Slippage Length Research Articles

Deriving Molecular Parameters of Interfaces Between Chemically Identical Polymers from Macroscopically Observed Phenomena

AbstractSummary: By utilizing model systems, macroscopically observable phenomena like friction or dewetting allow to identify and to quantify molecular interfacial parameters like molecular interpenetration depth, interfacial tension, or slippage length between grafted and free chemically identical polymers. We present experimental results, which permit to extract these parameters from simple contact angle measurements or by following the dewetting process in real time with a simple optical microscope. We also show how these model experiments can provide valuable insight and fundamental understanding of processes like polymeric friction and adhesion.

A theoretical model for quiescent coarsening in immiscible polymer blends

AbstractThe coalescence rate in immiscible polymer blends predicted by all existing models is two or three orders of magnitude lower than that observed experimentally. The model developed in this study considers for the first time that coarsening is driven by van der Waals forces and there is slippage at the interfacial boundaries between the moving particles and the matrix. The growth rate of the average radius of the particles, R, can be approximately expressed as where β is a function of the interfacial slippage length b, R, and the average surface distance between the particles h. The parameter b depends on the incompatibility and the degree of entanglement at the interface between the two polymers of the blend. The fact that the coarsening rate is decreased by the presence of a copolymer can be explained by a decrease in the value of b.

Droplet spreading: Intermediate scaling law by PDE methods

AbstractWe consider the spreading of a thin droplet of viscous liquid on a plane surface driven by capillarity. The standard lubrication approximation leads to an evolution equation for the film height h that is ill‐posed when the spreading is limited by the no‐slip boundary condition at the liquid‐solid interface due to a singularity at the moving contact line. The most common relaxation of the no‐slip boundary condition removes this singularity but introduces a new physical length scale: the slippage length b. It is believed that this microscopic‐length scale only enters logarithmically in the effective (that is, macroscopic) spreading behavior.In this paper, we rigorously show that the naively expected spreading rate is indeed only altered by a logarithmic term involving b. More precisely, we prove a scaling law for the diameter of the apparent (that is, macroscopic) support of the droplet in time. This is an intermediate scaling law: It takes an initial layer to “forget” the initial droplet shape, whereas after a long time, the droplet is so thin that its spreading is governed by the physics on the scale b.Our proof works by deriving suitable estimates for physically relevant integral quantities: the free energy, the length of the apparent support, and their respective rates of change. As opposed to matched asymptotic methods, this PDE approach closely mimics a simple heuristic argument based on the gradient flow structure. © 2002 John Wiley & Sons, Inc.

Real-time determination of the slippage length in autophobic polymer dewetting

We investigated the kinetics of autophobic dewetting, caused by differences in entropy, of a polymer melt slipping on a monolayer of end-grafted identical molecules (polymer brush). From simultaneous measures of the dewetted distance and the width of the resulting rim, we obtained in real time and quantitatively the slippage length and the contact angle, a measure of the "incompatibility" between identical molecules. Furthermore, we could directly relate a decrease in the slippage length in the course of the experiments at elevated temperatures to temporal or permanent attachment of polymers from the melt to the brush.

Kinetics of Autophobic Dewetting of Polymer Films

We experimentally investigated the retraction of poly(dimethylsiloxane) films of variable thickness on layers of chemically identical molecules, end-grafted onto a silicon substrate (autophobic dewetting of a melt-on-brush system). Measuring simultaneously the dewetted distance (d) and the width (w) of the rim formed by the collection of the retracted liquid, we were able to determine in situ and in real time (t) the contact angle, the velocity of retraction, and the energy dissipation mechanism at the melt−brush interface. The dewetting velocity decreased linearly with the width of the rim. Together with the characteristic thickness dependence and an exponent α of 2/3 for the power-law behavior of d ∼ tα, we concluded that the melt is slipping on the brush. The slippage length was on the order of 10 μm, indicating little interpenetration between melt and brush. We demonstrate that dewetting experiments represent a valuable tool for the characterization of static and kinetic properties of polymer−polymer interfaces.

Pulse propagation and optical-klystron free-electron-laser devices.

We derive the equation governing the evolution of the optical field amplitude of a free-electron-laser oscillator operating in the optical-klystron configuration. The equation includes short pulse effects, due to the finite length of the electron bunches, and are valid under the assumption of small signal regime and low gain. Stationary solutions of the supermode type, analogous to those of conventional free-electron-laser configurations, are shown to exist for this case, too. Analytical expressions for the optical pulse shape are derived, without any assumption of dominance of the dispersive section, in the case of the long bunch regime, namely when the bunch length is larger than the slippage length. We present useful gain formulas, including the combined effect of dispersive section and pulse effects, and discuss the limits of validity of our treatment.

経年劣化したアスファルト防水層のアスファルトのリサイクルの可能性

This paper describes the feasibility of recycling of the aged asphalt collected from membranes that are over service life. We developed a hot press technique to exclude asphalt from an aged roofing membrane. Some fundamental properties of the asphalt such as penetration, softening point and slippage length were clearly lowered. As reductions of resins, aromatics and saturated hydrocarbons were observed through a component analysis, process oil and new asphalt compound were added to the aged asphalt to recover the property. The roofing membrane constructed with the recycled asphalt reached again to the similar level in performance as new one.

Generation of ultrashort radiation pulses by injection locking a regenerative free-electron-laser amplifier

We demonstrate how a steady-state train of ultrashort radiation pulses can be produced utilizing a new free-electron laser (FEL) configuration, the injection-locked regenerative klystron amplifier (IRKA). This configuration consists of two elements: (1) a prebuncher, which microbunches the electron beams at the desired output wavelength, and (2) a multipass FEL operated at a very small cavity desynchronism and below the lasing threshold, in the regime of regenerative amplification. The regenerative amplifier is driven by the microbunched electron beam, so that the pulse-to-pulse stability is provided by the pre-buncher. The broad amplification bandwidth of this regenerative amplifier enables generation of ultrashort pulses, much shorter than a slippage length, with high efficiency. The IRKA configuration can produce such ultra-short radiation pulses while avoiding the chaotic dynamics that limits conventional FEL performance. {copyright} {ital 1997} {ital The American Physical Society}

Pulse-shaping in short-pulse FEL oscillators using multiple resonators

A novel method is proposed for the efficient production of optical pulses that are shorter than a slippage length. The concept uses short electron bunches and a multiple cavity FEL oscillator configuration.

Temporal structure of the CLIO laser micropulses in the two-color regime

By using sum-frequency generation in a Michelson arrangement, we have directly measured the temporal overlap between single-frequency micropulses in a two-color free-electron laser. As expected, the average separation appears to be related to the slippage length between the electrons and light when passing through the undulator. The two colors are then partly simultaneous, although there is not necessarily two-frequency bunching in the electron beam.

Optical power evolution in the Boeing 1 kW FEL oscillator

A four-dimensional simulation in x, y, z, and t, including betatron motion of the electrons, is used to study optical power evolution and the trapped-particle instability in the Boeing I kW FEL oscillator. Boeing is designing a visible, high power free electron laser (FEL) oscillator, to produce I kW average power at a wavelength A = 0.63 Rm [1]. The large electron beam current of 1-500 A will pass through an L = 5 m long, N = 220 period undulator, creating strong optical fields inside a resonator cavity. Simulations show this may lead to sideband growth and the onset of the trapped-particle instability. Increasing the outcoupling and tapering the undulator would lessen these effects. Fig. I shows the results from a multi-mode four-dimensional simulation in (x, y, , t) of the Boeing oscillator, for n = 50 passes. The longitudinal coordinate z is scaled to the slippage length NA, and the transverse coordinates (x, y) are scaled to the characteristic optical mode radius (LA/ITr) 2 . The model includes the betatron motion of the

Experimental indications for non-Gaussian transverse modes in the hole-coupled, short-pulse free-electron lasers of FELIX

The radial structure of intra-cavity light pulses is considered in the hole-coupled free-electron laser (FEL) oscillators of the Dutch FEL facility, FELIX. In a previous numerical study, it was shown that the radial profile can vary significantly over the light pulse, in particular when the electron pulses are short with respect to the slippage length. In this paper experimental indications are presented for the predicted transverse profile of the radiation. The decay of the power coupled out through the hole has been measured, after the electron beam was switched off, for the two different resonators employed in FELIX. These resonators differ in cavity length, mirror curvature and aperture radius, and in the width of the vacuum tube inside the undulator. The decay rate of the extracted radiation is interpreted according to the calculated intra-cavity mode structure from ELIXER. This simulation code describes the time-dependent radial profile in terms of a finite number of Gauss-Laguerre functions. Two extreme cases are discussed in further detail, one in which edge losses are large and one in which they are small.

Theoretical investigation of a waveguide application in a FEL with large μc

A free electron laser with a planar undulator, operating with a train of short electron pulses (3–6 ps) in the far infrared region (λ = 100–300 μm) was studied. The parameter μc defined as the ratio of the slippage length to the electron pulse length, can be rather large even for λ = 100 μm (μc ≈ 10). An increase in the radiation wavelength λ leads to an increase in both μc and diffraction losses.The introduction of a waveguide into the optical cavity provides an opportunity to decrease the diffraction losses. To analyze such systems a new code including pulse propagation through a waveguide was used. It was shown that the waveguide dispersion leads to a considerable variation of the pulse shape and an additional shift of the radiation pulse which can be comparable to the slippage length. This effect changes the optimal values of the cavity detuning and can even reduce the output power.Configurations with both circular and rectangular waveguides were analyzed. Results were compared with corresponding results without waveguides.

Spectrum, temporal structure, and fluctuations in a high-gain free-electron laser starting from noise.

We study the time structure, the frequency composition, and the shot to shot fluctuations of the radiation emitted by a free-electron laser starting from shot noise in the electron beam longitudinal distribution, taking into account slippage and finite bunch length effects. We find a very different behavior when the bunch length, ${\mathit{scrl}}_{\mathit{b}}$ is much longer thatn the cooperation length, ${\mathit{scrl}}_{\mathit{c}}$, or of the order of a few ${\mathit{scrl}}_{\mathit{c}}$. The field evolution is dominated by slippage effects in both cases, and shows the presence of superradiant spikes.

Preliminary consideration of a free electron laser operating at very large μc

A free electron laser with a planar undulator, operating with a train of short electron pulses (3–6 ps) in the far infrared region (λ = 100–300 μm) was studied. The parameter μc defined as the ratio of the slippage length to the electron pulse length, can be rather large even for λ = 100 μm (μc ≈ 10). An increase in the radiation wavelength λ leads to an increase in both μc and diffraction losses.The introduction of a waveguide into the optical cavity provides an opportunity to decrease the diffraction losses. To analyze such systems a new code including pulse propagation through a waveguide was used. It was shown that the waveguide dispersion leads to a considerable variation of the pulse shape and an additional shift of the radiation pulse which can be comparable to the slippage length. This effect changes the optimal values of the cavity detuning and can even reduce the output power.Configurations with both circular and rectangular waveguides were analyzed. Results were compared with corresponding results without waveguides.

Nonlinear short-pulse propagation in a free-electron laser

With one-dimensional time-dependent Maxwell-Lorentz equations, we have numerically investigated the nonlinear short-pulse propagation in a free-electron laser (FEL). Considering the pulsed electron beam and the cavity deturning, we describe a spiking behavior and the dissipative dynamics in a FEL oscillator. We show that the spiking behavior is well understood by superradiant pulse propagation and its dynamical regimes are closely related to a bifurcation and the chaotic transition in the nonlinear dissipative dynamics. The scaled synchrotron slippage distance (L syn /L s ), where L s is the slippage length and L syn is the slippage distance in a synchrotron period, plays an important role in determining the dynamical regimes

Limit cycle behaviour in FELIX

The free electron laser for infrared experiments (FELIX) operates at wavelengths up to λ = 110 μm. A radio-frequency linear accelerator is used to produce electron micropulses with a duration of about 3 ps. With N = 38 undulator periods, this puts FELIX well into the regime where the slippage length, Nλ, exceeds the electron micropulse length, and prominent short pulse effects are expected. One of these effects, stable limit cycle oscillations of the pulse energy, has not been detected experimentally before. Such oscillations occur when the saturated optical pulses move away from the electron pulses, due to the changing balance between lethargy and desynchronism, while new subpulses grow periodically. In FELIX, limit cycle behaviour is clearly demonstrated. The observations are in agreement with numerical simulations of the pulse propagation, and the oscillation period is given by a simple formula containing the slippage length and the desynchronism between optical and electron pulses. We also show how lethargic behaviour can be used to reduce the optical bandwidth of the FEL and to store optical energy in the optical cavity without saturation limiting the energy stored.

Optical spikes and superradiant pulse propagation in a free-electron laser

With one-dimensional nonlinear pulse propagation equations, we show numerically that the spiking behavior of free-electron lasers can be described by the superradiant pulse evolution. Two distinct dynamical regimes are defined by the characteristic length scales; slippage length ( L s) and slippage distance ( L syn) during one synchrotron period. In the superradiant regime ( L syn > L s), the superradiant pulse ( FWHM ≅ 1 2 L s ) is generated in the trailing slippage region of the electron pulse. In the spiking regime ( L syn≤ L s), the continuous pulse modulation ( FWHN ≅ 1 2 L s ) and the long-wavelength sidebands are observed. To compare with the experimental results, the realistic axial current profile and the shot noise are considered.

The Michelson resonator free-electron laser. II. Supermode structure and mirror detuning effects

For pt.I, see ibid., vol.29, no.2, p.452-64 (1993). Conventional mode-locked laser theory is applied to the longitudinal mode structure in an RF linac-driven Michelson resonator free-electron laser (FEL). A greatly simplified derivation of the small-signal small-gain FEL coupled mode equations is obtained. These equations are solved numerically in the frequency domain to study the supermode evolution in the presence of mode dependent cavity losses. The results are compared with simulations of the detuned Michelson resonator FEL using a pulse propagation code based on the Maxwell-Lorentz equations of motion. Increasing the interferometer detuning broadens and shifts the cavity detuning curve, narrows the supermode spectrum, and decreases the hypermode decay rates. The practical consequences of each of these effects are discussed. A simple theory describing the dependence of the hypermode decay rates on interferometer detuning, in which the decay rates are abruptly decreased beyond a critical detuning that depends primarily on the slippage length, is outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The 3-D FEL pulse propagation equation: An analytical treatment in the low-gain and small-signal regime

In this paper we show that the transverse mode evolution of a FEL operating with short pulses can be treated, in the small-signal and low-gain regime, using a relatively simple mathematical technique leading to a potentially fast numerical algorithm. We also point out that analytical solutions can be obtained for the cases where the slippage length is small compared to the longitudinal bunch length.