Session X18: Focus Session: Dynamics and Structures in Polymer Melts, Gels and Glasses

Elastomeric Photopolymers: Shaping Polymer Gels with Light

Polymer gels that possess a latent ability to change shape, which can be triggered in a spatially resolved manner using light---``elastomeric photopolymers''---have been developed to meet the need for materials that can be reshaped without direct contact, e.g., to non-invasively adjust an implanted lens in the human eye. The physics of diffusion and swelling in elastomers are applied to create a transparent silicone suitable for making a foldable intraocular lens that can be reshaped using near ultraviolet light. A crosslinked silicone matrix dictates the initial shape of the lens, while ``macromers''--short silicone chains with polymerizable end groups—and photoinitiator enable shape adjustment using light: polymerization of the macromer in the irradiated regions, followed by diffusion of free macromer causes local swelling. To predict shape change directly from irradiation profile, a theoretical treatment is presented that captures 1. shape change with no external forces, 2. coupling between diffusion and deformation, and 3. connection between thermodynamics, constitutive equations and equations of motion. Using continuum mechanics complemented with thermodynamics within the auspices of the finite element method, we develop a steady-state model which successfully captures the coupling between diffusion and deformation. Parameter values are drawn from our prior experimental studies of the mechanical properties, equilibrium swelling, penetrant diffusivities and interaction parameters in systematically varied polydimethylsiloxane (PDMS) networks and acrylate endcapped PDMS macromers. Preliminary computational studies show qualitative agreement with experimentally observed phenomena.   

Dynamics of Swollen Gel Layers Anchored to Solid Surfaces

Thin responsive hydrogel films are currently under development for biosensor applications. Photocrosslinkable poly(N-isopropylacrylamide) (PNIPAAm) based chains are spin coated as thin films (about 1 micron) and UV irradiated with variable doses to control the crosslink density. The obtained anchored gel layers can swell in ethanol or water up to about 10 microns for low crosslinking densities. Dynamics of the swollen layers and diffusion of different tracers (as analyte mimicks) are studied by dynamic light scattering (PCS) and fluorescence correlation spectroscopy (FCS). PCS resolved fast and slow diffusions, attributed to cooperative diffusion and long range concentration heterogeneities. Higher crosslink densities give rise to faster cooperative diffusion, i.e. short dynamic mesh sizes. FCS revealed the importance of electrostatic interactions between probe and negatively charged network. While a negatively charged dye senses local dynamics with a moderate slow down, a positively charged dye exhibited substantially retarded diffusion. Larger tracers are used to assess the size dependent gel penetrability, whereas large particles, trapped into the network, expectedly follow the network dynamics.   

Theory of the effect of deformation on the relaxation and mechanical properties of polymer glasses

Recently Saltzman and Schweizer have developed a statistical dynamical theory of segmental relaxation in deeply supercooled polymer melts by combining and extending methods of mode coupling, dynamic density functional and activated barrier hopping theories. The approach is built on the concept of a nanometer scale nonequilibrium free energy which quantifies dynamic localization due to interchain forces. We have now generalized this approach to treat quiescent relaxation, physical aging, and nonlinear mechanical properties in the nonequilibrium glass state. Applied stress weakens dynamical constraints in the effective free energy which accelerates alpha relaxation and softens the elastic modulus. A constitutive equation has been constructed which allows the prediction of dynamic yielding and mechanical response under constant strain rate, constant stress (creep), and other modes of deformation. Multiple predictions that fundamentally differ from the phenomenological Eyring model are made for the temperature and strain rate dependence of the dynamic yield stress and the deformation modified segmental relaxation time. Comparison of the theoretical results with experiments on PMMA reveals good agreement. The coupling of stress and aging, the strain softening effect, and large deformation strain hardening, can also be treated within our approach.   

Why Temperature Variation of the Chain Relaxation is Universal for Many Polymers?

Temperature variations of chain and segmental modes are traditionally described through corresponding friction coefficients. It is usually assumed that the same friction mechanism controls dynamics of both processes. As a result, their temperature dependence is expected to be the same. It is known, however, that segmental relaxation in many polymers varies faster than the chain one when temperature approaches Tg. We present an analysis of temperature variations of segmental and chain modes for different polymers. We demonstrate [1] that the chain relaxation shows universal temperature dependence for many polymers when it is presented vs Tg/T. Even polymers with strongly different temperature behavior of segmental dynamics (fragility) exhibit the same behavior for the chain relaxation. These results indicate complete decoupling in behavior of chain and segmental modes and emphasize our deficiency in understanding the microscopic mechanism of the chain friction coefficient. Possible mechanisms that lead to so universal behavior of chain relaxation are discussed at the end. \newline [1] Ding, Y., Sokolov, A.P., Macromolecules 2006, 39, 3322.   

Molecular dynamics simulations of layers of linear and branched alkanes under shear

We have previously studied the equilibrium structure and dynamical excitations in films of the linear alkane tetracosane ($n$-C$_{24}$H$_{50}$) and the branched alkane squalane (C$_{30}$H$_{62})$ in great detail$^{2}$. Here we report the results of nonequilibrium molecular dynamics simulations of these systems in order to compare the rheological properties of alkanes of the same length but with different architecture. The simulations were done in the NVT ensemble using the reverse nonequilibrium algorithm proposed by F. M\"{u}ller-Plathe et al.$^{3}$. The viscosity was calculated for different shear rates and compared with experimental values. Different structural parameters such as the mean end-to-end distance, the radius of gyration, and the angle of alignment of the molecules with the flow were studied as a function of the shear rate. $^{2}$A.D. Enevoldsen et al., J. Chem. Phys. 126, 104703-10 (2007); 126, 104704-17 (2007). $^{3}$F. M\"{u}ller-Plathe et al., Phys. Rev. E, \textbf{59}, 4894 (1998)   

On the influence of excluded volume in polymer melts

Flory's ideality hypothesis states that polymer chains in the melt have random walk like conformations as if there would be no excluded volume. However, it was shown recently that the excluded volume interaction induces corrections to scaling which are long range and which give rise to a power law decay of bond-bond correlation function [1] as well as to corrections to the Kratky plateau of the form factor [2]. In this presentation, we focus on the Rouse mode analysis by switching on the excluded volume potential gradually to study the crossover from phantom chains (representing perfect random walks described by the Rouse model) to real polymer melts [3]. In the melt, significant corrections have to be made to the static Rouse mode spectrum and consequences for the dynamics are briefly discussed. This gives also evidence that subdiffusive behaviour found in contradiction to the Rouse model is also caused by the excluded volume interaction. [1] J. Wittmer, H. Meyer, J. Baschnagel et. al. Phys. Rev. Lett. 93 (2004) 147801. Phys. Rev. E 76 (2007) 011803. [2] J. Wittmer et. al. EPL 77 (2007) 56003. [3] H. Meyer et. al. accepted at Eur. Phys. J. E (2007)   

Observation of Anomalous Viscosity in Entangled Polymer Films near the Glass Transition

We have studied the viscous relaxation of surface waves on molten polystyrene films of various molecular weights ($M_{W})$ using x-ray photon correlation spectroscopy. The relaxation time has been measured as a function of wave vector from high temperatures down to near the bulk glass transition temperature ($T_{g})$. We find a transition from a single exponential regime through a stretched exponential to another single exponential regime as the temperature decreases to $T_{g}$ where the effective viscosity saturates at that of chains with critical molecular weight for entanglement. These results are interpreted in terms of the freezing-out of relaxation modes involving full chains and large segments until only fluctuations of chain segments of critical entanglement length survive. We also find no evidence for a low-viscosity surface layer near $T_{g}$.   

Kohlrausch Parameter Determination for Simple Chain Models

The second Legendre polynomials of the end-to-end vector of freely jointed and freely rotating chains were extracted from molecular dynamics simulations and analyzed in terms of the Kohlrausch-Williams-Watts (KWW) function. Of particular interest is the variation of the stretching exponent, $\beta $, as a function of state point and, consequently, of the detailed compliance with time-temperature superposition. A new analysis methodology is introduced that permits the determination of $\beta $ at the needed level of precision. Detailed time-temperature superposition does not hold for freely-jointed or freely-rotating chain liquids. Indications of a breakdown in time-temperature superposition are also found in violations of Stokes-Einstein and Debye-Stokes-Einstein behavior.   

Understanding Fragility in Polymers

Glass transition in polymeric liquids is an important phenomenon that still remains poorly understood. It is accompanied by strongly non-Arrhenius temperature variations of segmental relaxation time \textit{$\tau$}$_{\alpha}$. The deviations of \textit{$\tau$}$_{\alpha}$ from Arrhenius behavior is described by the fragility parameter, $m$: $m=\delta \log \tau_\alpha$/$\delta (T_g$/$T$)$\vert_{T=Tg}$ where $T_{g}$ is the glass transition temperature. It appears that polymers are very fragile compared to small molecular weight liquids. However, there are some polymers that have intermediate fragility too. The reason for high fragility of polymers remains a topic of active discussion. We have studied various polymer systems using dielectric spectroscopy and dynamic mechanical analysis, and present an analysis of the results in the framework of chain flexibility, symmetry of the monomer and the packing efficiency of the polymer melt.   

Dye Reorientation as a Probe of Stress-induced Mobility in PMMA Glasses

To understand the response of molecular motions to deformation, we perform optical measurements of dye reorientation in PMMA glasses under stress. The reorientation of probes can be used to monitor the segmental dynamics of a polymer melt. We utilize this method to quantitatively determine the stress-induced mobility in PMMA glass during tensile creep deformation. At 377 K (Tg-18 K), a stress of 20 MPa accelerates the mobility by a factor of 100, while 11 MPa has almost no effect. After removing the stress, we observe that the enhanced mobility slowly disappears, even though the overall strain is still very large.   

On the effect of Molecular weight and Frequency dependence of Tg on the interpretation of Dynamic viscosity data

In this work, we re-plot dynamic data for a series of monodispersed Polystyrene melts, and their blends, obtained at constant temperature and variable frequency $\omega$, to enable a new analysis at constant (T-Tg) instead, where Tg is made a function of Mn and $\omega$. Tg ($\omega)$ is determined by DMA, from the shift of the max of E'' with $\omega $. Tg increases rapidly with $\omega $ and levels off at higher $\omega$. The Mn dependence of Tg varies in a similar way, quickly plateaus off at approximately M=2 Me, consistent with a free volume interpretation. It is shown that correction for the Tg dependence on Mn and $\omega$ does play an important role in the determination of the scaling parameters exponents, such as the molecular weight dependence exponent for M$<$ 2 Me data, or the low frequency tail representative of the terminal behavior for blends of monodispersed samples. The paper concludes that a true separation of the variables to determine the independent effect of structural (local) and molecular weight (scaling) factors, can only be done at constant (T-Tg). The incidence of Tg($\omega $, ${\rm M})$ on the superposition at low $\omega$, is also reviewed.   

Influence of pressure (density) on fast dynamics in polymers

Understanding the microscopic nature of the fast dynamics in disordered materials is still a challenge. In particular, the origin of the collective vibrations, the so-called Boson peak, remains a subject of active discussion. It's known that Boson peak spectra change significantly under pressure. Analysing the role of density in the Boson peak might help to unravel its microscopic nature. In this work, we use light scattering to study influence of pressure (up to 1.5GPa) on fast dynamics in different polymers. In all cases, the observed shift of the Boson peak frequency with pressure is significantly stronger than change of sound velocities. This result clearly indicates that elastic continuum approximation cannot describe the pressure-induced variations. We demonstrate that the main variation of the Boson peak amplitude is due to changes of the Debye level, although detailed quantitative analysis is not possible due to the light-to-vibration coupling coefficient, which also varies with pressure. Analysis also shows there is a correlation between pressure-induced changes in the Boson peak frequency and amplitude.   

Visualization and Analysis of the Dynamics of Methanol Transport in Poly(Methyl Methacrylate)

The relative rates of the diffusional and relaxational processes during the absorption of penetrant molecules in glassy polymers determine the nature of the transport process and lead to a myriad of transport phenomena, such as Fickian, Case II, and anomalous absorption behavior. Many proposed models account for the majority of anomalous behavior that has been observed. However, there is still a disconnect between theory and experiment, as data must be fit to the model and adjustable parameters determined. We propose that a better understanding of the dynamics of penetrant transport in glassy polymers can be achieved by careful and detailed investigations into the role the polymeric network structure plays in influencing the transport mechanism. We introduce a novel technique to visualize and quantify transport dynamics and mechanisms in- situ. High-resolution X-ray computed tomography, a completely nondestructive technique that can be used to visualize features in the interior of opaque solids, has been successfully adapted to examine the transport dynamics of methanol into glassy poly (methyl methacrylate) discs synthesized by an iniferter- mediated free radical polymerization. In addition to tracking methanol absorption and dimensional swelling, the time- dependent concentration profiles within the polymer disc were determined.