Predicting the formation,structure and elastomeric properties of end‐linked polymer networks

The molecular structures and macroscopic properties of network polymers depend more closely on reactant structures (molar masses, functionalities, chain flexibilities) and reaction conditions (dilution, proportions of different reactants) than do those of linear polymers. To understand and predict elastomeric properties, it is important to be able to model, statistically, the molecular growth leading to network formation. A new Monte‐Carlo network polymerisation algorithm has been developed, using Flory‐Stockmayer random‐reaction statistics with intramolecular reaction allowed on a correctly weighted basis. The algorithm simulates, as a function of extent of reaction, the formation of all of the connections in a reaction mixture and counts all the ring structures. It also enables polymerisations and network structures to be simulated efficiently up to complete reaction. Comparisons of predictions from the algorithm with experimental data from end‐linking polymerisations show the importance of accounting for the whole distribution of sizes of ring structure in determining reductions in elastic modulus. An important new factor, x, is introduced in the interpretation of experimental data. It is the fractional loss in elasticity per chain in loop structures larger than the smallest.     

Network formation and properties: Rate theory description of effects of ring formation on elastic shear modulus of RA2 + RB3 networks

The rate theory of RA₂+RB₃ polymerization has been developed to enable the concentrations of the smallest inelastic loops and the resulting reductions in elastic shear modulus at complete reaction to be evaluated. Reduction in modulus is expressed as M_c/M°_c, the effective molar mass of chains between elastically active junction points (M_c) relative to that for the perfect network for given reactants (M°_c). Calculations have been carried out for stoichiometric reaction mixtures and the concentration of loops is characterized by λ, a ring-forming parameter. λ = P_ab/C_Ao, where C_Ao is the initial concentration of A-groups and P_ab = (3/(2πvb²))^3/2/N_Av, with v the number of bonds in the chain forming the smallest loop, b the effective bond length of the chain, and N_Av Avogadro's number. P_ab is equal to the mutual concentration, assuming Gaussian statistics, of the A- and B-groups at the two ends of the linear sub-chain of v bonds. Loop formation increases as λ increases, that is, as the initial concentration of reactive groups (C_Ao) decreases, or, at constant C_Ao, as the molar mass of reactants (v) or their chain stiffness (b) decreases. Comparison with existing experimental data on two series of polyurethane networks formed from hexamethylene diisocyanate and two polyoxypropylene triols at different initial dilutions shows that the values of P_ab decrease with increases in initial dilution and molar mass of triol. The decrease with molar mass is entirely accounted for by changes in v and the variation with dilution shows that the approximation of counting only smallest loops improves as dilution increases.     

Concept of hard clusters in the interpretation of thermal and mechanical properties of polyurethane and polyurethane acrylate networks

Polyurethane (PU) and polyurethane acrylate (PUA) networks based on hydroxyl-terminated polycaprolactone (PCL), 1,3-bis-2,2′(2-isocyanatopropyl)benzene (m-TMXDI), trimethylolpropane (TMP) for PU or hydroxyethyl methacrylate (HEMA) for PUA were synthesized. Glass transition temperature, T_g, dynamic mechanical relaxation, α, and equilibrium tensile modulus, E′, were measured to compare the two kinds of networks. To explain thermal and mechanical properties of networks, the concept of hard clusters has been introduced. PU networks exhibit a single-phase structure with modulus and T_g dependent on the concentration of elastically active network chains (EANC) per unit volume calculated by considering hard crosslink clusters. The rigidity of the clusters comes from small diisocyanate and trimethylolpropane units connected by urethane bonds. They are embedded in a continuous soft phase of macrodiol urethane. Physical equivalence between several kinds of network models has been demonstrated for full conversion of isocyanate-alcohol reaction. PUA networks exhibit thermodynamically one-phase structures that become a two-phase structure for high molar mass of macrodiol when the molar fraction of isocyanate groups increases. For those networks, the calculated modulus considering clusters based on polyacrylate chains seems to be a good way to approach the experimental value of the equilibrium modulus. For the same molar ratio of OH to NCO groups the range of dynamic moduli is larger for PUA than for PU. This difference can be explained by a different concentration of crosslinks in the networks. © 1996 John Wiley & Sons, Inc.     

Modeling viscoelastic properties of triblock copolymers: A DPD simulation study

Gel systems based on self‐assembled, amphiphilic ABA triblock copolymers in midblock‐selective solvent form stable, spatially extended networks with controllable morphology and tunable viscoelastic behavior. In this work, we systematically evaluate the mechanical properties of these gels using morphology calculations, and a nonequilibrium oscillatory shear technique based on the dissipative particle dynamics (DPD) method. Our simulations demonstrate that low molecular weight triblock copolymers with incompatible blocks self‐assemble into micelles connected with bridges and loop‐like chains comprised of the solvent‐selective polymer midblocks. The fraction of bridges, ?_b, generally increases with increasing relative volume of the midblock, x, defined as the ratio of midblock and endblock volumes ( ). For our model, ?_b reaches a plateau at approximately x > 9 for a strongly selective solvent. At this limit, the value of ?_b increases from 0.40 to about 0.66 as the copolymer concentration, c, increases from 0.2 to 0.5; however, this increase is less significant at higher concentrations. The elastic response of the gel studied here is comparable with the Rouse modulus. The elastic modulus increases with polymer concentration, and it exhibits a broad peak within 6 < x < 12. Finally, we present an approximate method to predict the elastic modulus of unentangled ABA triblock copolymers based solely on the morphology of the micellar gel, which can be gleaned from equilibrium DPD simulations. We demonstrate that our simulation results are in good qualitative agreement with other theoretical predictions and experimental data. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 15–25, 2010     

First principles study of structural,electronic, elastic and thermal properties of YX (X = Cd,In, Au,Hg and Tl) intermetallics

The structural, electronic, elastic and thermal properties of YX (X = Cd, In, Au, Hg and Tl) intermetallic compounds crystallizing in B₂-type structure have been studied using first principles density functional theory within generalized gradient approximation (GGA) for the exchange correlation potential. Amongst all the YX compounds, YIn is stable in distorted tetragonal (P4/mmm) CuAu-type structure at ambient pressure with very small energy difference of 0.00681 Ry. but it undergoes to CsCl-type (B₂ phase) structure at 23.3 GPa. Rest of the compounds are stable in B₂ structure at ambient condition. The values of elastic moduli as a function of pressure are also reported. The ductility of these compounds has been analyzed using the Pugh rule. Our calculated results indicate that YTl is the most ductile amongst all the B₂-YX compounds. YAu is the hardest and less compressible compound due to the largest bulk modulus. The elastic properties such as Young's modulus (E), Poisson's ratio (σ) and anisotropic ratio (A) are also predicted. The anisotropic factor is found to be unity for YHg which shows that this compound is isotropic.     

Elasticity and structure of chemically crosslinked polyurethanes

A combination of electron-microscopy, light-scattering, and stress-birefringence studies on chemically crosslinked polyurethanes point toward the existence of rodlike regions (“bundles”), approximately 3000–8000 Å in length and involving about 5% of the volume, in which molecular orientations are correlated. The elastic behavior of these networks—as indeed that of most rubberlike networks—deviates substantially from the Gaussian behavior. The empirical representation of the data in Mooney-Rivlin plots yields C₁ and C₂ constants which depend on the type of imposed strain. It is thus impossible to identify C₁ with the Gaussian behavior and C₂ with the deviation there-from. Instead, it is found that the elastic behavior can be adequately described if it is assumed that, as a result of the bundle structure, about 5% of the segments of each chain are not free to assume the normal random-walk configurations. The determination of the number of chains in the network from the elastic behavior remains ambiguous, however, and the behavior upon swelling is not (yet) adequately reproduced by the theory. It is conceivable that in many cases deviations from Gaussian elasticity behavior may be caused by an intermolecular structuring effect, rather than by various minor deficiencies in the Gaussian model for the single chain statistics or by anisotropic excluded volume effects, as has been proposed in the past. In the present case, the amount of bundle structure, as well as the C₂/C₁ values, increase with the number of urethane couplings per chain, and this suggests that the interaction of the highly polar urethane couplings is responsible for the structuring. In other networks one often finds a dependence of C₂/C₁ on the previous history of the sample, which suggests that an accidentally trapped order may be responsible for the elastic behavior.     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

Electrocrystallization of Tetra‐ and Hexa‐coordinated Silver(II) Compounds Based on 4,4′‐Dimethyl‐2,2′‐Bipyridine Ligand – Single Crystal Structures and Magnetic Studies

In this paper we report on the potential dependent electrocrystallization of [Ag(4,4′‐dimethyl‐2,2′‐bipyridine)₂(NO₃)₂] ( 1 ) and Ag(4,4′‐dimethyl‐2,2′‐bipyridine)(NO₃)₂ ( 2 ) from the same electrolytic bath. Thus it has been shown for the first time that the coordination number of silver ion to ligands can be tuned by the electrocrystallization potential. The single crystal structure analysis [ 1 : C2/c, a = 18.6308(15), b = 14.5708(12), c = 11.5867(10) Å, β = 126.5910(10)°, Z = 4, R = 3.9 %] [ 2 : P2₁/c, a = 8.5865(11) b = 11.0157(14) c = 16.4554(10) Å, β = 111.102(10), Z = 4 , R = 3.5 %] show divalent silver to be in an approximately square planar surrounding. Both complexes are paramagnetic following Curie's law with magnetic moments of 1.86 μ_B and 1.72 μ_B respectively.     

Structural,elastic and electronic properties of β′ phase precipitate in Mg–Gd alloy system investigated via first-principles calculation

The β′ phase precipitate in Mg–Gd alloy system has been investigated by means of first-principles calculation within the generalized gradient approximation. The lattice parameters are determined theoretically by structural optimization of full relaxation, and the Mg₇Gd is found to be energetically more stable compared with the Mg₁₅Gd from the calculated formation energy. The nine independent elastic constants are calculated, indicating the proposed Mg₁₅Gd structure in literature is mechanically unstable. Then the polycrystalline bulk modulus B, Young's modulus E, shear modulus G, Poisson ratio ν of Mg₇Gd are gained by the Voigt–Reuss–Hill (VRH) approximation. The ductility and plasticity, especially elastic anisotropy are discussed in details. Based on the electronic density of states and charge density distribution, the covalent bonding and metallic bonding are exhibited in Mg₇Gd compound. Last, the Debye temperature is also calculated for the investigation in the future.     

Effect of composition changes on properties and defect structure of crystalline Sm-doped ZrO<Subscript>2</Subscript>

Polymorphous structure, electrical conductivity, absorption coefficient, refractive index, and mechanical characteristics of crystalline system ZrO₂ + x Sm₂O₃ (x = 4–43 mol %) is investigated. Vickers microhardness is investigated by the well-known quasi-static indentation method. Plastic microhardness and the effective elastic modulus are studied by the depth-sensing indentation technique. Special attention is devoted to the ordered defect fluorite structure, pyrochlore phase Sm₂Zr₂O₇, observed for x = 43 mol %. Potential applications of the investigated system are discussed. Published in Russian in Elektrokhimiya, 2007, Vol. 43, No. 4, pp. 402–411. The text was submitted by the authors in English.     

Structural, electronic and elastic properties of MAX phases M2GaN (M = Ti, V and Cr)

Based on first-principles total energy calculations, we have investigated the systematic trends for structural, electronic and elastic properties of the MAX phases M₂GaN depending on the type of M transition metal (M are Ti, V and Cr). The optimized zero pressure geometrical parameters: the two unit cell lengths (a, c), the internal coordinate z and the bulk modulus are calculated. The results for the lattice constants are in agreement with the available experimental data. The band structures show that all studied materials are electrical conductors. The analysis of the site-projected l-decomposed density of states shows that bonding is due to M d-N p and M d-Ga p hybridizations. The elastic constants are calculated using the static finite strain technique. The shear modulus C₄₄, which is directly related to the hardness, reaches its maximum when the valence electron concentration is in the range 10.5–11.0. The isotropic elastic moduli, namely, bulk modulus (B), shear modulus (G), Young's modulus (E) and Poisson's ratio (σ) are calculated in framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline M₂GaN aggregates. We estimated the Debye temperature of M₂GaN from the average sound velocity. This is the first quantitative theoretical prediction of the electronic structures, and elastic constants and related properties for Ti₂GaN, V₂GaN and Cr₂GaN compounds that require experimental confirmation.     

Electrochemical Synthesis and Structure Analysis of Neocoenzyme B12 – An Epimer of Coenzyme B12 with a Remarkably Flexible Organometallic Group

In neocoenzyme B₁₂ (=(5′-deoxy-5′-adenosyl)-13-epicob(III)alamin; 5 ), an epimer of coenzyme B₁₂ ( 1 ), the organometallic group and a propanamide side chain of the vitamin-B₁₂ ligand compete for the same region in space. Interesting consequences for structure and organometallic reactivity of this isomer of 1 are to be expected. Neocoenzyme B₁₂ ( 5 ; 89% yield) and methyl-13-epicobalamin ( 6 ; 88% yield) were prepared from neovitamin B₁₂ ( 4 ) by electrochemical means (Fig. 3). The solution structure of the organometallic neovitamin-B₁₂ derivative 5 was analyzed by homonuclear and heteronuclear NMR spectroscopy. Comparison of the structures of 1 and 5 informed on the structural consequences of the epimerization at C(13) and revealed a remarkable flexibility of the organometallic group in 5 . In 5 , both sterically interacting functionalities (organometallic group and propanamide side chain at C(13)) adapt their conformations dynamically to avoid significant mutual clashes. As one consequence of this structural adaptation, the major conformations of 5 feature counterclockwise and clockwise reorientations of the organometallic ligand with respect to its crystallographically determined position in coenzyme B₁₂ ( 1 ). One of the dominant conformers of 5 exhibits an orientation of the organometallic functionality similar to that found in the crystal structure of the coenzyme-B₁₂-dependent methylmalonyl CoA mutase. The present NMR study also revealed the significant population of syn-conformers of the organometallic adenosine group, another remarkable feature of the solution structure of 5 .     

Formation of T‐Shaped versus Charge‐Transfer Molecular Adducts in the Reactions Between Bis(thiocarbonyl) Donors and Br2 and I2

The reactions of 4,5,6,7‐tetrathiocino‐[1,2‐b:3,4‐b′]‐1,3,8,10‐tetrasubstituted‐diimidazolyl‐2,9‐dithiones (R₂,R′₂‐todit; 1 : R=R′=Et; 2 : R=R′=Ph; 3 : R=Et, R′=Ph) with Br₂ exclusively afforded 1:1 and 1:2 “T‐shaped” adducts, as established by FT‐Raman spectroscopy and single‐crystal X‐ray diffraction in the case of complex 1? 2 Br₂. On the other hand, the reactions of compounds 1 – 3 with molecular I₂ provided charge‐transfer (CT) “spoke” adducts, among which the solvated species 3? 2 I₂ ? (1?x)I₂ ? x CH₂Cl₂ (x=0.94) and ( 3 )₂ ? 7 I₂ ? x CH₂Cl_2, (x=0.66) were structurally characterized. The nature of all of the reaction products was elucidated based on elemental analysis and FT‐Raman spectroscopy and supported by theoretical calculations at the DFT level.     

Ab initio calculations of the structural and elastic properties of CoSi2

Under GGA, the geometry, energy, electronic structure, and elastic properties of the CoSi₂ have been investigated by using ab initio plane-wave ultrasoft pseudopotential method. The calculated equilibrium lattice parameter a and elastic stiffness constants c ₁₁, c ₁₂, and c ₄₄ are in better agreement with the experimental values than those obtained by both the VAMP and FLAPW with LDA. For engineering and technological applications, the isotropic elastic properties, including the shear modulus G, the bulk modulus B, Young’s modulus E, and Poisson’s ratio , are also calculated for polycrystalline CoSi₂ with Voigt, Reuss, and Hill approximations. The lower Poisson’s ratio of 0.327 means an increase in the volume is associated with the uniaxial tensile deformation and the higher ratio of bulk modulus to shear modulus B/G of 2.56 indicates the ductility of CoSi₂ which is in accordance with the metallic property of CoSi₂ obtained by the density of states.     

Prediction of structure and properties of end-linked networks

Rate theory has been developed for RA₂+RB₄ polymerisations including intramolecular reaction and the general behaviour of RA₃, RA and stoichiometric RA₂+RB₃ and RA₂+RB₄ polymerisations compared regarding the moduli of networks formed at complete reaction. The predictions for RA₂+RB₃ and RA₂+RB₄ polymerisations are used to analyse existing experimental data on gel points and moduli in polyurethane polymerisations and networks. By fitting experimental gel points, improved predictions of moduli at complete reaction are achieved.     

Controlling molecular mobility and ductile–brittle transitions of polycarbonate copolymers

To control molecular mobility and study its effects on mechanical properties, we synthesized two series of poly(ester carbonate) and polycarbonate copolymers with different linkages: (B_xt)_n (x = 3, 5, 7, 9) and (B_xT)_n (x = 1, 3, 5, 7, 9), where t represents the terephthalate, T represents the tetramethyl bisphenol A carbonate linkages, and B is the conventional bisphenol‐A (BPA) carbonate. These two series of materials have distinct differences in their relaxation behaviors and chain mobility, as indicated by the π‐flip motion of the phenylene rings in the B_x blocks. Uniaxial tensile tests of the copolymers indicate that the brittle–ductile transition (BDT) temperatures of the copolymers are correlated to whether the γ‐relaxation peaks due to the B_x sequence is fully established. The materials possessing more fully established low‐temperature γ peaks give rise to a lower BDT. Also, the locations of the γ peaks are correlated to the ring flips of the B_x blocks of polymer chains. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1730–1740, 2001     

Stress relaxation under large step equibiaxial elongation for low‐density polyethylene

The stress relaxation under large step equibiaxial elongation for low‐density polyethylene with long‐chain branches revealed that the time‐strain separability holds in relaxation modulus G_B(t, ε_B), and damping function h_B(ε_B) exhibits weaker equibiaxial elongational strain ε_B dependence than that predicted by the Doi–Edwards theory without the independent alignment approximation. Dependencies of damping function h(γ) for step shear deformation and h_B(ε_B) on stretch ratio α of polymer contour length and orientation of a polymer chain in direction of the maximum orientation were evaluated, and it was found that the α dependencies of h(γ) and h_B(ε_B) are different, whereas dependencies of h(γ) and h_B(ε_B) on the orientation coincide fairly well. These results indicate that the damping is dominated by the chain orientation rather than α. This implies that withdrawal of long‐chain branches into tube of a backbone chain occurs when the orientation of the long‐chain branches is large and friction force against the branch point withdrawal is small. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1275–1284, 2009     

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

Self‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with R_g ∝ lequation/tex2gif-stack-1.gif.

Conformation of a polyion chain for l_B = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.     

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     

Agarose Sols and Gels Revisited

Agarose sols have been seen for long as solutions of flexible chains that, on cooling, produce thermoreversible gels through double-helix formation. Investigations of the chain conformation in the sol state by small-angle neutron scattering reveals instead a rigid chain with a very large persistence length (l_p > 9 nm). The chain cross-section radius and mass per unit length correspond to characteristics of helices as those described by Foord and Atkins. These results lead one to a reappraisal of the occurrence of double helices in the gelation process, as they rather suggest a transition of the type loose-single helix⇒tight single helix. Studies of gels from agarose/water/cosolvent where the cosolvent is Dimethyl Sulfoxide (DMSO), Dimethyl Formamide (DMF), and Methyl Formamide (MF) have led one to conclude on the formation of agarose/water/ cosolvent ternary complexes. The contrast variation method by neutron scattering gives further support to this assumption. Finally, determination of the gel nanostructure allows one to account for the two regimes observed for the variation of the elastic modulus vs concentration.