Influence of solvent size on the mechanical properties and rheology of polydimethylsiloxane-based polymeric gels

Soft polymeric gels have utility in a broad range of medical, industrial, and military applications, which has led to an extensive research investment over the past several decades. While most gel research exploits a cross-linked polymer network swollen with small molecule solvents, this article systematically investigates the impact of the solvent molecular weight on the resulting gel mechanical properties. The model polymer gel was composed of a chemically cross-linked polydimethylsiloxane (PDMS) network loaded with a non-reactive PDMS solvent. In addition to investigating the impact of solvent loading, the solvent molecular weight was varied from 423,000 g/mol to 1250 g/mol, broadly spanning the molecular weight of entanglement for PDMS (MW_ENT ∼29,000 g/mol). The gels exhibited a strong frequency dependent mechanical response when the solvent molecular weight >MW_ENT. In addition, scaling factors of shear storage modulus versus solvent loading displayed a distinct decrease from the theoretical value for networks formed in a theta solvent of 2.3 with increasing measurement frequency and solvent molecular weight. The frequency dependent shear storage modulus could be shifted by the ratio of solvent molecular weights to the 3.4 power to form a master curve at a particular solvent loading indicating that mobility of entangled solvent plays a critical role for the mechanical response. In addition, the incorporation of entangled solvent can increase the toughness of the PDMS gels.     

The mechanism of cavitation-induced polymer scission; experimental and computational verification

In this paper we describe qualitatively and quantitatively the non-random scission of polymers by ultrasound. Scission experiments have been performed using monodisperse polymethyl methacrylate dissolved in methyl methacrylate, showing that fracture occurs close to the center of the polymer chain. A mechanism is proposed for this non-random fracture, from which it can be concluded that complete stretching of the polymer chains is required before breakage can occur. The developed model, which is a combination of strain rate and drag force calculations, predicts a limiting molecular weight, which has experimentally been confirmed. The scission rate depends almost quadratically on the molecular weight, which is derived by modeling the experimental time-dependent molecular weight distributions. This dependence supports the requirement of complete stretching of the polymer chain before breakage. The developed degradation model is also capable to describe the effects of various process variables on cavitation-induced polymer scission.     

Change in molecular weight of hyaluronic acid during measurement with a cone-plate rotational viscometer

It was shown using a cone-plate rotational viscometer that the apparent viscosity of a dilute aqueous solution of sodium hyaluronate decreased gradually during the measurement. Hyaluronic acid (HA) forms a characteristic network by entanglements coupling, so two hypotheses could be postulated from the reduction of viscosity due to shearing stress. One was that disentanglement of the temporary network occurred, and the other was that scission of HA chains was responsible. In this study, the reason for the reduction in viscosity was clarified using high-performance gel permeation chromatography with low-angle laser light scattering. It was thus demonstrated that chain scission occurred during the viscometric measurement. On the assumption that the HA degradation was caused by shearing stress, the effects of shearing rate, the initial molecular weight, salt, and polymer concentrations of samples were investigated. High molecular weight HA chains were preferably severed. From the change in polydispersity of the samples it was inferred that due to the viscoelasticity of HA solution scission behavior would differ, depending on the shearing rate. Also, the salt and polymer concentrations were found to exert large influences on the degradation. Thus, it was concluded that the scission rate was related to the expansion of HA molecules in solution. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:2199–2206, 1998     

Effects of solvent and concentration on scission of polymers with high-speed stirring

The effects of solvent and concentration on scission of polymers such as poly(methyl methacrylate) (PMMA) and polystyrene (PSt) in solution by high-speed stirring were investigated. Solvents were chloroform (good), benzene (intermediate), and ethyl acetate (poor) for PMMA and methyl ethyl ketone (good), toluene (intermediate) and dioxane (poor) for PSt, respectively. Concentration was varied from 0.04 to 2% w/v. The rate of scission of polymer chains was higher and the final molecular weight was lower in a good solvent than in a poor solvent at a low concentration for both polymers, but vice versa at a high concentration except for PSt in methyl ethyl ketone. Concentration dependence of the scission was large in a good solvent but small in a poor one. Polymer chains were ruptured to lower molecular weights with decreasing concentration, regardless of kind of polymer and solvent, showing that they were more easily broken in the isolated state.     

Characteristics of zwitterionic sulfobetaine acrylamide polymer and the hydrogels prepared by free-radical polymerization and effects of physical and chemical crosslinks on the UCST

A zwitterionic sulfobetaine polymer, poly(N,N-dimethyl(acrylamidopropyl) ammonium propane sulfonate) (poly(DMAAPS)), and the hydrogels of this polymer were synthesized by free-radical polymerization in an aqueous redox system using a wide range of monomer concentrations (C_m). The resulting polymers were characterized in terms of polymer yield, intrinsic viscosity, molecular weight, gel fraction, and thermoresponsive phase-transition behavior. Parameters in the Mark–Houwink–Sakurada equation, including the molecular-weight exponent α, were determined for poly(DMAAPS) in 0.1 M NaCl aqueous solution. The physical state and transparency of the poly(DMAAPS) samples were strongly dependent on C_m and temperature. At higher values of C_m (i.e. above a critical molecular weight), poly(DMAAPS) became a gel comprising a physically crosslinked network consisting of entangled polymer chains and interchain associations of the zwitterionic groups. The poly(DMAAPS) solutions or gels exhibited a thermoresponsive phase transition with an upper critical solution temperature (UCST). The gels obtained were completely soluble in aqueous NaCl solution at ambient temperature as well as in water at temperatures above UCST. The effects of molecular weight, chemical crosslink density and copolymerization on the UCST were also elucidated.     

Structural and mechanical properties of advanced polymer gels with rigid side-chains using coarse-grained molecular dynamics

Computational modeling was utilized to design complex polymer networks and gels which display enhanced and tunable mechanical properties. Our approach focuses on overcoming traditional design limitations often encountered in the formulation of simple, single polymer networks. Here, we use a coarse-grained model to study an end-linked flexible polymer network diluted with branched polymer solvent chains, where the latter chains are composed of rigid side-chains or “spikes” attached to a flexible backbone. In order to reduce the entropy penalty of the flexible polymer chains these rigid “spikes” will aggregate into clusters, but the extent of aggregation was shown to depend on the size and distribution of the rigid side-chains. When the “spikes” are short, we observe a lower degree of aggregation, while long “spikes” will aggregate to form an additional secondary network. As a result, the tensile relaxation modulus of the latter system is considerably greater than the modulus of conventional gels and is approximately constant, forming an equilibrium zone for a broad range of time. In this system, the attached long “spikes” create a continuous phase that contributes to a simultaneous increase in tensile stress, relaxation modulus and fracture resistance. Elastic properties and deformation mechanisms of these branched polymers were also studied under tensile deformation at various strain rates. Through this study we show that the architecture of this branched polymer can be optimized and thus the elastic properties of these advanced polymer networks can be tuned for specific applications.     

Brittle–ductile transition of double network hydrogels: Mechanical balance of two networks as the key factor

Tough double network (DN) hydrogels are a kind of interpenetrating network (IPN) gels with a contrasting structure; they consist of a rigid and brittle 1st network with dilute, densely cross-linked short chains and a soft and ductile 2nd network with concentrated, loosely cross-linked long chains. In this work, we focus on how the brittle gel changes into a tough one by increasing the amount of ductile component. By comparing the molecular structures of the individual first network and second network gels, we found that the true key mechanical factor that governs the brittle–ductile transition is the fracture stress ratio of the two networks, σ_f,2/σ_f,1. This ratio is related to the density ratio of elastically effective polymer strands of the two networks, ν_e,2/ν_e,1, where the inter-network topological entanglement makes dominant contribution to ν_e,2. When ν_e,2/ν_e,1 < k = 3.8−9.5, the second network fractures right after the fracture of the first network, and the gels are brittle. When ν_e,2/ν_e,1 > k, only the first network fractures. As a result, the brittle first network serves as sacrificial bonds, imparting toughness of DN gels. The study also confirms that the load transfer between the two networks is via inter-network topological entanglement. This result provides essential information to design tough materials based on the double network concept.     

PH-induced structure change of poly(vinyl alcohol) hydrogel crosslinked with poly(acrylic acid)

The structure of the hydrogel of poly(vinyl alcohol) (PVA) and poly(acrylic acid) (PAA) was investigated by small angle X-ray scattering (SAXS) of synchrotron radiation. A physically crosslinked blend gel, which was prepared by repetitive freezing and thawing of an aqueous solution of PVA and PAA, could be chemically crosslinked by esterfication of PVA with PAA even in the hydrogel state. The chemical crosslinking induced the destruction of physical crosslinks into a folded structure, indicating that the chemical crosslinking proceeds at the sites around the physical crosslinks that contain PVA and PAA in much higher concentration than other portion of the gel. The pH-induced structure changes of the PVA hydrogels, chemically crosslinked with poly(acrylic acid) (PAA) were investigated by SAXS on the samples of various chemical crosslinking time. The gels were shrunk at pH4, and swollen at pH8. The results of SAXS showed, that the Porod slope changed with chemical crosslinking time from -3.5 to ?2.9 at pH4, and from ?2.9 to ?2.4 at pH8. The results suggest that a folded structure as a structural domain, which is characterized by fractally rough interface, tends to change into the structure that corresponds to percolation cluster, particularly at pH8. The gels immersed in pH8 showed a remarkable structure change accompanying swelling. The results revealed that a conformational change of PAA chains, induced by the pH change, can be explained by the presence of a structural domain in the gel network, where both PVA chains and PAA chains get entangled and partially form a interpenetrating polymer network(IPN).     

Physical model of interface and interphase performance in composite materials and bonded polymers

The ‘rheological model’ of adhesion developed by Gent and Schultz significantly broadened the applicability of the thermodynamic model of adhesion by accounting not only for the thermodynamic energy of adhesion, but also for the irreversibly dissipated energy occurring during viscoelastic and plastic deformations occurring in the deformed materials and at the crack tip. This paper provides a review of further, most recent and significant developments of the physical models of adhesion proposed by de Gennes, Léger, Brochard-Wyart and others. It analyzes the theoretical background and experimental results concerning the enhancement of adhesion by surface-grafted molecular chains. These are anchored at the substrate surface and entangled with the crosslinked network of the adjacent polymer. The extraction of the entangled connector molecular chains, when grafted at the optimum surface density, provides significant increase in the bond strength or fracture energy. It occurs due to the energy dissipation taking place during extraction and deformation or fracture of strained macromolecular chains at the propagating crack's tip zone.     

Molecular weight dependence of the fracture toughness of glassy polymers arising from crack propagation through a craze

We investigate criteria for craze failure at a crack tip and the dependence of craze failure on the molecular weight of the polymer. Our micromechanics model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load bearing capacity so that they can transfer stress between the main fibrils. This load transfer mechanism allows the normal stress on the fibrils directly ahead of the crack tip in the center of the craze to reach the breaking stress of the polymer chains. We solve for stress field near the crack trip and use it to relate craze failure to the external loading and microstructural quantities such as the craze widening (drawing) stress, the fibril spacing, the molecular weight, and the force to break a single polymer chain. The relationship between energy flow to the crack tip due to external loading and the work of local fracture by fibril breakdown is also obtained. Our analysis shows that the normal stress acting on the fibrils at the crack tip increases linearly as the square root of the craze thickness, assuming that the normal stress distribution is uniform and is equal to the drawing stress acting on the craze-bulk interface. The critical crack opening displacement, and hence the fracture toghness is shown to be proportional to [1–(M_e/qM_n)]², where M_e is the entanglement molecular weight, M_n is the number average molecular weight of polymer before crazing, and q is the fraction of entangled strands that do not undergo chain scission in forming the craze.     

Role of the Amorphous Morphology in Physical Properties of Ultra High Molecular Weight Polyethylene

The role of amorphous layer in the physical properties of ultra high molecular weight polyethylene (UHMWPE) was investigated. It revealed that the thicker amorphous layer would promote the toughness of polyethylene, but make a negative effect on the rigidity of the polymer. Furthermore, it would be easier for semicrystalline polymers with less entangled chains to bring out the interlamellar slippage that would absorb more energy during the deformation. Finally, promotion of the physical properties of UHMWPE was also achieved with the assistant of nano-modification and an excellent relativity between the physical properties and the amorphous thickness (la) was obtained.     

Flow-assisted degradation in dilute polystyrene solutions

The flow-assisted degradation behavior of polystyrene was studied as a function of solvent, polymer concentration, molecular weight, and molecular weight distribution. To obtain data at concentrations as low as 100 parts per million by weight, turbulent drag reduction measurements were used to augment the usual analytical techniques of viscosity and gel permeation chromatography. Turbulent flow measurements were found to be a valuable technique for evaluating the effects of degradation: the drag reduction onset point provides information about the largest molecules in the sample while the flow rate dependence is related to the shape of the top part of the molecular weight distribution. For the polymers and flow conditions studied, the degradation causes a shift in the distribution to lower molecular weights with little change in the shape. This suggests a complex mechanism where the probability of bond scission is not random but varies along the polymer backbone.     

Deformation and toughness of polymeric systems: 3. Influence of crosslink density

In part 1 of this series the phenomenon of a critical ligament thickness (ID_c) below which brittle polymers become ductile was investigated for polystyrene (PS). Using the thermoplastic polystyrene-poly(2,6-dimethyl-1,4-phenylene ether) (PS-PPE) model system, it was demonstrated in part 2 of this series that the absolute value of ID_c as well as the maximum toughness (i.e. maximum strain to break) was dependent on the network density of the polymer used. In this study the toughness and ID_c of crosslinked thermosetting polymers were investigated using epoxides based on the diglycidyl ether of bisphenol A as a model system. The crosslink density (v_c) is varied between values comparable with (v_c = 9 × 10²⁵ chains m⁻³), up to values much higher than (v_c = 235 × 10²⁵ chains m⁻³), the entanglement density in the thermoplastic PS-PPE system. The maximum macroscopic toughness proportional to the strain to break (λ_macr) or given by the slow-speed fracture toughness (G_Ic) and the notched high-speed tensile toughness (G_h) of core-shell rubber-modified epoxides uniquely increases with an increasing molecular weight between crosslinks (M_c). Only by using extreme testing conditions (notched high-speed impact testing), could the ID_c of a limited range of epoxides be determined: 0.21 μm (v_c = 9 × 10²⁵ chains m⁻³) ≤ ID_c ≤ 0.29 μm (v_c = 14 × 10²⁵ chains m⁻³). Both the experimentally determined values of ID_c and the toughness of the epoxides compare well with the values determined for the entangled thermoplastic PS-PPE model system in the same range of network densities, elucidating the principal similarity of the influence of entanglements and crosslinks on the deformation processes. Good agreement was observed between the experimentally determined values of ID_c of the epoxides and the values predicted by the simple model introduced in part 2 of this series.     

Linear viscoelastic relaxation modulus of polydisperse poly(dimethylsiloxane) melts containing unentangled chains

This work analyzes the relationship between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and its molecular weight distribution (MWD) when a fraction of the sample contains chains with molecular weight M lower than the effective critical molecular weight between entanglements Mc_eff. This effective critical parameter is defined in terms of the critical molecular weight between entanglements M_c of the bulk polymer that forms the physical network and the effective mass fraction Wc_eff of the unentangled chains. In the terminal zone of the linear viscoelastic response, the double reptation mixing rule for blended entangled chains and a modified law for the relaxation time of chains in a polydisperse matrix are considered, where the effect of chains with M<Mc_eff is included. Although chain reptation with contour length fluctuations and tube constraint release are still the relevant mechanisms of chain relaxation in the terminal zone when the polydispersity is high, it is found that the presence of a fraction of molecules with M<Mc_eff modifies substantially the tube constrain release mode of chain relaxation. In this sense, a modified relaxation law for polymer chains in a polydisperse entangled melt that includes the effect of the MWD of unentangled chains is proposed. This law is validated with rheometric data of linear viscoelasticity for well-characterized polydimethylsiloxane (PDMS) blends and their MWD obtained from size exclusion chromatography. The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mc_eff. This mechanism is independent from the MWD. The unentangled chains with M<Mc_eff occluded in the polymer network also follow Rouse modes of relaxation although they exhibit dependence on the MWD.     

Molecular structure and morphology of crosslinked polyethylene in an aged hot-water pipe

Internally pressurized crosslinked polyethylene (XLPE) pipes fail according to one of the three following mechanisms: (a) stage I fracture occurs at the highest stresses and is ductile when large defects are absent; (b) stage II fracture is brittle and occurs at intermediate stress levels; (c) stage III fracture occurs at the lowest stress levels and is brittle. It has been assumed that the material in a pipe which fails according to the last mechanism is chemically degraded. This paper presents data obtained by thermal analysis, X-ray diffraction, infrared spectroscopy, and gel permeation chromatography on samples taken at different radial positions from a pipe of XLPE (crosslinked by peroxide) which failed according to the stage III mechanism after 17,136 h when subjected to 2.62 MPa hoop stress at 110°C (internal water/external air). These data are compared with data from samples of an unexposed reference pipe. Highly degraded brown spots, referred to as “oxidation spots”, are visible in the aged pipe. The puncture fracture occurred in one of these oxidation spots. The increase in melting point and crystallinity, the decrease in fold surface free energy, the almost invariant crystal unit cell, the decrease in gel content, the decrease in molecular weight of the soluble fraction and the formation of carbonyl arid hydroxyl groups at the inner wall in the aged pipe compared with the properties of the unexposed pipe are consistent with an oxidative degradation of the amorphous chain segments including scission of entangled chains and interlamellar tie chains. The latter is the main reason for the major reduction in strength of the aged pipe leading to stage III failure. The thickness of the inner wall layer of highly oxidized material was about 5 mm in the oxidation spots and only 0.5 mm elsewhere in the aged 10 mm thick pipe.     

Rheological behaviors of randomly crosslinked low density polyethylene and its gel network

Dicumy peroxide (DCP) modification of low density polyethylene (LDPE) below gel point (GP) produces modified LDPE (mLDPE) with wide molecular weight distributions while the random crosslinking beyond GP yields crosslinked LDPE (XLPE). Molecular weight distributions of mLDPE below GP and the sol-fractions of XLPE above GP were investigated. The sol-fractions in XLPE were extracted to prepare XLPE gels of different crosslinking densities. Both XLPE and the gels were subjected to shear action for studying dynamic rheology and relaxation modulus in the linearity region for revealing the role of entanglements and dangling chains to viscoelasticity of the randomly crosslinked network. The results revealed that the sol-fractions with molecular weight much higher than entanglement molecular weight contributed to equilibrium modulus in addition to the gel network, which lowered the DCP dosage for appearance of critical gel behavior of XLPE in comparison with the XLPE gel. However, rheological method yielded critical DCP dosages for appearance of apparent gel behaviors far beyond the chemical GP from the extraction experiment. The sol-fraction residing in the network gave rise to additional contribution to relaxation modulus of XLPE, shortening network relaxation time and improving equilibrium modulus.     

The Sizes of Polymer Molecules and the GPC Separation

Abstract

This introductory review explains in simplest terms the separation mechanism in GPC and the concept of size as its discriminant. Sample molecules permeate the gel to different degrees depending on their size and are kept out of the solvent stream in the interstices in correspondingly different time ratios. For rigid molecules the size is determined either by the volume or by the most prominent linear dimension. A better approximation seems to be Giddings's “mean external length.”

With polymers the decisive size parameter is the hydrodynamic volume. Its calculation from molecular weight must take into account the coiling of the polymer, its flexibility, and its interaction with the solvent. Another important consideration is the statistical nature of polymer properties which results in average values for molecular weight and size. Chain statistics yield polymer sizes that are compatible with pore dimensions of appropriate gels.     

Controlled Mesoporosity in SiOC via Chemically Bonded Polymeric “Spacers”

Silicon oxycarbides with controlled porosity in the mesopore range have been obtained through high‐temperature pyrolysis of newly developed reactive siloxane formulations. The starting gels have been synthesized via Pt catalyzed hydrosilylation reaction between polyhydromethylsiloxane (PHMS) and vinyl‐terminated polydimethylsiloxane (PDMS) of different molecular weights in the presence of tetravinyltetramethylcyclotetrasiloxane as a crosslinking enhancer. In our approach, the PDMS serves the double purpose of size‐controlling templating agent as well as solvent at the early stages of the synthesis. During the curing step, the vinyl‐terminated PDMS is chemically bonded to the preceramic network through the extremely efficient hydrosilylation reaction and “solidify.” Accordingly, its removal during pyrolysis occurs through decomposition of a solid phase with retention of the formed porosity. The structural and morphological evolution of the preceramic gels containing the molecular spacers have been investigated as a function of the thermal treatment temperature by N₂ physisorption measurements, thermogravimetry, and SEM analyses. The results show that the pore size distribution of the resulting SiOCs depends on the molecular weight of the PDMS and is directly related to the molecular volume assumimg that the PDMS chains are entangled into spheroidal shapes. The total pore volume is related to the initial amount of templating PDMS assuming its complete decomposition during pyrolysis.     

Toughening of an epoxy anhydride resin system using an epoxidized hyperbranched polymer

This paper reports on the use of an epoxidized hyperbranched polymer (HBP) as an additive to an epoxy anhydride resin system. The hyperbranched polymer used was an aliphatic polyester with a molecular weight of around 10 500 g mol^?1. The epoxy resin mixture used was a combination of a difunctional diglycidyl ether of bisphenol A (DGEBA) epoxy and an epoxy novolac, and was cured with a catalysed anhydride curing agent. It has been shown that, at a concentration range of 0 to 20 wt% addition, the HBP is able to almost double the fracture toughness, with little evidence of any deleterious effects upon processing and the durability of the cured resin system. The flexural modulus and stress, however, were found to both decrease by about 30% as a result of HBP addition while the T_g was found to decrease by about 10%. The processability of the uncured resin systems has been investigated by using rheological and calorimetric techniques and it was found that the processability window, as determined by the gel time and viscosity changes, was relatively unaffected by HBP addition. The fracture surfaces were evaluated by using scanning electron microscopy which showed that the unique structure of the HBP facilitates an enhanced interaction with the polymer matrix to achieve excellent toughness enhancement of the polymer matrix. The durability of the epoxy network has been investigated via thermogravimetric analysis (TGA) and solvent uptake, and the HBP has been shown to have little systematic deleterious effect upon the degradation temperatures and the total amount of solvent absorbed. Copyright © 2003 Society of Chemical Industry