Elastomeric properties of end-linked networks of high cross-link functionality. Accounting for possible changes in effective functionality with extent of reaction and chain-length distribution

This study reanalyzes some elastomeric properties in elongation reported for poly(dimethylsiloxane) (PDMS) networks of high cross-link functionality which had been prepared by using multifunctional siloxane oligomers to end link vinyl-terminated PDMS chains. The extent of reaction of the vinyl end groupsP _vi spanned the range of 0.40 to 0.95. These networks had elongation moduli that significantly exceeded the values predicted by the Flory-Erman theory, except at very low values ofP _vi. Trends in their stress-strain isotherms, as characterized by the Mooney-Rivlin constants 2C ₂ and the ratio 2C ₂/C₁, also appeared to be different from those predicted by theory. Neglected in such standard analyses, however, was the fact that the segments between cross-links along the junction precursor molecules can themselves act as short network chains, contributing to the modulus and giving a strongly bimodal distribution of both network chain lengths and cross-link functionalities. Of particular interest is the apparent change in functionality with extent of reaction and chain length distribution. The results thus obtained do suggest strong dependence of the observed values of the phantom modulus on the network chain-length distribution, particularly at very small values of the ratio of the length of the short chains to the long ones. Calculations based on recognition of these complications can be used to characterize more realistically the deformation of such networks. The results give much better agreement with experiment. Such behavior could be an important characteristic of elastomeric networks in general.Also, a preliminary attempt was made to bridge theory with experiment based on Kloczkowski, Mark, and Erman's recent theory of fluctuations of junctions in regular bimodal networks. The agreement between theory and experiment thus obtained is rather satisfactory and lends further support to assumptions that take into account the possibly bimodal nature of these high-functionality networks.     

Strain birefringence studies on poly(vinyl acetate) networks

Atactic poly(vinyl acetate) prepared in a free-radical polymerization was crosslinked by means of benzoyl peroxide. The resulting elastomeric networks were studied in elongation, both unswollen and swollen with triethylbenzene, over the range 0–90°C. The most important experimental results obtained were values of the network birefringence, which is negative, as was recently also found to be the case for networks of atactic poly(methyl acrylate).Calculations carried out to interpret the birefringence were based on Monte Carlo simulations of the atactic structure, and on the rotational isomeric-state theory of chain configurations. The agreement between theory and experiment was very good, in fact much better than has usually been observed for other polymers studied to date.     

Densely crosslinked polycarbosiloxanes. II: Thermal and mechanical properties

The thermal and mechanical properties of two densely crosslinked polycarbosiloxane systems were investigated in relation to the molecular structure. The networks were prepared from functional branched prepolymers and crosslinked via a hydrosilylation curing reaction. The prepolymers having only vinyl functionalities (poly[phenylmethylvinyl]siloxanes) were crosslinked by using crosslinking agents with reactive silicon–hydrogen groups. In prepolymers having both silicon–vinyl and silicon–hydrogen groups (poly[phenylmethylvinylhydro)]siloxanes crosslinking took place intermolecularly. The thermal and mechanical properties of the polymer networks were found to be dependent on the phenyl  Si O_3/2 (branches) content in the prepolymer, the number of elastically effective crosslinks, the elastically effective network chain density and molecular weight between crosslinks, length of the chain segments introduced by the hydrosilylation crosslinking reaction, and the number of dangling ends. As a consequence of the dense crosslinking, the mechanical properties were also strongly dependent on the glass transition temperature. A tough–brittle transition was observed around the glass transition temperature of the polymer networks. The properties of the poly(phenylmethylvinylhydro)siloxane networks were found to be superior to those of the poly(phenylmethylvinyl)siloxane networks. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1311–1331, 1997     

Effect of chain stiffness and entanglements on the elastic behavior of end-linked elastomers

The effect of chain stiffness and entanglements on the elastic behavior and microscopic structure of cross-linked polymer networks was studied using Monte Carlo simulations. We investigated the behavior of entangled and entanglement-free networks at various degrees of chain stiffness and densities. Based on previous results that indicated that trapped entanglements prevent strain-induced order-disorder transitions in semiflexible chain networks, we prepared the entangled networks by end-linking the chains in very dilute conditions so as to minimize the extent of trapped entanglements. We also considered the entanglement-free case by using a "diamond" structure. We found that the presence of even a very small amount of trapped entanglements is enough to prevent a discontinuous strain-induced transition to an ordered phase. In these mildly entangled networks, a nematiclike order is eventually attained at high extensions but the elastic response remains continuous and the cross-links remain uniformly distributed through the simulation box. The entanglement-free diamond networks on the other hand show discontinuities in their stress-strain data. Networks at higher densities exhibit a more stable ordered phase and show an unusual staircaselike stress-strain curve. This is the result of a stepwise extension mechanism in which the chains form ordered domains that exclude the cross-links. Extension is achieved by increasing the number of these ordered domains in the strain direction. Cross-links aggregate in the spaces between these ordered domains and form periodic bands. Each vertical upturn in the stress-strain data corresponds to the existence of an integer number of ordered domains. This stepwise elastic behavior is found to be similar to that exhibited by some tough natural materials.     

Radical processes in the pyrolysis of acetylene

The literature on the pyrolysis of acetylene below 1000 K is reviewed and it is shown that the reaction is a radical chain polymerization initiated by H atoms. The induction period is examined and shown to arise from a rapid autocatalysis produced by the very first product, vinyl acetylene. Data from studies of acetylene polymerization induced by vinyl acetylene and styrene are examined and shown to be in good qualitative agreement with the radical chain process presented. Measured and where needed, estimated rate constants are given to produce numerical estimates of chain length, rates of polymerization, induction period, and rates of initiation. It is further shown that all the products of the polymerization are capable of efficiently initiating chains in the system. An examination of the possible kinetics of vinylidene shows that it does not play any role in acetylene chemistry.     

Intrachain reaction of a pair of reactive groups attached to polymer ends. II. Monte carlo study on the intrachain reaction proceeding on trans/cis-polysarcosine chain.

Monte Carlo calculation was performed to evaluate the ring-closure probability of short polysarcosine chains. Calculations were made for unperturbed trans- non-self-intersecting trans-, and non-self-intersecting trans- and non-self-intersecting trans/cis-polysarcosine chains. In the latter case, the main chain amide bond was allowed to take cis as well as trans conformations. The ring-closure probability for unperturbed trans-polysarcosine chains was found to be substantially greater than for non-self-intersecting trans chains. Virtually no difference was observed between the ring-closure probability was used to estimate the cyclization constant, i.e., the ratio of rate constant for the intramolecular reaction of the two groups attached to the polymer ends to that of the intermolecular one. The results were compared with the experimental data for the intrachain reaction proceeding on polysarcosine chain reported in the first paper of this series. The Monte Carlo results roughly reproduced the experimental data and the calculated chain length dependence was consistent with the observed one for longer chains.     

Dependence of the moduli of random bimodal networks on chain-length distribution

There have now been a number of experimental studies on the preparation and elastomeric properties of random bimodal networks of polydimethylsiloxane. The mole per cent of the short chains and their molecular masses covered a wide range, thus resulting in various polydisperse chain-length distributions. The networks were studied with regard to their stress-strain isotherms in elongation, and values of their moduli in the large-deformation (phantom) limit were found to depend on the chain-length distribution. This Important result is in disagreement with phantom network theory, which assumes the elastic modulus is dependent only on the mean value of chain lengths such that the cycle rank of the network is preserved. The effective functionality of the long chains was found to depend on the number of short chains present. Better agreement with experiment was obtained when account was taken of the connectivity of the very short chains, in what is essentially a bimodal distribution of both network chain lengths and cross-link functionalities. Relevant here is the fact that as the degree of chemical cross-linking Increases, the shear modulus G moves away from the affine limit, toward the phantom limit. This increase toward phantom behavior is presumably due to the fact that the mutual interspersion of chains is less when the chains are shorter, even in the small-strain region.     

Effect of stiffness on the micellization behavior of model H4T4 surfactant chains

The micellization behavior of a series of model surfactants, all with four head and tail groups (H4T4) but with different degrees of chain stiffness, was studied using grand canonical Monte Carlo simulations on a cubic lattice. The critical micelle concentration, micellar size, and thermodynamics of micellization were examined. In all cases investigated, the critical micelle concentration was found to increase with increasing temperature as observed for nonionic surfactants in apolar or slightly polar solvents. At a fixed reduced temperature and increasing chain stiffness, in agreement with previous observations, it was found that the critical micelle concentration decreased and the average micelle size increased. This behavior is qualitatively consistent with that experimentally observed when comparing hydrogenated and homologous fluorinated surfactants. Thermodynamic considerations based on the analysis of the temperature dependence of the critical micelle concentration indicated that both effects could be interpreted as arising from an increased number of heterocontacts between hydrophobic portions of stiff surfactants and a lower entropic cost on packing rigid chains. Structural analysis that was also based on considering the inner micellar radial dependence of the surfactant head and tail site fraction distributions suggested that, on stiffening the molecular backbone, the resulting micellar aggregates grew, without appreciable deviations from spherical symmetry. Stiffer surfactants led to a slightly denser micellar core because of better packing.     

Molecular aspects of polymer network deformation - small angle neutron scattering and NMR studies

Poly(1,4-butadiene) networks obtained by a 4-functional random cross-linking reaction over a broad range of polymer concentration were studied by small angle neutron scattering(SANS), ²H NMR and Monte Carlo(MC) simulation in the isotropic and uniaxially deformed state. The defect structure of the networks has been characterized by MC simulation of the cross-linking reaction. The anisotropy of the radius of gyration in deformed networks determined from SANS has been analyzed by the theory of Ullman. It was found that the number of active cross-links per chain is in agreement with MC and that the chain deformation follows phantom behaviour. The local orientation as measured by ²H NMR is related to the global anisotropy of the network by a MC calculation of oriented chains. The ²H NMR line shape of the deformed network is analyzed in terms of two relaxation processes arising from interior parts of the chains and from segments at chain ends. The mobility of both decrease with strain. It was found that the orientation connected to the first process shows the classical strain dependence of rubber elasticity, whereas the second exhibits a weaker dependence on strain.     

The modulus of randomly-crosslinked poly(dimethylsiloxane) networks

In several published studies, randomly crosslinked networks were prepared from poly(dimethylziloxane) by the selective crosslinking of vinyl side chains with a silicon-hydride crosslinking agent. Stress-strain measurements on these elastomers gave values of the elongation modulus in the limits of small and large deformations which exceeded those predicted by the Flory-Erman theory. Although these unexpectedly large values at the small-strain limit have frequently been attributed to contributions from trapped entanglements, the present analysis interprets them as simply arising from contributions from short chains inadvertently introduced from the silicon-hydride crosslinking agent. In this interpretation there is a bimodal distribution of network chain lengths and, possibly, of crosslink functionalities as well. The present analysis gives results in good agreement with experiment.     

Bulk hydrosilylation reaction of poly(dimethylsiloxane) chains catalyzed by a platinum salt: Effect of the initial concentration of reactive groups on the final extent of reaction

Model silicone networks obtained by curing linear poly(dimethylsiloxane) (PDMS) chains with end‐vinyl groups, (B₂), with a polyfunctional silane‐terminated crosslinker of functionality f, (A_f), through a hydrosilylation reaction have been widely used. In these networks, the principal characteristics of their ultimate molecular structure are strongly affected by the final extent of reaction reached during the crosslinking reaction. This work analyzes the effect of the initial concentration of the reactive end groups on the maximum attainable extent of reaction under normal bulk crosslinking conditions. This was accomplished by examining the reaction between linear B₂ PDMS chains with difunctional and trifunctional silanes. The experimental results were fitted by an exponential equation to have an empirical equation able to predict the maximum extent of reaction to be obtained as a function of the initial concentration of reactive groups. Molecular parameters relevant to this study, such as the degree of polymerization, the weight‐average molecular weight for the A₂ + B₂ system, or the weight fraction of solubles for the A₃ + B₂ system, were calculated with a mean field theory (recursive approach). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1099–1106, 2003     

Polymerization of vinyl chloride in the presence of precipitants. I

The kinetics of bulk and precipitation polymerization of vinyl chloride has been studied over wide range of reaction temperature by using γ-ray induced initiation. The autoacceleration effect, which has been observed by many investigators in the case of chemically initiated bulk polymerization of vinyl chloride above 40°C and has been the most controversial aspect of the bulk polymerization of vinyl chloride, was found to disappear in the bulk polymerization below 0°C. In the bulk polymerization at 40°C, the autoacceleration effect was observed up to 20%, in agreement with the results of previous investigators, and a pronounced effect of the size of polymer particles on the time–conversion curve was observed. The kinetics of precipitation polymerization of vinyl chloride in the presence of some nonsolvents was successfully described by a oneparameter equation. A kinetic scheme, which clearly explains the zero-order reaction behavior of bulk polymerization at low temperature and the kinetic behavior of precipitation polymerization described by the empirical equation, is proposed. The autoacceleration effect in the bulk polymerization at 40°C was considered to be essentially the same phenomenon as the small retardation period observed in the bulk polymerization at low temperature.     

Synthesis of 4-Alkyl-4-alkoxybutenolides Having Unsaturated Side Chains via Chromium Carbene Complex Photochemistry: (+)-Cerulenin

The photochemical reaction between optically active ene carbamates and chromium alkoxycarbene complexes containing unsaturated aliphatic side chains was further developed. Although remote olefinic groups, including conjugated dienes, were tolerated, a homoallylic side chain underwent intramolecular reaction to give a strained cyclobutanone. (+)-Cerulenin was synthesized utilizing the photochemical reaction of an alkynylcarbene complex with an optically active ene carbamate and the bis(pi-crotyl)nickel halide alkylation of a vinyl bromide as key steps.     

Precision synthesis of graft copolymers via living cationic polymerization of p‐acetoxystyrene followed by friedel–crafts‐type termination reaction

This study describes a novel precision synthesis strategy for graft copolymers using Friedel–Crafts‐type termination reaction between a cationically prepared poly(styrene derivative) and the naphthyl side groups from a poly(vinyl ether) main chain. The pendant alkoxynaphthyl groups on the poly(vinyl ether) efficiently terminated the living cationic polymerization of p‐acetoxystyrene (AcOSt) with SnCl₄ in the presence of ethyl acetate as an added base. This research provides the first example of a well‐defined graft copolymer prepared using this method. The resulting polymer contained 40 poly‐(AcOSt) branches, as calculated from the M_w determined via gel permeation chromatography–MALS analysis, which was in good agreement with the estimated number of branches obtained from ¹H NMR analysis. The acetoxy groups in the grafted poly(AcOSt) chains were easily converted into phenolic hydroxy groups under basic conditions. The as‐obtained graft copolymer with poly(p‐hydroxystyrene) side chains exhibited a pH‐sensitive phase separation in water. The synthetic method for preparing the graft copolymers was also effective in the living cationic polymerizations of other styrene derivatives. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4675–4683     

Kinetics of the Photopolymerization of Vinyl Monomers by Bis(Isopropylxanthogen) Disulfide. Design of Block Copolymers

Bis(isopropylxanthogen) disulfide (BX) has been used as a photoinitiator with various vinyl monomers at 30°C. The kinetics of polymerization of styrene (St) and methyl methacrylate (MMA) at 30°C were studied for various concentrations of monomer and initiator. The observed deviations in polymerization rate from simple kinetic theory could be explained in terms of primary radical termination. The fraction of primary radical terminating chains was obtained as a function of various concentrations. The ratio of the rate constants for chain initiation and chain termination by a primary radical was determined to be 3.34 ± 10⁷ for St and 2.60 ± 10⁷ for MMA. The number-average degree of polymerization (DP _n) of polymers obtained by photopolym-erization with BX was found to increase linearly with conversion. However, the DP _n extrapolated to zero conversion was in good agreement with that calculated on the basis of the kinetic scheme. It was found that BX had interesting properties for the design of block copolymers, i.e., BX acts as a terminator and a chain transfer agent as well as an initiator in these polymerizations. The polymers obtained with BX contained two reactive isopropyl xanthate groups bonded at their chain ends, which could also act as macrophotoinitiators.     

Cationic Grafting of Vinyl Polymers onto a Carbon Whisker,Initiated by Acylium Perchlorate Groups Introduced onto the Surface

Abstract

The cationic graft polymerization of vinyl monomers onto a carbon whisker, vapor-grown carbon fiber, initiated by acylium perchlorate groups introduced onto the surface, was investigated. The introduction of acylium perchlorate groups onto a carbon whisker was achieved by the treatment of a carbon whisker having acyl chloride groups, which were introduced by the reaction of surface carboxyl groups with thionyl chloride, with silver perchlorate in nitrobenzene. It was found that the cationic polymerization of vinyl monomers, such as styrene, indene, N-vinyl-2-pyrrolidone, and n-butyl vinyl ether, is initiated by acylium perchlorate groups on a carbon whisker. In the polymerization, the corresponding vinyl polymers were grafted onto a carbon-whisker surface based on the propagation of polymer from the surface: the percentage of grafting of polystyrene and polyindene reached 42.5 and 100.3%, respectively. The percentage of polystyrene grafting decreased with increasing polymerization temperature because of preferential chain transfer reactions at higher temperatures. Polymer-grafted carbon whisker gave a stable colloidal dispersion in a good solvent for grafted polymer.     

Elastomers having high functionality cross links viewed as bimodal networks. An alternative interpretation in terms of bimodal chain-length distributions

Several groups have now prepared poly(dimethylsiloxane) networks of high cross-link functionality by end-linking vinyl-terminated chains by means of Si? H groups in siloxane oligomers (CH₃)₃SiO[SiHCH₃O]_xSi(CH₃)₃. The elongation moduli of these networks were generally found to be considerably larger than the values predicted from the functionality and number density of the cross links (based on the stoichiometry of the end-linking reaction). Not all the Si? H groups in an oligomer are used in the end-linking reaction, however, and the segments between cross-links can themselves act as short network chains. The connectivity of these short chains to the long ones, in what is essentially a bimodal distribution, has been neglected in analyses to date. They are taken into account in the present analysis, giving much better agreement between experiment and theory. The stress-strain behavior for such very short chains can be characterized by the use of Monte Carlo methods and the Fixman-Alben non-Gaussian distribution. This alternative analysis seems useful in reproducing the experimental observations, but further experimental and theoretical will be required to remove some remaining ambiguities. © 1995 John Wiley & Sons, Inc.     

Computational annealing of simulated unimodal and bimodal networks

A conjugate gradient Monte Carlo algorithm was used to simulate the annealing of two and three dimensional end-linked unimodal and bimodal polydimethylsiloxane networks. Equilibrium is satisfied at every crosslink during network energy minimization resulting in distinct differences in network characteristics from classical assumptions. Annealed unimodal networks were found to retain the uniformly dispersed arrangement of crosslinks generated during the crosslinking algorithm. Radial distribution functions of chain vector lengths for various unimodal systems show a shift in the mean chain length from the rms length prior to annealing to shorter lengths upon annealing. Short chains in bimodal networks cluster during the annealing process in agreement with experimental investigations of short chain agglomeration in the literature. This work provides the first predictions of bimodal chain network clustering via simulated network formation and demonstrates the critical role of network annealing in determining the initial configurations of deformable elastomeric networks. This information is extremely useful in the development of accurate constitutive models of bimodal networks.