Model networks of end-linked polydimethylsiloxane chains. XIV. Stress-strain,thermoelastic, and birefringence measurements on the bimodal networks at very low temperatures

Bimodal networks consisting of very short and relatively long poiydimethylsiloxane (PDMS) chains were studied from 30 to ?52°C in an attempt to elucidate the anomalous increases in modulus [f^*] exhibited by such elastomeric materials at high elongations. Temperature was found to have very little effect on (i) the elongation at which the upturn in [f^*] becomes discernible, (ii) the elongation at which rupture occurs, and (iii) the total increase in [f^*] up to the rupture point. The standard force-temperature (“thermoelastic”) plots were linear, but gave values of the energetic contribution to the total force which were significantly smaller than those universally obtained on unimodal, long-chain PDMS networks. Birefringence-temperature relations were also found to be linear, and yielded values of the optical-configuration parameter and its temperature coefficient which were in satisfactory agreement with the corresponding values reported for unimodal PDMS networks. These results indicate that even at very low temperatures the observed increases in modulus (and consequent improvements in ultimate strength) are due to non-Gaussian effects arising from limited chain extensibility, rather than from intermolecular reinforcing effects such as strain-induced crystallization.     

Fracture of model polyurethane elastomeric networks

Fracture properties of model elastomeric networks of polyurethane have been investigated with a double‐edge notch geometry. The networks were synthesized from monodisperse end‐functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect‐free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M_n = 4 kg mol^?1), an entangled network of longer chains (M_n = 8 kg mol^?1) and a bimodal network with 8 kg mol^?1 and 1 kg mol^?1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network. Fracture experiments were carried out at different strain rates and temperatures and showed for all three networks a marked decrease in fracture toughness with increasing temperature and decreasing strain rate which mirrored reasonably well the rate and temperature dependence of tan δ, the dissipative factor. However the proportionality factor between tan δ, and G_IC was very material dependent and the shift factors obtained for the master curves of the viscoelastic properties could not be used to build fracture energy master curves. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Model networks of end-linked polydimethylsiloxane chains

Summary Elastomeric networks of high extensibility were prepared by end-linking mixtures of vinyl-terminated polydimethylsiloxane chains having molecular weights of approximately 600 and 11,000 g mol^–1, with silanes chosen to give junction functionalities ranging from 3 to 8. The resulting bimodal networks were studied in elongation, at 25 °C, to their rupture points, and in swelling equilibrium in benzene at room temperature. The elongation moduli [f ^*] were found to be in satisfactory agreement with previous results obtained by end-linking hydroxyl-terminated polydimethylsiloxane chains. Values of [f ^*] at low and moderate deformations gave relatively low values of the ratio of elasticity constants 2C ₂/2C ₁, which is a measure of the extent to which the elongation changes from approximately affine to nonaffine as the elongation increases. The low values obtained for this ratio are presumably due to diminished interpenetration of configurational domains in the case of very short chains. In spite of its small magnitude, 2C ₂/2C ₁ does show some decrease with increase in , as predicted by the recent molecular theory of rubberlike elasticity developed by Flory. The swelling equilibrium results were also found to be in satisfactory agreement with theory. The elongation moduli increased significantly at high elongations, and the values of the elongation at which the upturn was first discernible were very nearly independent of , This is consistent with the interpretation of this anomalous behaviour in terms of limited chain extensibility. The maximum extensibility generally decreased somewhat with increase in and this caused a decrease in both the ultimate strength and the toughness of the elastomer, as measured by the energy required for rupture.     

Elastic behavior of bimodal poly(dimethylsiloxane) networks

The rubberlike elastic behavior of bimodal poly(dimethylsiloxane) (PDMS) networks was investigated by the Monte Carlo simulation method and enumeration calculation method on the basis of the rotational‐isomeric‐state (RIS) model. These bimodal PDMS networks consist of short chains (chain length from 10 to 20) as well as long chains (chain length equal to 150). For long PDMS chains, through generating many PDMS conformations in the equilibrium state using the Monte Carlo simulation method we can obtain the average Helmholtz free energy and the average energy. For short PDMS chains with chain lengths from 10 to 20, as the total number of conformations is only from 6.56 × 10³ to 3.87 × 10⁸, we adopt the enumeration calculation method. The deformation is partitioned nonaffinely between the long and short chains, and this partitioning can be determined by requiring the free energy of the deformed network to be minimized. Chain dimensions and thermodynamic statistical properties of bimodal PDMS networks at various elongation ratios are discussed. We find that elastic force f increases with elongation ratio λ; the energy contribution f_u to elastic force is significant, and the ratio of ranges from 0.15 to 0.36 at T = 343 K. In the meantime, elastic force f increases with the average energy 〈U〉. The energy change in the process of tensile elongation is taken over, which has been ignored in previous theories. Our calculations may provide some insights into the phenomena of rubberlike elasticity of bimodal networks. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 105–114, 2002     

Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles

Monte Carlo computer simulations were carried out on filled networks of poly(dimethylsiloxane) (PDMS), which were modeled as composites of crosslinked chains and randomly arranged spherical filler particles. The primary concern of the investigation was the effect of the excluded volume of these particles on the elastomeric properties of the polymers. Calculations were carried out for PDMS chains with different molecular masses between crosslinks, and for filler particles with different sizes and at various volume percentages. Distributions of end-to-end vectors for both unfilled and filled networks were obtained using Monte Carlo simulations based on rotational isomeric state (RIS) theory. More extended configurations, with a higher end-to-end distance, were observed for networks filled with smaller particles. The nominal stress f* and the modulus or reduced nominal stress [f*] were calculated from the distributions of end-to-end vectors using the Mark-Curro approach. Relatively small filler particles were found to increase the non-Gaussian behavior and to increase the normalized moduli above the reference value of unity. Temperature effects on the stress were also investigated. © 1996 John Wiley & Sons, Inc.     

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.     

Model networks of end-linked polydimethylsiloxane chains. XI. Use of very short network chains to improve ultimate properties

Elastomeric networks were prepared by tetrafunctionally end-linking mixtures of various proportions of relatively long and very short polydimethylsiloxane (PDMS) chains. The former had a number-average molecular weight of 18,500 and the latter either 660 or 220 g mole^?1. The series of (unfilled) bimodal networks thus prepared were studied in elongation to the rupture point at 25°C, and in swelling equilibrium in benzene at room temperature. Elasticity constants characterizing the Gaussian regions of the stress–strain isotherms, and values of the degree of equilibrium swelling were used to evaluate the most recent molecular theories of rubberlike elasticity. The isotherms also gave values of the elongation at which the modulus begins to increase anomalously because of limited chain extensibility, and values of the elongation and nominal stress at the point of rupture. These results were interpreted in terms of the known configurational characteristics of the constituent PDMS chains. Values of the energy or work required for rupture were used as an overall measure of the “toughness” of the networks. The very short chains were found to give a marked increase in toughness, through an increase in ultimate strength without the usual corresponding decrease in maximum extensibility. A variety of additional experiments will be required in order to elucidate the molecular origins of this important effect.     

Rubber elasticity in the range of small uniaxial tensions and compressions. Results for poly(dimethylsiloxane)

Results of uniaxial tension and compression experiments are reported on crosslinked polydimethylsiloxane (PDMS) networks in the unswollen state over the range 0.5 < α^?1 < 1.2 where α is the extension ratio. Curves representing the reduced force [f] = f(V⁰/V)^1/3(α – α^?2)^?1 plotted against α^?1 can be approximated by straight lines for 0.5 < α^?1 < 0.9, in agreement with the phenomenological Mooney equation. As α^?1 approaches 1, however, they tend to level off and continue into the α^?1 > 1 region with decreasing slope. These results are in agreement with the predictions of recent elasticity theories that incorporate the effect of junction-chain entanglements in the elastic free energy.     

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.     

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.     

Increase of the average reactivity of active species due to a shift to the more reactive species in ionic propagation accompanied by termination

The presented simulations demonstrate that in polymerizations proceeding on two kinds of species, differing in reactivity and being in equilibrium, the expected decrease of the rate of polymerization due to termination may happen to be compensated by the relative increase of concentration of the more reactive species. This takes place, for instance, in the polymerization proceeding simultaneously on ions and ion pairs if ions are more reactive. Because of termination the total concentration of ionic species during the course of polymerization decreases while the proportion of ions increases due to increasing dilution. The maximum compensation is observed when simultaneously k_(ions)/k_{(ion pairs)} → and K_d/[I]₀ → 0, where k are the propagation rate constants, K_d is the equilibrium constant of dissociation and [I]₀ is the starting concentration of initiator. Then, the degree of compensation (the ratio of the rate with compensation to the rate without termination) is becoming equal to ([P*]/[P*]₀)^1/2, where [P*] is the actual, total concentration of the growing species and [P*]₀ is the initial total concentration (before any termination has taken place).     

Silicone networks with junctions of high functionality and the theory of rubber elasticity

Results of Krik, Bidstrup, Merrill, and Meyers on polydimethylsiloxane networks of high functionality ? yield values of the reduced force [f*] in the high-extension limit that are directly proportional to (v_s/V) (1 ? 2/?) where v_s/V is the number of effective chains in volume V. The contention that trapped entanglements contribute significantly to the modulus is refuted by adherence of the results to this proportionality down to the lowest degrees of interlinking. Features of the relationship of stress to strain that appear to be in conflict with current theory are attributable to crowding of chains about the junctions of high functionality and of large linear dimension in the networks investigated by these authors.     

The effect of swelling on the stress-strain isotherms and ultimate properties of polydimethylsiloxane networks in elongation

Summary Gamma radiation was used to prepare three cross-linked, unfilled samples of highly elastomeric polydimethylsiloxane. Portions of each sample were studied in elongation to their rupture points, at 30 °C, in both the unswollen state and swollen with low molecular weight dimethylsiloxane fluid. Values of the volume fraction ν₂ of polymer in the networks ranged from 1.00 to 0.40. None of the stress-strain isotherms obtained showed any upturn in the reduced force or modulus [f ^*] at high elongation, an observation in agreement with the conclusion that such increases in [f ^*], when observed, are due to strain-induced crystallization. All of the isotherms were well represented by the semi-empirical equation [f ^*]=2C ₁+2C ₂ α ⁻¹, whereα is the elongation, and 2C ₁ and 2C ₂ are the Mooney-Rivlin constants. Values of 2C ₂, which serves as a measure of the extent to which [f ^*] varies with elongation, showed a decrease with decrease in ν₂, and generally also with decrease in degree of cross-linking. The ultimate properties reported were the valuesλ _r and [f ^*], of the total elongation and the reduced force, respectively, at the rupture point. Decrease in degree of cross-linking causes a significant increase inλ _r and a significant decrease in [f ^*] _r ; decrease in ν₂, however, has only a relatively small effect onλ _r and [f ^*] _r . With 3 figures and 1 table     

Elastomeric Properties of Polysiloxane Networks. Bimodal Elastomers that are Spatially Inhomogeneous and Others that are Very Broadly Multimodal

End‐linking poly(dimethylsiloxane) was used to prepare bimodal elastomers networks so as to have inhomogeneous nanostructures, and also to prepare others having very broadly multimodal chain‐length distributions. Macroscopic phase separation, probably high crosslink density clusters, was observed to occur in some of the bimodal networks. The mechanical properties in simple extension and in equilibrium swelling were measured. The bimodal elastomers that were not obviously inhomogeneous showed very good mechanical properties, but the macroscopically phase‐separated networks, and the broadly multimodal network were weak. Analysis of the Mooney‐Rivlin profiles suggests that the reinforcing mechanism could have a structural component in addition to that from the limited extensibilities of the short chains. The mechanical properties and the extents of swelling support the cluster conjecture, in accord with previous morphological studies on spatially‐inhomogeneous polysiloxane elastomers.     

Unimodal and bimodal networks of poly(dimethyl-siloxane) in pure shear

Model networks of poly(dimethylsiloxane) (PDMS) were prepared by tetrafunctionally endlinking hydroxyl-terminated chains of various molecular weights. Some networks were prepared from mixtures of chains so as to yield a bimodal distribution of network chain lengths and, in some cases, these networks were prepared in solution. The stress–strain behavior of these unimodal and bimodal networks was studied in pure shear, which was imposed by stretching a sheet of the network having a large ratio of width to length in the direction perpendicular to the width. The pure-shear moduli of both types of networks generally were found to depend markedly on strain. Stress–strain isotherms for unimodal networks prepared from chains of one or the other of two molecular weights were well interpreted using the constrained-junction model of Flory and Erman. The bimodal networks showed large increases in the pure-shear modulus at high strains which were similar to those reported for uniaxial extension and compression. Endlinking in solution decreases the modulus in general and its upturn in particular, presumably because of diminished chain-junction entangling.     

Chain segment ordering in uniaxially strained networks: A deuterium NMR investigation

The deuterium NMR (²H-NMR) is used for probing the chain segment orientation in polymer networks under uniaxial stress. The method is based on the observation of an incomplete time averaging of quadrupolar interactions affixed to deuterated segments. The samples are end-linked polydimethylsiloxane networks. The ²H-NMR experiments are performed either on labelled network chains or an labelled probe polymer chains dissolved in the network. The basic results are the following: — The induced uniaxial order is related to a uniaxial dynamics of chain segments around the direction of the applied constraint. — A permanent orientation is observed on free polymer chains dissolved in the deformed networks. — The mean degrees of orientational order induced along short and long chains in bimodal networks are the same. These experimental facts appear as evidences for cooperative orientational couplings between chain segments in the deformed networks.     

Star‐shaped polymers by Ru(II)‐catalyzed living radical polymerization. II. Effective reaction conditions and characterization by multi‐angle laser light scattering/size exclusion chromatography and small‐angle X‐ray scattering

Star poly(methyl methacrylate)s (P*) of various arm lengths and core sizes were synthesized in high yields by the polymer linking reaction in Ru(II)‐catalyzed living radical polymerization. The yields of the star polymers were strongly dependent on the reaction conditions and increased under the following conditions: (1) at a higher overall concentration of arm chains ([P*]), (2) with a larger degree of polymerization (DP) of the arm chains (arm length), and (3) with a larger ratio (r) of linking agents to P* (core size). In particular, the yields sharply increased in a short time at a higher temperature, in a polar solution, and at a higher complex concentration after the addition of linking agents. These star polymers were then analyzed by multi‐angle laser light scattering to determine the weight‐average molecular weight (3.8 × 10³ to 1.5 × 10⁶), the number of arm chains per molecule (f = 4–63), and the radius of gyration (R_z = 2–22 nm), which also depended on the reaction conditions (e.g., f and R_z increased as [P*], DP, and r increased). Small‐angle X‐ray scattering analyses of the star polymers showed that they consisted of spheres for which the radius of the microgel core was 2.7 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2245–2255, 2002     

Activation and racemization of trifluoroacetate esters in the cationic polymerization of styrene

1-Phenylethyl trifluoroacetate ( 1 ) does not react directly with styrene but it is readily incorporated into polymer chains in the presence of an excess of trifluoroacetic acid. The proportion of the nondeuterated 1-phenylethyl end groups in the polymerization of deuterated styrene coinitiated with the acid was much higher than the proportion of the end groups formed by direct incorporation of the acidic protons ([CH₃? CHPh? CD₂? CDPh? …] > [HCD₂? CDPh? CH₂? CDPh? …]). The racemization of the optically active ester-(pseudo-first order rate constant at [HA]₀ = 0.79 mol/L at 20°C equals k^R = 1.7 × 10^?4 S^?1) is more rapid than the incorporation of the ester into polymer chains (k^E = 1.5 × 10^?4 mol^?1 Ls^?1, [M]₀ < 0.4 mol L^?1, i.e., k^R > k^E · [M]). These results and the complete loss of the optical activity in the final polymer indicate that the ester is activated by the acid but it is incorporated into polymer chain via ionic intermediates.     

Effect of temperature of liquid sulphur on kinetics of transformation of chains in its amorphous modification

The rate of transformation of the chains in amorphous sulphur was examined by calorimetry at 298 K. The amorphous samples were remelted at the temperatureT _f in the range from 458 to 573 K. Increase ofT _f decreased the transformation rate. The results satisfy the equationX=1-exp[-(kt)^z] (X=transformation degree,t=time, andk andz=constants). A one-stage transformation was observed for samples remelted atT _f473 K. ForT _f 523 K, transformation in two stages was observed.The effects ofT _f on the kinetics of nucleation and the growth of the nuclei are discussed.