Long‐range order in physical networks of gel‐forming triblock copolymer solutions

Structural studies on physical gels, based on a triblock copolymer and a solvent selective for its midblocks, are presented. Gel formation in such systems arises due to interconnected microdomains that form the junctions in a three‐dimensional network. Small angle X‐ray scattering studies revealed that the physical networks show either short‐range order, described by an effective hard sphere model, or long‐range order, where junctions are arranged on a cubic lattice. The emerging morphology depends on the thermal conditions during preparation of such systems, which essentially reflects a competition among microdomain ordering and formation of the physical network. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1833–1840, 1999     

Local mobility in network junctions of gels based on hydrophobically modified polyacrylamides

Spin-probe ESR spectroscopy is employed to study the local mobility in junctions of physical networks in gels of hydrophobically modified polyacrylamides. These junctions are formed owing to self-association of alkyl groups containing 12 carbon atoms. It is shown that, irrespective of the mode of covalent binding between the alkyl groups and the polymer backbone (via either ester or amide groups) and the degree of macromolecule blockiness, the local mobility in the gel network junctions is almost an order of magnitude lower than that in the hydrophobic core of a micelle of the low-molecular-mass surfactant sodium dodecyl sulfate.     

Molecular structure and morphology of membrane-forming copolymers of tolylene diurea and poly(dimethylsiloxane)

The molecular structure of tolylene diurea and poly(dimethylsiloxane) copolymers has been studied by the methods of mechanical and dielectric losses, photoelasticity, and X-ray analysis. The above copolymers are found to experience microphase separation. The radius of gyration of domains formed by the hard blocks based on tolylene diurea was estimated as R ≈ 30 Å. Hard blocks connected by the hydrogen bonds in domains are shown to be perpendicular to directions of the maximum extension of domains. The proposed molecular model of a membrane based on the above copolymer includes a molecular network composed of flexible poly(dimethylsiloxane) chains connected by physical junctions; the above physical junctions are domains formed by the thermodynamically hard blocks of tolylene diurea.     

Comparison of results from the more informative version of TMA with other methods of polymer testing

Summary Several characteristics of the topological regions determined by the more informative version of TMA for cured rubbers based on NR/CPE and NR/ENR blends as well as PA6/cured rubber blends correlate with static and dynamic mechanical properties. These rubbers differ substantially in the structure of their network and the related topological structure because CPE does not participate in cross-links when ENR can do it. The physical interactions caused by these additives also vary, due to the different polarity that influences the formation of physical networking junctions. In blends of PA6 and cured rubber the networking junctions are assumed as being physical nature only. From these facts and the above-mentioned results it could be preliminarily concluded that the correlation depends on the formulation and related structure of the composite, and on which of the characteristics have been compared. To understand the reasons for the existence, or lack of, correlation observed, further investigations are needed.     

In situ forming physical hydrogels for three-dimensional tissue morphogenesis

In situ forming physical hydrogels are formed through a biologically benign reaction between two multi-arm macromers, one containing terminal thiol and the other containing terminal vinyl sulfone groups. One macromer is self-assembled through a coiled-coil domain; and the physical junction of this macromer confers the physical nature to the whole network. Unlike covalently cross-linked hydrogels in which material degradation is a prerequisite for three-dimensional cell movement, these physical hydrogels have junctions that undergo reversible dissociation and re-association, constitutively opening paths for cell movement. Epithelial cells encapsulated in these hydrogels can form hollow spherical cysts without the need for material degradation.     

General dynamic theory of macromolecular networks. II. Dynamics of network deformation

On the basis of the general concepts of a macromolecular network as defined in the preceding paper, a detailed analysis of forces acting on a network chain is given. In all types of networks the chain tension involves elastic, diffusional, contact friction and internal viscosity terms; in entanglement networks there appears also an additional term associated with chain–chain friction at entanglement junctions. The force balance equation for a tetrafunctional network junction is derived. It is shown that exact formulation of this equation requires knowledge of the simultaneous configurations of all the network chains in the system. For energetic networks, solution of the force balance equation is not required for the determination of the distribution function; and the dynamics of such networks can be discussed in terms of a distribution function for a single chain. On the other hand, for entanglement and contact networks, where the force balance equation is a source of information about sliding rates, some simplified equations can be formulated and solved, by using a 4(N + 1)-dimensional distribution function for a single macromolecule with N network junctions. It is shown that for both network classes with nonlocalized junctions the position of a network chain within the macromolecule plays an essential role and is a source of the effects of molecular weight on the physical behavior of the system. The analysis of forces acting on a network chain reveals also some essential differences in the dynamic behavior of energetic, entanglement and contact networks and thus confirms the significance of the classification proposed in the preceding paper.     

Application of the Gaussian theory of elastomeric networks to native proteins: analysis of fluctuations and the dynamic scattering function

The junctions of an elastomeric network fluctuate about well-defined mean positions under the effects of covalently-bonded chains attached to the junctions. The residues of native proteins fluctuate about well-defined mean positions under the Lennard-Jones, dipole moment, hydrogen bond and electrostatic forces exerted by spatially neighbouring residues. Both an elastomer and a native protein are elastic bodies in this respect, and therefore share many structural features. The magnitude of fluctuations of the junctions in networks is significant, leading to their well-known interesting features. The ratio of root-mean-square fluctuations of the distance between two spatially neighbouring residues to the distance between them is of the same order of magnitude as that between two network junctions joined by a network chain. Based on the analogy of the network and protein structure, the method of evaluating the fluctuations of residues and the dynamic coherent and incoherent scattering functions is described and sample calculations for two model proteins are presented.     

Effects of added surfactants on thermoreversible gelation of associating polymer solutions

The influence of added surfactants on physical properties of associating polymer solutions was examined by a new statistical‐mechanical theory of associating polymer solutions with multiple junctions and by computer simulation. The sol–gel transition line, the spinodal line, and the number of elastically effective chains in the mixed networks were calculated as functions of the concentration of added surfactants. All of them exhibited nonmonotonic behavior as a result of the following two competing mechanisms. One was the formation of new mixed micelles by binding surfactants onto the polymer associative groups. These micelles serve as crosslink junctions and promote gelation. The other was the replacement of polymer associative groups in the already formed network junctions by added surfactants. Such replacement lowers connectivity of junctions and destroys networks. The critical micelle concentration was also calculated. The results are compared with the reported experimental data on poly(ethylene oxide)‐based associating polymers and hydrophobically modified cellulose derivatives. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 733–751, 2004     

Photochromism of diarylethene: Effect of polymer environment and effects on surfaces

A diarylethene (DAE) study using thermodynamical physical chemistry, elemental fractal analysis, and quantum chemistry is presented. Attention is focused on the ways the polymer environment affects DAE photochromism and on the ways that DAE photochromism affects surfaces. Non-constant quantum yields in single-molecule measurements, selective metal deposition, and a super-water-repellent fractal surface are discussed after a short summary of the latest experimental results concerning photochromism in DAE molecules.     

Effect of annealing on the viscoelastic and viscoplastic responses of low‐density polyethylene

Two series of tensile tests with constant crosshead speeds (ranging from 5 to 200 mm/min) and tensile relaxation tests (at strains from 0.03 to 0.09) were performed on low‐density polyethylene in the subyield region of deformations at room temperature. Mechanical tests were carried out on nonannealed specimens and on samples annealed for 24 h at the temperatures T = 50, 60, 70, 80, and 100 °C. Constitutive equations were derived for the time‐dependent response of semicrystalline polymers at isothermal deformations with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical crosslinks, and lamellar blocks). The network is thought of as an ensemble of mesoregions linked with each other. The viscoelastic behavior of a polymer is modeled as a thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects sliding of junctions in the network with respect to their reference positions driven by macrostrains. Stress‐strain relations involve five material constants that were found by fitting the observations. Fair agreement was demonstrated between the experimental data and the results of numerical simulation. This study focuses on the effects of strain rate and annealing temperature on the adjustable parameters in the constitutive equations. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1638–1655, 2003     

Scattering form factors for self-assembled network junctions

The equilibrium microstructures in microemulsions and other self-assembled systems show complex, connected shapes such as symmetric bicontinuous spongelike structures and asymmetric bicontinuous networks formed by cylinders interconnected at junctions. In microemulsions, these cylinder network microstructures may mediate the structural transition from a spherical or globular phase to the bicontinuous microstructure. To understand the structural and statistical properties of such cylinder network microstructures as measured by scattering experiments, models are needed to extract the real-space structure from the scattering data. In this paper, we calculate the scattering functions appropriate for cylinder network microstructures. We focus on such networks that contain a high density of network junctions that connect the cylindrical elements. In this limit, the network microstructure can be regarded as an assembly of randomly oriented, closed packed network junctions (i.e., the cylinder scattering contributions are neglected). Accordingly, the scattering spectrum of the network microstructure can be calculated as the product of the junction number density, the junction form factor, which describes the scattering from the surface of a single junction, and a structure factor, which describes the local correlations of different junctions due to junction interactions (including their excluded volume). This approach is applied to analyze the scattering data from a bicontinuous microemulsion with equal volumes of water and oil. In a second approach, we included the cylinder scattering contribution in the junction form factor by calculating the scattering intensity of Y junctions to which three rods with spherical cross section are attached. The respective theoretical predictions are compared with results of neutron scattering measurements on a water-in-oil microemulsion with a connected microstructure.     

Local mobility and rheological characteristics of gels based on hydrophobically modified poly(acrylamides)

For hydrophobically modified poly(acryl amide), we analyze the effect of various parameters of the macromolecular structure (number and length of side hydrophobic groups, content of charged groups, type of bonding between side chains and the polymer backbone, and the degree of blocking of hydrophobic groups distributed along the chain) on the local mobility of physical network junctions and rheological characteristics of gels. We have found that the local mobility measured by the method of spin-probe EPR spectroscopy is either independent or it slightly depends on the above parameters. At the same time, these parameters exert a strong effect on the rheological characteristics of gels. This disagreement can be explained by the fact that local mobility of junctions is primarily controlled by the intermolecular interactions of hydrophobic groups and by the covalent bonding between these groups and a macromolecule. However, the rheological characteristics depend on the number of junctions, their dimensions, and other parameters.     

Theory of relaxation spectra and dielectric relaxation of rigid rodlike particles incorporated in a polymer network

The theory of molecular mobility and relaxation spectra is developed for rodlike particles embedded in a polymer network with allowance for the involvement of the particles in collective network dynamics through topological entanglements with network fragments. A regular cubic coarse-grained network model is used, where the motion of junctions describes the mobility of large fragments (domains) of the initial network with a size equal to the distance between adjacent rodlike particles. The involvement of the rods in collective network dynamics is taken into account by introducing an effective quasi-elastic potential acting between the rods and junctions of the coarse-grained network and preventing long-distance diffusion of the embedded particles. The viscoelastic parameters of the coarse-grained (“renormalized”) network are functions of the viscoelastic characteristics of the initial network. The relaxation time spectra are calculated as well as the frequency dependences of the dielectric loss factor of the embedded particles that possess a permanent dipole moment directed along the major axis of each rod. Depending on the ratio between the viscoelastic characteristics of the rods and the network, the frequency dependence of the dielectric loss factor may have two maxima. The high-frequency maximum corresponds to local orientational movements of particles at fixed junctions of the coarse-grained network, which correspond to the position of the domain centers in the initial network. The low-frequency maximum corresponds to movements of particles involved in large-scale dynamics of network fragments. The dependence of the dielectric loss factor on the ratio between the viscoelastic parameters of the rods and the network is studied.     

Estimating the molecular mass between epoxy-amine network junctions from glass-transition-temperature data

The average molecular mass between network junctions is estimated for several epoxy-amine systems of various compositions with comparable molecular masses of the epoxy oligomer and the curing agent. This estimation is based on the experimental data on glass-transition temperatures of curing epoxy-amine mixtures. The constant that relates these physicochemical characteristics is dependent on the nature of the epoxy-amine system and the rigidity of polymer chains located between network junctions. Correlations are found between the constant and the glass-transition temperature of the crosslinked epoxy-amine system and between the constant and the difference in the glass-transition temperatures of uncured and ultimately cured epoxy-amine systems.     

Dielectric relaxation of polymer networks built from macromolecules with dipole moment directed along the end-to-end chain vector

The dielectric relaxation properties are considered for polymer networks built from polar macromolecules with the dipole moment directed along the end-to-end chain vector. The viscoeleastic cubic model of a regular network is used. The fixed average volume of a polymer network is ensured by the effective internal pressure. The dynamic models of polymer networks with external and interchain friction are studied. Two cases are considered: (1) polar chains cross-linked in a network at their ends, and (2) a densely cross-linked network with many network junctions per polar chain. The expressions for the autocorrelation functions of the total dipole moment of a network, which determine the dielectric susceptibility, are calculated. The relaxation spectrum of the autocorrelation function consists of two regions: the high-frequency relaxation spectrum of a chain fragment between two neighbouring junctions (intrachain relaxation spectrum) and the lowfrequency interchain relaxation spectrum. The interchain relaxation spectrum is determined by cooperative motions of chains which form a network. The characteristic time of this spectrum for networks of type (1) is the relaxation time of a chain between junctions τ_min. For networks of type (2) a second time scale τ₁ exists, which corresponds to motions inside the volume occupied by a single long polar chain included in a network. It leads to different time behaviour of the autocorrelation functions for both network models. The existence of only interchain friction in the network model leads to a cut-off of the relaxation spectrum at the time τ_max depending on the volume of viscous interchain interactions.     

Deformation of elastomeric polyolefin spherulites

The ethylene‐octene block copolymers in this study consist of long crystallizable sequences with low comonomer content alternating with rubbery amorphous blocks with high comonomer content. The crystallizable blocks form lamellae that organize into space‐filling spherulites even when the fraction of crystallizable block is so low that the crystallinity is only 7%. These unusual spherulites are highly elastic and recover from strains as high as 300%. This new class of thermoplastic elastomers is fundamentally different from conventional elastomeric olefin copolymers that depend on isolated, fringed micellar‐like crystals to provide the junctions for the elastomeric network. The elastomeric block copolymers are shown to be unique in that a hierarchical organization of space‐filling lamellar spherulites provides the junctions for the elastomeric network. The deformation of the elastic spherulites is readily studied with small angle light scattering, wide angle X‐ray diffractograms, and atomic force microscopy. At strains in excess of 300%, the spherulites break up into a fibrillar structure following lamellar deformation processes that are similar to those established for high density ethylenic polymers. The crystalline transformation produces a stiffer elastomer that exhibits complete recovery on subsequent loadings. Similar experiments on elastomeric random ethylene‐octene copolymers where fringed micellar crystals provide the physical crosslinks that connect the rubbery, amorphous chain segments reveal significant differences. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1313–1330, 2009     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

Simple presentation of network theory of rubber,with a discussion of other theories

The approximations implicit in the use of the Gaussian network model for soft rubber are discussed. It is shown that the form of the stress–strain curve can be derived for this model simply, and without special assumptions about the form or behavior of the network. The common assumption that the network junctions are fixed, or can be treated as fixed, is discussed. It is shown that this picture of the situation is unrealistic: the junctions have a Brownian motion comparable to that of any portion of the intervening molecular segments. The introduction of this assumption is not generally admissible, but it will not affect the outcome of certain types of calculation; in particular, one can foresee that it need not affect the calculated form of the stress-strain curve. A particularly simple and straightforward calculation of the network entropy on this basis is given. Wall's theory of rubber is analysed. It is shown that Wall's postulates are not consistent with the network structure of rubber, and in general lead to different results.