Curing theory of Af- Ag type free radical polymerization (III)

Evaluation of defects in the polymer network is important to characterize the polymer materials, in which there always exist the defects that affect the physical and chemical properties of polymer network. Taking A_f- A_g type nonlinear free radical polymerization as an example, one type of defects called dangling loops in the gel network is investigated by means of the statistical theory of polymeric reactions. The number of dangling loops and the probability of its formation are obtained by analyzing the polymer network structure in detail.     

Curing theory of A_f-A_g type free radical polymerization (Ⅲ)——The evaluation of network defects

Evaluation of defects in the polymer network is important to characterize the polymer materials, in which there always exist the defects that affect the physical and chemical properties of polymer network. Taking Af-Ag type nonlinear free radical polymerization as an example, one type of defects called dangling loops in the gel network is investigated by means of the statistical theory of polymeric reactions. The number of dangling loops and the probability of its formation are obtained by analyzing the polymer network structure in detail.     

Novel amphiphilic network polymers consisting of nonpolar,short primary polymer chains and polar,long crosslink units: Influence of characteristic dangling chains on swelling behavior of resulting amphiphilic gels

Novel amphiphilic network polymers consisting of nonpolar, short primary polymer chains and polar, long crosslink units were prepared, and the swelling behavior of resulting amphiphilic gels is discussed by focusing on the influence of characteristic dangling chains; that is, benzyl methacrylate (BzMA) was copolymerized with tricosaethylene glycol dimethacrylate [CH₂?C(CH₃)CO(OCH₂CH₂)₂₃OCOC(CH₃)?CH₂, PEGDMA‐23] in the presence of lauryl mercaptan as a chain‐transfer agent because BzMA forms nonpolar, short primary polymer chains and PEGDMA‐23 as a crosslinker contains a polar, long poly(oxyethylene) unit. The enhanced incorporation of dangling chains into the network polymer was brought by shortening the primary polymer chain length, and copolymerization with methoxytricosaethylene glycol methacrylate, a mono‐ene counterpart of PEGDMA‐23, enforced the incorporation of flexible dangling poly(oxyethylene) chains into the network polymer, although the former dangling chains as terminal parts of primary poly(BzMA) chains were rather rigid. Then, the influence of characteristic dangling chains on the swelling behavior of amphiphilic gels was examined in mixed solvents consisting of nonpolar t‐butylbenzene and polar methanol. The profiles of the solvent‐component dependencies of the swelling ratios were characteristic of amphiphilic gels. The introduction of dangling poly(oxyethylene) chains led not only to an increased swelling ratio but also to sharpened swelling behavior of amphiphilic gels. The swelling response of amphiphilic gels was checked by changing the external solvent polarity. The dangling chains with freely mobile end segments influenced the swelling response of gels. The amphiphilic gels with less entangled, collapsed crosslink units exhibited faster swelling response than the ones with more entangled, collapsed primary polymer chains. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2192–2201, 2004     

Af型自由基均聚反应的固化理论(Ⅲ)──高分子凝胶网络缺陷

应用高分子反应统计理论,分析了高分子网络的形成过程,讨论了A_f型自由基均聚反应凝胶网络中的缺陷悬吊环的数目及其形成几率.     

Curing theory of A f -A g type free radical polymerization (II)

By means of the polymer statistical thrury. the A _f -A _g type nonlinear free radical polymerization is investigated to give the number of effective elastic chains, the number of effective elastic mers and the average length for the elastic chains. The corresponding quantities for the dangling chains, the number of effective cross-linkage and the mod-ulus are also obtained. Furthrrmore, the nurnber- and weight-fractions of elastic chains are deduced. Project supported by the National Natural Science Foundation of China (Grant No. 29673018), the Ph. D. funds of the State Education Commission of China.     

Characterization of PDMS model junctions and networks by solution and solid-state silicon-29 NMR spectroscopy

The application of ²⁹Si solution and solid-state cross-polarization/magic-angle spinning (CP/MAS) nuclear magnetic resonance (NMR) techniques to the study of structural features in polydimethylsiloxane (PDMS) model endlinked elastomeric networks is explored. The relationship between the topological (network) functionality of a structural moiety, which determines network mechanical properties, and its chemical (spectral) functionality, which is reported by the NMR, is discussed. The second-order spectral shifts corresponding to topographical functionality variation within a chemical functionality class are usually sufficiently well resolved in these networks to allow positive identification of a variety of structural features. The basic PDMS repeat unit, ? OSi(CH₃)₂? , is found to possess an axially symmetric chemical shift tensor with σ_∥ = ?56.8 ppm downfield from TMS, and σ_⊥ = ?4.4 ppm. This axial symmetry does not result from rapid reorientation about the chain axis. The NMR spectrum reveals defects in model endlinked networks. In the case of vinyl-endlinked systems, the defects are ascribed to the formation of elastically ineffective loops. Hydroxyl-endlinked systems contain either loops or else trifunctional junctions (hydrolyzed before chain coupling could take place) and dangling chain ends. The CP/MAS technique provides an order-of-magnitude reduction over standard solution techniques in the time to acquire a spectrum from a network not containing paramagnetic doping. ¹³C spectra of PDMS systems are not as informative as ²⁹Si spectra.     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

Crosslinking Index,Molecular Weight Distribution and Rubber Equilibrium Shear Modulus During Polyfunctional Crosslinking of Existing Polymer, 6. Primary Polymer with a Schulz–Zimm Distribution of Molecular Weights

A network model for the crosslinking of already existing polymer molecules with a so‐called Schulz–Zimm distribution of their molecular weights is presented. It is an extension of previously developed statistical network models applied to the crosslinking of primary polymers with several other molecular weight distributions and with crosslinks of any functionality. The model results in the possibility to obtain more insight into the structure of polymers, especially those with narrow distributions of the molecular weight. In more detail, the model can give a perspective on structural network parameters such as the weight fractions of ideal network, of dangling polymer ends, and of those molecules not connected to the network, i. e., the sol fraction, the number of crosslinks in which a polymer molecule is bound, the functionality of the crosslinks, or the average molar mass of the polymer molecules in between the crosslinks M̄_c. Results of calculations are shown for a hypothetical crosslinking process of polymers with various molecular weight distributions. Moreover, the dependency of the network parameters on the polydispersity index and the type of molecular weight distribution is shown. Finally the increase of the functionality of the crosslinks during the ageing process of a 9.9% poly(vinyl chloride) gel as a function of the polydispersity index of the molecular weight distribution is presented.     

Fluorination of poly(p-phenylene) using TbF4 as fluorinating agent

The fluorination using TbF₄ as fluorinating agent was successfully performed on poly(p-phenylene). The method allows the fluorine content of the polymer to be controlled and the formation of structural defects, such as dangling bonds, to be significantly decreased by comparison with the direct fluorination using pure F₂ gas. The aromatic character of the phenyl ring is partly maintained through the fluorination contrary to the direct fluorination (using pure F₂ gas), for which a quasi-perfluorination and a partial decomposition of the polymer occur. Complementary analytical techniques have been used, such as ¹⁹F and ¹³C solid state NMR, FT-IR and EPR to compare the samples as a function of the reaction conditions.     

Toughness of polymeric networks: The limited importance of crosslink density

Four series of polymeric model networks were prepared with bimodal chain length distribution between crosslink points and two types of dangling chains as network defects. In the last series the crosslink density was changed without a large change in the chemical composition. The fracture toughness of those networks were compared with that of the defect–free networks. The fracture toughness of the various networks is surprisingly little influenced by the introduction of defects. Neither bimodality, nor dangling chains, nor a high sol fraction alters the toughness of the network. A good correlation between K_Ic and the weight fraction of polyether is observed. A much smaller dependence of K_Ic on the strand density can be deduced. The yield stress is high and approximately invariant for all systems studied. It is concluded that the toughness of a polymeric network does not seem to be influenced by its perfection and only to a small extent by its degree of crosslinking.     

A New Type of Macroscopically Oriented Smectic‐A Liquid Crystal Elastomer

Smectic‐A liquid single crystal elastomers (S_A‐LSCE) are materials where the rubber elasticity of the polymer network is combined with the one‐dimensional positional long‐range order of mesogenic groups which are covalently attached to the network. In the systems investigated so far, a mechanical deformation of the network causes significant reorientation processes of the layered structure. We present a new type of S_A‐LSCE in which this structure remains unaffected on mechanical deformation both parallel and perpendicular to the director. The thermoelastic behavior, macroscopic dimensions, and stress–strain measurements parallel as well as perpendicular to the director are investigated. X‐ray studies confirm that a deformation parallel and perpendicular to the layer normal does not alter the macroscopically ordered lamellar structure with respect to the order parameter and the layer correlation length. We propose a simple picture where defects within the lamellar structure might account for these findings.

     

Nonhomogeneous state of stress,strain, and swelling in amorphous polymer networks

The total free energy of an amorphous, crosslinked polymer is given as ΔA = ΔA_mix + ΔA_el, where ΔA_mix indicates the free energy of mixing of the crosslinked polymer and the solvent to which the network is exposed throughout the deformation process; ΔA_el indicates the elastic free energy of the network as a function of strain, including the effect of dilation with the solvent. The explicit forms of the mixing and the elastic free energies are obtained from the molecular theory of rubber elasticity. Recent developments in this field allow accurate representation of the behavior of swollen networks under strain. Expressions for the stress in terms of strain and swelling ratio are obtained from the free energy. Formulation of boundary-value problems are discussed. Bending of a cuboid subject to the action of a swelling agent is analyzed as an example. Material parameters are chosen for a crosslinked amorphous network. The distribution of stresses, strains, and solvent in the bent cuboid are calculated numerically. The magnitude of moments applied at the two ends are calculated for different degrees of flexure. Results are compared with those obtained for the same network in the dry state.     

Curing theory of A f -A g type free radical polymerization (I)

By means of polymer statistical theory, the sol fraction and the gelation condition of A _f -A _g type nonlinear free radical polymerization are obtained by introducing the probabilities with respect to initiation and chain addition. With Lagrange expansion theorem, the equilibrium number fraction distribution of A _f -A_g type is obtained, and its invariant property is proved. Moreover, the evaluation of average polymer quantities for post-gel regime is simplified by this invariant property. Project supported by the National Natural Science Foundation of China (Grant No. 29673018), and the Ph.D.-funds of the State Education Commission of China.     

Straightforward preparation of polymers based on oligodimethylsiloxane and alkylamine

Novel oligodimethylsiloxane‐based polymers with alkyl side chain were synthesized in bulk by step‐growth polymerization between α,ω‐glycidyl ether oligodimethylsiloxanes and a monoalkylamine in the absence of catalyst and at temperatures ranging between 80 and 180 °C. Matrix assisted laser desorption ionization time of flight results attested for the high reactivity of the amine functions with the glycidyl groups and revealed that the main polymer structure was (A₂B₂)_n type with alkyl moieties as dangling chains. No etherification was observed during the reaction even at high temperatures and the nature of the end groups strongly depended on the molar ratio between glycidyl and amine functions. Polymerization reactions were followed by ¹H NMR and the kinetics of the glycidyl‐amine reaction pointed out the dependence of temperature, molar ratio, and the molar mass of the oligodimethylsiloxane. High conversion rates were obtained, especially with the lowest molecular weight oligodimethylsiloxane. An optimized kinetic model derived from the Horie's model was discussed and permitted to correctly fit the experimental data. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Quantitative Prediction of Concentration Effects in Steric Exclusion Chromatography

Abstract

A semiempirical model, based on a previous one quantitatively describing the dependence of the elution volume, V(c_A), on the concentration of injected polymer, c_A, in exclusion chromatography (SEC) at dilute solutions, has been developed. In the derived equation, concentration effects are mainly governed by the Huggins' coefficient, k_A, and by the quadratic coefficient in the polynomial expansion of the reduced specific viscosity, k_A. Because of the incertitudes on reliable k_A and k_A' values, these are respectively removed from the model through she Imai's equation and the empirical correlation k_A' + 0.122=k_A, here obtained. Thus, A predicted elution volumes besides polymer concentration only depend on the polymer intrinsic viscosity and on its unperturbed dimensions constant,K_θ. The polymer concentration range of model applicability is up to Jerately diluted polymer solutions, as a comparison between predicted and experimental elution volumes for diverse literature systems shows.     

The effect of molecular weight heterogeneity on the second virial coefficient of linear polymers in good solvents

The effect of molecular weight heterogeneity on the second virial coefficient A₂ in good solvents is studied for binary mixtures of monodisperse poly(α-methylstyrenes). It is concluded that A₂ for polymer mixtures passes through a maximum with variation of the mixing ration. From comparison with the data, it is concluded that no available theory quantitatively explains both the molecular weight dependence of A₂ of monodisperse polymer and the variation of A₂ of mixtures with the mixing ratio. The interpenetration function for two polymer coils with different molecular weights is discussed on the assumption that the thermodynamic interaction between two polymer coils in good solvents can be approximated by a hard-sphere model.     

Comparison of the force field in various pyrochlore families. II. Phases presenting structural defects

A previous study of various A₂B₂O₆O′ pyrochlore families by vibrational spectroscopy allowed the analysis of the ir and Raman spectra and the force fields of pyrochlore phases presenting structural defects. The spectra of the following compounds were compared: (i) ideal pyrochlore Cd₂Ta₂O₇, (ii) lacunary Tl₂Ta₂O₆, (iii) nonstoichiometric Pb_1.5Ta₂O_6.5, and (iv) Pb_2.3Ta₂O_7.3 exhibiting regular shear planes. If the tridimensional network of TaO₆ octahedra is not modified and the perturbations concern only the A₄O′ tetrahedra network, a slight modification of the vibrational spectra and a weak decrease in the TaO stretching and OTaO bending force constants are observed. But, if the octahedra network is perturbed, large modifications appear on the spectra, revealing unambiguously the existence of new types of bonds created by the defects in the structure. The Raman intense lines observed in the low frequency range in lead compounds is also discussed.     

Dynamic - mechanical properties of poly(oxypropylene)di-amine-diepoxide and poly(oxypropylene)triamine-diepoxide networks and their relationship to the structure of elastically active network chains

The effect of the initial mole ratio of reactive components on the shape and position of dynamic mechanical functions in the main transition and rubbery region was investigated for two series of networks made from poly(oxypropylene)diamine (D-400)-diglycidyl ether of Bisphenol A (DGEBA) and poly(oxypropylene)-triamine (T-403)-DGEBA. The networks were prepared with an excess of amine groups up to the highest conversion of epoxy groups; the ratio ^rH = 2 [ NH₂ ]₀/ [E]₀ ranged from unity to 2,1 for networks from D-400 and from unity to 3,5 for networks from T-403. By using the theory of branching processes, structural parameters of these networks were calculated, in particular, the molecular weights of elastically active network chains (EANC's) including dangling chains, of backbone EANC's and of dangling chains. A comparison between theory and experiment led to the following conclusions: (a) the mechanical behaviour in the rubberlike region can be described either by using an affine deformation model (front factor A = 1), or by means of a phantom model (A = (f_e-2)/f_e, f_e being functionality of the crosslink) with the contribution of permanent interchain interactions; (b) the temperature and frequency position of viscoelastic functions in the main transition region is conclusively affected by the concentration of EANC's; (c) the shape of visco-elastic functions, especially of retardation spectra in the main transition and rubbery region, depends on the detailed structure of EANC's, but it cannot be decided from the result which structural parameter has the strongest effect on the shape of the functions.     

The Structure and Stability of Magic Carbon Clusters Observed in Graphene Chemical Vapor Deposition Growth on Ru(0001) and Rh(111) Surfaces

To improve the atomically controlled growth of graphene by chemical vapor deposition (CVD), understanding the evolution from various carbon species to a graphene nucleus on various catalyst surfaces is essential. Experimentally, an ultrastable carbon cluster on Ru(0001) and Rh(111) surfaces was observed, while its structure and formation process were still under debate. Using ab initio calculations and kinetic analyses, we disclose a specific type of carbon cluster, composed of a C₂₁ core and a few dangling C atoms, which is exceptional stable in a size range from 21 to 27 C atoms. The most stable one of them, an isomer of C₂₄ characterized by three dangling C atoms attached to the C₂₁ core (denoted as C₂₁‐3C), is the most promising candidate of the experimental observation. The ultrastability of C₂₁‐3C originates from both the stable core and the appropriate passivation of the dangling carbon atoms by the catalyst surface.     

Topology and chemistry of polyoxometalates: Inorganic polymers formed by connecting octahedral units,hetero- and isopolyanions,and their structural stability

The structure of inorganic polymers such as hetero- and isopolyanions formed by connecting some MO₆ octahedra is topologically discussed on the basis of the mode of connectivity of the octahedral components. The path in the inorganic polymer and the closed loop in the polyanion, which are contours continuously linked by trans-located bridging vertices (oxygens) in each constituent octahedron, are discussed. The previously reported three rationalizations of the polyanion structure are standardized; the first is Lipscomb's proposal on the number of terminal vertices within each octahedral unit of actual polyanions, the second is Pope's classification of all polyanions according to Lipscomb's proposal, and the third is our presentation of the structural stability based on the number of closed loops. A topological definition of a polyanion is provided by the Lipscomb-Pope condition; the polyanion is a condensation compound of some octahedral units where each octahedron has one or two mutually cis-located terminal oxygens. The structure of the polyanion skeleton is determined by the combination of the structural parameters A, B and C, where A is the number of MO₆ octahedral components constituting the polyanion skeleton, B the number of MO₆ units constituting the closed loop, and C the number of closed loops. The closed loop is directly related to the mode of connectivity of the octahedral units and significantly contributes to the structural stability. The combination of the structural parameters A, B and C represents the topological character of the polyanion. The topological isomer with an identical combination is distinguished from the chemical isomer with an identical composition.