-order associations, in which the planar macrocycles sandwich the carbohydrate guests. The less planar C₂-symmetrical receptor (S,S,R)- 3 formed stable 1 : 1 complexes with binding free enthalpies of up to ΔG⁰=−5.0 kcal mol⁻¹ (Table 2). With diastereoselectivities up to Δ(ΔG⁰)=1.3 kcal mol⁻¹ and enantioselectivities of Δ(ΔG⁰)=0.9 kcal mol⁻¹, (S,S,R)- 3 is among the most selective artificial carbohydrate receptors known.     

The kinetics of the decarboxylation of n-butylmalonic acid in alkanols and amines

Rate constants and activation parameters are reported for the decarboxylation of n-butylmalonic acid in four normal alkanols (hexanol? 1, octanol? 1, decanol? 1, and dodecanol? 1) and in five amines (aniline, N-methylaniline, N-ethylaniline, N-n-propylaniline, and N-n-butylaniline). Both ΔH? and ΔS? of the reaction in both homologous series decrease regularly with increasing length of the hydrocarbon chain of solvent. If we compare data for the reaction in alkanol–amine pairs containing the same total number of carbon atoms in the molecule, we find that the ΔH? values are identical, but that the value of ΔS? is 0.8 eu/mole higher for the reaction in the amines as compared with the alcohol. The rate constant, at all temperatures, is 1.5 times as large in the amine as it is in the corresponding alcohol. Empirical equations are deduced relating the parameters ΔH? ΔS? ΔG? and k of the reaction to the parameters n and T, where n is the total number of carbon atoms in the solvent molecule and T is the absolute temperature. The results reported herein are compared with previously reported data for malonic acid.     

The spread of unicyclic graphs with given size of maximum matchings

The spread s(G) of a graph G is defined as s(G) = max _i,j |λ _i − λ _j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U ^*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U ^*(n,k), and the graph with the largest spread in U(n,k).      

Konstitution und absolute Konfiguration der Rhoeadin-Alkaloide (+)-Alpinigenin und (+)-cis-Alpinigenin

The constitution and absolute configuration of the rhoeadine alkaloids (+)-alpinigenine and (+)-cis-alpinigenine. The fundamental structure of the hemi-acetal phenylbenzazepine alkaloid (+)-alpinigenine ( 1 ), isolated from Papaver bracteatum LINDL ., was derived essentially from ¹H-NMR.- and mass-spectra of 1 and its derivatives 7, 10 and 14 (cf. Scheme 2). The positioning of the four methoxy groups in the two aromatic rings could be deduced from the ¹H-NMR.-spectra of the N-oxides 14 and 15 in which, as a result of favourable sterical and conformational behaviour, an interaction exists between the N-oxide oxygen atom and one of the two ortho protons in ring C. The B/D-trans-fused 1 undergoes isomerization in 1N HCl to cis-alpinigenine ( 16 ). A stereochemical correlation between bases in the trans-and cis-series was enabled via an Emde degradation of the corresponding methylacetal-methyliodides 21 resp. 19 leading to the enantiomeric isochroman derivatives 22 resp. 23 which are achiral at C (2) (Scheme 4). The configuration at C (14) in the hemi-acetals (eg. 1 and 16 ) and the methyl ethers (eg. 7 and 8 ) is discussed in detail (cf. Scheme 7). (+)-Alpinigenine ( 1 ) has the (1S, 2R, 14R) configuration and (+)-cis-alpinigenine ( 16 ), in chloroform or acetone solution, the (1R, 2R, 14R) configuration.     

NMR Detection of Phase Transition in a ZSM-5 Silicalite Caused by the Adsorbed Hexane and Decane Molecules

Times of longitudinal T _1b and transverse T _2b magnetic relaxation of hexane and decane molecules in micropores of ZSM-5 silicalite were measured as functions of the content of these liquid n-alkanes in zeolite and of temperature. The stepwise changes in the T _1b and T _2b times were revealed in the region of 8% content of hydrocarbons. The observed changes in the concentration and temperature dependences of T _1b and T _2b times are explained by the rearrangement of silicalite crystal lattice under the action of adsorbed molecules.     

Determination of Retention Factors of s-Triazines Homologous Series in Water Using a Numerical Method Basing on Ościk's Equation

The retention factors in pure water for a homologous series of s-triazines were calculated by a numerical method basing on Ościk's equation and were correlated with log k _w values obtained by linear and parabolic extrapolation. Chromatographic data (log k _w ) were compared with the software-calculated partition coefficients in the n-octanol/water system (Alog P, IAlog P, clog P, log P _Kowin , xlog P, log P _ACD and log P _Chem.Off.) as alternative hydrophobicity indices. The effect of organic modifier (methanol and acetonitrile) and its concentration in the mobile phase used for log k _w evaluation were investigated. Very good linear correlations were found between log k _w values calculated by the numerical method and log P _ACD , log P _Chem.Off . and clog P values, independent of organic modifier type.

     

Sorption and diffusion of HTO and cesium in crushed granite compacted to different lengths

In this study, batch and through-diffusion experiments have been performed in order to determine the distribution coefficients (K _d ), apparent diffusion coefficients (D _a ) and retardation factor (Rf), respectively. Both apparent and effective diffusion coefficient (D _a and D _e ) of Cs were obtained by accumulative concentration method developed by Crank (1975). In addition, a non-reactive radionuclide, HTO, was initially conducted in through-diffusion experiment for assessing the ability of radionuclide retardation. The distribution coefficients (K _d ) obtained by batch tests in 14 days under aerobic and anaerobic systems were 2.06 and 3.52 ml/g. Moreover, it is found in through-diffusion test that Rf = 4.12 and 4.40 and K _d = 0.97 and 1.06 of Cs did not have an obvious discrepancy in a length/diameter/ (L/D) ratio of 0.44 and 1.78. However, Rf and K _d revealed a larger difference in an L/D ratio closing to 1 due to the geometric change of one-dimension diffusive hypothesis. Therefore, it demonstrates that Rf and K _d obtained by through-diffusion experiments only could be achieved at a lower or larger L/D ratio and would be reliable for long-term performance assessment.     

Molecular orbital study of the Q–e scheme in free radical copolymerization

Molecular orbital calculations were used to study free radical polymerization. Calculations show that the monomer is activated during the reaction and the pi bond becomes a diradical. The radical on the carbon that is about to form the new bond is called the e radical in this article. The other is the Q radical. For different monomers it is shown indirectly that changes in the energies of formation of the Q and e radicals are related to changes in the Q and e terms in the empirical Q–e scheme of Alfrey and Price. The polar effect in the Q–e scheme involves the e-radical, unpaired electron density. Specifically, the Q–e sum (e_x + e_y) is correlated with the e radical spin density. Also the e term is correlated with the electron density on the unsubstituted carbon of the monomer. The relationship of the Q radical to the adjacent substituent is shown by correlating ln Q values with the energy of addition of a hydrogen atom to a monomer. These relationships give theoretical meaning to the Q–e terms and allow calculation of Q and e values from molecular orbital properties for small monomers.     

Lipophilic Diamides as Ionophores for Alkali and Alkaline Earth Metal Cations

A series of lipophilic N, N, N′,N′-tetrasubstituted diamides were prepared and their selectivity in solvent polymeric membranes was studied, cis-N, N, N′, N′-Tetraisobutylcyclohexane-1,2-dicarboxamide induces a selectivity in membranes for Li⁺over alkaline earth metal cations and other alkali metal cations by a factor of about 1000 and 100 respectively. The ionophore N, N′-diheptyl-N,N′-dimethylethylmalonamide is an attractive candidate for the use in microelectrodes for the determination of intracellular Mg²⁺-activities.     

Fragmentation‐related phosphinylations using 2‐aryl‐2‐phosphabicyclo[2.2.2]oct‐ 5‐ene‐ and ‐octa‐5,7‐diene 2‐oxides

A series of new P‐methylphenyl P‐heterocycles are introduced. The para and ortho substituted 2,5‐dihydro‐1H‐phosphole oxides ( 1a and 1b ) were converted to the double‐bond isomers ( A and B ) of 1,2‐dihydrophosphinine oxides ( 3a and 3b ) via the corresponding phosphabicyclo[3.1.0]hexane oxides ( 2a or 2b ). Isomeric mixture ( A and B ) of the dihydrophosphinine oxides ( 3a and 3b ) gave, in turn, the isomers ( A and B ) of phosphabicyclo[2.2.2]oct‐5‐enes ( 4a and 4b ) or a phosphabicyclo[2.2.2]octa‐5,7‐diene ( 5 ) in Diels‐Alder reaction with dienophiles. The bridged P‐heterocycles ( 4 and 5 ) were useful in the photo‐ or thermoinduced fragmentation‐related phosphinylation of hydroxy compounds and amines. The new precursors ( 4a and 4b ) were applied in mechanistic investigations. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:443–451, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10176     

Synthesis, X-Ray Diffraction Data, and 1H and 13C NMR Spectra of N-(N-Arylsulfonylimidoyl)-1,4-benzoquinonimines Derived from N-Aroyl(acetyl)-1,4-benzoquinonimines

Oxidation of N-(N-arylsulfonylimidoyl)-4-aminophenols gave the corresponding N-[N-arylsulfonylimidoyl)-1,4-benzoquinonimines, derivatives of N-aroyl- and N-acetyl-1,4-benzoquinonimines. The structure of the products was studied by the X-ray diffraction method and ¹H and ¹³C NMR spectroscopy. N-(N-Arylsulfonylimidoyl)-1,4-benzoquinonimines were found to undergo fast (on the NMR time scale) Z E isomerization about the CÍN bond in the quinonimine fragment. N-(N-Arylsulfonylacetimidoyl)-1,4-benzoquinonimines in solution give rise to dynamic Z E-isomerization with respect to the CÍN bond in the N-arylsulfonylacetimidoyl fragment.     

PHOTOREAaIVITY OF CHLORAMPHENICOL in vitro AND in vivo

Abstract The negative side effects of chlorarnphenicol (CAP) mostly involve blood dyscrasias (e.g. irreversible nondose-dependent aplastic anemia), allergic skin reactions and eye damage. To learn the cause of these side effects, most research focuses on metabolically formed nitroso- and hydroxylamino derivatives in the predisposed patient. In previous investigations it was demonstrated that photochemical decomposition of CAP in vitro by UV-A leads to formation of p-nitrobenzaldehyde (pNB), p-nitrobenzoic acid (pNBA) and p-nitrosobenzoic acid (pNOBA); the latter comprises up to 45 mol% of the starting amount of CAP. Incubation of these photoproducts in rat blood showed that pNB and pNOBA rapidly react and that PNBA is stable under these conditions. Reaction products from pNB (half-life 1.7 min) proved to be pNBA and p-nitrobenzyl alcohol (pNBOH) while pNOBA (half-life 3.7 min) was converted into p-aminobenzoic acid (pABA). Exposure of CAP in rat blood to UV-A yielded the same end products: pNBA, PABA and pNBOH. To estimate the amount of oxidative stress generated in vivo by these compounds, the ability to form methemoglobin (MetHb) in erythrocytes was tested; only pNOBA and p-hydroxylaminobenzoic acid (pHABA), a possible intermediate in the decomposition of pNOBA, proved to be reactive. Ultraviolet-A exposure of rats, after intraperitoneal injection of CAP, led to 3.6 times the basic level of MetHb. In addition, covalent binding of ³H-labeled CAP photoproducts to the skin of the back and to the ears was found, which was 9.1 and 3.2 times higher, respectively, than the dark values. Toxicity toward bone marrow cells of all photoproducts was established in vitro. p-Nitrobenzaldehyde, pNOBA andpHABA were 20, 6 and 6 times more toxic than CAP, respectively. These results show that photodecomposition of CAP in vivo does occur. Its reactive photoproducts are able to cause damage that may lead to (systemic) side effects. The latter is supported by the fact that the nature of the reactive products, nitroso- and hydroxylamino derivatives, is the same as the expected metabolites.     

Acute Toxicity of Cresols to Pseudomonas — An Initial Oxygen Uptake Method

Acute toxicity of cresols to both Pseudomonas I and II was estimated by an initial oxygen uptake method. Inhibition studies of toluene and cresols on the oxidation of either benzoate by Pseudomnas I or phenol by Pseudomonas II were analyzed and expressed as oxygen uptake rates. Double reciprocal plots for the inhibiton by cresols of oxygen uptake in Pseudomonas, two physical constants, Vmaxi and Ki, were obtained. The Vmaxi of o?, m? and p-cresol were 80%, 81% and 57% of Vmax in Pseudomnas I, and 10%, 25% and 36% in Pseudomonas II, respectively. Thus, the toxicity to Pseudomonas I decreases in the order p- > o- ≥ m-cresol, whereas to Pseudomonas II, the order is changed to o- > m- > p-cresol. This difference in the toxicity order is probably due to the allosteric effect of p-cresol towards Pseudomonas II. Inasmuch as most compounds inhibit noncompetively, the relative toxicity of different compounds can be estimated by a new toxicity parameter RI (relative inhibition) which is defined as 100/Ki. By comparing the RI value of each compound, the toxicity to Pseudomonas I decreases in the order m-chlorophenol > p-cresol > p-chlorophenol > o-cresol ≥ m-cresol > o-chlorophenol > toluene > phenol.     

Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

Effect of diffusion on rates and molecular weights in graft polymerization

A theoretical analysis has been made of the graft polymerization process in terms of the quantitative interrelationship between the initiation rate R_i, the k_p/k_t^1/ ratio of the monomer, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, and the diffusivity D of the monomer in the polymer. It is shown how the values of these parameters in any grafting system interact to lead to diffusion-controlled graft polymerization. Whether graft polymerization is diffusion-free or diffusion-controlled depends on the values of K_p, d, k_p/k_p^1/2, and L as gathered in the parameter A = [(K_p/k_t^1/2)R_i, D,/^1/2] L/2. When the values of the various terms are such that A is less than 0.1 (i.e., D is large while R_i, k_p, and L are small), the reaction is diffusion-free. When A is greater than 3 (i.e., D is small while R_i, k_p, and L are large), the reaction is diffusion-controlled. The derived equations showing the relationship between kinetic and diffusional parameters are theoretically applicable to all grafting systems, i.e., for all monomer-polymer combinations under all conditions of reaction temperature, radiation intensity and polymer film thickness. The theoretical analysis has been verified for the rate and degree of polymerization for the radiation-induced graft polymerization of styrene to polyethylene.