Lateral Length Scale Research Articles

Novel transparent nano‐ to micro‐heterogeneous substrates for in‐situ cell migration study

Transparent substrates having heterogeneities ranging from nanometer to micrometer lateral length scale were fabricated to study cell migration. The surfaces were generated using thin films of block copolymers and homopolymer blends on ultra smooth transparent polyethylene terephthalate films. Results show that the lateral size scale of the surface heterogeneities affects fibroblast (NIH-3T3) adhesion, spreading and motility. More specifically, fibroblasts migrate faster on micron-sized than on nanometer-sized heterogeneities. Cell movements and morphology on the micron patterned surfaces resemble cells cultured in a 3D environment. These surfaces, therefore, can potentially be utilized as models to study cell behavior in physiologically relevant conditions which can add to our fundamental understanding of cell-substrate interactions and facilitate development of surfaces for medical devices.

The propagation of water waves across a laterally sheared current

This paper studies surface gravity waves propagating across a shearing current in water of constant depth according to linear theory. The approach adopted is to represent the current by a series of vortex sheets separating regions of constant velocity. In each such region the method of solution employed is one of expansion in terms of eigenfunctions. These are then matched at the boundaries between regions. This leads to a large set of linear algebraic equations to solve for the coefficients. The results are then compared with those obtained using simpler semi-analytic theories which neglect the evanescent modes and can be described as analogues of the mild-slope equation. The general conclusion is that these simple approaches are accurate when the wavelength of the incident waves is much less than the lateral length scale over which the current varies but become less and less accurate as the wavelength increases.

Regular Surface Patterns on Rayleigh-Taylor Unstable Evaporating Films Heated from Below

We study a thin liquid film with a free surface on the underside of a cooled horizontal substrate. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase below, regular surface patterns in the form of long-wave hexagons having a well-defined lateral length scale are observed. This is in sharp contrast to the case without evaporation where rupture or coarsening to larger and larger patterns is seen in the long time limit. In this way, evaporation could be used for regular structuring of the film surface. Finally, we estimate the finite wave length for the simplified case of an extended Cahn-Hilliard equation.

Erratum: Contact Instability in Adhesion and Debonding of Thin Elastic Films [Phys. Rev. Lett.97, 018303 (2006)

Based on experiments and 3-D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths and cavities, all of which have the same lateral pattern length scale, close to \lambda/H ~ 3 for thick films, H > 1 micrometer. The linear stability analysis and experiments show a new thin film regime where \lambda/H \approx 3+ 2 (\gamma/3 \mu H)^(1/4) (\gamma is surface tension, \mu is shear modulus) because of significant surface energy penalty (for example, \lambda/H = 6 for H = 200 nm; \mu = 1MPa).

Contact Instability in Adhesion and Debonding of Thin Elastic Films

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).

Examination of large-scale structures in turbulent microchannel flow

Microscopic particle image velocimetry was performed on turbulent flow in microchannels of various diameters and aspect ratios to evaluate the characteristics of large-scale turbulent structures. Spatial correlations of velocity fluctuations were measured along the channel centerlines and at four other locations, and characteristic turbulent length scales were defined. For square microchannels, excellent agreement was observed between the measured length scales and results for macro-scale duct flow. Along the centerline of the square microchannels the normalized longitudinal length scale, 2Lxuu/W, ranged from 0.30 to 0.37, the lateral length scale, 2Lyuu/W, ranged from 0.16 to 0.18, and the ratio between the two length scales, Lxuu/Lyuu ranged from 1.88 to 2.00, results which agree well with macroscale results. Results for non-square microchannels indicate that as aspect ratio increases, the ratio Lxuu/Lyuu also increases, ranging from 2.29 for an aspect ratio of 2.09 up to 3.75 for an aspect ratio of 5.68. Measurements were repeated at various distances from the side walls of the microchannels. For the square microchannels the turbulent structures are smaller near the side walls than near the center of the microchannel with 2Lxuu/W ranging from 0.30 to 0.38 along the centerline, but dropping to 0.04–0.06 at y/(W/2)=0.94. Similar results were observed for the rectangular microchannels. For the rectangular microchannels 2Lxuu/W ranged from 0.32 to 0.42, compared to 0.30–0.38 for the square microchannels.

New Growth Mode through Decorated Twin Boundaries

Scanning tunneling microscopy and low energy electron diffraction were used to investigate the growth of partly twinned Ir thin films on Ir(111). A transition from the expected layer-by-layer to a defect dominated growth mode with a fixed lateral length scale and increasing roughness is observed. During growth, the majority of the film is stably transformed to twinned stacking. This transition is initiated by the energetic avoidance of the formation of intrinsic stacking faults compared to two independent twin faults. The atomistic details of the defect kinetics are outlined.

Stress-induced wrinkling of sputtered SiO2 films on polymethylmethacrylate

Compressively stressed SiO2 films are deposited by rf magnetron sputtering onto polymethylmethacrylate- (PMMA) coated Si substrates. The oxide film roughens by wrinkling during deposition; wrinkling is enabled by the viscous flow of the PMMA layer. The nanoscale lateral length scale of the wrinkling, ∼120nm, is established during the first few nanometers of film deposition and is controlled by the thickness and stress of the SiO2 film at the onset of the instability. Continued deposition of SiO2 leads to a rapid increase and then saturation of the rms roughness at ∼5nm.

Calcium-Induced Changes to the Molecular Conformation and Aggregate Structure of β-Casein at the Air−Water Interface

The influence of calcium on interactions of beta-casein at the air-water interface has been studied by several techniques, including interfacial rheology, atomic force microscopy (AFM), infrared reflectance-absorbance spectroscopy (IRRAS), and zeta potential measurements. In the absence of calcium, a weak interfacial gel forms after about 2.5 h. Also in the absence of calcium, the adsorbed beta-casein film exhibits some degree of both intra- and intermolecular structural organization. For example, IRRAS spectra show a measurable amount of alpha-helix content, and AFM images indicate the presence of interfacial aggregates with a characteristic lateral length scale of 20-30 nm, which we interpret as hemimicelles. Upon the addition of calcium, particularly at Ca:beta-casein molar ratios above approximately 5:1, a stronger interfacial gel forms more quickly; for example, the interfacial shear moduli increase twice as rapidly. Also under these conditions (5:1 Ca:beta-casein ratio) there is little evidence of structural organization; i.e., the alpha-helix peaks are very weak, and AFM images show a disordered, but continuous film, without distinct hemimicelles. On the basis of these findings, we hypothesize that calcium binding destabilizes the coupled intra- and intermolecular structural organization, and that the loss of organization permits more rapid interfacial gelation. These phenomena are characteristic of the air-water interface; they are not accompanied by analogous structural changes in bulk solution.

Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields

The unsteady interaction of a moving shock wave with nearly homogeneous and isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock tube facility. Rectangular grids of various mesh sizes were used to generate turbulence with Reynolds numbers based on Taylor's microscale ranging from 260 to 1300. The interaction has been investigated by measuring the three-dimensional velocity and vorticity vectors, the full velocity gradient and rate-of-strain tensors with instrumentation of high temporal and spatial resolution. This allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause. Fluctuations of all velocity gradients in the longitudinal direction are amplified significantly downstream of the interaction. Fluctuations of the velocity gradients in the lateral directions show no change or a minor reduction through the interaction. Root mean square values of the lateral vorticity components indicate a 25% amplification on average, which appears to be very weakly dependent on the shock strength. The transmission of the longitudinal vorticity fluctuations through the shock appears to be less affected by the interaction than the fluctuations of the lateral components. Non-dissipative vortex tubes and irrotational dissipative motions are more intense in the region downstream of the shock. There is also a significant increase in the number of events with intense rotational and dissipative motions. Integral length scales and Taylor's microscales were reduced after the interaction with the shock in all investigated flow cases. The integral length scales in the lateral direction increase at low Mach numbers and decrease during strong interactions. It appears that in the weakest of the present interactions, turbulent eddies are compressed drastically in the longitudinal direction while their extent in the normal direction remains relatively the same. As the shock strength increases the lateral integral length scales increase while the longitudinal ones decrease. At the strongest interaction of the present flow cases turbulent eddies are compressed in both directions. However, even at the highest Mach number the issue is more complicated since amplification of the lateral scales has been observed in flows with fine grids. Thus the outcome of the interaction strongly depends on the initial conditions.

Coupling of wrinkle patterns to microsphere-array lithographic patterns.

We report a method to modulate spontaneously formed microwrinkle patterns on a metal-capped elastomer surface by introducing lithographic patterns (structures) on the original surface as spatial triggers for directed wrinkling. The lithographic patterns are designed to have approximately the same lateral length scales as the characteristic wavelength of the microwrinkles by utilizing self-assembled two-dimensional microsphere arrays with hexagonal packing as a lithographic mask. When the lateral periodicity of the lithographic pattern is close to the wavelength of wrinkles, a novel directional order originating from the hexagonal packing of microspheres is induced. Otherwise, the wrinkle crests tend to form along the small ridges of the lithographic structure. The compression direction-dependent and reversible ordering of wrinkle patterns by compressive strain is also found for patterns with directional order.

Nanosecond freezing of water under multiple shock wave compression: Optical transmission and imaging measurements

Water samples were subjected to multiple shock wave compressions, generating peak pressures of 1-5 GPa on nanosecond time scales. This loading process approximates isentropic compression and leads to temperatures where the ice VII phase is more stable than the liquid phase above 2 GPa. Time resolved optical transmission and imaging measurements were performed to determine the solidification rate under such conditions. Freezing occurred faster at higher pressures as water was compressed further into the ice VII phase, in agreement with classical micleation theory. Water consistently froze when in contact with a silica window, whereas no solidification occurred in the presence of sapphire windows. The transition was determined to be a surface initiated process--freezing began via heterogeneous nucleation at the water/window interface and propagated over thicknesses greater than 0.01 mm. The first optical images of freezing on nanosecond time scales were obtained. These images demonstrate heterogeneous nucleation and irregular solid growth over 0.01-0.10 mm lateral length scales and are consistent with latent heat emission during the transformation. The combination of optical transmission and imaging measurements presented here provide the first consistent evidence for freezing on short time scales.

Fibroblast adhesion to micro- and nano-heterogeneous topography using diblock copolymers and homopolymers.

Polymeric substrates of different surface chemistry and length scales were found to have profound influence on cell adhesion. The adhesion of fibroblasts on surfaces of oxidized polystyrene (PS), on surfaces modified with random copolymers of PS and poly(methyl methacrylate) [P(S-r-MMA)] with topographic features, and chemically patterned surfaces that varied in lateral length scales from nanometers to microns were studied. Surfaces with heterogeneous topographies were generated from thin film mixtures of a block copolymer, PS-b-MMA, with homopolymers of PS and PMMA. The two homopolymers macroscopically phase separated and, with the addition of diblock copolymer, the size scales of the phases decreased to nanometer dimensions. Cell spreading area analysis showed that a thin film of oxidized PS surface promoted adhesion whereas a thin film of P(S-r-MMA) surface did not. Fibroblast adhesion was examined on surfaces in which the lateral length scale varied from 60 nm to 6 microm. It was found that, as the lateral length scale between the oxidized PS surfaces decreased, cell spreading area and degree of actin stress fiber formation increased. In addition, scanning electron microscopy was used to evaluate the location of filopodia and lamellipodia. It was found that most of the filopodia and lamellipodia interacted with the oxidized PS surfaces. This can be attributed to both chemical and topographic surface interactions that prevent cells from interacting with the P(S-r-MMA) at the base of the topographic features.

High-resolution measurement of phase singularities produced by computer-generated holograms

We present measurements of the intensity as well as the phase distribution in the various diffraction orders of computer-generated holograms designed to generate a higher order Gauss–Laguerre beam. For the direct measurement of the phase distribution in the diffraction orders a high-resolution interferometer is used, which allows access to a lateral length scale for the localization of phase singularities below the wavelength. It is experimentally shown that in beams that carry multiple singularities, the dislocations do not degenerate. This effect cannot be seen by analyzing only the intensity distribution of the laser beam.

Synchrotron radiation studies of the dynamics of polymer films

X-ray photon correlation spectroscopy, an emerging technique for studying the slowdynamics of condensed matter, has been employed to probe surface fluctuations on thinsupported polymer films as a function of in-plane wavevector, film thickness, temperature,and molecular weight of the polymer. The measurements were performed on thinpolystyrene (PS) films of thicknesses ranging from 84 to 333 nm above the glasstransition temperature. The lateral length scales probed are at least ten timessmaller than those accessible in conventional dynamic light scattering. We findexcellent agreement between the measured surface dynamics and the theory ofoverdamped thermal capillary waves on thin viscoelastic films. The values of theviscosity obtained from these data show good agreement with those of bulk PS.

Fluctuation microscopy studies of medium-range ordering in amorphous diamond-like carbon films

In this letter, we report fluctuation microscopy studies of medium-range ordering in amorphous diamond-like carbon films and the effect of annealing on this ordering. Annealed and unannealed diamond-like carbon films have almost identical short-range order. Our fluctuation microscopy results, however, indicate the presence of medium range order or clustering in the films on a lateral length scale that exceeds 1 nm. Within the clustered regions, the dominant local ordering appears to be diamond-like, and graphite-like ordering is not observed. Thermal annealing up to 600 °C leads to an increase in diamond-like clustering with no onset of graphite-like clustering. However, after high temperature annealing up to 1000 °C, graphite-like clustering becomes apparent as a result of the conversion of diamond-like carbon to graphite-like carbon. The results on the as-deposited films and films annealed up to 600 °C suggest that a spontaneous medium range ordering process occurs in diamond-like carbon films during and subsequent to film growth, and this may play an important role in stress relaxation.

Patterning-based investigation of the length-scale dependence of the surface evolution during multilayer epitaxial growth

We describe an investigation of the lateral length scale dependence of the evolution of topographical corrugations during multilayer molecular beam epitaxial growth in the GaAs/AlAs multilayer system. By patterning the substrate at series of well-defined spatial periods, we are able to study selectively the changes which occur as a function of lateral period over a wide range of corrugation amplitudes. A critical pattern period, which increases monotonically with thickness, separates an initial long spatial period regime where roughness is amplified, from a later, short spatial period regime in which the topography of the growing surface smoothes out.

Polymer film dynamics using X-ray photon correlation spectroscopy

A new method of X-ray photon correlation spectroscopy (XPCS) is applied for probing the dynamics of surface height fluctuations as a function of lateral length scale in supported polymer films. The short wavelength and slow time scales characteristic of XPCS extend the phase space accessible to scattering studies beyond some restrictions by light and neutron. Measurements were carried out on polystyrene films of thicknesses ranging from 84 to 333 nm at temperatures above the PS glass transition temperature. We present the experimental verification of the theoretical predictions for the thickness, wave vector and temperature dependence of the capillary wave relaxation times for supported polymeric films above the glass transition temperature.

Interrupted coarsening of anisotropic step meander.

We report on the effect of anisotropy on the step meandering instability on vicinal surfaces during molecular beam epitaxy growth. A scenario of interrupted coarsening is found: the lateral length scale of the structure first significantly increases with time and then freezes at a larger length scale. The wavelength selection mechanism results from a nontrivial nonlinear effect of anisotropy. Anisotropy also leads to solutions which drift sideways, resulting from the loss of the back-front symmetry of the meander and the nonvariational character of dynamics.

Roughness effects on the double-layer charge capacitance: the case of Helmholtz layer induced roughness attenuation

For electrical double layers, the presence of a Helmholtz layer could lead to electrode roughness attenuation. The latter is assumed of self-affine type which is characterized by the roughness amplitude w, the correlation length ξ, and the roughness exponent H. For sufficiently rough metal electrode surfaces ( H≪1 and/or ratios w/ ξ⩾0.1) the diffuse/Helmholtz layer interface would not have the same roughness parameters with the metal electrode surface. If the latter is smoothened at lateral length scales smaller than a healing length Λ (≪ ξ), the diffuse charge capacitance decreases and approaches values close to that of the Gouy–Chapman theory for flat electrodes.