Session Q45: Elastomers and Gels

Can a Rheological Experiment Distinguish Between a Gel and a Soft Glass? If yes, which Experiment?

Generic rheological differences between gels and soft glasses appear most pronounced in the \textit{immediate approach of the liquid-to-solid transition from the liquid side}. Two model systems of known linear viscoelasticitywere chosen to exemplify the two material classes: a crosslinking PDMS represents gelation and a concentrated, aqueous suspension represents the soft glass transition. The longest relaxation time and the zero shear viscosity diverge for both materials, which look very similar in this way. However, the relaxation time spectrum and its expression as complex modulus, with components G' and G'', provide a clear distinction between gelation and the soft glass transition. While the long-time component of the relaxation time spectrum follows a powerlaw in time for both, log $H\sim n$ log $t$, their powerlaw exponent $n $is of different sign: negative $n$ for the critical gel (material at the gel point) (Chambon et al. Polym Bull 13:499--503, 1885; Winter et al. J Rheology 30:367--382, 1986; Chambon et al. J Rheol 31:683--697, 1987) and positive $n$ for the soft glass (Siebenb\"{u}rger et al. J Rheology 53:707-720, 2009; Winter et al. Rheol Acta 48:747--753). The powerlaw spectrum is cut off by the diverging, longest relaxation time (called ``alpha relaxation time'' for the soft glass) in the approach of the liquid-to-solid transition. In summary, relaxation data provide a clear distinction between these two classes of materials.   

Effects of crosslinker concentration and chemical disorder on the nonlinear mechanics of thermoreversibly associating networks

We present simulation studies of thermoreversibly associating polymer networks that relate dramatic differences in nonlinear mechanics (e.\ g.\ creep and fracture) to differences in crosslinker placement and consequent differences in the equilibrium structure and quiescent dynamics of these systems. Our results illustrate how the greater structural and dynamical heterogeneity in systems possessing randomly placed crosslinkers leads to higher mobility, increased creep compliance and decreased fracture toughness in comparison to systems with uniformly spaced crosslinkers. Further quiescent-dynamical slowdown and mechanical property enhancement may be obtained through well-defined but nonuniform placement of crosslinkers. The variation of properties with crosslinker concentration $c$ and parent chain length $N$ is also investigated. Increasing characteristic chemical distances between crosslinkers decreases effects arising from network ``loops,'' the prevalence of which is closely associated with chemical order. At fixed $c$, while differences associated with chemical (dis)order decrease with increasing $N$, they remain dramatic in the $N \sim N_e$ regime which is often used in practical applications.   

Mechanically induced oscillations in Belousov-Zhabotinsky gels

Belousov-Zhabotinsky (BZ) gels are a unique class of stimuli-responsive materials that exhibit periodic changes in both color and size due to the self-oscillating kinetics of the BZ reduction-oxidation reaction. Such oscillations last for several hours, ending when a steady-state is reached in which the chemical reactants have been depleted. Here, we demonstrate that a depleted, non-oscillating BZ gel can be mechanically resuscitated, extending the oscillatory functionality of the material. These results represent the first experimental demonstration of mechanically induced oscillations in N-isopropylacrylamide-Ru(bpy)$_{3}$ gels. We characterize this phenomenon by quantifying the critical stress required to trigger oscillations, and the dependence of period and amplitude for triggered oscillations as a function of malonic acid concentration. Lastly, we demonstrate sensor applications comprising arrays of discrete BZ gel discs in which individual gels oscillate in color upon compression and have the capacity to transmit chemical signals away from the deformation site.   

Nonlinear Elasticity of Entangled Polymer Networks

We develop a microscopic model for elasticity of entangled polymer networks. The classical models of rubber elasticity (affine network and phantom network models) take into account only the effect of cross-links, but not the entanglements between polymer chains. For uniaxial deformation, the entanglement effects can be characterized by the dependence of Mooney ratio on network deformation. Constrained network models (such as constrained-junction and diffused-constraint models), tube models (such as Edwards' tube and nonaffine tube models) as well as phenomenological models (such as Mooney- Rivlin model) have been proposed to capture the experimentally observed dependence of Mooney ratio on network deformation. One of the latest efforts in the field is the slip-tube model, in which the entanglements are represented by slip-rings that can glide along the network chains but elastically constrained in space. The model we study improves over the original slip-tube model by taking into account harmonic interactions along the chain between such slip-links. We analytically and numerically solve the new microscopic model and present our results in comparisons with experimental and simulation data for both uniaxial and biaxial deformation.   

Coarse grain modeling of the high-rate stress-strain behavior for select model Poly[urethane urea] (PUU) elastomers

Microphase-separated PUU, which consists of 4,4'-dicyclohexylmethane diisocyanate, diethyltoluenediamine and poly[tetramethylene oxide](PTMO), exhibits versatile mechanical properties making them an excellent choice for potential applications in the form of films, adhesives, coatings and matrix materials for composites. To elucidate the effects of composition, including the hard segment content {\&} molecular weight of PTMO, on rate-dependent mechanical deformation in the high strain-rate regime ($>>$ 10$^{5}$/s) the stress-strain behavior for PUU at various rates are calculated for four model systems using a coarse-grain model. Pair interactions between topologically non-connected particles are described by the standard truncated Lennard-Jones (LJ) pair potential, where bonded particles interact according to the standard FENE/LJ potential. An angle harmonic potential is also used to enforce the rigidity of the hard segments, and the system is evolved using molecular dynamics. Stress-strain curves are calculated at various strain-rates and qualitatively agree with experimental results when extrapolated to higher rate. Further analysis of the morphology is also performed to characterize the morphology and discern its connection to the calculated mechanical properties.   

Swelling Behavior of Crosslinked Rubber: Does the Peak in Dilational Modulus Exist?

Previous work\footnote{G.B. McKenna and J.M. Crissman.J. Polym. Sci., Part B: Polym. Phys. 35, 817 (1997).} has shown that when handled properly, Frenkel\footnote{J. Frenkel, Acta Phys. USSR, 9, 235 (1938); Rubber Chem. Technol., 13, 264 (1940).}-Flory-Rehner\footnote{P. J. Flory and J. J. Rehner, Jr., J. Chem. Phys.,11, 521 (1943).}(FFR) theory is an excellent model to explain swelling behavior with the exception of failing to describe the peak of the swelling activity parameter S, or dilational modulus. This peak was first observed by Gee et al.\footnote{G. Gee, J. B. M. Herbert, and R. C. Roberts, Polymer, 6, 541 (1965).} and has eluded explanations. In the present work, we explored the importance of fitting procedure to the isopiestic data on the presence of the peak of S. We found the peak in S disappears when using a FFR model based fit instead of the empirical or polynomial fits used previously. We take model material parameters and show that adding less than 1{\%} random error to the theoretical curves can lead to the peak in S. Our findings suggest strongly that the ``peak'' in S is due to experimental errors that are amplified by the fitting method.   

Microphase Separation and Dynamics of Elastomeric Polyureas

Polyureas, consisting of alternating polyether soft segments and urea-containing hard segments, are of interest for shock and other energy absorbing applications. The properties of these materials are strongly influenced by microphase separation of the hard and soft segments, which is rather incomplete. Bulk- and solution-polymerized polyureas based on oligomeric polytetramethylene oxide and methylene diphenyl diisocyanate were investigated, and the role of PTMO molecular weight was identified. The morphology was characterized using atomic force microscopy and quantitative degrees of phase separation were determined from small-angle X-ray scattering. Dielectric relaxation spectroscopy and dynamic mechanical analysis were used to probe the dynamics. Particular attention was paid to the segmental dynamics of the soft phase, which has been proposed to be a major contributor to shock energy absorption in these materials.   

Opening and Closing of Nanocavities under Stress in Soft Nanocomposites: A Real Time Small Angle X-ray Scattering (SAXS) Observation

Cavitation occurring at the nanometer length scale has been recently demonstrated conclusively in rubbers$^{1}$. Real time SAXS with synchrotron radiation is employed to probe the structure changes in carbon black filled styrene-butadiene rubber (SBR) under uniaxial tension. The scattering invariant Q($\lambda )$, where $\lambda $ is the extension ratio, increases sharply, which we attribute to void formation, above a critical true stress ($\sim $25 MPa) that is roughly independent of both filler content and crosslinking density. During step-cycle tests Q decreases on unloading to Q$_{0}$, its value before any testing, and does not increase again until $\lambda $ exceeds the maximum previous $\lambda =\lambda _{max}$, showing that the voids close upon unloading and only reappear upon reloading when $\lambda \quad > \quad \lambda _{max}$ (Mullins effect). We attribute the increase of the scattering invariant once $\lambda $ exceeds $\lambda _{max}$ to the creation of new voids rather than to the reopening of old ones. The scattering of the voids in the region q $<$ 0.1 nm$^{-1}$ can be separated from that of the carbon black particles and provides information on average void size and shape.   

Reversible shape memory

An ``Achilles' heel'' of shape memory materials is that shape transformations triggered by an external stimulus are usually irreversible. Here we present a new concept of reversible transitions between two well-defined shapes by controlling hierarchic crystallization of a dual-network elastomer. The reversibility was demonstrated for different types of shape transformations including rod bending, winding of a helical coil, and widening an aperture. The distinct feature of the reversible shape alterations is that both counter-shapes are infinitely stable at a temperature of exploitation. Shape reversibility is highly desirable property in many practical applications such as non-surgical removal of a previously inserted catheter and handfree wrapping up of an earlier unraveled solar sail on a space shuttle.   

Inscribing dynamical patterns within heterogeneous self-oscillating gels.

Grafting the ruthenium catalyst to the network of swollen chemo-responsive polymer gel creates a new class of materials, which exhibit the autonomous, coupled chemical and mechanical oscillations induced by the ongoing Belousov-Zhabotinsky (BZ) reaction. The mechanical oscillations occur due to the hydrating effect of the oxidized Ru that causes the gel to swell and de-swell repeatedly. It was predicted previously that compartmentalization of BZ gels in a nonresponsive gel matrix would enable a researcher to create gel-based devices with the functionality inscribed by the configuration of the Ru-containing patches. Recently, the heterogeneous gels were fabricated that encompass the disk-shaped BZ patches. It was demonstrated experimentally for the first time that the direction of propagation of the chemo-mechanical waves in an array of the BZ patches can be controlled by varying the ruthenium content and size of the patches. Here, we present the results of computational modeling of such heterogeneous self-oscillating gels. We discuss how the catalyst concentration, patch size, and inter- patch distance affect the synchronization of oscillations in the neighboring BZ gels, and how the synchronization effects can be utilized to control the dynamical behavior of the entire system.   

Swelling instabilities in patterned, microscale gels

Hydrogels facilitate reconfigurable structures with response integrated at the material level. Response is engendered by a competing mechanism: the elasticity of the network ounterbalances expansion by the solvent. If the strength of expansion can be controlled by an environmental cue, the hydrogel can be adjusted in situ. The equilibrium state occurs when the osmotic stress exerted by the solvent in the gel equals the osmotic pressure of the solvent outside the gel. For a free structure, the equilibrium state corresponds to homogenous swelling. If a free surface of the gel is mechanically constrained, however, the dimensions available for the relief of the osmotic stress are reduced, resulting in non-uniform or inhomogeneous swelling. In this study, we demonstrate how mechanical constraints impose differential gel swelling and buckling in patterned gels. Depending on the initial geometry of the constrained gel, three general modes of swelling-induced deformation can be observed: lateral differential swelling, bulk sinusoidal buckling, and surface wrinkling. Through confocal microscopy and 3D image rendering, the mechanics of swelling has been evaluated in the context of linear elasticity theory.   

Thermoresponsive hydrogels from ABC triblock terpolymers

We have prepared novel thermoreversible ABC hydrogels from poly(ethylene-alt-propylene)-b-poly(ethylene oxide)-b-poly(N-isopropylacrylamide) (PEP-PEO-PNIPAm) triblock terpolymers. The terpolymers form micelles in water at low temperatures with hydrophobic PEP cores surrounded by hydrophilic PEO-PNIPAm coronas, and these micelles subsequently associate to form a hydrogel upon heating above the lower critical solution temperature (LCST) of PNIPAm. The separation of micellization and gelation leads to the formation of a two-compartment network with exclusively bridging conformations for the PEO midblocks. Therefore, gelation can be achieved at a much lower concentration, with better mechanical properties and a sharper sol-gel transition, when compared with ABA triblock copolymer hydrogels from PNIPAm-PEO-PNIPAm. The results highlight the intricate nanostructures and new properties available from ABC terpolymer hydrogels.   

Single Quantum Dot Tracking in Heterogeneous Polyacrylamide Hydrogels

Structural heterogeneity within polymer gels plays an important role in determining their material properties, yet is difficult to characterize by established methods. Single particle tracking measurements can provide highly localized information on the diffusion dynamics of tracer particles, and therefore on the material properties of the medium. We use tailored core-shell quantum dots (QDs) with hydrophilic ligands to characterize polyacrylamide hydrogels with varying crosslink density. We find that QDs show sub-diffusive behavior and non-Gaussian displacement distributions, consistent with prior reports on diffusive behavior in other heterogeneous media. We also consider the distribution of particle caging times, which is dictated by the potential energy barriers to escape pores, and therefore provides insight into structural heterogeneity. Specifically, we find that gels with a higher density of crosslinks yield broader distributions of caging times, indicating greater heterogeneity of these networks.   

Modeling Photo-Reconfiguration and Directed Motion of Spirobenzopyran- Containing Polymer Gels

We develop a computational model to simulate the behavior of photo-responsive polymer gels that contain spirobenzopyran (SP) chromophores. Using this model, we design three-dimensional samples with dynamically reconfigurable morphologies and photo-induced motility. In the dark, the SP moieties assume an open ring conformation and are hydrophilic; under illumination with blue light, the chromophores assume a closed ring conformation and are hydrophobic. This collapse of the gels is caused by the decrease in hydration due to conformational changes and not by a light-induced heating of the polymer network. We demonstrate that these gels can be effectively patterned remotely and reversibly with light by illuminating the sample through photomasks. We also show that by introducing variations in crosslink density within the gels during their preparation, as well as introducing temperature gradients, we have additional means of guiding the dynamic behavior of these versatile, responsive systems. Furthermore, we demonstrate that one can use a mobile light source to move multiple gel pieces to a specific location. The results point to a novel method for controlling the self-organization of soft, reconfigurable materials.   

Gelation of Copolymers Photo-crosslinked by Pendent Benzophenones

Copolymers containing pendent benzophenone (BP) groups provide a simple and powerful route to crosslinkable polymer films. While the solution state photo-chemistry of BP is well established, and crosslinking of polymers blended with BP has been studied in detail, the process of crosslinking by covalently attached BP has received comparatively little attention. We have prepared copolymers of BP with several different monomers, and studied gelation as a function of BP content and degree of photochemical conversion. Understanding the influence of polymer chemistry on crosslinking efficiency allows the appropriate choice of materials for nanostructured photo-crosslinkable polymer films and reactive polymer blends.