Cross-linking Junctions Research Articles

Theoretical Study of Molecular Association and Thermoreversible Gelation in Polymers

This paper reviews our recent theoretical studies of molecular association and thermoreversible gelation in polymer solutions and blends. We first classify fundamental types of association, and propose their static and dynamic characterization. We then develope general theory of associating polymers to study phase transitions induced by molecular association. These transitions include macro- and microphase separation, micellization, hydration, thermoreversible gelation and liquid-crystalization. As for the origin of associative forces, we focus on hydrogen bonding and hydrophobic aggregation. Detailed study on thermoreversible gelation with multiple cross-link junctions is presented. Paying special attention to the multiplicity and sequence length of the network junctions, we derive phase diagrams with coexisting gelation and phase separation, and compare them with experimental data. Local and global structures of the gel networks are studied from molecular point of view. The theory is applied to more complex thermoreversible gels such as binary networks (interpenetrating networks, alternating networks and randomely mixed networks), hydrated networks with high-temperature gelation, gelation strongly coupled to polymer conformational transitions such as coil-to-helix transition. To study dynamics of thermoreversible gels, a simple transient network model is introduced, and creation and annihilation of junctions in the networks are theoretically described. Stationary non-linear viscosity and the dynamic mechanical moduli are calculated as functions of the shear rate, frequency and the chain disengagement rate. From the peak of the loss modulus, the lifetime τ× of the junction is estimated, and from the high frequency plateau of the storage modulus, the number of elastically effective chains in the network is found. Transient phenomena such as stress relaxation and stress overshoot are also theoretically studied. Results are compared with the recent experimental reports on the rheological study of hydrophobically modified water-soluble polymers.

Theoretical and Computational Study of Thermoreversible Gelation

Abstract This paper reviews recent theoretical and computational studies of thermoreversible gelation with multiple cross-link junctions in associating polymers. Paying special attention to the multiplicity and sequence length of the network junctions, we derive phase diagrams with coexisting gelation and phase separation. Local and global structures of the gel networks are studied. The conventional Eldridge–Ferry method is extended to allow for simultaneous evaluation of multiplicity and sequence length (or enthalpy of the cross-links), and applied to the experimental gel melting curves of poly(vinylalcohol) in water. On the basis of the Scanlan–Case criterion, we calculate the number of elastically effective chains and of dangling ends in the network as functions of polymer concentration and temperature. The effect of added surfactants on the formation of thermoreversible gels (surfactant-mediated gelation) in hydrophobically modified associating polymer solutions is also studied under the assumption of the existence of a minimum multiplicity required for stable cross-links. Competition between intramolecular micellization and intermolecular cross-linking is also studied with special attention to the formation of flower micelles.

Crystallization of the polyethylene block in polystyrene-b-polyethylene-b-polycaprolactone triblock copolymers, 1. Self-nucleation behavior

The self-nucleation of branched polyethylene chains of different degrees of chain mobility was studied. The polyethylene block (PE block) within poly(styrene-b-ethylene-b-caprolactone) triblock copolymers (SEC) of varying compositions was studied. Differential scanning calorimetry was used to determine the self-nucleation domains as a function of the self-nucleation temperature (Ts). The self-nucleation behavior of PE chains within SEC block copolymers was found to be anomalous in comparison to the classical self-nucleation behavior exhibited by homopolymers. When the degree of chain constraint is high, as in the case where the SEC copolymer only contains 15% of PE, domain II (only self-nucleation domain) completely disappears and annealing can take place before self-nucleation occurs. This means that chain constraint complicates the self-nucleation process and this situation persists until, upon decreasing the self-nucleation temperature (Ts), annealing has generated crystals that are big enough to act as self-nuclei for the less restricted portions of the chain. If the PE content in the copolymer is very low (15%), two crystal populations can be distinguished. This may reflect the differences in diffusion of the PE chain segments close to the interfaces with the other two blocks and those segments that are close to the middle of the PE block. The influence of chain constraint on determining the difficulty of the chains to self-nucleate was further explored using a crosslinked low-density polyethylene (XLDPE). In this case, crosslinking junctions instead of covalent links with other blocks restrict chain mobility. Nevertheless, a similar difficulty in self-nucleation was found as in the case of the PE block within SEC triblock copolymers in contrast to neat LDPE, a polymer that exhibited the classical self-nucleation behavior with the usual three domains.

Crystallization of the polyethylene block in polystyrene-b-polyethylene-b-polycaprolactone triblock copolymers, 1. Self-nucleation behavior

The self-nucleation of branched polyethylene chains of different degrees of chain mobility was studied. The polyethylene block (PE block) within poly(styrene-b-ethylene-b-caprolactone) triblock copolymers (SEC) of varying compositions was studied. Differential scanning caloriometry was used to determine the self-nucleation domains as a function of the self-nucleation temperature (T s ). The self-nucleation behavior of PE chains within SEC block copolymers was found to be anomalous in comparison to the classical self-nucleation behavior exhibited by homopolymers. When the degree of chain constraint is high, as in the the case where the SEC copolymer only contains 15% of PE, domain II (only self-nucleation domain) completely disappears and annealing can take place before self-nucleation occurs. This means that chain constraint complicates the self-nucleation process and this situation persists until, upon decreasing the self-nucleation temperature (T s ), annealing has generated crystals tha are big enough to act a self-nuclei for the less restricted portions of the chain. If the PE content in the copolymer is very low (15%), two crystal populations can be distinguished. This may reflect the differences in diffusion of the PE chain segments close to the interfaces with the other two blocks and those segments that are close to the middle of the PE block. the influence of chain constraint on determining the difficulty of the chains to self-nucleate was further explored using a crosslinked low-density polyethylene (XLDPE). In this case, crosslinking junctions instead of covalent links with other blocks restrict chain mobility. Nevertheless, a similar difficulty in self-nucleation was found as in the case of the PE block within SEC triblock copolymers in contrast to neat LDPE, a polymer that exhibited the classical self-nucleation behavior with the usual three domains.

Thermoreversible Gelation Strongly Coupled to Polymer Conformational Transition

The effect of polymer conformational transition on thermoreversible gelation with multiple cross-link junctions in natural and synthetic polymers is studied on the basis of the recent theory of associating polymers. The effective number of associative groups carried by each chain in such solutions is not a fixed number but varies with conformation change induced by the temperature and other environmental conditions. Transition from intra- to intermolecular bonding due to denaturation of some proteins on heating leads to high-temperature gelation, while coil-to-helix transition (or coil-to-globule transition), followed by aggregation of helices (globules), leads to low-temperature gelation. We calculate the sol/gel transition concentration as a function of temperature and find that, in both cases, it is not a monotonic function but takes a minimum value at an intermediate temperature. At low temperatures gelation is prevented due to the lack of active groups or due to the strict restriction in helix sequence selection. Typical phase diagrams in which sol/gel transition coexists with phase separation are derived.

Intramolecular and intermolecular association in thermoreversible gelation of hydrophobically modified associating polymers

In the thermoreversible gelation of hydrophobically modified water-soluble associating polymers, intramolecular association competes with intermolecular association. The former leads to intramolecular micelles with hydrophobic cores decorated by loops of hydrophilic chains. Loop formation prevents an intermolecular cross-linking. This paper theoretically details the effect of small loops on the sol/gel transition with multiple cross-link junctions in associating polymer solutions. In the case of telechelic associating polymers, the problem is shown to be mathematically equivalent to the mixture of monofunctional and bifunctional polymers. The gelation concentration changes with a parameter describing the probability of a single loop formation. Relative populations of the six fundamental chain categories are derived as a function of the total polymer concentration with special attention to the formation of flower micelles. For polymers carrying many hydrophobes, Monte Carlo computer simulation is carried out by using model chains to see how intramolecular micellization competes with intermolecular cross-linking.

The effect of uniaxial deformation on swollen gels

The effect of uniaxial deformation on swollen gels is investigated. The elastic contribution is obtained by a extension of the modified Flory model proposed previously. Following Bastide, it is assumed that the deformation occurs by a process of topological rearrangements of the cross-link junctions. Consequently, the contracted junction affine model is used to describe the relationship between the macroscopic deformation and the resulting chain deformation. Using this simple approach, we examine the effect of deformation on the relative degree of swelling ( φ g /φ gm ) and the packing factor.

Thermoreversible gelation of associating polymers

This paper studies sol/gel transition of associating polymers with multiple cross-link junctions. Paying special attention to the multiplicity and sequence length of the network junctions, we derive phase diagrams and analyze molecular structure of the networks. The conventional Eldridge–Ferry method is extended to evaluate multiplicity, as well as enthalpy, of the cross links, and applied to the experimental gel melting curves of poly(vinyl alcohol) in water. The effect of added surfactants on the formation of reversible gels in hydrophobically modified polymer solutions is also studied under the assumption of the existence of a minimum multiplicity required for stable cross-links. On the basis of the transient network model with temporal junctions, we calculate dynamic mechanical moduli, average lifetime of a junction, the number of elastically effective chains and of dangling ends as functions of the strength of the association constant, polymer concentration and the temperature. We compare the results with the experimentally measured moduli of hydrophobically modified poly(ethylene oxide).

Effects of hydroxy compounds on gel formation of gelatin

Network formation of gelatin gel is known to consist of three-dimensionally cross-linked triple helices among polypeptide chains. The effects of added low molecular weight mono-ols, diols and polyols on the higher-order structure formation of gelatin chains were investigated using the following measurements: melting temperature, viscoelasticity and spin-lattice relaxation time (Ti) of H217O of gels, and circular dichroism spectra of diluted gelatin solutions. Furthermore, hydration behaviors of these hydroxy compounds were evaluated from the dynamic hydration numbers (nDHN) derived from T1 of H217O in the solutions. It was found that network structures of gelatin gels containing hydoxy compounds were influenced by the number and position of hydroxyl groups as well as the number of carbon atoms of these coexisting compounds. The effect of hydroxyl groups of hydroxy compounds was considered to stabilize the helices among gelatin chains. Especially, the addition of polyols with large number of hydroxyl groups increased the number of cross-linking junctions in the gel networks, which consist of the aggregation among the helices. On the contrary, the effect of carbon atoms of hydroxy compounds is to disturb the formation of the helices and the aggregation among the helices.

Structure of polyelectrolyte hydrogels studied by SANS

The structure of hydrogels based on sodium polyacrylate and crosslinked by different low- and high-molecular-weight compounds is studied by small-angle neutron scattering (SANS). It is shown that the size of heterogeneities in the vicinity of crosslinking junctions does not depend on the molecular weight of the polyfunctional crosslinking agents used. The dependence of heterogeneity dimensions on the gel concentration (or degree of swelling) was measured. It showed a maximum which was interpreted by analogy to the concentration behaviour of specific viscosity of polyelectrolyte solutions.

Rotational Dynamics of Naphthalene-Labeled Cross-link Junctions in Poly(dimethylsiloxane) Elastomers

A series of end-linked poly(dimethylsiloxane) (PDMS) networks were prepared with different cross-link functionalities and molecular weights. This was achieved by simultaneous end-linking and self-condensation of a trifunctional silane cross-link precursor. These networks had a nonpolar naphthalene chromophore covalently attached to a fraction of the cross-link junctions. We probe the time-dependent reorientation of the naphthalene, and infer reorientation of the cross-links, by determining the time-dependence of the fluorescence depolarization in the picosecond time domain. A two-step relaxation model describes the orientational dynamics. Fast, partial depolarization in a restricted geometry is superimposed on a slower relaxation that completely depolarizes the fluorescence. We determine the two rotational diffusion constants at temperatures varying from 235 to 298 K, while we vary network parameters such as cross-link density, molecular weight, and macroscopic strain. These diffusion constants have an Arrhenius activation energy of 11.4 ( 0.8 kJ/mol. The fast relaxation is driven by motions of a few chain segments; this process is dominated by the density of the network polymer around the labeled cross-links. The slower, complete reorientation is driven by cooperative motions of a larger number of chain segments connected to the cross-link that are insensitive to steric constraints in the immediate vicinity of the cross-links. I. Introduction Model networks of known molecular weight between crosslinks, Mc, and cross-link functionality, , are used to test molecular theories of rubber elasticity. These networks can be prepared by end-linking telechelic polymers using a-functional cross-linking precursor. For this study, we prepared PDMS elastomers through the condensation reaction of hydroxyterminated PDMS with hydrolyzed trifunctional alkoxysilanes. In the presence of water and a catalyst this reaction is not quantitative, since the hydrolyzed alkoxysilanes will react with each other in a self-condensation reaction, forming silane clusters with an effective average functionality avg > , resulting in an elastically active cross-link density, Ia. The relative rates of the end-linking and homopolymerization reactions will determine the size and functionality distribution of the cross-link junctions and other network structure parameters. By manipulation of the stoichiometry, the resulting PDMS network structure and, hence, the mechanical, transport, and swelling properties can be controlled. We determine the swelling behavior of the various PDMS networks and use swelling theory to make assumptions about the network structure.

Photophysical studies of probes bound to cross-link junctions in poly(dimethylsiloxane) elastomers and nanocomposites

Abstract

Statistical mechanics of macromolecular networks without replicas

We report on a novel approach to the Deam-Edwards model for interacting polymeric networks without using replicas. Our approach utilizes the fact that a network modelled from a single non-interacting Gaussian chain of macroscopic size can be solved exactly, even for randomly distributed crosslinking junctions. We derive an {\it exact} expression for the partition function of such a generalized Gaussian structure in the presence of random external fields and for its scattering function $S_0$. We show that $S_0$ of a randomly crosslinked Gaussian network (RCGN) is a self-averaging quantity and depends only on crosslink concentration $M/N$, where $M$ and $N$ are the total numbers of crosslinks and monomers. From our derivation we find that the radius of gyration $R_{\mbox{\tiny g}}$ of a RCGN is of the universal form $R_{\mbox{\tiny g}}^2=(0.26 \pm 0.01)a^2 N/M$, with $a$ being the Kuhn length. To treat the excluded volume effect in a systematic, perturbative manner, we expand the Deam-Edwards partition function in terms of density fluctuations analogous to the theory of linear polymers. For a highly crosslinked interacting network we derive an expression for the free energy of the system in terms of $S_0$ which has the same role in our model as the Debye function for linear polymers. Our ideas are easily generalized to crosslinked polymer blends which are treated within a modified version of Leibler's mean field theory for block copolymers.

Selective Sorption and Solvation in Dansyl-Labeled Poly(dimethylsiloxane) Networks Swollen in Binary Solvent Mixtures

Poly(dimethylsiloxane) (PDMS) networks were fluorescently labeled with the 1-(dimethylamino)-5-naphthalenesulfonyl (dansyl) chromophore. The networks were prepared by end-linking silanol-terminated PDMS with a mixture of methyltriethoxysilane (MTES) and N-((triethoxysilyl)propyl)dansylamide (DTES). The selective sorption behavior of these networks swollen in binary mixtures of 1,4-dioxane and a series of water and linear alcohols was studied. Refractometry and equilibrium swelling measurements were used to determine the amounts of PDMS and solvent components inside the swollen networks. We find that the cosolvency behavior of the solvent mixture depends on the alkyl chain length of the amphiprotic solvent. Steady-state fluorescence spectra of the dansyl compound dissolved in binary solvent mixtures are compared to the fluorescence of dansyl-labeled networks swollen with the same solvent mixture. Differences in emission energy are related to differences in the polarity of the solvation shells surrounding the dansyl moieties. The composition around the labeled cross-link junctions is compared with the bulk composition to determine spatial heterogeneity in the distribution of solvent and polymer molecules. We find that while dioxane is preferentially sorbed, the alcohols preferentially solvate the fluorescent moieties. Water has a tendency to cluster inside the networks that is stronger than its tendency to preferentially solvate dansyl.

Reactive Blending via Metal-Olefin Coordination in Diene Polymers. Solid-State Properties That Support the Concept of a Network Structure

This study focuses on the properties of solid films formed from tetrahydrofuran solutions containing diene polymers, polybutadiene or polyisoprene, and an inorganic salt, bis(acetonitrile)-dichloropalladium(II). Upon mixing, effective cross-links are formed, because the acetonitrile ligands of the palladium salt are displaced by olefinic pendant groups of the polymers. Infrared data measured herein and previous studies of the chemistry of palladium compounds suggest that a Heck-like mechanism is operative to generate chemical cross-links via palladium-catalyzed reactions. The swelling behavior of polybutadiene and polyisoprene was studied in various solvents. In both cases, equilibrium swelling ratios decrease with an increase in salt content, indirectly supporting the concept of a network structure. Using the Flory-Rehner relation, the number-average molecular weight between cross-link junction points (M c ) was calculated from the swelling data. Relative to the undiluted polymers, the mechanical properties of polybutadiene and polyisoprene solid films show a dramatic increase of 3 orders of magnitude in Young's modulus of elasticity when the palladium salt content is 4 mol %. Thermogravimetric measurements show that an increase in the transition-metal salt (PdCl 2 ) content, as well as annealing at 80 °C, enhances the thermal stability of solid films. The glass transition temperatures (T g ) of solid films determined by differential scanning calorimetry increase with PdCl 2 content until the thermal plateau is achieved between 1 and 3 mol % palladium salt, where the increase in T g (i.e., ΔT g ) is approximately 100 °C relative to the undiluted polymer.

Structure of Poly(vinyl alcohol) Gels Studied by Wide- and Small-Angle Neutron Scattering

The structure of poly(vinyl alcohol) (PVA) gels formed in a mixture of deuterated DMSO and heavy water at 23°C has been investigated. It was directly confirmed from the wide-angle neutron scattering measurements that cross-linking points or junction points in the gels are crystallites. In the small-angle scattering measurements, it was found that the scattering intensity I(Q) decreases with Q according to the -4th power law (Porod's law) in the Q range above 0.05 A -1 where Q=4π sin θ/λ (2θ and λ are scattering angle and wavelength of neutron, respectively), suggesting that the surface of the crystallites has a clear boundary

Measurement of crosslinking degree for electron beam irradiated block copolymers

AbstractThe molecular weight between crosslinking junctions (Mc) of styrene‐butadiene‐styrene (SBS) and that of styrene‐isoprene‐styrene (SIS) irradiated by electron beams (5 Mrad to 100 Mrad) was measured by dynamic modulus, glass transition temperature, static modulus, and swelling. The change in dynamic modulus at low temperature was smaller than that at high temperature in both SBS and SIS. The shift of Tg to higher temperature was observed in both SBS, and SIS systems except for 100 Mrad of SIS. Both dynamic and static moduli increased with irradiation doses, however, the change of static modulus was smaller than that of dynamic one. Those mechanical measurements were compared with the swelling measurements and discussed.

Junction Dynamics and the Elasticity of Networks

The restrictions on the configurations available to the cross-link junctions of a network, arising from its presence in a dense phase, have a well-established effect on the mechanical properties of elastomers. These constraints give rive to intermolecular cooperativity of the junction motions and hence can be well described by models of constraint dynamics in relaxation phenomena. This connection between junction dynamics and elasticity of networks is illustrated by comparing the predictions of the coupling model of relaxation with the constrained junction model of Flory. The comparison is borne out by recent 31 P NMR results on network

Segmental order in uniaxially strained bimodal polymer networks: a deuterium-NMR study

The segmental orientational order generated in bimodal poly(dimethylsiloxane) networks under uniaxial stress is probed using 2 H-NMR. The induced segmental order is measured either on «short» chains (M n = 3000 g /mol) or on «long» chains (M n = 25000 g/mol). The segmental orientation is very similar for both kinds of chains and decreases linearly as the volume fraction Φ L of «long» chain increases. A mean field analysis including orientational correlations between segments is developed and accounts for these observations. Additionally, this study has been carried out on twosets of samples with different crosslinkers. It shows clearly that the induced orientational order depends on the nature of the crosslinking junctions

A simple model for the swelling of polymer networks

The Flory–Rehner approach to the solvent swelling of polymer networks is modified so as to abandon the affine deformation assumption. Instead, it is assumed that swelling occurs by a process of disinterspersion of cross-link junctions, and relationships between chain expansion and segment concentration are established using the ideas of de Gennes. Using this approach, we also examine osmotic deswelling, aspects of phase equilibria, and the maximum observed in differential swelling measurements.