Estimation of flocculation structure in filled polymer composites by dynamic rheological measurements

 The frequency and concentration dependences of the storage modulus (G ^′) for carbon black and short-carbon-fiber-filled polymer composites were investigated by means of dynamic rheological measurements. It was found that G ^′ at low frequencies and amplitudes could be used as a sensitive experimental parameter for detecting the flocculation structure of the ultra-fine-particle-filled polymer composites. Correlation of electrical resistivity of the composites to the relative storage modulus, G ^′ _r(=G ^′ _c/ G ^′ _p), revealed that the three-dimensional interparticle networks start to construct through the matrix when G ^′ _r increases to 7 regardless of the composite systems. Quantitative calculations in order to determine the flocculation structure were carried out by means of the modified Kerner equation. A plot of the calculated value, defined as the floc index A, dependence of electrical resistivity for various systems was found to be a universal curve. Accordingly, we suggest that A might universally correspond to the flocculation structure of the filler, which is independent of the nature of the filler, the molecular weight, the chemical composition of the polymer and the temperature at which the measurement is made. This method is particularly effective for estimating the flocculation structure of ultra-fine-particle-filled polymer composites no matter whether the filler is conductive or not. Received: 26 May 1999/Accepted in revised form: 28 September 1999     

Short‐term dynamics of isotopic composition of leaf‐respired CO2 upon darkening: measurements and implications

Recent advances in understanding the metabolic origin and the temporal dynamics in δ¹³C of dark‐respired CO₂ (δ¹³C_res) have led to an increasing awareness of the importance of plant isotopic fractionation in respiratory processes. Pronounced dynamics in δ¹³C_res have been observed in a number of species and three main hypotheses have been proposed: first, diurnal changes in δ¹³C of respiratory substrates; second, post‐photosynthetic discrimination in respiratory pathways; and third, dynamic decarboxylation of enriched carbon pools during the post‐illumination respiration period. Since different functional groups exhibit distinct diurnal patterns in δ¹³C_res (ranging from 0 to 10‰ diurnal increase), we explored these hypotheses for different ecotypes and environmental (i.e. growth light) conditions. Mass balance calculations revealed that the effect of respiratory substrates on diurnal changes in δ¹³C_res was negligible in all investigated species. Further, rapid post‐illumination changes in δ¹³C_res (30 min), which increased from 2.6‰ to 5‰ over the course of the day, were examined by positional ¹³C‐labelling to quantify changes in pyruvate dehydrogenase (PDH) and Krebs cycle (KC) activity. We investigated the origin of these dynamics with Rayleigh mass balance calculations based on theoretical assumptions on fractionation processes. Neither the estimated changes of PDH and KC, nor decarboxylation of a malate pool entirely explained the observed pattern in δ¹³C_res. However, a Rayleigh fractionation of ¹²C‐discriminating enzymes and/or a rapid decline in the decarboxylation rate of an enriched substrate pool may explain the post‐illumination peak in δ¹³C_res. These results are highly relevant since δ¹³C_res is used in large‐scale carbon cycle studies. Copyright © 2009 John Wiley & Sons, Ltd.     

Interfacial bonding,energy dissipation,and adhesion

Thin sheets of several elastomers have been adhered together by C? C or S? S interfacial bonds and peeled apart at various rates and temperatures. For C? C bonding, values of the work G required per unit area to separate the sheets could be superposed to form a master curve versus peel rate using Williams-Landel-Ferry (WLF) temperature shift factors. Threshold values G_o at low rates and high temperatures ranged from virtually zero for nonbonded sheets up to the tear strength of the sheet itself, 50-80 J/m², for fully interlinked sheets, in proportion to the density of interfacial bonds. The strength thus appears to be the sum of two terms: G_o and a viscoelastic loss function which itself is approximately proportional to G_o. By comparing the dependence of G upon rate of peel with the dependence of dynamic shear modulus μ′ upon oscillation frequency, an effective length of the fracture zone was deduced. It was extremely small in all cases, only about 1 Å. With sulfur interlinks, values of G were larger at all peel rates and varied more with temperature than predicted by the WLF relation. This is attributed to a concomitant decrease in S? S bond strength with temperature, and an increase in energy dissipation as the weaker sulfur bonds fail. © 1994 John Wiley & Sons, Inc.     

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.     

Development of gel permeation chromatography for polymer characterization. II. Universal calibration

GPC appearance volumes have been determined for a series of linear polyethylene, polystyrene, and polybutadiene fractions (M_w/M_n < 1.1) in trichlorobenzene at 130°C. and for the latter two series in tetrahydrofuran at 23°C. A polymer-type independent relationship between appearance volumes and the equivalent hydrodynamic radii of the polymer molecules has been demonstrated. The equivalent hydrodynamic radius is calculated from intrinsic viscosity data. It is proposed that this relationship can be used to construct a universal GPC calibration curve for polymers that assume a spherical conformation in solution. Methods for applying the universal curve to the determination of molecular weight averages and molecular weight distribution are described. In addition, a method is outlined by which the universal calibration curve can be empolyed for determining number-average Mark-Houwink constants from polydisperse samples.     

Functionally Rigid and Degenerate Molecular Shuttles

The preparation and dynamic behavior of two functionally rigid and degenerate [2]rotaxanes ( 1⋅ 4 PF₆ and 2⋅ 4 PF₆) in which a π-electron deficient tetracationic cyclophane, cyclobis(paraquat-p-phenylene) (CBPQT⁴⁺) ring, shuttles back and forth between two π-electron-rich naphthalene (NP) stations by making the passage along an ethynyl-phenylene-(PH)-ethynyl or butadiyne rod, are described. The [2]rotaxanes were synthesized by using the clipping approach to template-directed synthesis, and were characterized by NMR spectroscopic and mass spectrometric analyses. ¹H NMR spectra of both [2]rotaxanes show evidence for the formation of mechanically interlocked structures, resulting in the upfield shifts of the resonances for key protons on the dumbbell-shaped components. In particular, the signals for the peri protons on the NP units in the dumbbell-shaped components experienced significant upfield shifts at low temperatures, just as has been observed in the flexible [2]rotaxanes. Interestingly, the resonances for the same protons did not exhibit a significant upfield shift at 298 K, but rather only a modest shift. This phenomenon arises from the much reduced binding of the ethynyl-NP unit compared to the 1,5-dioxy-NP unit. This effect, in turn, increases the shuttling rate when compared to the 1,5-dioxy-NP-based rotaxane systems investigated previously. The kinetic and thermodynamic data of the shuttling behavior of the CBPQT⁴⁺ ring between the NP units were obtained by variable-temperature NMR spectroscopy and using the coalescence method to calculate the free energies of activation (ΔG_c^≠) of 9.6 and 10.3 kcal mol⁻¹ for 1⋅ 4 PF₆ and 2⋅ 4 PF₆, respectively, probed by using the rotaxane's α-bipyridinium protons. The solid-state structure of the free dumbbell-shaped compound ( 3 ) shows the fully rigid ethynyl-PH-ethynyl linker with a length (8.1 Å) twice as long as that (3.8 Å) of the butadiyne linker. Full-atomistic simulations were carried out with the DREIDING force field (FF) to probe the degenerate molecular shuttling processes, and afforded shuttling energy barriers (ΔG^≠=10.4 kcal mol⁻¹ for 1⋅ 4 PF₆ and 2⋅ 4 PF₆) that are in good agreement with the experimental values (ΔG_c^≠=9.6 and 10.3 kcal mol⁻¹ for 1⋅ 4 PF₆ and 2⋅ 4 PF₆, respectively, probed by using their α-bipyridinium protons).     

Relationship between the positive temperature coefficient of resistivity and dynamic rheological behavior for carbon black‐filled high‐density polyethylene

Studies on the relationship between resistivity and dynamic rheological properties of carbon black‐filled high‐density polyethylene (CB/HDPE) composites were carried out. Change of resistivity ρ is associated with the dynamic modulus before the positive temperature coefficient/negative temperature coefficient (PTC/NTC) transition temperature. When the temperature approaches the melting point of HDPE, ρ increases rapidly with a decreasing modulus, corresponding to PTC transition. The resistivity‐dynamic viscoelasticity relationship in the PTC region can be divided into two parts in which the changes of ρ with storage modulus G′ and loss modulus G″ can be described by the scaling laws given by the critical storage modulus and loss modulus G′_c and G″_c; adjustable parameters ρ′_1c, ρ′_2c, ρ″_1c and ρ″_2c; and nonlinear exponents n and m, respectively. The accordance between the experimental data and the scaling functions of the dimensionless quantities (G′/G′_c ? 1) and (G″/G″_c ? 1) in the PTC transition region suggests that the ρ jump may be the result of a modulus‐induced percolation. G′_c and G″_c increase, but the four scaling resistivitis, ρ′_1c, ρ′_2c, ρ″_1c, and ρ″_2c, decrease with increasing CB concentration, implying that the microstructure change of the composites is the determinant factor for the PTC behavior and the resistivity‐dynamic modulus relationship. However, ρ′_2c and ρ″_2c exhibit no scaling dependence. It is suggested that a threshold concentration exists for the modulus of the composites on the basis of examining the plot of both G′_c and G″_c against CB concentration. The scaling laws G′ ～ Φ^x and G″ ～ Φ^y hold for the concentration dependence of the critical modulus when Φ > Φ_c and the estimated values of x and y are 1.10 ± 0.10 and 0.89 ± 0.29, respectively. The resistivity‐dynamic modulus can shift to form a master curve. The horizontal factors a_G′ and a_G″ and the vertical factors a′ and a″ are relevant to the concentration dependence of the dynamic modulus or PTC behavior. It is believed that the former would be involved in changing the mechanical microstructure formed by the complicated interaction of CB particle and polymer segments, and the latter would be involved in the overall changes of conducting a network during the PTC transition region. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 983–992, 2003     

Infrared spectroscopy of ethylene–vinyl chloride copolymers

This paper continues an investigation into the ethylene–vinyl chloride copolymers prepared by partial reduction of poly(vinyl chloride). The infrared spectra of the copolymers have been obtained and the individual resonances assigned. Each infrared band has been quantitatively analyzed in terms of peak position (cm^?1) and intensity, and correlations with the sequence microstructure (dyad, triads, etc.) have been determined. The infrared resonances have been found to be sensitive to long sequences; i.e., (V)_x or (E)_x where x ≥ 10. Sequences of up to 10–15 monomer units were seen to affect the position (cm^?1) and intensity of C? H stretching and bending frequencies. Methylene rocking bands between 850 and 700 cm^?1 were observed to be sequence dependent with ? V(E)_xV? resonanting at 860, 750, or 730 cm^?1 for x = 0, 1 and 2, or ≥3, respectively. The C? Cl stretching resonances, which are well known for their conformational complexity in pure PVC, were found to be dominated by sequence length effects reducing to two bands at 665 and 610 cm^?1 characteristic of and isolated ? CH? Cl unit in a long methylene chain.     

Relating fracture energy to entanglements at partially miscible polymer interfaces

A new model has been developed to calculate the areal chain density of entanglements (Σ_eff) at partially miscible polymer–polymer interfaces. The model for Σ_eff is based on a stochastic approach that considers the miscibility of the system. The values agree between Σ_eff calculated from the model and literature values for the reinforced interfaces. Using Σ_eff calculated from the model, the interfacial width, and the average distance between entanglements, an equation for the fracture energy of nonreinforced polymer interfaces is proposed. This equation is used to model the transition from chain pullout to crazing. As a function of system miscibility, the model for Σ_eff also accurately predicts a maximum in mode I fracture energy (G_c) as a result of the transition from gradient‐driven to miscibility‐limited interdiffusion, which is observed experimentally. As Σ_eff increases, the fracture energy increases accordingly. Compared with a recent model developed by Brown, the new model correctly predicts a reduced G_c (attributed to chain pullout) when the interfacial width is less than the average distance between entanglements. Theoretical predictions of the change in fracture energy with respect to interfacial width agree with the experimental measurements. Finally, it is postulated that the use of a miscibility criterion for G_c may reveal the universal nature of the pullout to crazing transition. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2292–2302, 2002     

Influences of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile solutions around the sol-gel threshold

Viscoelastic experiments were performed to study the influence of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile (PAN) solutions around the sol-gel threshold. The dynamic critical parameters around the sol-gel threshold were determined using dynamic rheometer. The sol-gel transition takes place at a critical gel temperature at which the scaling law of G′(ω) ∼ G″(ω) ∝ ωⁿ holds, allowing an accurate determination of the critical gel temperature by means of the frequency independence of the loss tangent. Although the gel points of PAN solutions increase with increasing H₂O content, the results show that the scaling exponent n at the gel point is found to be universal for all ternary PAN solutions, which is independent of temperature and H₂O content, indicating the similarity of the fractal structure in the critical PAN gels. The gelation of ternary PAN solutions induced by adding a nonsolvent and by decreasing the temperature is demonstrated to be a thermoreversible process, which implies that the PAN gels are physical gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2637–2643, 2008     

Effect of nematic ordering on the elasticity and yielding in disordered polymeric solids

The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τ_Y/G between the shear yield strength τ_Y and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τ_Y/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769     

Compression elastic modulus of neutral,ionic, and amphoteric hydrogels based on N‐vinylimidazole

Several hydrogels of N‐vinylimidazole and sodium styrenesulfonate have been prepared by radical cross‐linking copolymerization in aqueous solution, using N,N′‐methylene‐bisacrylamide as crosslinker. Depending on composition, these hydrogels were neutral, amphoteric, cationic or anionic. Compression‐strain measurements were performed on samples as‐synthesized and swollen in deionized water or in acid aqueous solutions, with and without salt. It was thus found that the cross‐linking densities determined by compression measurements on as‐synthesized samples are in good accordance with those calculated by means of the model of polymer networks with pendant vinyl groups. A non‐Gaussian parameter (β) was introduced to explain that the elastic moduli (G) of samples swollen at equilibrium are larger than predicted by the Gaussian model. The β values of the neutral or ionized systems increase with swelling and fall into a single curve, which denotes a common behavior. Swelling has two opposite effects on G; on the one hand G decreases because the polymer volume fraction diminish and the system shifts from the affine limit to the phantom one; on the other, β increases and contributes to increasing G. The balance of those two opposite effects determines the variation of G with swelling. The possible contribution of ionic crosslinks to ν_e for the polyampholyte and for the polycation wearing divalent counteranions was discussed. A peculiar system is poly(sodium styrenesulfonate), whose cross‐linking density is much lower than expected. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1078–1087, 2009     

The superposition of small deformations on large deformations: Measurements of the incremental relaxation modulus for a polyisobutylene solution

The incremental relaxation modulus ΔG(t) for a concentrated solution of polyisobutylene has been determined from step-shear experiments in which a small deformation Δγ was superimposed on a large deformation γ₁; ΔG(t) was found to decrease with increasing γ₁ and to increase with the time t_e after the imposition of the large deformation. It was also observed that the “apparent relaxation specturm” associated with δG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic relaxation modulus G(t). The results are well described by the nonlinear constitutive equation of the BKZ elastic fluid theory.     

Saturated vapor pressure of individual substance. Supplement to interpretations and procedures for processing experimental polythermal data

A universal (that is, actual for any reaction) interconnection between enthalpy (∆_r H), entropy (∆_r S), and Gibbs energy (∆_r G) was applied to the analysis of the formation of saturated vapor of individual condensed (liquid and solid) substances. This allowed us to specify the conceptual and metrological sense of thermodynamic parameters available for estimation within the framework of tensimetric investigations. Proposals for the procedures of experimental data processing were made. The informativity of the approach was illustrated by the example showing the results of processing two arrays of primary data obtained using the static and the flow methods for crystal hafnium(IV) dipivaloylmethanate.     

DFT plus PCM calculation for pairing specificity of Watson–Crick‐type bases in aqueous solutions

This study is aimed at explaining the preference for AT and CG pairings and the possible insertion of other tautomeric DNA base pairs such as G_enolT, that respect energetic and steric requirements including at least two hydrogen bonds and 11 ± 0.5Å distance between the 9‐CH₃ of purine and 5‐CH₃ of pyrimidine. The calculated free energy of formation ΔΔG at the DFT B3LYP/6‐31G*‐PCM/BEM level pointed out the CG and AT pairs as the most favored, followed closely by G_enolT, in good agreement with Michaelis–Menten first order kinetics (CG ≈ AT > G_enolT). Unusual DNA base pairs complexes such as AG (BEM) and CT (PCM) resulted to be stable, but it is very difficult to assume that they are likely to be included in the double strand DNA. The calculated enthalpy and dipole moments of isolated DNA bases agree well with experiment. The free energy of hydration, ΔG_hyd, was found to depend on the electrostatic term, while cavitation‐dispersion components are almost constant. The stability of DNA complexes in water resulted from PCM calculations is markedly influenced by the free energy of hydration. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

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.     

Electrical transport properties of liquid alloys

Two complementary mechanisms have been proposed for relatively high temperature superconductor MgB₂. While the first is the electron–phonon mechanism of BCS theory, advocated strongly by Pickett and co-workers, the second, by Bianconi et al., invokes Feshbach shape resonances. While we cannot presently discount the second mechanism, and while both proposals exploit the multiband nature of the electronic structure of MgB₂, we show here that five body-centred cubic (bcc) transition metals, whose superconducting transition temperature correlate intimately with elastic constants and therefore are plainly BCS-like in character, lie on a curve which has MgB₂ at the high T _c end. Any alternative mechanism to electron–phonon interaction in MgB₂ will need to account quantitatively for this circumstance.     

The influence of cytosine methylation on the chemoselectivity of benzo[a]pyrene diol epoxide‐oligonucleotide adducts determined using nanoLC/MS/MS

Benzo[a]pyrene is a major carcinogen implicated in human lung cancer. Almost 60% of human lung cancers have a mutation in the p53 tumor suppressor gene at several specific codons. An on‐line nanoLC/MS/MS method using a monolithic nanocolumn was applied to investigate the chemoselectivity of the carcinogenic diol epoxide metabolite, ( ± )‐(7R,8S,9S,10R)‐benzo[a]pyrene 7,8‐diol 9,10‐epoxide [( ± )‐anti‐benzo[a]pyrene diol epoxide (BPDE)], which was reacted in vitro with a synthesized 14‐mer double stranded oligonucleotide (5′‐ACCCG₅CG₇TCCG₁₁CG₁₃C‐3′/5′‐GCGCGGGCGCGGGT‐3′) derived from the p53 gene. This sequence contained codons 157 and 158, which are considered mutational ‘hot spots’ and have also been reported as chemical ‘hot spots’ for the formation of BPDE‐DNA adducts. In evaluating the effect of cytosine methylation on BPDE‐DNA adduct binding, it was found that codon 156, containing the nucleobase G₅ instead of the mutational hot spot codons 157 (G₇) and 158 (G₁₁), was the preferential chemoselective binding site for BPDE. In all permethylated cases studied, the relative ratio for adduction was found to be G₅? G₁₁ > G₁₃ > G₇. Permethylation of CpG dinucleotide sites on either the nontranscribed or complementary strand did not change the order of sequence preference but did enhance the relative adduction level of the G₁₁ CpG site (codon 158) approximately two‐fold versus the unmethylated oligomer. Permethylation of all CpG dinucleotide sites on the duplex changed the order of relative adduction to G₅? G₇ > G₁₁ > G₁₃. The three‐ to four‐fold increase in adduction at the mutational hot spot codon 157 (G₇) relative to the unmethylated or single‐stranded permethylated cases suggests a possible relationship between the state of methylation and adduct formation for a particular mutation site in the p53 gene. Using this method, only 125 ng (30 pmol) of adducted oligonucleotide was analyzed with minimal sample cleanup and high chromatographic resolution of positional isomers in a single chromatographic run. Copyright © 2009 John Wiley & Sons, Ltd.