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.     

Structure and Conformation of β‐Oligopeptide Derivatives with Simple Proteinogenic Side Chains: Circular Dichroism and Molecular Dynamics Investigations

A careful CD analysis (Figs. 1 – 3 and 5; MeOH or H₂O solutions) of β‐oligopeptides ( 1 – 6 , B , C ) containing four to seven β‐amino acids reveals that seemingly small structural changes cause a switch from the CD pattern (maxima of opposite sign near 215 and 200 nm) associated with a 3₁₄‐helical structure to the CD pattern (single Cotton effect at ca. 205 nm) considered characteristic of a so‐called 12/10‐helical structure, but also exhibited by a β‐peptide adopting a hair‐pin conformation with a ten‐membered H‐bonded ring as the turn motif. Comparison of these CD spectra with those of the trans‐2‐aminocyclohexanecarboxamide oligomers, which give rise to the long‐wavelength Cotton effect only, suggests that the H‐bonded 14‐, 12‐, and 10‐membered ring conformations of the β‐peptides, and not just the entire helix structures, might actually generate the Cotton effects. This interpretation would be compatible with our previous NMR structure determinations of β‐peptides and with previously reported temperature dependences of CD and NMR spectra of β‐peptides. To further substantiate this suggestion, we have performed a statistical analysis of the β‐peptidic conformations generated by molecular‐dynamics calculations (GROMOS96) for a β‐hexapeptide ( C ; the 12/10 helix) and a β‐heptapeptide ( 6 ; the 3₁₄ helix) in MeOH (Figs. 6 – 9). Up to 400,000 conformations at 0.5‐ps intervals were analyzed from up to 200‐ns simulations (at 298 to 360 K). The analysis reveals the co‐existence of the various H‐bonded rings. Remarkably, the central section of the β‐peptide 6 (containing a β^2,3‐amino‐acid residue of like‐configuration!) adopts a ten‐membered‐ring conformation for ca. 5% of the simulation time, while the central section of the β‐peptide C adopts a 14‐membered‐ring conformation for ca. 3% of the time, according to this computational analysis. Further experimental and theoretical work will be necessary to find out to which extent the components (H‐bonded rings) and the entire helical secondary structures of β‐peptides contribute to the observed Cotton effects.     

Preparation and X-ray structures of complexes of 18-membered crown ethers with polyfunctional guests: Urea and (O-alkyliso)uronium salts

The preparation and X-ray structure determinations of six complexes of urea and (O-n-butyliso)uronium salts with crown ethers are presented. Urea forms isostructural 5:1 adducts with 18-crown-6 (1) and aza-18-crown-6 (2), in which two urea molecules are each hydrogen bonded to two neighbouring hetero atoms of the macroring. The remaining urea molecules form two-dimensional layers alternating with crown ether layers. In both complexes the macroring has theg ⁺ g ⁺ a ag ^– a ag ^– a g ^– g ^– a ag ⁺ a ag ⁺ a conformation withC _i symmetry. In the solid 1:1 complex of O-n-butylisouronium picrate with 18-crown-6 (3) two types of conformations of the macroring were observed: theg ⁺ g ⁺ a ag ^– a ag ⁺ a ag ^– g ^– ag ^– a ag ⁺ a conformation with approximateC _m symmetry and to a lesser extent theg ⁺ g ⁺ a ag ^– a ag ⁺ a g ⁺ g ⁺ a ag ^– a ag ⁺ a conformation with approximateC ₂ symmetry. Both conformations allow the guest to form three hydrogen bonds to the macrocyclic host. Three complexes of 18-crown-6 and uronium salts have been prepared and characterized by X-ray crystallography. The 1:1 complexes with uronium nitrate (4) and uronium picrate (5) both exhibit the sameC ₂ conformation and the same hydrogen bonding scheme as in the least occupied form of the previous complex. A 1:2 complex with uroniump-toluenesulphonate (6) has a different hydrogen bonding scheme (two hydrogen bonds per cation to neighbouring oxygen atoms of the macroring) and a different conformation of the host molecule (theag ⁺ a ag ^– a ag ⁺ a ag ^– a ag ⁺ a ag ^– a conformation with almostD _3d symmetry). An attempt to prepare a solid uronium nitrate complex with diaza-18-crown-6 in the same way as the 18-crown-6·uronium nitrate (1:1) complex did not yield the expected result. Instead X-ray analysis revealed that the uronium ion is dissociated, resulting in the nitrate salt of the diprotonated diaza crown ether (7). Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82058 (26 pages).     

β‐Peptidic Secondary Structures Fortified and Enforced by Zn2+ Complexation – On the Way to β‐Peptidic Zinc Fingers?

The correlation between β²‐, β³‐, and β^2,3‐amino acid‐residue configuration and stability of helix and hairpin‐turn secondary structures of peptides consisting of homologated proteinogenic amino acids is analyzed (Figs. 1–3). To test the power of Zn²⁺ ions in fortifying and/or enforcing secondary structures of β‐peptides, a β‐decapeptide, 1 , four β‐octapeptides, 2 – 5 , and a β‐hexadecapeptide, 10 , have been devised and synthesized. The design was such that the peptides would a) fold to a 14‐helix ( 1 and 3 ) or a hairpin turn ( 2 and 4 ), or form neither of these two secondary structures (i.e., 5 ), and b) carry the side chains of cysteine and histidine in positions, which will allow Zn²⁺ ions to use their extraordinary affinity for RS^? and the imidazole N‐atoms for stabilizing or destabilizing the intrinsic secondary structures of the peptides. The β‐hexadecapeptide 10 was designed to a) fold to a turn, to which a 14‐helical structure is attached through a β‐dipeptide spacer, and b) contain two cysteine and two histidine side chains for Zn complexation, in order to possibly mimic a Zn‐finger motif. While CD spectra (Figs. 6–8 and 17) and ESI mass spectra (Figs. 9 and 18) are compatible with the expected effects of Zn²⁺ ions in all cases, it was shown by detailed NMR analyses of three of the peptides, i.e., 2, 3, 5 , in the absence and presence of ZnCl₂, that i) β‐peptide 2 forms a hairpin turn in H₂O, even without Zn complexation to the terminal β³hHis and β³hCys side chains (Fig. 11), ii) β‐peptide 3 , which is present as a 14‐helix in MeOH, is forced to a hairpin‐turn structure by Zn complexation in H₂O (Fig. 12), and iii) β‐peptide 5 is poorly ordered in CD₃OH (Fig. 13) and in H₂O (Fig. 14), with far‐remote β³hCys and β³hHis residues, and has a distorted turn structure in the presence of Zn²⁺ ions in H₂O, with proximate terminal Cys and His side chains (Fig. 15).     

Markovian approach to nonlinear polymer formation: Free-radical crosslinking copolymerization

A Markovian model is used to extend the Flory/Stockmayer gelation theory to nonequilibrium reaction systems, by taking free-radical crosslinking copolymerization of vinyl and divinyl monomer as an example. Free-radical polymerizations are kinetically controlled; therefore, each primary polymer molecule experiences a different history of crosslinked structure formation. By assuming that the primary chains with identical birth time conform to the same chain connection probabilities, the nonlinear structural development can be viewed as a system in which the primary chains formed at different birth times are combined into nonlinear polymers in accordance with the first-order Markov chain statistics. According to the present Markovian model, the weight-average chain length, P̄_w is given by a matrix formula, P̄_w = W _p( E — Q )⁻¹ l where W _p is the row vector that concerns the weight contribution of a primary chain, E is a unit matrix, Q is the transition matrix representing the chain connection statistics, and I is a column vector whose elements are all unity. For an equilibrium system, W _p = P̄_wp (weight-average chain length of the primary chains), E = 1, Q = ρP̄_wp (ρ is the crosslinking density), and I = 1; therefore, the present formula reduces to the Flory/Stockmayer equation, P̄_w = P̄_wp/(1 − ρP̄_wp). The criterion for the onset of gelation is simply stated as a point at which the largest eigenvalue of the transition matrix Q reaches unity, i.e., det( E − Q ) = 0. The present Markovian approach elucidates important characteristics of the kinetically controlled network formation, and provides greater insight into nonequilibrium gelling systems.     

Unitary group approach to general system partitioning. I. Calculation of U(n = n1 + n2): U(n1) × u(n2) reduced matrix elements and reduced wigner coefficients

This paper is the first in a series of two directed toward a unitary calculus for group-function-type approaches to the many-electron correlation problem. In this paper we present a complete derivation of the matrix elements of the U(n = n₁ + n₂) generators, for the representations approapriate to many-electron systems, in a basis symmetry adapted to the subgroup U(n₁) × U(n₂). Explicit formulae for the fundamental U(n):U(n₁) × U(n₂) reduced Wigner coefficients, which are needed for the general multishell problem, are also obtained. The symmetry properties of the reduced Wigner coefficients and reduced matrix elements are investigated, and a suitable phase convention is given.     

Proposed relationship between the exponents γ and η at liquid–vapour critical point via the dimensionality d

In earlier work, Ma [S.K. MA, Phys. Rev. Lett., 29, 1311 (1972)] has studied the critical exponents γ and η for charged and neutral Bose gases. Here we use the result of Ma, valid for general dimensionality d but only to O(m ^?1), where m is the number of components of the Bose field, to write a relation between γ(d) and η(d) to O(m ^?1). This then motivates, but now for the Ising model, a relationship between the critical exponents γ and η, via the dimensionality d. We finally demonstrate a connection between the two renormalisation group eigenvalues y _t and y _h , via the critical exponent δ with a dimensional dependence.     

Solvation effect in the thermal decomposition of 2,2′‐azoisobutyronitrile in the three‐component system

The thermal decomposition rate constant (k_d ) of 2,2′‐azoisobutyronitrile in acrylonitrile (AN; monomer A)–methyl methacrylate (MM; monomer B) comonomer mixtures in N,N‐dimethylformamide (DMF) as a function of the comonomer mixture composition and its concentration in the solvent at 60 °C was studied. The dependences k_d = f(x_A ,C) [x_A (mole fraction of A in the comonomer mixture) = A/(A + B) = A/C, where C is the comonomer mixture concentration] have a different course as a function of C: from a curve k_d = f(x_A ) approaching the straight line (C = 2 mol · dm⁻³) to a convex curve possessing a maximum at a point x_A = 0.7 (C = 4 mol · dm⁻³) to a curve with a flattened wide maximum within the range of x_A = 0.2–0.8 (C = 7 mol · dm⁻³) to a curve with the shape of a lying s (C = 9 mol · dm⁻³). All the courses of the experimental dependences k_d = f(x_A ,C) can be explained with a hypothesis of initiator solvation by the comonomers AN and MM and the solvent DMF. The existing solvated forms, their relative stability constants, the thermal decomposition rate constants, and the relative contents in the system were determined. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2156–2166, 2000     

A partial recurrence relation for reduced class coefficients of the symmetric group

An expression for the product of a single-cycle class [(1)^{N - P}(p)]_N and an arbitrary class [(1)^l1(2)^l …? (N)^lN]_N of the symmetric group has recently been conjectured. This expression involves a sum over a relatively small number of reduced class sums, depending on p indices. A further conjecture is formulated and demonstrated, according to which reduced class coefficients (RCCS ) involving cycles whose length is expressed by means of a single index can be related to corresponding coefficients in the product of [(1)^{N - P+1}(p - 1)]_N with an arbitrary class sum. Consequently, the problem of evaluating the general class sum product reduces to that of obtaining a relatively small set of fundamental RCCS containing no single-index cycles. The conjectures mentioned can be used to evaluate the product [(1)^{N - p}(p)]_N · [(1)^{N - q}(q)]_N in terms of fundamental RCCS that can all be obtained from the product [(r)]_r · [(r)]_r, where r = min(p, q). For the latter product, we use a result due to Boccara.     

Transamidation reactions. Part 11. N-substituted 3-aminopropanenitriles and 2-aminoacetonitriles as Schiff-base equivalents

In presence of a strong base, the 13-membered cyclic compound 3 yielded, by loss of acetonitrile or its equivalent, the bicyclic product 5 instead of the 17-membered compound 4 as expected (Scheme 2). Investigation of model compounds (Scheme 4) and of model reactions (Schemes 5 and 6) led to the conclusion that the reaction proceeds via an intermediate formaldehyde imine; a Schiff base, e.g. 3b (Scheme 5), which reacts intra- and intermolecularly with a nucleophile to form a Mannich-type product. It seems to be a general principle that N-substituted 3-aminopropanenitrile and 2-aminoacetonitrile derivatives behave in the presence of a strong base as Schiff -base equivalents (Schemes 5 and 6).     

Structure‐dependent conductivity and microhardness of metal‐filled PVC composites

Metal‐filled composites of a commercial PVC (polyvinyl chloride) powder (mean particle size d_p ≈ 100 microns) and a metal powder (mean particle size d_f about 100 microns for copper, Cu, and about 10 microns for nickel, Ni) prepared by mechanical mixing in a ball mill, subsequent hot‐pressing at 443 K and rapid cooling to 300 K, were characterized by the room‐temperature measurements of electrical conductivity σ, density ρ and microhardness H. The sudden jumps of about 17 orders of magnitude followed by a much slower growth up to the limiting filler fraction ϕ* on the log σ vs. ϕ plots are the evidence for the onset of percolation transitions, at filler volume contents ϕ_c1 = 0.05 and 0.04 for PVC/Cu and PVC/Ni, respectively. For both systems, the values of H exhibited an initial steep increase up to ϕ_c2 = 0.07, followed by an apparent plateau extending up to ϕ = 0.18. However, drastic differences in the patterns of composition dependence of H were observed at higher metal loadings, i.e., a continuous increase of H up to the leveling‐off at ϕ* for PVC/Cu, in contrast to a sudden drop of H at ϕ = 0.20 and subsequent slow increase for PVC/Ni. For both composites the apparent density ρ′ of a polymer matrix remained the same as that of the neat PVC in the composition interval ϕ < 0.20, while at ϕ* > 0.20 a precipitous drop of ρ₁ was observed due to the formation of polymer‐free voids between filler particles (crowding effect) as ϕ approaches ϕ*. The observed effects were analyzed in terms of a tentative model envisaging cross‐overs from “dilute suspension regime” to “semi‐dilute suspension regime” in the concentration range ϕ_c1 to ϕ_c2, and from “semi‐dilute suspension regime” to “concentrated suspension regime” above ϕ = 0.20. Different behavior in this latter regime was explained by intrinsic differences in the structure of conductive infinite clusters between mixtures of particles of about the same size (PVC/Cu) and of widely different sizes (PVC/Ni).     

Amorphous blends of poly(zwitterions) and zwitterionomers of the ammonioalkoxydicyanoethenolate type with some alkali metal salts

Poly(zwitterions) and zwitterionomers of the ammonioethoxydicyanoethenolate type (functional dipolar unit R ₃N⁺–(CH ₂) ₂–O–CO–C^?–(CN) ₂, µ = 25.9 D) show the very specific property of solvation of some alkali metal salts to yield amorphous blends. For homopolymers in the (meth)acrylic series, solvation is observed up to a ratio r = [salt]/[zwitterion] of 1 for LiClO ₄ and NaSCN and of 0.5 for NaCF ₃SO ₃: it results in a significant plasticization (increasing order LiClO ₄ < NaSCN < NaCF ₃SO ₃) and in the development in some cases of a poorly defined (lamellar?) local order, as evidenced by the presence of a single broad peak in the small‐angle x‐ray scattering (SAXS) patterns (Bragg distances of about 15–20 Å). For the amorphous blend of a biphasic poly(tetramethyleneoxide) segmented zwitterionomer and NaCF ₃SO ₃ (r = 0.5), selective solvation of the salt in the hard zwitterionic domains induces a transition from a lamellar structure (zwitterionic sublayer of about 9 Å thickness) to an hexagonal packing of ionic‐zwitterionic cylinders (radius of about 15 Å). Ionic conductivity, measured in a narrow range of temperature just above the glass transition temperature, is characterized for most systems by an activation energy of about 1–1.8 eV; the drastic decrease of the conductivity by a factor of 10 ³, when going from the homopolymer to the zwitterionomer blends, is typical of the inhibition of the ionic percolation process by the lack of connectivity of the ionic‐zwitterionic domains. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

Photochemical reaction mechanism of cyclobutanone: CASSCF study

The photochemical reaction channels of cyclobutanone have been studied at the CASSCF level with a 6‐31G* basis set. Starting from the n‐π* excited‐state (S₁) cyclobutanone, the three reactions can take place: decarbonylation (produce CO and cyclopropane or propylene), cycloelimination (produce ketene and ethylene), and ring expansion (produce oxacarbene). Our computation indicates that decarbonylation products CO and triplet trimethylene are formed on the triplet n‐π* excited state (T₁) in a stepwise way via a biradical intermediate after intersystem crossing (ISC) to T₁ from S₁. And, then, the triplet trimethylene undergoes a second ISC to the ground state (S₀) to produce the singlet trimethylene from which cyclopropane can be produced rapidly only overcoming a 1 to 2‐kcal/mol barrier while propylene can be formed as a secondary product. The cycloelimination products ketene and ethylene are formed on the S₀ in a concerted mechanism after internal conversion (IC) to S₀ from S₁ via a biradical conical intersection. The reaction channels corresponding to ring expansion on the S₀, T₁, and S₁ states have also been discussed, and the likeliest reaction path is that oxacarbene is formed on the ground state following S₁/S₀ internal conversion. The surface topology of cyclobutanone on the S₁ surface is characterized by a transition state separating the minimum from the S₁/S₀ conical intersection, which is consistent with the previous computations and can explain the wavelength dependence of the fluorescence emission yield. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Flow of polymer chains and segregation in a flow field with a hybrid simulation

Effects of a flow field (E) on segregation and flow of polymer chains are studied in two dimensions using a hybrid (discrete‐to‐continuum) simulation. The flow rate (j) of polymer chains is found to increase monotonically with E, a linear response in the low field regime followed by a slow approach to saturation in the high field regime. The effective chain permeability (ϕ_c = j/E) varies nonmonotonically on increasing the field E, with a maximum (ϕ_cm) at a characteristic value of the field (in the range 0.2 < E < 2); ϕ_cm depends on the chain length. Chain aggregates exhibit an anisotropic mass distribution due to the field with a molecular bridging at high fields. The longitudinal component of the radius of gyration (R_gx) exhibits a crossover from a random walk (RW) (R_gx ˜ L_c^1/2) at E = 0 to an elongated conformation (R_gx ˜L_c) at E ⪈ 0.2; the transverse component changes from R_gy ˜ L_c^1/2 to R_gy ˜ L_c^1/3. The width of the radial distribution function (ρ(r)) of the monomers increases while its peak varies nonmonotonically with E and is consistent with the observation of anisotropic mass distribution.     

Effect of Cluster Deformations in the DLCA Modeling of the Sol-Gel Process

The diffusion limited cluster-cluster aggregation (DLCA) model is modified by including cluster deformations during aggregation, with a tuning flexibility parameter F. A three-dimensional computer simulation is presented, which starts from a collection of f-functional monomers randomly distributed in a cubic box with a volumic fraction c (concentration) and which uses the highly efficient bond fluctuation algorithm to describe the cluster deformations. It is shown that, for F 0, there exists a well defined threshold value of the volumic fraction below which the realization of all intra-aggregate bonding possibilities prevents the formation of a gelling network. For c > c _g , a true sol-gel transition occurs at a characteristic time t _g , after which an infinite cluster (which is self connected via the boundary conditions) appears. In contrast to DLCA, t _g does not increase as the box size increases. The transition at c _g is characterized by a divergence of the final clusters size for c<c _g and a divergence of the gel time for c>c _g . Several other numerical results are reported.     

Magnetic Orbitals and Mechanisms of Exchange II. Superexchange

Summary. In a first step, we examine the concept of magnetic orbital which is very useful to treat the mechanism of superexchange. After that, we recall the general broad lines of the first historical model proposed by Anderson. In a second step, we develop a new general treatment for superexchange, in the case of the centrosymmetrical model AXB, where A and B are metal cations and X a common bridging ligand (with here, for simplification, A = B, without transfer between cations). It allows one to retrieve the expression of exchange energy J vs. key molecular integrals, as respectively proposed by several authors such as Anderson on the one hand, Hay, Thibeault, and Hoffmann on the other one, and, finally, Kahn and Briat. This model may be easily generalized to the case where a transfer does exist between both cations, with A = B or A ≠ B. An erratum to this article is available at .     

The Implications of (2S,4S)‐Hydroxyproline 4‐O‐Glycosylation for Prolyl Amide Isomerization

The conformations of peptides and proteins are often influenced by glycans O‐linked to serine (Ser) or threonine (Thr). (2S,4R)‐4‐Hydroxyproline (Hyp), together with L ‐proline (Pro), are interesting targets for O‐glycosylation because they have a unique influence on peptide and protein conformation. In previous work we found that glycosylation of Hyp does not affect the N‐terminal amide trans/cis ratios (K_trans/cis) or the rates of amide isomerization in model amides. The stereoisomer of Hyp—(2S,4S)‐4‐hydroxyproline (hyp)—is rarely found in nature, and has a different influence both on the conformation of the pyrrolidine ring and on K_trans/cis. Glycans attached to hyp would be expected to be projected from the opposite face of the prolyl side chain relative to Hyp; the impact this would have on K_trans/cis was unknown. Measurements of ³J coupling constants indicate that the glycan has little impact on the C^γ‐endo conformation produced by hyp. As a result, it was found that the D ‐galactose residue extending from a C^γ‐endo pucker affects both K_trans/cis and the rate of isomerization, which is not found to occur when it is projected from a C^γ‐exo pucker; this reflects the different environments delineated by the proline side chain. The enthalpic contributions to the stabilization of the trans amide isomer may be due to disruption of intramolecular interactions present in hyp; the change in enthalpy is balanced by a decrease in entropy incurred upon glycosylation. Because the different stereoisomers—Hyp and hyp—project the O‐linked carbohydrates in opposite spatial orientations, these glycosylated amino acids may be useful for understanding of how the projection of a glycan from the peptide or protein backbone exerts its influence.     

Relaxations in thermosets. IX. Ionic conductivity and gelation of DGEBA-based thermosets cured with pure and mixed amines

The results obtained during the isothermal curing of diglycidyl ether of bisphenol-A-based thermosets cross-linked with pure diaminodiphenyl methane and pure diaminodiphenyl sulfone and with their mixtures have been analyzed to determine how the dc conductivity changes with time during the conversion of its liquid to a gel. The complex permittivity data are first analyzed to show that ac measurements can be used to obtain the ionic conductivity over a considerable period of the curing process. The procedure allows one to obtain the dc conductivity without having data as a function of frequency. The shape of the complex plane plots of the electrical modulus are semicircles, but with small deviations that appear at long times during the curing process. The dielectric consequences of the chemical changes with time during the cross-linking of the thermoset are analogous to the frequency dependence of the complex permittivity of a liquid. The analysis shows that the dc conductivity σ_o of a thermoset during its cure follows a power law, σ_o∝ (t_g—t)^x, where t is the curing time (t < t_g). The results can also be described equally well by a new equation, σ_o ∝ exp[—B/(t_o—t)], where x, t_g, B, and t_o are empirical constants all of which vary with the temperature of the cure. t_g is close to the time for gelation known from independent studies and t_o is close to but longer than the time for vitrification. These conclusions are discussed in terms of scaling concepts for the gelation phenomenon.     

A necessary and sufficient condition for the existence of real coupling coefficients for a finite group

We establish a theorem which gives a necessary and sufficient condition for a set of matrix irreps of a finite group to admit real coupling (Clebsch–Gordan) coefficients. The proof is based on the method used by Feit to prove that a full set of coupling coefficients for a finite group determines the group up to isomorphism. A consequence of the theorem is that a finite group with real coupling coefficients is necessarily quasiambivalent. The theorem is used to demonstrate that real coupling coefficients do not exist for the point-group hierarchies T ? D₂ and I ? T or for the double-group hierarchies I* ? D₃*, I* ? D₅*, and O* ? D₃*.