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.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Molecular dimensions and melt rheology of an all‐aromatic liquid crystalline polymer

The molecular dimensions and melt rheology of a thermotropic all‐aromatic liquid crystalline polyester (TLCP) composed of p‐hydroxy benzoic acid, hydroquinone, terephthalic acid, and 2,4‐naphthalenedicarboxylic acid is examined. The Mark–Houwink exponent (α) of 0.95 is estimated for the TLCP. The persistence length estimated from molecular weight (M) and intrinsic viscosity ([η]) data using the Bohdanecky–Bushin equation is about 95 Å, whereas that estimated from light scattering data is 117 Å. These persistence lengths and the observed α value, both higher than those for flexible polymers, suggest that the present TLCP is a semirigid polymer. The zero shear melt viscosity (η₀) varies with approximately M⁶ for molecular weight M > 3 × 10⁴ g/mol; below this molecular weight, η₀ varies almost linearly with M. Widely different entanglement molecular weights (M_e) are predicted, depending on the method used; the plateau modulus estimates M_e of about 8 × 10⁵ g/mol, whereas the ratio of mean square end‐to‐end distance and molecular weight (〈R²〉₀/M) predicts M_e's either too small (0.33 g/mol) or too large (2.5 × 10⁶ g/mol), depending on the theory used. Although the change in the molecular weight dependency of melt viscosity appears to be associated with the onset of entanglement coupling of the semirigid molecules, its origin needs further investigation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2378–2389, 2001     

THE 31P NMR SPECTRA OF ISOMERIC DIAMINOHEXA-CHLOROCYCLOTETRAPHOSPHAZATETRAENES; EXAMPLES OF A2B2 AND AA'BB' SPIN SYSTEMS

Abstract

The ³¹P nmr spectra of 2,4- and 2,6-diamino-derivatives of octachlorocyclotetraphosphazatetraene, N₄P₄Cl₆(NR¹R²)₂ (R¹ = H, R² = Bu^t; R¹ = H, R² = CH₂Ph; R¹ = Me, R² = Ph), have been measured. The 2,4- and 2,6-isomers were analysed as AA'BB' and A₂B₂ spin systems respectively. In the 2,4-isomers the spin-spin couplings ²J(PNP) and ⁴J(PNPNP) were of opposite sign.     

Kinetics of methyl methacrylate and n‐butyl acrylate copolymerization mediated by 2‐cyanoprop‐2‐yl dithiobenzoate as a RAFT agent

The RAFT (co)polymerization kinetics of methyl methacrylate (MMA) and n‐butyl acrylate (BA) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was studied with various RAFT concentrations and monomer compositions. The homopolymerization of MMA gave the highest rate. Increasing the BA fraction f_BA dramatically decreased the copolymerization rate. The rate reached the lowest point at f_MMA ～ 0.2. This observation is in sharp contrast to the conventional RAFT‐free copolymerization, where BA homopolymerization gave the highest rate and the copolymerization rate decreased monotonously with increasing f_MMA. This peculiar phenomenon can be explained by the RAFT retardation effect. The RAFT copolymerization rate can be described by 〈R_p〉/〈R_p〉₀ = (1 + 2(〈k_c〉/〈k_t〉)〈K〉)[RAFT]₀)^?0.5, where 〈R_p〉₀ is the RAFT‐free copolymerization rate and 〈K〉 is the apparent addition–fragmentation equilibrium coefficient. A theoretical expression of 〈K〉 based on a terminal model of addition and fragmentation reactions was derived and successfully applied to predict the RAFT copolymerization kinetics with the rate parameters obtained from the homopolymerization systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3098–3111, 2007     

Relationship between fracture toughness and intrinsic deformation parameters in isotropic and flow‐oriented linear low‐density polyethylene

The fracture toughness of isotropic and flow‐oriented linear low‐density polyethylene (LLDPE) is evaluated by the Essential Work of Fracture (EWF) concept, with a special setup of CCD camera to monitor the process of deformation. Allowing for the molecular orientation, flow‐oriented sample, prepared via melt extrusion drawing, is stretched parallel (oriented‐0°) and perpendicular (oriented‐90°) to its original melt extrusion drawing direction, respectively. The obtained values of specific EFW w_e are 34.6, 10.2, and 4.2 N/mm for the oriented‐0°, isotropic and oriented‐90° sample, respectively. With knowledge of intrinsic deformation parameters deduced from uniaxial tensile tests, moreover, a relationship between specific EFW w_e the ratio of true yield stress to strain hardening modulus σ_ty/G is well established. It means that the fracture toughness of polyethylene is determined by both crystalline and amorphous parts, rather than by one of them. Moreover, the true yield stress seems to be nondecisive factors determining the fracture toughness of polyethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2880–2887, 2006     

Zur Reaktion von tert-Butyl-phosphaalkin mit Molybdänkomplexen

Reaction of tert -Butyl-phosphaalkyne with Molybdenum Complexes The reaction of tBuC≡P with [(CH₃CN)₃Mo(CO)₃] leads to the complex [Mo(CO)₄〈Mo(CO)₂(η⁴-P₃CtBu){η⁴-P₂(CtBu)₂}〉] 1 as well as to the alkyne complexes [Mo(CO)₄〈{P₃(CtBu)₂}{Mo(CO)₂(CtBu)}{η³-P₂(CtBu)₂}〉] 2 and [Mo(CtBu){η⁴-P₂(CtBu)₂(CO)}{η⁵-P₃(CtBu)₂}] 3 . All compounds are characterized by X-ray structural analysis, by NMR- and IR spectroscopy and by mass spectrometry. In complex 1 a 1,3-diphosphacyclobutadiene and a 1,2,4-triphosphacyclobutadiene are connected by two molybdenum carbonyl centres. In 2 a 1,3-diphosphacyclobutadiene is π- and a novel 1,2,4-triphospholyl ligand is σ-bonded at two Mo centres. A characteristic feature of 3 besides a π co-ordinated 1,2,4-triphospholyl ligand is a 3,4-diphosphacyclopentadienone as ligand, formed via CO insertion during the cyclodimerisation of two phosphaalkynes.     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

Unusual Bonding and Properties in Main Group Element Chemistry: Rational Synthesis,Characterization, and Experimental Electron Density Determination of Mixed‐Valent Tetraphosphetes

Five dispirocyclic λ³,λ⁵‐tetraphosphetes [{R₂Si(NR¹)(NR²)P₂}₂] (R¹ = R² and R¹ ≠ R²) are easily prepared in almost quantitative yields via photolysis of the respective bis(trimethylsilyl)phosphanyldiazaphosphasiletidines with intense visible light. These deep‐yellow low‐coordinate phosphorus compounds can be considered as the first higher congeners of the well‐known cyclodiphosphazenes. The tetraphosphetes are remarkably stable in air and show unexpected molecular properties related to the unique bonding situation of the central four‐π‐electron four‐membered phosphorus ring. The extent of rhombic distortion of the central P₄ ring is remarkable due to an unusually acute angle at the σ²‐phosphorus atoms. All of the P?P bonds are approximately equal in length. The distances are in the middle of the range given by phosphorus single and double bonds. The anisotropic absorption of visible light that can easily be observed in the case of the yellow/colorless dichroic crystals of [{Me₂Si(NtBu)(NtBu)P₂}₂] and the exceptional ³¹P NMR chemical shift of the σ²‐phosphorus atoms are the most remarkable features of the λ³,λ⁵‐tetraphosphetes. In the case of [{Me₂Si(NtBu)(NtBu)P₂}₂], the Hansen–Coppens multipole model is applied to extract the electron density from high‐resolution X‐ray diffraction data obtained at 100 K. Static deformation density and topological analysis reveal a unique bonding situation in the central unsaturated P₄ fragment characterized by polar σ‐bonding, pronounced out‐of‐ring non‐bonding lone pair density on the σ²‐phosphorus atoms, and an additional non‐classical three‐center back‐bonding contribution.     

Stress overshoot of polymer solutions at high rates of shear

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow were investigated for polystyrene solutions. The magnitudes of shear corresponding to these stresses, γ_σm and γ_Nm, for entangled as well as nonentangled solutions were universal functions of γ˙τ_eq, respectively, and γ_Nm was approximately equal to 2γ_σm at any rate of shear, γ˙. Here τ_eq = τ_R for nonentangled systems and τ_eq = 2τ_R for entangled systems, where τ_R is the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. Only concentrated solutions exhibited stress overshoot at low reduced rates of shear, γ˙τ_eq < 1. The behavior at very low rates, γ˙τ_eq < 0.2, was consistent with the Doi–Edwards tube model theory for entangled polymers. At high rates, γ˙τ_eq > 1, γ_σm and γ_Nm were approximately proportional to γ˙τ_eq. At very high rates of shear, the peak of σ is located at t = τ_R, possibly indicating that the polymer chain shrinks with a characteristic time τ_R in dilute solutions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1917–1925, 2000     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimensions 〈R²〉 of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration ϕ is enhanced in a slit relative to the bulk. The global dimensions of chains also change with ϕ in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on the three‐dimensional surface 〈R²〉(D,ϕ) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions 〈R_y²〉/〈R_x²〉, reaches high values at strong confinements, where coils form quasi‐two‐dimensional pancakes. The concentration‐induced reduction of the global chain dimensions in good solvents is almost fully transmitted to the parallel component 〈R_y²〉. The computed effects of concentration and confinement were compared with the predictions of mean‐field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end‐to‐end distance R perpendicular and parallel to the plates, W (R_x) and W (R_y), were calculated. The function W (R_x) combined with the concentration profile ϕ (x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution functions W (R_x) and W (R_y), the highly anisotropic force‐elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.     

Viscoelasticity of textile fibers at finite strains

Experimental data obtained from stress–strain curves of five different textile fibers, at a series of different, constant strain rates covering a range of 6^1/2 decades have been used to study two methods of nonlinear viscoelastic analysis proposed elsewhere. According to the first of these, time and strain effects are factorizable so that stress σ, strain ε and time t are related by the equation σf₁(ε)/ε = f(t),. This is shown to be unsatisfactory with the present materials, but an empirical modification to σf₁(ε)/ε = f₂(ε) + f(t) is satisfactory. According to the second, general nonlinear viscoelastic behavior can be described by an equation which reduces to the form σ/ε = F₁(t) + εF₂(t) + ε²F₃(t) + when applied to extension at a constant strain rate. This series is shown to be strongly divergent except at fairly small stains. In fact, if it is truncated after about three terms, which are as many as can be estimated with any significance in the present experiments, it is applicable only to strains of about 3–4% and less. Numerical techniques which enable standard statistical procedures to be used have been devised to perform the above analyses and are described in detail.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

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 theoretical analysis of rheodielectric response of type‐A polymer chains

For type‐A polymer chains having type‐A dipoles parallel along the chain backbone (such as cis‐polyisoprene), a theoretical analysis was conducted for the rheodielectric response to relate this response to the chain dynamics. The rheodielectric response in the shear gradient direction (y direction) under steady shear was analyzed on the basis of a Langevin equation. It turned out that the relaxation time is exactly the same for the rheodielectric relaxation function and the end‐to‐end vector autocorrelation function defined in the shear gradient direction and that the relaxation mode distribution also coincides for these functions at least up to second order of the shear rate (corresponding to the lowest order of nonlinearities of these functions). Consequently, the Green‐Kubo theorem holds satisfactorily, and the rheodielectric intensity is proportional to the squared chain size in y direction, 〈R〉, averaged over the time‐independent conformational distribution function under steady shear. The situation is more complicated under large amplitude oscillatory strain (LAOS) because the conformational distribution function f_LAOS is synchronized with LAOS to oscillate at the LAOS frequency, Ω. The rheodielectric response under LAOS was found to detect this oscillation of f_LAOS being coupled with the oscillation of the electric field, E(t) = E₀sin ωt, and thus, split into a series of components oscillating at frequencies ω and ω ± βΩ (β = 1, 2, …). Consequently, the rheodielectric intensity under LAOS, evaluated from the component oscillating at ω, is no longer proportional to 〈R〉. However, the relative mode distribution and relaxation time of this component can be directly related to those of the end‐to‐end vector correlation averaged over a nonoscillatory part of f_LAOS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1039–1057, 2009