Van der Waals

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation.  [c.66]

Dieterici s equation A modification of van der Waals equation, in which account is taken of the pressure gradient at the boundary of the gas. It is written  [c.136]

Utilization of equations of state derived from the Van der Waals model has led to spectacular progress in the accuracy of calculations at medium and high pressure.  [c.152]

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)  [c.56]

The function of thermodynamics is to provide phenomenological relationships whose validity has the authority of the laws of thermodynamics themselves. One may proceed further, however, if specific models or additional assumptions are made. For example, the use of the van der Waals equation of state allows an analysis of how P - p in Eq. III-40 should vary across the interface Tolman [36,37] made an early calculation of this type. There has been a high degree of development of statistical thermodynamics in this field (see Ref. 47 and the General References and also Sections XV-4 and XVI-3). A great advantage of this approach is that one may derive thermodynamic properties from knowledge of the intermolecular forces in the fluid. Many physical systems can be approximated with model interaction potential energies a widely used system comprises attractive hard spheres where rigid spheres of diameter b interact with an attractive potential energy, att( )-  [c.61]

The classic theory due to van der Waals provides an important phenomenological link between the structure of an interface and its interfacial tension [50-52]. The expression  [c.61]

The gradient model has been combined with two equations of state to successfully model the temperature dependence of the surface tension of polar and nonpolar fluids [54]. Widom and Tavan have modeled the surface tension of liquid He near the X transition with a modified van der Waals theory [55].  [c.62]

One may, of course, use a two-dimensional modification of the van der Waals equation  [c.85]

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191].  [c.132]

In particular, comparisons between fluorinated amphiphiles and their hydrogenated counterparts reveal the influence of chain stiffness in the former producing solids having molecules with constant tilt from close packing to coexistence [178]. Molecular flexibility is further probed in simulations of partially fluorinated alkane amphiphiles where disorder in the hydrocarbon portion of the chain produces more disordered monolayers than their purely hydrogenated or fluorinated counterparts [216]. Finally, a nonpolar long-chain molecule, perfluoro- -eicosane, forms stable monolayers much like their amphiphilic counterparts [220]. Rice and co-workers suggest that van der Waals forces (see Chapter VI) are sufficient to stabilize such a monolayer. Gao and Rice [216,221] have studied the phase behavior of long-chain heterogeneous amphiphiles via grazing  [c.135]

The problem is that [c.206]

Much of chemistry is concerned with the short-range wave-mechanical force responsible for the chemical bond. Our emphasis here is on the less chemically specific attractions, often called van der Waals forces, that cause condensation of a vapor to a liquid. An important component of such forces is the dispersion force, another wave-mechanical force acting between both polar and nonpolar materials. Recent developments in this area include the ability to measure  [c.225]

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here.  [c.228]

Contributions to van der Waals s Interactions between Neutral Molecules  [c.230]

Microscopic analyses of the van der Waals interaction have been made for many geometries, including, a spherical colloid in a cylindrical pore [14] and in a spherical cavity [15] and for flat plates with conical or spherical asperities [16,17].  [c.234]

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances  [c.240]

Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.) Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)
The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range.  [c.250]

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface.  [c.264]

Mounting a fine tip to a piezoelectrically positioned cantilever spring provides the means to measure surface forces in the range from 10 to 10 N. The atomic force microscope (AFM) illustrated in Fig. VIII-measures deflections in the cantilever due to capillary (Chapter II), electrostatic (Chapter V), van der Waals (Chapter VI), and frictional (Chapter XII) forces between the tip and the surface. Not restricted to conducting surfaces, AFM measurements can be made on organic and inorganic surfaces and immersed in liquids [9,50]. Conical tips of silicon have points of 5-50 nm (radius of curvature) however, numerous probes have been used including attaching a several micrometer colloidal particle to a cantilever as described by Butt and co-workers [50] and Ducker and co-workers [51].  [c.297]

In molecular beam epitaxy, evaporated atoms are directed toward a crystalline surface in an ultra-high-vacuum chamber, where in situ surface analysis may be performed (Chapter VIII). While epitaxial growth often requires lattice matching between the surface and the growing crystal phase, van der Waals interactions (see Chapter VI) dominate the growth of semiconductors and appear to relax the lattice matching constraint [106, 107]. Armstrong and co-workers have grown semiconductor GaSe and MoSei films on GaP(lll) after passivating the surface in a solution containing sulfur. The sulfur passivation creates a chemically unreactive smooth surface for the growth of semiconductor films. Molecular beam epitaxy of organic molecules creates ordered ultrathin films of large aromatic molecules on metals, insulators, and semiconductors [108] wherein the oiganic molecules are packed more closely than in films grown by Langmuir-Blodgett or self-assembly techniques (see Chapters XI and XV). Higher den-  [c.341]

There is always some degree of adsorption of a gas or vapor at the solid-gas interface for vapors at pressures approaching the saturation pressure, the amount of adsorption can be quite large and may approach or exceed the point of monolayer formation. This type of adsorption, that of vapors near their saturation pressure, is called physical adsorption-, the forces responsible for it are similar in nature to those acting in condensation processes in general and may be somewhat loosely termed van der Waals forces, discussed in Chapter VII. The very large volume of literature associated with this subject is covered in some detail in Chapter XVII.  [c.350]

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79].  [c.454]

The thermodynamics of Ae wetting transition as the critical point is approached has been treated for simple fluids [10-12] and polymer solutions [13], and the influence of vapor adsorption on wetting has been addressed [14]. Widom has modeled the prewetting transition with a van der Waals-like theory and studied the boundary tension between two coexisting surface phases [15]. The line tension at the three phase contact line may diverge as the wetting transition is approached [16]. The importance of the precursor film (see Section X-7A) on wetting behavior was first realized by Marmur and Lelah in 1980 in their discovery of the dependence of spreading rates on the size of the solid surface [17]. The existence of this film has since received considerable attention [1, 18, 19].  [c.466]

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence.  [c.508]

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42).  [c.508]

The key physical elements in a molecular thermodynamic analysis are the interaction potentials between the molecules. The intermolecular forces have a profound influence on interfacial phenomena where properties change dramatically over molecular length scales. This is addressed in Chapters V and VI, where electrostatic and long-range forces are discussed these inteimolec-ular attractions and repulsions play a recurring role throughout the book. An important characteristic of an interface is that it is directional. Properties vary differently both along and perpendicular to an interface. This aspect is responsible for many of the fascinating phenomena occurring at interfaces and also provides leverage in the study of long-range forces. As described in Chapter VI, it is possible, for example, to measure directly the van der Waals force iKtween two surfaces. This area is one in which surface physical chemists have made fundamental contributions to physical chemistry as a whole.  [c.1]

The three phases of Fig. IV-4 meet at a line, point J in the figure the line is circular in this case. There exists correspondingly a line tension X, expressed as force or as energy per unit length. Line tension can be either positive or negative from a theoretical point of view experimental estimates have ranged from -10 to +10 dyn for various systems (see Ref. 64). A complication is that various authors have used different defining equations (see Ref. 65 and also Section X-5B). Neumann and co-workers have proposed a means to measure the line tension from the shape of the meniscus formed near a wall comprising vertical stripes of different wettability [66]. Kerins and Widom [67] applied three models including the van der Waals theory (Section III-2B) to the density profiles near the three-phase contact line and find both possitive and negative line tensions.  [c.113]

Direct force measurements on the SFA by Israelachvili and co-workers and others also confirm DLVO theory for many cases [59-62]. An example of a force measurement is shown as a plot of force over radius, F/R, versus surface separation in Fig. VI-6 for lipid bilayer-coated surfaces in two salt solutions at two ionic strengths. The inset shows the effect of the van der Waals force at small separations. Note that the ordinate scale may be converted to erg/cm or N/m for two effective planar surfaces using the Deijaguin approximation, Eq. VI-27 (see Problem Vl-7).t Interestingly, good agreement was also found with surfactant solutions well above the critical micelle concentration (see Section XII-5B) [63], although the micelles and their counterions do not contribute to the electrostatic screening [64]. A complete range of behavior was found as neat liquid ethylammonium nitrate was diluted with water [65]. Generally the DLVO potential works well until one gets to separations on the order of the Stem layer (see Section V-3), where the hydrated ions can eliminate the primary minimum  [c.242]

A molecular crystal is one whose lattice sites are occupied by molecules, as opposed to atoms or monatomic ions, and the great majority of solids belong in this category. Included would be numerous salts, such as BaS04, involving a molecular ion most nonionic inorganic compounds, as, for example, CO2 and H2O and all organic compounds. Theoretical treatment is difficult. Relatively long-range van der Waals forces (see Chapter VI) are involved surface distortion now includes surface reorientation effects. Surface states, called polaritons, have been studied by Rice and co-workers in the case of anthracene [73].  [c.269]

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3).  [c.270]

Good, van Oss, and Caudhury [208-210] generalized this approach to include three different surface tension components from Lifshitz-van der Waals (dispersion) and electron-donor/electron-acceptor polar interactions. They have tested this model on several materials to find these surface tension components [29, 138, 211, 212]. These approaches have recently been disputed on thermodynamic grounds [213] and based on experimental measurements [214, 215].  [c.376]

More recently, emphasis has been given to adhesion between the polymer and substrate as a major explanation for friction [33], the other contribution being from elastic hysteresis (see Section XII-2E). The adhesion may be mostly due to van der Waals forces, but in some cases there is a contribution from electrostatic charging. Yethiraj and co-workers have carried out simulations of polymers combining Monte Carlo methods with density functional theory [34,35], They show segmental depletions and enhancements near solid walls, which may help provide a molecular explanation for friction and adhesion in polymers. Brochard-Wyart and de Gennes have shown that the stretching transition polymers attached to a surface will experience at a critical shear rate will result in significant slippage and a consequently reduced friction [36].  [c.442]

Eventually the top of a draining film becomes thinner than the wavelength of visible light and appears black in reflected light. Black films are of particular interest because their properties are governed by surface chemical interactions, mainly the electrostatic repulsion and van der Waals attraction (Section VI-3), between the surfactant layers [186, 187]. In fact, the study of horizontal, nondraining films provides one means of investigating intermolecular forces [188-190], or the resultant disjoining pressure [191, 192]. Early observations by Perrin [193] later confirmed by Mysels and co-workers [194] and by Overbeek [189] indicated that black films coexist in patches of varying thickness with stepwise transitions between regions. This stratification has been further quantified by Exerowa and co-workers [195], Platikanov and co-workers [196] and experiments by Wasan and co-workers on films containing colloidal particles showed the stratification [197] and illustrated its mechanism [198, 199]. The thinnest of these black films, the Newton black film, is on the order of 4 nm, or about the thickness of a soap bilayer. Recent x-ray scattering studies [196, 200] showed the inaccuracies in optical measurements of such thin films.  [c.522]

See pages that mention the term Van der Waals : [c.16]    [c.136]    [c.417]    [c.417]    [c.417]    [c.50]    [c.61]    [c.109]    [c.134]    [c.230]    [c.230]    [c.237]    [c.247]    [c.265]    [c.267]    [c.342]    [c.376]   
Physical chemistry of surfaces (0) -- [ c.0 ]

Chemoinformatics (2003) -- [ c.340 ]

Molecular modelling Principles and applications (2001) -- [ c.166 ]

Computational chemistry (2001) -- [ c.50 , c.51 , c.52 , c.111 ]