intermediate frequencies, T u (q) interpolates smoothly between these two limiting behaviours 12 .The behaviour seen in Fig. 2 is consistent with KTB dynamics, if we identify the crossover with T KTB of an isolated bilayer. Above T KTB , the conductivity is predicted to scale according to 13±15 :The scaling function S(q/) is constrained by the physics of the high-and low-frequency limits. As q= !`, S must approach i/q in order for j to assume its superconducting form, equation (1). At low frequencies, S approaches a real constant S 1 (0) which characterizes the d.c. conductivity of the normal state. By comparing the measured complex conductivity to equation (2), we can extract both the phase stiffness and correlation time at each temperature. To analyse the experimental data in terms of equation (2), we note that the phase angle of the complex conductivity, J [ tan 2 1 j 2 =j 1 , equals the phase angle of S(q/). Therefore J depends only on the single parameter , and is independent of T 0 u . With the appropriate choice of (T), all the measured values of J should collapse to a single curve when plotted as a function of the normalized frequency q/. Knowing (T), T 0 u is obtained from a collapse of the normalized conductivity magnitude, (~=k B T 0 v jjqj=j Q , to jSq=j. Figure 3 shows the collapse of the data to the phase angle and magnitude of S. As anticipated, S approaches a real constant in the limit q= ! 0, and approaches i/q as q= !`.When analysed further, the data reveal a con®rmation of thermal generation of vortices in the normal state. In the KTB picture we expect that the d.c. conductivity will equal k B T/n f D© 2 0 , which is thè¯u x-¯ow' conductivity of n f free vortices with quantized¯ux © 0 , and diffusivity D (ref. 16). Together with equation (2), this implies that is a linear function of n f , that is, 0 n f a vc =£, where a vc is the area of a vortex core, £ [ T=T 0 u is the reduced temperature, and 0 [ p 2 S 1 0D=a vc . Moreover, we expect that n f will be a thermally activated function, except for T very close to T KTB . The activation energy is simply Ck B T 0 u , where C is a non-universal constant of order unity. It follows that the¯uctuation frequency depends exponentially on the reciprocal of the reduced temperature, 0 =£exp 2 2C=£. The inset to Fig. 3 is a plot of log(£) versus 1/£ which shows that the exponential relation is observed over nearly four orders of magnitude. This is direct evidence that vanishing of phase coherence in our samples re¯ects the dynamics of thermally generated vortices. From the slope and intercept of a straight-line ®t we obtain C 2:23 and 0 1:14 3 10 14 s 2 1 .In Fig. 4 we present the behaviour of the bare stiffness and phasecorrelation time obtained from our measurement and modelling of j(q). The main panel contrasts T 0 u with the dynamical stiffness T u (q) measured at 150 and 400 GHz. The inset shows t as a function of temperature together with hatching that highlights the region where t ,~=k B T.The parameters displayed in Fig. 4 suggest that while phase ...

Generally, line widths are reduced by increasing the contact angle and by reducing the inlet/substrate velocity ratio. The conditions providing the minimum stable line width are bounded by a regime of capillary instability -we anticipate that this instability could be exploited to create periodic arrays of dots.The advantages of h4PL are that we can use computer-aided design to define any arbitrary 2-D pattern and that we can use any desired combination of surfactant and functional silane as ink to selectively define different functionalities at different locations. However ikiPL is a serial technique: In situations where it is desirable to create an entire pattern with the same functionality, it would be preferable to employ a parallel technique in which the deposition process occurred simultaneously in multiple locations. Schem~~( Figure 3) illustrates a rapid, parallel patterning procedure, dip-coating on patterned SAMS.This procedure uses micro-contact printing20 or electrochemical patteming2 1 of hydroxyl-and methyl-terminated SAMS to define hydrophilic and hydrophobic patterns on the substrate surfi~ce. ..,&., .-, ,., ., ...<. !.-.7 '?--..-., hydrophilic patterns in seconds. As described for A4PL, further evaporation accompanying the dip-coating operation induces self-assembly of silic~surfac~t mesophases.The patterned dip-coating procedure may be conducted with organic dyes or functional silanes (see Table 1). Scheme 2 illustrates patterned deposition of a propyl-amine derivatized cubic mesophase followed by a conjugation reaction with a pH-sensitive dye, 5,6-carboxyfluorescein, succinimidyl ester (5,6-FAM, SE). The uniform continuous porosity of the amine-derivatized and dye-conjugated films is confirmed by TEM and surface acoustic wave (SAW)-based nitrogen sorption isotherms22 of the corresponding films deposited on SAW substrates (Figure 4). The reduction in film porosity after dye conjugation reflects the volume occupied by the attached dye moieties. The patterned, functional array can be used to monitor the pH of fluids introduced at arbitrary locations and transported by capillary flow into the imaging cell. Figure 4a shows the fluorescence image of an array contacted with three different aqueous solutions prepared at pH 4.8, 7.7, and 12.0. Figure 4b shows the corresponding emission spectra and provides a comparison with solution data. In combination, the fluorescence image ( Fig. 4a) and plan-view and cross-sectional TEM micrographs (Figures 3 and 4c) of the dye-conjugated film demonstrate the uniformity of macro-and mesoscale features achievable by this evaporation-induced, de-wetting and self-assembly route. In comparison, films formed by nucleation and growth of thin film mesophases on patterned SANIS1 are observed to have nonhomogeneous, globular morphologies.Finally we can create patterned nanostructures by combining E]SA with a variety of aerosol processing schemes. For example, Figure 5 compares an optical micrograph of a macroscopic array of spots formed by inkjet printing LIPlo~1lon a sili...

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