Transient Polymer Networks Research Articles

Dynamics in Supramolecular Polymer Networks Formed by Associating Telechelic Chains

We present hybrid molecular dynamics/Monte Carlo simulations of supramolecular networks formed by unentangled telechelic chains with sticky end monomers (or stickers) of finite functionality. The reversible bonding between sticky monomers leads to the formation of sticker clusters with well-defined size distribution, which in turn work as cross-links for transient polymer networks. We study the kinetics of sticky monomer association, the topological structure, and the resulting dynamic and rheological behavior of the supramolecular systems as a function of the sticker bonding energy e and the parent polymer chain length. Percolated transient networks are formed above a threshold bonding energy around 4.3kBT. At high bonding energies e ≥ 10kBT, the majority of the stickers are fully reacted and the fraction of open stickers is less than 1%. The conventional picture of a single sticker hopping from one cluster to another is energetically unfavorable. We find the dynamic and rheological behavior of such stro...

Self-Diffusion of Associating Star-Shaped Polymers

The dynamics of associating bonds in transient polymer networks exerts a paramount influence on their relaxation and time-dependent mechanical properties. In particular, diffusive motion of polymers mediated by the dissociation and association equilibrium of reversible junctions can affect the materials’ structural stability, dynamic mechanical properties, and a broad spectrum of functionality that arises from the constant motion of polymer chains. In this work, forced Rayleigh scattering is used to measure the diffusion of terpyridine end-functionalized four-arm poly(ethylene glycol) polymers transiently interlinked by zinc ions in organic solvent across a wide range of length and time scales. Phenomenological superdiffusion, where the scaling of the squared length dimension vs time has a power-law exponent larger than one, is demonstrated as an intrinsic feature of these networks due to the interplay of chain dissociation and diffusion. Outside the superdiffusive regime, normal Fickian diffusion is reco...

Stress Relaxation, Dynamics, and Plasticity of Transient Polymer Networks

We propose a theoretical framework for dealing with a transient polymer network undergoing small deformations, based on the rate of breaking and re-forming of network crosslinks and the evolving elastic reference state. In this framework, the characteristics of the deformed transient network at microscopic and macroscopic scales are naturally unified. Microscopically, the breakage rate of the crosslinks is affected by the local force acting on the chain. Macroscopically, we use the classical continuum model for rubber elasticity to describe the structure of the deformation energy, whose reference state is defined dynamically according to when crosslinks are broken and formed. With this, the constitutive relation can be obtained. We study three applications of the theory in uniaxial stretching geometry: for the stress relaxation after an instantaneous step strain is imposed, for the stress overshoot and subsequent decay in the plastic regime when a strain ramp is applied, and for the cycle of stretching and release. We compare the model predictions with experimental data on stress relaxation and stress overshoot in physically bonded thermoplastic elastomers and in vitrimer networks.

Effect of Supramolecular Interchain Sticking on the Low-Frequency Relaxation of Transient Polymer Networks.

Supramolecular polymer networks and gels often exhibit three effects in rheology as a function of increasing strength and extent of transient chain interlinkage: (i) the longest relaxation time increases, (ii) the elastic part of the complex shear modulus on timescales longer than that increases, and (iii) the frequency-dependent power-law scaling of this modulus gets shallower in this regime. In a recent report, these effects have been systematically assessed by comparing transient polymer networks derived from a common precursor modified with different extents of a common hydrogen-bonding supramolecular sticker. In this communication, complementary studies are discussed that are based on a set of polymers also derived from a common precursor but all modified with the same extent (4.8%) of very different supramolecular crosslinking motifs. This comparison reveals that effect (iii) can be rationalized by exacerbation of polydispersity effects to the relaxation time spectrum if supramolecular interchain sticking is present. In addition, effect (ii) is addressable to a simple thermodynamic argument that appraises the supramolecular sticking contribution to the elastic part of the shear modulus in the relaxation regime.

Dynamics of Entangled Linear Supramolecular Chains with Sticky Side Groups: Influence of Hindered Fluctuations

The design and effective application of supramolecular transient polymer networks based on the assembly of entangled polymer building blocks requires not only precise description of relaxation mechanisms of the chain segments but also inclusion of the kinetics of reversible formation and breakage of reversible supramolecular interactions. In this work we extend the tube-based time marching algorithm to the entangled associative polymers with sticky side groups, with special emphasis on the effect of hindered fluctuations, besides sticky Rouse and sticky reptation. Two different approaches are introduced for inclusion of hindered fluctuations comprising fluctuations with extra penalty for deeper segments and stepwise fluctuations by extra friction. It is shown that there is a transition zone in dynamic moduli between the characteristic lifetime of the stickers and emergence of the final relaxation slopes, which can be characterized by almost parallel drop of loss and storage moduli with slope of 0.5 that c...

Single-Chain Conformation for Interacting Poly(N-isopropylacrylamide) in Aqueous Solution

The demixing phase behavior of Poly(N-isopropylacrylamide) (PNIPAM) aqueous solution is investigated using small-angle neutron scattering. This polymer phase separates upon heating and demixes around 32 ∘C. The pre-transition temperature range is characterized by two scattering modes; a low-Q (large-scale) signal and a high-Q dissolved chains signal. In order to get insight into this pre-transition region, especially the origin of the low-Q (large-scale) structure, the zero average contrast method is used in order to isolate single-chain conformations even in the demixing polymers transition region. This method consists of measuring deuterated and non-deuterated polymers dissolved in mixtures of deuterated and non-deuterated water for which the polymer scattering length density matches the solvent scattering length density. A fixed 4% polymer mass fraction is used in a contrast variation series where the d-water/h-water fraction is varied in order to determine the match point. The zero average contrast (match point) sample displays pure single-chain scattering with no interchain contributions. Our measurements prove that the large scale structure in this polymer solution is due to a transient polymer network formed through hydrophobic segment-segment interactions. Scattering intensity increases when the temperature gets close to the phase boundary. While the apparent radius of gyration increases substantially at the Lower Critical Solution Temperature (LCST) transition due to strong interchain correlation, the single-chain true radius of gyration has been found to decrease slightly with temperature when approaching the transition.

Relaxation and Dynamics in Transient Polymer Model Networks

Supramolecular polymer networks have promising potential to serve as self-healing soft materials. To benefit from this ability, quantitative understanding of the underlying mechanisms of macromolecular dynamics and transient association must be achieved. A key to obtaining such understanding is to understand the dynamics and relaxation of supramolecular polymer networks, which is often complexed by inhomogeneous polymer-network structures. To overcome this limitation, we use a set of regular star-shaped poly(ethylene glycol) polymers end-capped with terpyridine groups that can transiently coordinate to different metal ions, thereby forming transient supramolecular polymer networks with determined homogeneous architectures and determined binding strength. We study these networks in view of their mechanics, dynamics, and relaxation from both macroscopic and microscopic perspectives through the use of rheology, dynamic light scattering, and fluorescence recovery after photobleaching. These studies reveal tha...

Photothermal Deformation of a Transient Polymer Network

Gold nanoparticles (GNPs) are embedded in a highly entangled solution of an ultrahigh molar mass polymer (polystyrene Mw = 16 800 kg/mol in toluene). When an isolated GNP is heated by a focused laser beam, the solvent is attracted to and the polymer is pushed away from the particle surface by thermophoretic forces, thereby elastically deforming the transient polymer network. Because of the long disentanglement time, the randomly distributed GNPs are trapped in the meshes of the transient polymer network and allow for a visual observation of the network deformation field using an optical microscope. The observed displacement field of the meshes is of long-ranged nature and only limited by the finite size of the cuvette, despite of the local heating of a single submicrometer-sized GNP.

Viscoelastic interface motion in semidilute polymer solutions

We study interface motion in phase separated semidilute polymer solutions near the critical point. We derive the non-Markovian equation for motion of an interface taking into account the viscoelastic effects due to the transient polymer network and the hydrodynamic interaction between interfaces. This equation indicates that the velocity of an interface is affected by the history of the past velocity when the characteristic length scale of domains is shorter than , where d0 is the capillary length and ξve is the viscoelastic length. We also study growth of a droplet in metastable polymer solutions. The growth is much decelerated when the radius of a droplet is smaller than .

Effects of component molecular weight on the viscoelastic properties of thermoreversible supramolecular ion gels via hydrogen bonding

We describe a thermoreversible supramolecular ion gel system consisting of a poly(2-vinylpyridine-b-ethylene oxide-b-2-vinylpyridine) (P2VP-PEO-P2VP) triblock copolymer, a poly(4-vinylphenol) (PVPh) linear homopolymer, and a room-temperature ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([EMI][TFSA]). Aggregates of intermolecularly hydrogen-bonded PVPh cross-linkers form cross-links, connecting P2VP-PEO-P2VP triblock chains into a transient polymer network through hydrogen bonding with the P2VP endblocks. The viscoelastic properties of the resulting gels are strongly temperature-dependent, as manifested by the 15 orders of magnitude variation in the longest relaxation time (τ1) from the gel temperature (Tgel) down to room temperature. Wide temperature- and frequency-independent rubbery plateaus are distinct, indicating the formation of a well-defined network structure. The applicability of time-temperature superposition to this system is striking, suggesting the invariance of the underlying relaxation mechanism. The terminal relaxation dynamics of these hydrogen-bonded supramolecular networks is dramatically retarded upon increasing the P2VP endblock length. In contrast, their viscoelastic properties are relatively insensitive to the PVPh cross-linker length. These results are consistent with the hypothesis that τ1 is determined by the average lifetime of a P2VP ↔ PVPh association, which is directly related to the number of hydrogen bonds involved. Besides their potential applications in various electrochemical devices, these materials might also be used in surface coatings, where thermally reversible and sensitive viscoelastic properties are highly advantageous.

Fracture and Self-Healing in a Well-Defined Self-Assembled Polymer Network

We studied shear-induced fracture and self-healing of well-defined transient polymer networks formed by telechelic polypeptides, with nodes formed by collagen-like triple helices. When these gels are sheared at a rate that is higher than the inverse relaxation time of the nodes, fracture occurs at a critical stress which increases logarithmically with increasing shear rate. When a constant stress is applied, fracture occurs after a delay time that decreases exponentially with increasing stress. These observations indicate that fracture in these systems is due to stress-activated rupture of triple-helical junctions. After rupture, the physical gels heal completely.

Intermittent dynamics in transient polymer networks under shear: Signs of self-organized criticality

In this paper we demonstrate an unusual behavior in the shear-banded flow of a viscoelastic fluid. We report large and patterned fluctuations in the shear stress in an apparently fluid material undergoing steady shear, which we interpret as an intermittent and microscopic fracture and self-healing process. The statistical pattern of the fluctuations is indicative of self-organized criticality, and their magnitude can be directly related to the constitutive instability that underlies the shear banding.

Failure-mode transition in transient polymer networks with particle-based simulations

Transient polymer networks are known to undergo a wide variety of viscoelastic flow instabilities. In this paper we investigate two of these flow failure modes: shear banding and melt fracture. Using particle-based simulations we reveal a transition from gradient banding to fracture in transient polymer networks with reversible associative nodes. We discuss the failure-mode transition on the basis of an energetic and a kinetic approach to fracturing in soft materials.

Brownian particles in transient polymer networks

We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings.

Rouse Dynamics of Colloids Bound to Polymer Networks

We present experimental evidence of a transition in the short-time Brownian motion of colloids from diffusive to subdiffusive, Rouse-like. This transition is seen for particles that are bound, through physical adsorption, to transient polymer networks. The characteristic Rouse scaling of the mean square particle displacement with radical t, found in the experiments, is rationalized using an analytical bead-spring model of a large particle anchored to a set of polymer chains.

Local and Global Dynamics of Transient Polymer Networks and Swollen Gels Anchored on Solid Surfaces

We employ fluorescence correlation spectroscopy to study length dependent dynamics in transient and grafted cross-linked poly(N-isopropylacrylamide) (PNIPAAm) networks at different concentrations and cross-link densities, respectively. For nondilute PNIPAAm solutions, the molecular diffusants appear to sense local dynamics on the length scale of the mesh size obtained from photon correlation spectroscopy, whereas a polymer probe, comparable to the PNIPAAm size, reveals global chain motions. The relation of the tracer Brownian diffusion to the mesh size can be utilized to characterize permanently cross-linked and grafted PNIPAAm networks.

Molecular origin of shear thickening in transient polymer networks: A molecular dynamics study

This paper proposes a simple model of transient networks of telechelic associating polymers for molecular simulations and reports the main results obtained by molecular dynamics on the rheological properties of the transient networks. The steady shear viscosity obtained by the non-equilibrium molecular dynamics simulation exhibits shear thickening at moderate shear rates and shear thinning at larger shear rates. The behavior is similar to that observed in experiments of telechelic associating polymers. By analyzing the distribution function of the end-to-end vector of bridge chains as a function of the shear rate, we find that shear thickening is mainly caused by the stress from the bridge chains highly stretched by shear flow. We also find that fracture of the transient network occurs in the shear-thinning regime at high shear rates.

Rheological study of transient polymer networks crosslinked by two-component associative groups—Inversion of the gel skeletal structure

On the basis of transient network theory, we study linear viscoelasticity of physical gels formed by polymers that carry two different species of associative groups. The simplest but an important case, discussed in this paper, treats linear chains carrying two A functional groups at both ends and one B group at the center of the chain. It turns out that the complex modulus is described by the two-mode Maxwell model when condition βA≫βB or βA≪βB holds, where βi (i=A,B) is the detaching rate of an i associative group from the junction. In the latter case, two rubbery plateaus appear in the storage modulus, and structural transformations from a network of A backbone to that of connected B micelles are expected to occur at characteristic frequency of ω≃βA+βB.

Theory of Transient Polymer Networks Crosslinked by Two Different Associative Groups

Co-associating polymers (CAP) are new type of polymers carrying two different species of associative groups along the polymer backbone. Transient gels of CAP show many new interesting thermodynamical and rheological properties such as network inversion, reentrant gelation etc. In this paper, we study linear viscoelasticity of physical gels formed by CAP on the basis of transient network theory. Model CAP to be treated here are difunctional (A-B) and trifunctional (A-A-B) linear polymers, where A and B stand for the associative groups. It turns out that the dynamic shear moduli of difunctional (heterotelechelic) A-B polymers behave like a Maxwell fluid with a single relaxation time τAB=1/(βA+βB), where βi(i =A, B) are the dissociation rates of associative groups from the network junctions. On the other hand, shear moduli of trifunctional A-A-B polymers are well described by the two-mode Maxwell model with two relaxation times τAB and τAA=1/(2βA) when A groups are much less frequently dissociated from the junctions compared with B groups. In such case, structural transformations of the network are expected to occur at a characteristic frequency ω≈1/ τAB where two distinct rubbery plateaux meet.

Complex formed in the system hydrophobically modified polyethylene glycol/methylated α-cyclodextrin/water. An NMR diffusometry study

In aqueous solutions hydrophobically modified polyethylene glycol (HM-PEG) forms a transient polymer network held together by intermolecular hydrophobic associations. In the present investigation we have used NMR-diffusometry to study how the addition of methylated alpha-cyclodextrin (M-alpha-CD) influences the polymer network. The addit on of M-alpha-CD resulted in an increased mean self-diffusion of HM-PEG, DHM-PEG, which is referred to a degradation of the polymer network when hydrophobic associations are disrupted due to complex formation between the hydrophobic groups of HM-PEG and M-alpha-CD. Addition of small amounts of M-alpha-CD results in a dramatic increase in DHM-PEG. Upon further addition of M-a-CD the increase in DHM-PEG is less dramatic and at excess M-alpha-CD, DHM-PEG levels off and equals the mean self-diffusion coefficient for unmodified PEG with the same molecular weight. The suggested interpretation is that the addition of the first molecules of M-alpha-CD mainly reduces the probability for hydrophobic associations inter-connecting different clusters of polymer micelles whereas at higher M-alpha-CD concentrations a disengagement of the individual clusters into separate HM-PEG molecules becomes important. (C) 2003 Elsevier B.V. All rights reserved. (Less)