Hydrodynamic surface modes on concentrated polymer solutions and gels

Crossover of surface waves and capillary-viscous-elastic transition in soft biomaterials detected by resonant acoustic rheometry

Viscoelastic properties of hydrogels are important for their application in science and industry. However, rheological assessment of soft hydrogel biomaterials is challenging due to their complex, rapid, and often time-dependent behaviors. Resonant acoustic rheometry (RAR) is a newly developed technique capable of inducing and measuring resonant surface waves in samples in a non-contact fashion. By applying RAR at high temporal resolution during thrombin-induced fibrin gelation and ultraviolet-initiated polyethylene glycol (PEG) polymerization, we observed distinct changes in both frequency and amplitude of the resonant surface waves as the materials changed over time. RAR detected a series of capillary-elastic, capillary-viscous, and visco-elastic transitions that are uniquely manifested as crossover of different types of surface waves in the temporally evolving materials. These results reveal the dynamic interplay of surface tension, viscosity, and elasticity that is controlled by the kinetics of polymerization and crosslinking during hydrogel formation. RAR overcomes many limitations of conventional rheological approaches by offering a new way to comprehensively and longitudinally characterize soft materials during dynamic processes.

Dynamic behaviours of epoxy resin thin films during the curing process

Epoxy resin thin films are widely used in applications such as coating materials, insulator films, and adhesives; accordingly, investigations of their physical properties have garnered increasing importance. Although the physical properties of thermoset epoxy thin films are strongly affected by the curing conditions, such as the heating temperature and curing time, the dynamic properties during the curing process have not been studied thoroughly. In this study, we investigated the thermal fluctuations on the surface of epoxy resin thin films using grazing-incidence X-ray photon correlation spectroscopy, to elucidate the dynamic behaviours during the curing process. We thus succeeded in observing the freezing of capillary waves during the thermal curing process. These results are expected to facilitate a deeper understanding of the curing mechanisms of various thin films.

Surface viscosity in simple liquids

The response of Newtonian liquids to small perturbations is usually considered to be fully described by homogeneous transport coefficients like shear and dilatational viscosity. However, the presence of strong density gradients at the liquid/vapor boundary of fluids hints at the possible existence of an inhomogeneous viscosity. Here, we show that a surface viscosity emerges from the collective dynamics of interfacial layers in molecular simulations of simple liquids. We estimate the surface viscosity to be 8-16 times smaller than that of the bulk fluid at the thermodynamic point considered. This result can have important implications for reactions at liquid surfaces in atmospheric chemistry and catalysis.

Dynamics of active liquid interfaces

Controlling interfaces of phase-separating fluid mixtures is key to the creation of diverse functional soft materials. Traditionally, this is accomplished with surface-modifying chemical agents. Using experiment and theory, we studied how mechanical activity shapes soft interfaces that separate an active and a passive fluid. Chaotic flows in the active fluid give rise to giant interfacial fluctuations and noninertial propagating active waves. At high activities, stresses disrupt interface continuity and drive droplet generation, producing an emulsion-like active state composed of finite-sized droplets. When in contact with a solid boundary, active interfaces exhibit nonequilibrium wetting transitions, in which the fluid climbs the wall against gravity. These results demonstrate the promise of mechanically driven interfaces for creating a new class of soft active matter.

Active elastocapillarity in soft solids with negative surface tension

Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. Whereas active interfaces have been realized across many experimental systems, control of three-dimensional (3D) bulk materials remains a challenge. Here, we develop continuum theory and microscopic simulations that describe a 3D soft solid whose boundary experiences active surface stresses. The competition between active boundary and elastic bulk yields a broad range of previously unexplored phenomena, which are demonstrations of so-called active elastocapillarity. In contrast to thin shells and vesicles, we discover that bulk 3D elasticity controls snap-through transitions between different anisotropic shapes. These transitions meet at a critical point, allowing a universal classification via Landau theory. In addition, the active surface modifies elastic wave propagation to allow zero, or even negative, group velocities. These phenomena offer robust principles for programming shape change and functionality into active solids, from robotic metamaterials down to shape-shifting nanoparticles.

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a "drop vibration rheometer", suggesting future experiments using either ultrasonic levitation or a microgravity environment.

Light scattering by liquid surfaces, new developments

The surface light scattering technique is presented, highlighting recent technical improvements and describing studies of various types of surfaces. The technique is non-invasive, but delicate to handle and no commercial instruments are available yet. The technique gives however interesting information difficult to obtain otherwise, for instance on out-of-equilibrium surfaces, surfaces of very low tension, or systems close to solidification. Many studies were performed with monolayers of surface-active molecules at the surface of water. In this case, surface viscoelastic parameters can be determined at high frequencies (10 kHz- 1 MHz), complementing usefully the data obtained at lower frequencies with other techniques. As with these other techniques, inconsistencies such as negative surface viscosities are sometimes reported. The origin of these anomalies is not yet fully clarified. The problem deserves further work, in order to achieve a satisfactory description of the motion of surfactant or polymer-laden surfaces.

How capillarity affects the propagation of elastic waves in soft gels

Elastic waves propagating at the interface of soft solids can be altered by the presence of external forces such as capillarity and gravity. We measure the dispersion relation of waves at the free surface of agarose gels with great accuracy, revealing the existence of multiple modes as well as an apparent dispersion. We disentangle the role of capillarity and elasticity by considering the three-dimensional nature of mechanical waves, achieving quantitative agreement between theoretical predictions and experiments. Notably, our results show that capillarity plays an important role for wave numbers smaller than expected from balancing elastic and capillary forces. We further confirm the efficiency of our approach by including the effect of gravity in our predictions and quantitatively comparing it to experiments.

Surface Response of a Polymer Network: Semi-infinite Network

We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology: the extraction of viscoelastic moduli and intrinsic length scales from the motions of tracer particles lying on the surface without doping the bulk material.

The elastic Rayleigh drop

Bioprinting technologies rely on the formation of soft gel drops for printing tissue scaffolds and the dynamics of these drops can affect the process. A model is developed to describe the oscillations of a spherical gel drop with finite shear modulus, whose interface is held by surface tension. The governing elastodynamic equations are derived and a solution is constructed using displacement potentials decomposed into a spherical harmonic basis. The resulting nonlinear characteristic equation depends upon two dimensionless numbers, elastocapillary and compressibility, and admits two types of solutions, (i) spheroidal (or shape change) modes and (ii) torsional (rotational) modes. The torsional modes are unaffected by capillarity, whereas the frequency of shape oscillations depend upon both the elastocapillary and compressibility numbers. Two asymptotic dispersion relationships are derived and the limiting cases of the inviscid Rayleigh drop and elastic globe are recovered. For a fixed polar wavenumber, there exists an infinity of radial modes that each transition from an elasticity wave to a capillary wave upon increasing the elastocapillary number. At the transition, there is a qualitative change in the deformation field and a set of recirculation vortices develop at the free surface. Two special modes that concern volume oscillations and translational motion are characterized. A new instability is documented that reflects the balance between surface tension and compressibility effects due to the elasticity of the drop.

Extracting the surface tension of soft gels from elastocapillary wave behavior

Mechanically-excited waves appear as surface patterns on soft agarose gels. We experimentally quantify the dispersion relationship for these waves over a range of shear modulus in the transition zone where the surface energy (capillarity) is comparable to the elastic energy of the solid. Rayleigh waves and capillary-gravity waves are recovered as limiting cases. Gravitational forces appear as a pre-stress through the self-weight of the gel and are important. We show the experimental data fits well to a proposed dispersion relationship which differs from that typically used in studies of capillary to elastic wave crossover. We use this combined theoretical and experimental analysis to develop a new technique for measuring the surface tension of soft materials, which has been historically difficult to measure directly.

Free Surface Relaxations of Star-Shaped Polymer Films

The surface relaxation dynamics of supported star-shaped polymer thin films are shown to be slower than the bulk, persisting up to temperatures at least 50 K above the bulk glass transition temperature T_{g}^{bulk}. This behavior, exhibited by star-shaped polystyrenes with functionality f=8 arms and molecular weights per arm M_{arm} Collapse

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Grants

• 9999-NIST Intramural NIST DOC

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Affiliation(s)

Emmanouil Glynos Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, P.O. Box 1385, 711 10 Heraklion, Crete, Greece
Kyle J. Johnson Department of Material Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA
Bradley Frieberg Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
Alexandros Chremos Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
Suresh Narayanan Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Zografou, 15771, Athens Greece
Georgios Sakellariou National Renewable Energy Laboratory (NREL), Golden, Colorado 80401, USA
Peter F. Green Department of Material Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Biointeraces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA National Renewable Energy Laboratory (NREL), Golden, Colorado 80401, USA

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Surface hydrodynamics of viscoelastic fluids and soft solids: Surfing bulk rheology on capillary and Rayleigh waves

From the recent advent of the new soft-micro technologies, the hydrodynamic theory of surface modes propagating on viscoelastic bodies has reinvigorated this field of technology with interesting predictions and new possible applications, so recovering its scientific interest very limited at birth to the academic scope. Today, a myriad of soft small objects, deformable meso- and micro-structures, and macroscopically viscoelastic bodies fabricated from colloids and polymers are already available in the materials catalogue. Thus, one can envisage a constellation of new soft objects fabricated by-design with a functional dynamics based on the mechanical interplay of the viscoelastic material with the medium through their interfaces. In this review, we recapitulate the field from its birth and theoretical foundation in the latest 1980s up today, through its flourishing in the 90s from the prediction of extraordinary Rayleigh modes in coexistence with ordinary capillary waves on the surface of viscoelastic fluids, a fact first confirmed in experiments by Dominique Langevin and me with soft gels [Monroy and Langevin, Phys. Rev. Lett. 81, 3167 (1998)]. With this observational discovery at sight, we not only settled the theory previously formulated a few years before, but mainly opened a new field of applications with soft materials where the mechanical interplay between surface and bulk motions matters. Also, new unpublished results from surface wave experiments performed with soft colloids are reported in this contribution, in which the analytic methods of wave surfing synthetized together with the concept of coexisting capillary-shear modes are claimed as an integrated tool to insightfully scrutinize the bulk rheology of soft solids and viscoelastic fluids. This dedicatory to the figure of Dominique Langevin includes an appraisal of the relevant theoretical aspects of the surface hydrodynamics of viscoelastic fluids, and the coverage of the most important experimental results obtained during the three decades of research on this field.

Dynamics of ultra-thin polystyrene with and without a (artificial) dead layer studied by resonance enhanced dynamic light scattering

Using non-invasive, marker-free resonance enhanced dynamic light scattering, the dynamics of capillary waves on ultrathin polystyrene films' coupling to the viscoelastic and mechanical properties have been studied. The dynamics of ultrathin polymer films is still debated. In particular the question of what influence either the solid substrate and/or the fluid-gas interface has on the dynamics and the mechanical properties of films of glass forming liquids as polymers is in the focus of the present research. As a consequence, e.g., viscosity close to interfaces and thus the average viscosity of very thin films are prone to change. This study is focused on atactic, non-entangled polystyrene thin films on the gold surface. A slow dynamic mode was observed with Vogel-Fulcher-Tammann temperature dependence, slowing down with decreasing film thickness. We tentatively attribute this relaxation mode to overdamped capillary waves because of its temperature dependence and the dispersion with a wave vector which was found. No signs of a more mobile layer at the air/polymer interface or of a "dead layer" at the solid/polymer interface were found. Therefore we investigated the influence of an artificially created dead layer on the capillary wave dynamics by introducing covalently bound polystyrene polymer brushes as anchors. The dynamics was slowed down to a degree more than expected from theoretical work on the increase of density close to the solid liquid interface-instead of a "dead layer" of 2 nm, the interaction seems to extend more than 10 nm into the polymer.

Frequency dispersion of small-amplitude capillary waves in viscous fluids

This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of capillary waves in the underdamped regime is proposed, including predictions for the wave number of critical damping based on a harmonic-oscillator model. The scaling resulting from this parametrization leads to a self-similar solution of the frequency dispersion of capillary waves that covers the entire underdamped regime, which allows an accurate evaluation of the frequency at a given wave number, irrespective of the fluid properties. This similarity also reveals characteristic features of capillary waves, for instance that critical damping occurs when the characteristic time scales of dispersive and dissipative mechanisms are balanced. In addition, the presented results suggest that the widely adopted hydrodynamic theory for damped capillary waves does not accurately predict the dispersion when viscous damping is significant, and an alternative definition of the damping rate, which provides consistent accuracy in the underdamped regime, is presented.

Interface deformations due to counter-rotating vortices: Viscous versus elastic media

Capillary forces determine the shape of a liquid interface. Although often not considered, elastic solids with a free surface are also subjected to surface forces and these become important for materials of low Young's modulus. Here we consider two equivalent problems where a capillary free surface deforms due to vortices: (i) in a steady viscous flow [solved by Jeong and Moffatt, J. Fluid Mech. 241, 1 (1992)], and (ii) in an elastic medium. The equations of linear incompressible elasticity and viscous flow are strictly identical, and the two-dimensional problems that we consider are solved using complex variable methods. Despite the similarity, the kinematics of the free surface is very different for the viscous and elastic cases. We show for the present problem that these kinematics result in displacement and velocity fields of different topology. Unexpectedly, the resulting surface deflections are even of opposite sign.

X-ray photon correlation spectroscopy studies of surfaces and thin films

The technique of X-ray Photon Correlation Spectroscopy (XPCS) is reviewed as a method for studying the relatively slow dynamics of materials on time scales ranging from microseconds to thousands of seconds and length scales ranging from microns down to nanometers. We focus on the application of this technique to study dynamical fluctuations of surfaces, interfaces and thin films. We first discuss instrumental issues such as the effects of partial coherence (or alternatively finite instrumental resolution) and optimization of signal-to-noise ratios in the experiments. We then review what has been learned from recent XPCS studies of capillary wave fluctuations on liquid surfaces and polymer films, of nanoparticles used as probes to study the interior dynamics of polymer films, of liquid crystals and multilamellar surfactant films, and of metal surfaces, and magnetic domain wall fluctuations in antiferromagnets. We then discuss studies of non-equilibrium dynamics described by 2-time correlation functions. Finally, we briefly speculate on possible future XPCS experiments at new synchrotron sources currently under development including studies of dynamics on time scales down to femtoseconds.

Anomalous surface relaxations of branched-polymer melts

The dynamics of thermally stimulated surface fluctuations of 100 nm thick films of long-branched polymers are measured for the first time. In contrast to comparable films of linear or cyclic chains that show no change in viscosity upon confinement, films of 6-pom, 6-star, and 6-end end-branched stars show viscosities, inferred from x-ray photon correlation spectroscopy, as much as 100 times higher than in the bulk. This difference varies in magnitude with chain architecture. Branching has a profound effect on confinement, even for these unentangled chains.

Interfacial roughening in nonideal fluids: dynamic scaling in the weak- and strong-damping regime

Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260 (1995)], where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case.

Capillary waves of compressible fluids

The interplay of thermal noise and molecular forces is responsible for surprising features of liquids on sub-micrometer lengths-in particular at interfaces. Not only does the surface tension depend on the size of an applied distortion and nanoscopic thin liquid films dewet faster than would be expected from hydrodynamics, but also the dispersion relation of capillary waves differ at the nanoscale from the familiar macroscopic behavior. Starting with the stochastic Navier-Stokes equation we study the coupling of capillary waves to acoustic surface waves which is possible in compressible fluids. We find propagating 'acoustic-capillary waves' at nanometer wavelengths where in incompressible fluids capillary waves are overdamped.

Surface waves on non-Newtonian viscoelastic liquids

In the present work, we study the dynamics of thermally excited fluctuations on the surface of non-Newtonian viscoelastic liquids, which shows complex behaviors such as crossover between the capillary wave and the elastic wave, and the coexistence of several modes. We show that the power spectrum is separated into surface localized modes and the bulk shear modes, and they are decomposed further into several modes using the partial fraction expansion. The peak positions of these modes are characterized by roots of a polynomial equation. We calculate the decomposition of the surface wave spectra numerically, and discuss evolution of constituent peaks with liquid parameters.

Surface Waves and Rosensweig Instability in Isotropic Ferrogels

We derive the dispersion relation of surface waves for isotropic magnetic gels in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluids by taking into account elasticity, additionally.

Ultraflat templated polymer surfaces

The roughness of spin-cast polymer films arises from thermally activated capillary waves during preparation and typically amounts to about 0.5 nm(rms) measured on a micrometer-sized surface area. Templating from atomically flat mica substrates allows the creation of polymer films with a surface roughness approaching the molecular scale. Three regimes of spatial frequencies are identified in which the roughness is controlled by different physical mechanisms. We find that frozen-in elastic pressure waves ultimately limit the flatness of polymer films.

Entanglement effects in capillary waves on liquid polymer films

Overdamped surface capillary wave relaxations on molten polymer films were measured using x-ray photon correlation spectroscopy. We found a transition from a single through a stretched to another single exponential regime as the temperature is decreased from well above to near the bulk glass transition temperature. A universal scaling of the dynamics was discovered over a wide range of film thicknesses, temperatures, and molecular weights (except in the multiple relaxation regime). These observations are justified by hydrodynamic theory and the time-temperature superposition principle by considering an effective viscosity instead of the bulk zero shear viscosity.

Thermal and non-thermal fluctuations in active polar gels

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.

Surface tension and elasticity of gel studied with laser-induced surface-deformation spectroscopy

The laser manipulation technique was effectively used for agarose solutions and the frequency specstrum of the surface response to the periodical laser irradiation yielded shear elasticity G and surface tension sigma in the gel. The laser spot size, from 60 mum to 200 mum in radius, was chosen so that either the Rayleigh waves or the capillary waves, selectively excited, associated with G or sigma , respectively. The result of G showed a dependence on the agarose concentration that is consistent with the theoretical prediction of the percolation model, while sigma has little dependence on the concentration. The surface state of 0.2 wt.% agarose solution was controlled with sodium-dodecyl-sulfate (SDS) additives, and sigma of the gel and the sol was observed at different SDS concentrations: The result showed (i) sigma decreased with increasing SDS concentration up to 39 x 10-3 mol/l and kept a constant value thereafter, and (ii) the gel and the sol have the same value of sigma and the same dependence on the concentration. These results were considered from a viewpoint of surface pressure and a partially quantitative discussion was made on the surface adsorbed with SDS and agarose molecules.

Hydrodynamics of nanoscopic capillary waves

The dynamics of nanoscopic capillary waves on simple liquid surfaces is analyzed using molecular dynamics simulations. Each Fourier mode of the surface is obtained from the molecular positions, and its time behavior compared with the hydrodynamic prediction. We trace the transition from propagating to overdamped modes, at short wavelengths. The damping rate is in very good agreement with the hydrodynamic theory up to surprisingly small wavelengths, of about four molecular diameters, but only if the wave number dependent surface tension is considered. At shorter scales, surface tension hydrodynamics break down and we find a transition to a molecular diffusion regime.

Rosensweig instability of ferrogel thin films or membranes

We derive the dispersion relation of surface waves for magnetic gel membranes or thin films at the interface between two fluids in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluid and ferrogel free surfaces to take into account bending elasticity and intrinsic elastic and magnetic surface properties of the film or membrane, additionally. The latter is of interest for uniaxial ferrogel film or membranes, which show a locked-in permanent magnetization.

Evidence for viscoelastic effects in surface capillary waves of molten polymer films

The surface dynamics of supported ultrathin polystyrene films with thickness comparable to the radius of gyration were investigated by surface sensitive x-ray photon correlation spectroscopy. We show for the first time that the conventional model of capillary waves on a viscous liquid has to be modified to include the effects of a shear modulus in order to explain both static and dynamic scattering data from ultrathin molten polymer films.

Adsorbed gels versus brushes: viscoelastic differences

It is of fundamental importance to be able to easily distinguish between the viscoelastic properties of a molecular gel (noncovalent cross-linked three-dimensional polymer structure) and a brush (polymer structure that emanates from a surface in three dimensions without cross-linking). This has relevance in biology and in designing surfaces with desired chemical and viscoelastic properties for nano and genomic technology applications. Agarose and thiol-tagged poly(ethylene glycol) were chosen as model systems, as they are known, on adsorption, to behave like a molecular gel and brush, respectively. Here, we focus on their viscoelastic differences using a quartz crystal microbalance with dissipation monitoring (QCM-D). Changes in resonance frequency and dissipation for three overtones using QCM-D were fitted with the Voigt viscoelastic model to calculate the shear viscosity and shear modulus for the adsorbed agarose gel and the PEG brush. At a surface coverage of 500 ng/cm2, the shear viscosities and shear moduli were 0.0025 +/- 0.0002 Pa-s and 2.0 +/- 0.17 x 105 Pa and 0.0010 +/- 0.0001 Pa-s and 5.0 +/- 0.3 x 104 Pa for the gel and brush, respectively. Thus, the adsorbed agarose gel layer was far more rigid than that of the covalently bound PEG brush due to its cross-linked network. Also, the diffusivity of agarose and PEG in solution was compared during adsorption onto a bare gold surface. The estimated value for the effective diffusivity of the PEG (without a thiol tag) and of the agarose gel was on the order of 10(-11) and 10(-15) m2/s, respectively. This low diffusivity for agarose supports the contention that it exists as a molecular gel with a H-bonded cross-linked network in aqueous solution. With the methods used here, it is relatively easy to distinguish the differences in viscoelastic properties between an adsorbed gel and brush.

Capillary wave dynamics on supported viscoelastic films: single and double layers

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].

Surface and interfacial dynamics of polymeric bilayer films

The theory for surface dynamics of the thermally excited fluctuations on a homogenous single-layer film of arbitrary depth is generalized to describe surface and interfacial dynamics of polymeric liquid bilayer films in terms of susceptibilities, power spectra, and characteristic relaxation time constants. The effects on surface dynamics originating from viscosity inhomogeneities close to the surface and interfacial regions are investigated by the bilayer theory and compared with the surface dynamics of homogeneous single-layer films under nonslip and slip boundary conditions. Our bilayer theory can also be extended to study interfacial dynamics of more generalized multilayer systems. The effects of viscoelasticity and van der Waals interactions on surface and interfacial dynamics are also briefly discussed.

Light-induced deformation and instability of a liquid interface. II. Dynamics

We study the dynamics of the deformation of a soft liquid-liquid interface by the optical radiation pressure of a focused cw Gaussian laser beam. We measured the temporal evolution of both the hump height and the hump curvature by direct observation and by detecting the focusing effect of the hump acting as a lens. Extending the results of Yoshitake [J. Appl. Phys. 97, 024901 (2005)] to the case of liquid-liquid interfaces and to the Bo approximately =1 regime [Bo=(omega0/lc)2, , where omega0 is the beam waist and lc the capillary length], we show that, in the Bo<<1 and Bo approximately =1 ranges, the small-amplitude deformations are correctly described by a linear hydrodynamic theory predicting an overdamped dynamics. We also study the dynamics of the large-amplitude interface deformations at the onset of optohydrodynamic instability [Phys. Rev. Lett. 90, 144503 (2003)]. Using a simple, phenomenological model for the nonlinear evolution of the hump height, we interpret the observed interface dynamics at the instability onset as the signature of an imperfect subcritical instability.

Surface Light-Scattering at the Air−Liquid Interface: From Newtonian to Viscoelastic Polymer Solutions

The dynamics of the liquid-air interface of aqueous solutions of a tensioactive triblock copolymer (Pluronic F-68) has been studied using surface quasielastic light scattering over a broad range of concentrations and temperatures. Ancillary surface tension and bulk rheometry data have been obtained for the same system. The results show that the classical theoretical spectrum for monolayers on a Newtonian fluid can be applied only for concentrations below 4.10(-2) mM. For concentrations above c = 14 mM a clear peak centered at zero frequency appears in the spectrum. This feature is incompatible with the classical theoretical spectrum. The SQELS spectra have been described in terms of the theory of Wang and Huang [Wang, C. H.; Huang, Q. R. J. Chem. Phys. 1997, 107, 5898] considering that the loss modulus of the concentrated solutions shows the existence of two relaxation modes even at low frequencies. The theory is able to explain the existence of a peak centered at zero frequency in the spectra, and the theoretical spectra point out the existence of an elastic peak together with the capillary one. There is a reasonable agreement between the relaxation times and the product Gtau obtained from the fits of the SQELS spectra to the theory of Wang and Huang and those obtained from bulk rheology.

Signature of elasticity in the Faraday instability

We investigate the onset of the Faraday instability in a vertically vibrated wormlike micelle solution. In this strongly viscoelastic fluid, the critical acceleration and wave number are shown to present oscillations as a function of driving frequency and fluid height. This effect, unseen in either in simple fluids or in previous experiments on polymeric fluids, is interpreted in terms of standing elastic waves between the disturbed surface and the container bottom. It is shown that the model of Kumar [Phys. Rev. E 65, 026305 (2002)] for a viscoelastic fluid accounts qualitatively for our experimental observations. Explanations for quantitative discrepancies are proposed, such as the influence of the nonlinear rheological behavior of this complex fluid.

Capillary waves at the transition from propagating to overdamped behavior

We measure the dispersion relation of capillary waves on a liquid surface by heterodyne x-ray photon correlation spectroscopy near the transition from propagating to overdamped dynamic behavior. A strong deviation of the propagation frequency from the small-damping result omega(p) proportional, variant k(3/2) is observed long before the actual transition where ( partial differential omega(p)/ partial differential k)<0 and omega(p) tends to zero. This behavior is successfully described by expressions derived within linear response theory.