Internal friction spectra of polymer materials in complex stressed states

A procedure for the quantitative characterization of complex stressed states and their effect on the relaxation properties of polymer materials has been proposed. Throughout the temperature interval where the thermal degradation of polymers can be ignored, three measurements runs for recording internal friction spectra Δ(T) are performed. As has been shown for cellulose diacetate and poly(vinylformals), a difference between attenuation decrements Δ₁(T)–Δ₂(T) for the initial samples and the same samples in the second measurement cycle reflects the presence of cryptoheterogeneity. This difference achieves its maximum values at temperatures close to the glass transition temperature T _α but becomes noticeable even at temperatures several tens of degrees lower than T _α.     

The elastic potential function of slightly compressible rubberlike materials

In order to obtain an analytical expression for the stored energy function W of slightly compressible rubberlike materials, two recent results are used to obtain a unified expression where Γ_i are a new set of invariants, and H(Γ₁,Γ₂) is the shear part of the stored energy function which is now assumed to be a separate symmetric function of the modified stretch ratio, λ = λ_i/I, i.e., Various analytical forms of h(λ) are proposed. Also, a straightforward transformation technique is formulated such that one can easily relate the stress-strain relation in terms of modified stretch ratio λ to the new invariants Γ_i. Thus, by a combination of the above equations and the transformation technique, one may readily determine the elastic strain energy function of slightly compressible materials from careful measurements of the volume change in multiaxial deformations.     

Optimal use of the recurrence relations for the evaluation of molecular integrals over Cartesian Gaussian basis functions

We consider the tree search problem for the recurrence relation that appears in the evaluation of molecular integrals over Cartesian Gaussian basis functions. A systematic way of performing tree search is shown. By applying the result of tree searching to the LRL2 method of Lindh, Ryu, and Liu (LRL) (J. Chem. Phys., 95 , 5889 1991), which is an auxiliary function-based method, we obtain significant reductions of the floating point operations (FLOPS) counts in the K⁴ region. The resulting FLOPS counts in the K⁴ region are comparable up to [dd|dd] angular momentum cases to the LRL1 method of LRL, currently the method requiring least FLOPS for [dd|dd] and higher angular momentum basis functions. For [ff|ff], [gg|gg], [hh|hh], and [ii|ii] cases, the required FLOPS are 24, 40, 51, and 59%, respectively, less than the LRL1 method in the K⁴ region. These are the best FLOPS counts available in the literature for high angular momentum cases. Also, there will be no overhead in either the K² or K⁰ region in implementing the present scheme. This should lead to more efficient codes of integral evaluations for higher angular momentum cases than any other existing codes. © 1993 John Wiley & Sons, Inc.     

The expansion of hydrogen states in Gaussian orbitals

The convergence properties of Gaussian orbitals are studied by considering a very simple system, the hydrogen atom. We have variationally optimized even-tempered basis sets containing up to 60 s functions for the ground state and the first excited S state of the hydrogen atom, to an accuracy of 10^–15E_h. In addition, we have freely optimized the exponents in basis sets containing up to 12 Gaussians. We have studied the convergence of the total energy, the kinetic energy, the extent of the atom as measured by r², and the Fermi-contact interaction at the nucleus in these basis sets as well as in basis sets augmented with additional diffuse or steep functions.     

The Gaussian potential: Bound states in the continuum?

Simple variational solutions to the problem of a single particle in a Gaussian potential well inN dimensions,N being positive and real, are investigated. The system exhibits locally bound states in the continuum, which are demonstrated to be artifacts of the variational procedure. The relevance of the conclusions to recent studies of the possible existence of bound states in the continuum is discussed.     

Mechanochemical preparation of molecular and supramolecular organometallic materials and coordination networks

This Dalton Perspective deals with solvent-free reactions taking place within solids or between solids or involving a solid and a vapour. The focus is on reactions involving organometallic and coordination compounds and occurring via reassembling of non-covalent bonding, e.g. hydrogen bonds, and/or formation of ligand-metal coordination bonds. It is argued that reactions activated by mechanical mixing of solid reactants as well as those obtained by exposing a crystalline solid to a vapour can be exploited to "make crystals", which is the quintessence of crystal engineering. It is demonstrated through a number of examples that solvent-free methods, such as co-grinding, kneading, milling of molecular solids, or reactions of solid with vapours represent viable alternative, when not unique, routes for the preparation of novel molecular and supramolecular solids as well as for the preparation of polymorphic or solvate modifications of a same species. The structural characterization of the products requires the preparation of single crystals suitable for X-ray diffraction, a goal often achieved by seeding.     

The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks

The microstructural basis of the characteristic nonlinear mechanics of biopolymer networks remains unclear. We present a 3D network model of realistic, cross-linked semiflexible fibers to study strain-stiffening and the effect of fiber volume-occupancy. We identify two structural parameters, namely, network connectivity and fiber entanglements, that fully govern the nonlinear response from small to large strains. The results also reveal distinct deformation mechanisms at different length scales and, in particular, the contributions of heterogeneity at short length scales.     

Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. VII. Stress-birefringence relations

Crosslinks are introduced by γ irradiation into 1,2-polybutadiene while strained in uniaxial extension near T_g with stretch ratio λ₀, thereby trapping a proportion of the entanglements originally present. The stress at any subsequent strain λ is accurately given by the sum σ_N + σ_x, where σ_N is the stress contributed by a trapped entanglement network with λ = 1 as reference and a Mooney–Rivlin stress-strain relation, and σ_x is that contributed by a crosslink network with λ = λ₀ as reference and neo-Hookean stress-strain relation. The birefringence is accurately given as δn = ?_Nσ_N + ?_xσ_x, where the ?'s are the respective stress-optical coefficients. From measurements at λ = λ₀ where σ_x = 0, ?_N can be determined separately. For polymer with 88% 1,2 microstructure, ?_N and ?_x are nearly equal and independent of irradiation dose, though strongly dependent on temperature. For polymer with (95–96)% 1,2, ?_N and ?_x are different (even opposite in sign) and dependent on dose. This behavior is associated with a side reaction of cyclization by the γ irradiation, which is inhibited by the 1,4 moiety in the polymer with lesser 1,2 content. It is responsible for residual birefringence in the state of ease (λ = λ_s) where σ_N = –σ_x and the stress is zero.     

Tunable cross-linked copolymer networks for improvement of physical performance

The ability to tune the physical properties of polymeric materials through the different compositions in copolymer networks is suitable for the strategy of materials accompanied by combined high mechanical strength and stretchability simultaneously. Here, we developed a practical and straightforward strategy of a copolymer network structure via controlling the compositions of the acrylic-based urethane copolymers of diurethane acrylate (DUA) and diurethane cyclic acrylate (DUCA) with hydrogen-bonds through photo-polymerization. The copolymer networks led to the development of a physically cross-linked structure between the amide groups of DUA and/or DUCA and the hydroxyl groups of pentaerythritol ethoxylate (PEEL) by hydrogen-bonds. Based on the rheological analysis, the composition of the copolymer networks had a significant effect on the control of physical properties and development of cross-linked structure and thus led to the tunable comprehensive properties including high elastic modulus, high chain mobility and high recovery performance with a higher proportion of DUCA in the copolymer networks. Consequently, the tunable copolymer networks based on the developed physically cross-linked structure can improve the elastic properties, recovery performance, and healing ability simultaneously, providing significant progress in the fields of coating and adhesive.     

Gaussian expansion method for molecular integrals of molecular properties

The finite Gaussian Expansion method for molecular integrals proposed by Taketa, O-ohata and Huzinaga has been extended to the integrals of molecular properties. The integral formulas of so-called moment, field and field gradient integrals have been derived. It has been numerically shown that in order to evaluate the field and the field gradient integrals based on Slater type orbitals, eight- or ten-term Gaussian expansions are sufficient but this method fails to attain sufficient effective numbers for the moment integrals.     

The ellipsoidal Gaussian basis in molecular orbital theory

The ellipsoidal Gaussian basis function used in a minimal valence atomic orbital representation is compared with the double-zeta spherical Gaussian basis orbital representation for some seventeen molecules made up of first row atoms and hydrogen. Except for acetylene the double-zeta basis gives consistently better total electronic energies and generally better property values than the optimized ellipsoidal single zeta basis. Difference molecular density contour maps comparing the two basis sets, as well as other one-electron property values, indicate that the ellipsoidal basis exaggerates the transfer of charge from the atomic regions to the interatomic and lone pair regions of molecules. Apparently, the forced complete elliptization of the valence atomic orbital in the single-zeta representation does not allow the basis set sufficient flexibility to simultaneously represent both the basically spherical atomic part of these orbitals and the non-spherical molecular bond formation. Other properties and aspects of the ellipsoidal Gaussian basis are also discussed.     

Liquid crystal polysiloxane networks as materials for molecular imprinting technology: memory of the mesomorphic organization

A novel approach to the synthesis of molecularly imprinted polymers via non-covalent linkages has been studied. It relies on the use of thermotropic side group liquid crystal polymer networks. The polysiloxane networks obtained after extraction of the template preserved the mesomorphic organization set up in the presence of the guest molecule. A first batch rebinding analysis was performed: this study revealed that the imprinted polymer has a much greater affinity for the template molecule than has the non-imprinted polymer, and a significant selectivity.     

Liquid crystal polysiloxane networks as materials for molecular imprinting technology: memory of the mesomorphic organization

A novel approach to the synthesis of molecularly imprinted polymers via non-covalent linkages has been studied. It relies on the use of thermotropic side group liquid crystal polymer networks. The polysiloxane networks obtained after extraction of the template preserved the mesomorphic organization set up in the presence of the guest molecule. A first batch rebinding analysis was performed: this study revealed that the imprinted polymer has a much greater affinity for the template molecule than has the non-imprinted polymer, and a significant selectivity.     

Green's function formalism coupled with Gaussian broadening of discrete states for quantum transport: application to atomic and molecular wires

A Green's function formalism incorporating broadened density of states (DOS) is proposed for the calculation of electrical conductance. In cluster-molecule-cluster systems, broadened DOS of the clusters are defined as continuous DOS of electrodes and used to calculate Green's function of electrodes. This approach combined with density functional theory is applied to the electrical transmission of gold atomic wires and molecular wires consisting of benzene-1,4-dithiolate, benzene-1,4-dimethanethiolate, 4,4(')-bipyridine, hexane dithiolate, and octane dithiolate. The B3LYP, B3PW91, MPW1PW91, SVWN, and BPW91 functionals with the LANL2DZ, CEP, and SDD basis sets are employed in the calculation of conductance. The width parameter was successfully determined to reproduce the quantum unit of conductance 2e(2)/h in gold atomic wires. The combination of the B3LYP hybrid functional and the CEP-31G basis set is excellent in reproducing measured conductances of molecular wires by Tao et al. [Science 301, 1221 (2003); J. Am. Chem. Soc. 125, 16164 (2003); Nano Lett. 4, 267 (2004)].     

Atomic and molecular intracules for excited states

Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.     

Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions

Recurrence relations are derived for the evaluation of two-electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient ??(?). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.     

The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations

A new algorithm for density-functional-theory-based ab initio molecular dynamics simulations is presented. The Kohn–Sham orbitals are expanded in Gaussian-type functions and an augmented-plane-wave-type approach is used to represent the electronic density. This extends previous work of ours where the density was expanded only in plane waves. We describe the total density in a smooth extended part which we represent in plane waves as in our previous work and parts localised close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localised and extended part can be treated separately, achieving a computational cost for the calculation of the Kohn–Sham matrix that scales with the system size N as O(NlogN). Furthermore, we are able to reduce drastically the size of the plane-wave basis. In addition, we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calculations and for ab initio molecular dynamics simulations. Received: 15 December 1998 /Accepted: 18 February 1999 /Published online: 14 July 1999     

Group transfer polymerization in the bulk: linear polymers and randomly cross-linked networks

Linear homopolymers and randomly cross-linked homopolymer networks of 2-(dimethylamino)ethyl methacrylate of various molecular weights (MWs) were synthesized by group transfer polymerization in the bulk. 1-methoxy-1-(trimethylsiloxy)-2-methyl propene was used as the initiator, while tetrabutylammonium bibenzoate served as the catalyst. Ethylene glycol dimethacrylate was the cross-linker used for the network synthesis at an 8-fold molar excess with respect to the initiator. Gel permeation chromatography in tetrahydrofuran was used to characterize the linear homopolymers in terms of their MW and molecular weight distribution (MWD). Although the experimental MWs did not match the theoretical MWs, they were reasonably close to them. The MWDs were rather broad with polydispersity indices ranging between 1.5 and 1.9. The monomer conversion was relatively high, ranging from 97% to 74% for theoretical degrees of polymerization (DPs) from 5 to 500. No polymerization was observed for an attempted DP of 1000. Networks with molar ratios of monomer to initiator (nominal DPs) from 5 to 200 were prepared, while an attempted synthesis with a nominal DP of 500 did not yield a network. The networks were characterized in terms of their degree of swelling in water and the effects of DP, pH, salt concentration and temperature were investigated.