Volume surface tension

Figure 3.9 Illustration of the drop weight/volume surface tension method (shown here for a wetting contact angle).

In the second approach, which finds application in real systems, validity of the general Redlich-Kister equation for the excess property is supposed. For description of the composition dependence on the given property Y (molar volume, surface tension) in the system, the following equation is then used (e.g. for a ternary system)... 

Plot the boiling point against the product of (internal volume) / (surface tension) as suggested from the relation. 

As these cosolvents contain both hydrophilic and hydrophobic groups, the same molecule can induce opposite effects in water. The hydrophilic part can interact with water to form strong HBs, while the hydrophobic part may induce cooperative ordering in the system by a hydrophobic hydration effect. These two effects combine together to regulate the extensive HB network of water in their aqueous binary mixtures that is reflected in strong, often anomalous non-ideal behavior in many physical properties such as viscosity, density, dielectric constant, excess mixing volume, surface tension, heat of formation, etc. 

We start by supplying a thermodynamic definition of line tension [3]. Consider the three-phase system as shown in Fig. 13. Around the line of three-phase contact a cylinder is drawn with length L and radius R, and implicitly we assume that R and L approach infinity. The total free energy inside the cylinder comprises terms of the form pressure times volume, surface tension times surface area, and, finally, line tension times line length... 

Data on molar volumes, surface tensions, viscosities, thermal characteristics and related physical properties for fatty acids and their esters in the crystal and liquid states, which may be useful in interpreting experimental results on natural membranes, have been compiled (74, 75). 

The molecules of a liquid are held together by attractive forces. The sum of aU attractive forces on any molecule present in the bulk of a liquid averages zero. The net force (also known as cohesion force) on a surface molecule is a non-zero quantity in the direction towards the bulk (Figure 2.1). This is the force that must be counteracted to increase the surface area the energy consumed by this process is called surface energy. The unbalanced forces on the interface cause it to contract to a minimum surface area value. Therefore, water droplets are spherical because a sphere has the minimum surface area of all shapes for a given volume. Surface tension and surface free energy of a liquid are equal while the same is not true for a solid surface. 

Here a - surface tension pa - atmospheric pressure 9 - contact angle of crack s wall wetting by penetrant n - coefficient, characterizing residual filling of defect s hollow by a penetrant before developer s application IT and h - porosity and thickness of developer s layer respectively W - minimum width of crack s indication, which can be registered visually or with the use of special optical system. The peculiarity of the case Re < H is that the whole penetrant volume is extracted by a developer. As a result the whole penetrant s volume, which was trapped during the stage of penetrant application, imbibes developer s layer and forms an indication of a defect. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

This is a fairly accurate and convenient method for measuring the surface tension of a liquid-vapor or liquid-liquid interface. The procedure, in its simpli-est form, is to form drops of the liquid at the end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Recently developed computer-controlled devices track individual drop volumes to = 0.1 p [32]. 

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

Small drops or bubbles will tend to be spherical because surface forces depend on the area, which decreases as the square of the linear dimension, whereas distortions due to gravitational effects depend on the volume, which decreases as the cube of the linear dimension. Likewise, too, a drop of liquid in a second liquid of equal density will be spherical. However, when gravitational and surface tensional effects are comparable, then one can determine in principle the surface tension from measurements of the shape of the drop or bubble. The variations situations to which Eq. 11-16 applies are shown in Fig. 11-16. 

The automated pendant drop technique has been used as a film balance to study the surface tension of insoluble monolayers [75] (see Chapter IV). A motor-driven syringe allows changes in drop volume to study surface tension as a function of surface areas as in conventional film balance measurements. This approach is useful for materials available in limited quantities and it can be extended to study monolayers at liquid-liquid interfaces [76],... 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Here p/p° is the relative pressure of vapour in equilibrium with a meniscus having a radius of curvature r , and y and Vi are the surface tension and molar volume respectively, of the liquid adsorptive. R and T have their usual meanings. 

It would clearly be desirable to extend the scope of the Kelvin method to include a range of adsorptives having varied physical properties, especially surface tension, molar volume, molecular shape and size. This would enable the validity of the method and its attendant assumptions to be tested more adequately, and would also allow a variation in experimental technique, for example by permitting measurements at 298 K rather than 77 K. 

Equations for vapor pressure, liquid volume, saturated liquid density, liquid viscosity, heat capacity, and saturated Hquid surface tension are described in Refs. 13, 15, and 16. 

The primary site of action is postulated to be the Hpid matrix of cell membranes. The Hpid properties which are said to be altered vary from theory to theory and include enhancing membrane fluidity volume expansion melting of gel phases increasing membrane thickness, surface tension, and lateral surface pressure and encouraging the formation of polar dislocations (10,11). Most theories postulate that changes in the Hpids influence the activities of cmcial membrane proteins such as ion channels. The Hpid theories suffer from an important drawback at clinically used concentrations, the effects of inhalational anesthetics on Hpid bilayers are very small and essentially undetectable (6,12,13). 

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