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.     

Monte Carlo simulations of the spatial structure of end-linked bimodal polymer networks: part II

The article presents the results of Monte Carlo simulations of bimodal networks performed with the Bond-Fluctuation-Algorithm. First the sol-fractions of networks with different ratios of short chains were studied and found to be always less than 2%. Concerning clustering behaviour, we saw that while random networks always form a main cluster containing more than 95% of all chains, simulated networks with less than 80% short chains do not form a main cluster. The density profiles during the swelling process show that clustering is reflected in a lower swelling degree and a sharper transition zone between the inner part and the boundary regions of the network. Finally, comparing the density distributions of crosslinkers of unimodal and bimodal networks, we found that all unimodal networks have a more ordered structure in their interior than in the melt. On the other hand, bimodal networks, where the ratio between long and short chains leads to equal masses of the fractions, show a superposition of two separate density distribution peaks, leading to a broader distribution than the Gaussian distribution found for a melt.     

Stress-optical properties of bimodal polymer networks

The optical properties of bimodal poly(dimethylsiloxane) (PDMS) networks were studied with special emphasis on the non-linear stress optical properties exhibited by these materials. In particular the effect of chain length, and junction functionality on the strain induced birefringence was investigated. It is shown that for the non-linear properties to clearly manifest themselves a critical concentration of short chains is essential and that the junctions are tetra-functional. However, all bimodal compositions studied were found to exhibit a non-linear variation of birefringence with strain irrespective of the junction functionality. The optical properties of the unimodal networks were found to vary linearly with stress and strain as expected. The transition from non-linear to linear optical behavior on increasing the molecular weight of the short chains is also established.     

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.     

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.     

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     

The effect of network chain-length distribution,specifically bimodality,on strain-induced crystallization

Polyurethane elastomers were prepared from a series of poly(ethylene oxide) samples by end-linking the chains into “model” trifunctional networks. The molecular weight M_c between crosslinks in such networks is simply the number-average molecular weight M_n of the precursor polymer. End-linking samples separately gave networks with unimodal distributions of network chain lengths, whereas end-linking mixtures of two samples having very different values of M_n gave bimodal distributions with average values of M_c equal to the average value of M_n for the two samples. Stress-strain isotherms in elongation were obtained for these networks, both unswollen and swollen to various extents. Strain-induced crystallization was manifested in elastic properties that changed significantly with changes in temperature. Swelling has more complicated effects, since it causes deformation of the network chains as well as melting of some of the crystallites. Comparisons among stress-strain isotherms at constant M_c indicate that bimodality facilitates strain-induced crystallization.     

The distributions of chain lengths in a crosslinked polyisoprene network

A fundament of classical rubber elasticity theory is the Gaussian chain approximation formula, P(n,r) for the probability distribution of end-to-end distances of a polymer chain composed of n beads. It is considered to provide a realistic distribution of end-to-end distances, r, provided that the length of the polymer chain is much greater than its average end-to-end distance. By considering the number of beads (n) to be the independent variable, we can use P(n,r) to construct the probability distributions of network chain lengths, for fixed r. Since the network crosslinks reduce the probability for the occurrence of longer chains, the formula must be modified by a correction factor that takes this effect into account. We find that, both the shape of the n-probability distribution, its height, and the position of the peak vary significantly with r. We provide a numerical procedure for constructing networks that respect these distributions. The algorithm was implemented in a three-dimensional, random polymer-and-node network model to construct polyisoprene networks at two common crosslink densities. Although the procedure does not constrain the density, we find that the networks constructed have densities very close to the measured bulk density.     

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.     

Biaxial extension measurements on bimodal elastomeric networks

Bimodal elastomeric networks were prepared by tetrafunctionally endlinking mixtures of short and long hydroxyl-terminated poly (dimethylsiloxane) chains having number-average molecular weights of 500 and 18,000 g/mol^?1, respectively, over a composition range of 0–98 mol % of the short chains. Biaxial extension (compression) measurements were carried out by inflation of circular sheets of these materials at 23°C. The unimodal network (0 mol % short chains) showed the same behavior reported by other workers for noncrystal-lizable networks: as the compression increased, the reduced stress or modulus [f*] went through a rather slight maximum followed by a gradual leveling off to the rupture point. The bimodal networks, however, showed much more pronounced maxima with another, significant increase in [f*] at very high compressions. This final increase is presumably due to non-Gaussian effects from the very limited extensibility of the short chains, and thus parallels the upturns in [f*] frequently reported for bimodal networks at very high elongations.     

Detection of heterogeneities in dry and swollen polymer networks by proton low-field NMR spectroscopy

We report on the implementation of modern proton multiple-quantum NMR methods for the characterization of molecular order and dynamics in polymer networks and melts on cost-efficient low-resolution low-field NMR instrumentation. The method permits the extraction of chain order parameter distributions, and is therefore sensitive to a heterogeneity of cross-links and other topological constraints. Data from samples with bimodal network chain length distributions acquired at 20 MHz (0.47 T) are in quantitative agreement with results obtained at high field (500 MHz). It is shown for the first time that the chain order distribution is broadened upon swelling, providing evidence for the nontrivial nature of the swelling process.     

Bimetallic Chromium Catalysts with Chain Transfer Agents: A Route to Isotactic Poly(propylene oxide)s with Narrow Dispersities

Bimetallic chromium catalysts are investigated for the enantioselective polymerization of propylene oxide. The catalyst is composed of two salen chromium species linked by an alkyl chain, the length of which significantly impacts the rate of polymerization. While the use of a chloride initiator on the catalyst resulted in bimodal molecular weight distributions, switching to a trifluoroacetate initiating group and adding a diol chain transfer agent afforded polymers of controllable molecular weight with low, unimodal dispersities.     

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.     

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.     

Change in Collagen Fibril Diameter Distribution of Bovine Anterior Cruciate Ligament upon Injury Can Be Mimicked in a Nanostructured Scaffold

More than 200,000 people are suffering from Anterior Cruciate Ligament (ACL) related injuries each year in the US. There is an unmet clinical demand for improving biological attachment between grafts and the host tissue in addition to providing mechanical support. For biological graft integration, it is important to provide a physiologically feasible environment for the host cells to enable them to perform their duties. However, behavior of cells during ACL healing and the mechanism of ACL healing is not fully understood partly due to the absence of appropriate environment to test cell behavior both in vitro and in vivo. This study aims at (i) investigating the change in fibril diameter of bovine ACL tissue upon injury and (ii) fabricating nanofiber-based scaffolds to represent the morphology and structure of healthy and injured ACL tissues. We hypothesized that distribution and mean diameter of ACL fibrils will be altered upon injury. Findings revealed that the collagen fibril diameter distribution of bovine ACL changed from bimodal to unimodal upon injury with subsequent decrease in mean diameter. Polycaprolactone (PCL) scaffold fiber diameter distribution exhibited similar bimodal and unimodal distribution behavior to qualitatively represent the cases of healthy and injured ACL, respectively. The native ACL tissue demonstrated comparable modulus values only with the aligned bimodal PCL scaffolds. There was significant difference between mechanical properties of aligned bimodal and unaligned unimodal PCL scaffolds. We believe that the results obtained from measurements of diameter of collagen fibrils of native bovine ACL tissue can serve as a benchmark for scaffold design.     

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.     

Impact of Alkoxyl Tail of Fullerene Dyad Acceptor on Crystalline Microstructure for Efficient External Treatment-free Polymer Solar Cells with Poly(3-hexylthiophene) as Donor

A series of tri(alkoxyl)benzene-fullerene dyads(PCBB-Cn, n=4, 6, 8, 10, 12) with varied tri(alkoxyl) chain lengths was designed, synthesized and used as acceptor materials in polymer solar cells(PSCs). The five fullerene dyads possess similar absorption spectra in dilute solution, decreased glass-transition temperature(T_g) and gradually elevated lowest unoccupied molecular orbital(LUMO) energy levels from -3.87 eV to -3.73 eV with the increase of the alkoxy chain length. In the fabrication of PSCs with poly(3-hexylthiophene)(P3HT) as donor and the fullerene dyads as acceptor, PCBB-Cn with longer tri(alkoxyl) chains and lower T_g can induce crystalline structure of P3HT during spin-coating the photoactive layer at room temperature and form nanoscale phase separated interpenetrating network of P3HT:PCBB-Cn blend films, which results in the improvement of photovoltaic performance of PSCs. A power conversion efficiency of 3.03% for the PSCs based on P3HT:PCBB-C10 was obtained without thermal annealing or solvent annealing. The thermal and solvent annealing-free fabrication using the fullerene dyads as acceptor is very important for the roll to roll production of PSCs with flexible large area.     

Entanglement effects in model polymer networks

Many fundamental questions for the understanding of polymer networks are more suitably addressed by current computer simulations than by experiments. Details of the microscopic topology, such as the elastically active cluster or loop entanglements, can be identified as well as controlled. In particular, it is possible to isolate and quantify their effects on macroscopic observables such as the elastic modulus. The constraints due to connectivity and conserved topology are more clearly present for networks than for melts. Already for strand lengths between crosslinks which are relatively short, the effect of the conserved topology is important. The mode relaxation in a network is significantly different from that of a melt. For weakly crosslinked systems the melt entanglement length is the relevant scaling parameter. The elastic modulus of a long chain network under ideal conditions reaches an asymptotic value which is about 2.2 times smaller than the prediction of an affine model for a network made of strands of the melt entanglement length. An analysis of the stress reveals that in the linear regime the contribution from the excluded volume is dominant compared to that from the connectivity along the strands. For larger elongations, however, the non-linear elastic response is dominated by the chemically and topologically shortest paths through the system, where chemical crosslinks and topological entanglements between meshes of the network play a similarly important role.     

Nucleation and crystallization of H-shaped (PS)2PEG(PS)2 block copolymers

<正>A series of H-shaped(PS)_2PEG(PS)_2 block copolymers with different PS chain lengths were prepared.The influence of different confinements active on the crystallization and self-nucleation(SN) behavior of the PEG blocks was investigated by differential scanning calorimetry(DSC).When the content of the crystalline block was high,a classical SN behavior was obtained.The block copolymer with PEG content of 49%(by weight) showed a classical SN behavior with a narrow self-nucleation domain and had bimodal crystallization exotherms.When the PEG dispersed as separated microdomains in the block copolymer,the self-nucleation domain disappeared and only annealing was observed.     

Synthesis and investigation of polyphenyldimethylsiloxane block copolymers with bimodal chain length distribution of oligodimethylsiloxane blocks

Siloxane block copolymers containing linear dimethylsiloxane (DMS) and cyclolinear phenylsilsesquioxane blocks were synthesized. A peculiarity of the copolymers is a bimodal distribution of linear DMS blocks in the polymer chain. The results of X-ray diffraction. thermomechanical, and DSC studies of bimodal block copolymers indicate a higher degree of microphase separation of the blocks as compared to unimodal block copolymers. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1542–1546, September, 2000.