Surface tension threshold

As the production methods of MWCNTs is very efficient [8] (see Chaps. 2 and 12), it is an advantage to implement a filling procedure after the synthesis. A promising approach to fill CNT cavities, could exploit the capillary properties that have been revealed by Ajayan and lijima [9]. Subsequent studies by Dujardin et al.[10] allowed the estimations of a surface tension threshold in order to select materials that are good candidates to wet and fill CNTs. 

The capillary filling of CNTs is basically and usually described using macroscopic thermodynamic approximations. For example, Dujardin et al. [10] concluded that the surface-tension threshold value for filling a CNT was 100-200... 

The capillary effect in CNTs was reported originally by Ajayan and lijima [89], who obtained surface tension threshold values for NT wetting based on macroscopic surface tension concepts and immersion experiments of NTs in different liquids (solvents, metals, etc.) [98]. From their results, although liquids with low surface tension (<200 mN/m), including most common organic solvents would fill tubes, those with surface tension higher than 200 mN/m, such as metals, can neither wet CNTs nor initialize the capillary action [99]. 

The choice of the solvent also has a profound influence on the observed sonochemistry. The effect of vapor pressure has already been mentioned. Other Hquid properties, such as surface tension and viscosity, wiU alter the threshold of cavitation, but this is generaUy a minor concern. The chemical reactivity of the solvent is often much more important. No solvent is inert under the high temperature conditions of cavitation (50). One may minimize this problem, however, by using robust solvents that have low vapor pressures so as to minimize their concentration in the vapor phase of the cavitation event. Alternatively, one may wish to take advantage of such secondary reactions, for example, by using halocarbons for sonochemical halogenations. With ultrasonic irradiations in water, the observed aqueous sonochemistry is dominated by secondary reactions of OH- and H- formed from the sonolysis of water vapor in the cavitation zone (51—53). 

Choice of liquid Vapor pressure Surface tension Viscosity Chemical reactivity Intensity of collapse Transient cavitation threshold Transient cavitation threshold Primary or secondary sonochemistry... 

Yarin and Weiss[357] also determined the number and size of secondary droplets, as well as the total ejected mass during splashing. Their experimental observations by means of a computer-aided charge-coupled-device camera and video printer showed that the dependence of the critical impact velocity, at which splashing initiates, on the physical properties (density, viscosity, and surface tension) and the frequency of the droplet train is universal, and the threshold velocity may be estimated by ... 

The final factor to be considered here, and known to affect the cavitation threshold, is the temperature. In general, the threshold limit has been found to increase with decrease in temperature. This may in part be due to increases in either the surface tension (a) or viscosity (rj) of the liquid as the temperature decreases, or it may be due to the decreases in the liquid vapour pressure (P ). To best understand how these parameters (a, q, Py) affect the cavitation threshold, let us consider an isolated bubble, of radius Rq, in water at a hydrostatic pressure (Pjj) of 1 atm. 

For water the surface tension varies with temperature as shown in Fig. 2.13 - i. e. a lowering of surface tension with increase in temperature. If it can be assumed that P, remains constant vdth increase in temperature then there will be a small increase in P and a lowering of the intensity (P ) necessary to cause cavitation. Obviously P, does not remain constant vdth increase in temperature but increases quite rapidly. Consequently there is a rapid rise in P with increase in temperature and the threshold decreases accordingly. The corollary is that liquids with high vapour pressures or low surface tensions cavitate at a lower intensity. 

Whilst vapour pressure may be the major solvent factor involved in the degradation process, there could also be a contribution from solvent viscosity or even, yet less likely, from surface tension. It has already been argued (see Section 2.6.2) that although an increase in viscosity raises the cavitation threshold, (i. e. makes cavitation more difficult), provided cavitation occurs, the pressure effects resulting from bubble collapse... 

Van der Waals forces between solid/gas interactions and the liquid/gas surface tension forces represent the limiting cases, but in general both the forces competitively affect the adsorption process. Therefore, in determining the surface fractal dimension by using the SP method, it is very important to use appropriate relation between CSP and <4n-r,sp- According to Ismail and Pfeifer,60 the threshold for the dominant forces between van der Waals forces and the liquid/gas surface tension forces is given as... 

For the same reason as above, excess solvent molecules in the cavitation bubble also seriously limit the applicability of many volatile organic solvents as a medium for sonochemical reactions [2,25,26]. In fact, water becomes a unique solvent in many cases, combining its low vapor pressure, high surface tension, and viscosity with a high yield of active radical output in solution. Its higher cavitation threshold results in subsequently higher final temperatures and pressures upon bubble collapse. Most environmental remediation problems deal with aqueous solutions, whereas organic solvents are mostly used in synthesis and polymer modifications processes. 

Fig. 10 a Surface tension of the surfactant solution (stars, right axis) and receding contact angle of the solutions (squares, circles, left axis) on a photoresist layer processed at the threshold dose corrected by the effect of swelling, b Wetting tension y v cos 0 calculated from the values given in (a). The dashed line marks the concentration ceff. Above a, the assumed distribution of the surfactant molecules at various concentrations is drawn schematically... 

To estimate the influence of the surfactant adsorption on the capillary forces, the wetting tension yiv cos was calculated from the values given in Fig. 10a. The results drawn in Fig. 10b show for both measurement series a minimum of the capillary forces exactly at the concentration ceff. The capillary forces are reduced by about 20% compared to water. This confirms the hypothesis that the reduction of the pattern collapse is caused by a hydropho-bizing of photoresist processed with the threshold dose by cationic surfactant adsorption. Unfortunately the inverse ADS A method could not be applied at relative surfactant concentrations >0.2 since the bubbles became unstable due to the lower surface tension. Thus it cannot be estimated how the wetting tension evolves at higher concentrations. 

Characteristics of the solvent. Solvent properties affect US-assisted digestion as they impose the cavitation threshold above which sonochemical effects are felt by the medium. Also, any phenomenon altering some solvent property can modify such a threshold. Thus, any change in temperature results in a change in solvent properties such as the vapour pressure, viscosity or surface tension, which affect cavitation and their effects as a result. 

The drop model of nuclei (section 2.4) proved to be useful to explain fission (Bohr and Wheeler, 1939) due to the surface tension of a liquid, a droplet assumes a spherical shape. If energy is supplied, the droplet begins to oscillate between spherical and elongated shapes. With increasing distortion, elongation passes a threshold and the droplet splits into two parts. In nuclei, the repulsive Coulomb forces, which... 

Surface tension (range 0.03-0.072 Nm ) Size of the nuclei (cavitation threshold) Low surface tension... 

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