Hamaker constant, effective

A common approach to treating retardation in dispersion forces is to define an effective Hamaker constant that is not constant but depends on separation distance. Lxioking back at Eq. VI-22, this defines the effective Hamaker constant... 

Thus, the spacing of the chains relative to the neutral, free, swollen size of the buoy blocks is, for a given chemical system and temperature, a unique function of the solvent-enhanced size asymmetry of the diblock polymer and a weak function of the effective Hamaker constant for adsorption. The degree of crowding of the nonadsorbing blocks, measured by a decrease in the left-hand side of Eq. 28, increases with increasing asymmetry of the block copolymer. 

From the above equation, the variation of equilibrium disjoining pressure and the radius of curvature of plateau border with position for a concentrated emulsion can be obtained. If the polarizabilities of the oil, water and the adsorbed protein layer (the effective Hamaker constants), the net charge of protein molecule, ionic strength, protein-solvent interaction and the thickness of the adsorbed protein layer are known, the disjoining pressure II(x/7) can be related to the film thickness using equations 9 -20. The variation of equilitnium film thickness with position in the emulsion can then be calculated. From the knowledge of r and Xp, the variation of cross sectional area of plateau border Qp and the continuous phase liquid holdup e with position can then be calculated using equations 7 and 21 respectively. The results of such calculations for different parameters are presented in the next session. 

Effective Hamaker constant, 234 Emulsifying activity index, 186,188/ Emulsions, concentrated oil-in-water, effea of interdroplet forces on centrifugal stability, 229-245 Enhancers of taste. See Taste enhancers Enzymatic modification of soy proteins, 181-190... 

Lastly, particle engineering as a method to improve suspension stability may be an alternative. Weers et al. and Dellamary et al. describe the use of hollow porous particles to decrease the attractive forces between particles in suspension (43,51). The similarities between the particles and the dispersing medium (the propellant system enters and fills the porous particles) reduces the effective Hamaker constant that corresponds to forces of attraction, and also makes the density difference between the propellant and the particles smaller. The FPF of these aerosols was reported to be around 70%. 

The effective Hamaker constant A2l2 is always positive, regardless of the relative magnitudes of Au and A. Thus identical particles exert a net attraction on one another due to van der Waals forces in a medium as well as under vacuum. 

It is understood that A in Equation (1) is the effective Hamaker constant A2I2 for the system. Of the variable parameters in this equation, it is the one over which we have least control its value is determined by the chemical nature of the dispersed and continuous phases. The presence of small amounts of solute in the continuous phase leads to a negligible alteration of the value of A for the solvent. 

This review indicates that good solvent conditions (in terms of either x or 0) result in a positive value for AGR. This is what would be expected from a model that assumes that the first encounter between particles with adsorbed layers is dominated by the polymers. Conversely, in a poor solvent AGR is negative and amounts to a contribution to the attraction between the core particles as far as flocculation is concerned. Under these conditions the polymer itself is at the threshold of phase separation. Van der Waals attraction between the core particles further promotes aggregation, but it is possible that coagulation could be induced in a poor solvent even if the medium decreases the effective Hamaker constant to zero. 

From a plot of log W versus log c determine the CCC value and T0 [by means of Eq. (53)]. Use the approximation for T0 given in Problem 6 to estimate for this colloid. Use the values of the CCC and T0 determined in Eqs. (5) and (6) to estimate the effective Hamaker constant Ain for polystyrene dispersed in water. Describe how A might be estimated using a more realistic model than that used in the derivation of Eqs. (5) and (6). 

MackorJ used the model outlined in Example 13.6 to derive the expression AGR = NkBT( — d/L) for the repulsion per unit area of particles carrying N rods of length L when the surfaces are separated by a distance d. Assuming this repulsion equals the van der Waals attraction when the particle separation is 1.5 nm, calculate the effective Hamaker constant in this system if L = 2.5 nm. Select a reasonable value for Win this calculation and justify your choice. 

The presence of a liquid dispersion medium, rather than a vacuum (or air), between the particles (as considered so far) notably lowers the van der Waals interaction energy. The constant A in equations (8.8)-(8.10) must be replaced by an effective Hamaker constant. Consider the interaction between two particles, 1 and 2, in a dispersion medium, 3. When the particles are far apart (Figure 8.1a),... 

For a typical experimental hydrosol critical coagulation concentration at 25°C of 0.1 mol dm-3 for z = 1, and, again, taking if/d = 75 mV, the effective Hamaker constant, A, is calculated to be equal to 8 X 10 20 J. This is consistent with the order of magnitude of A which is predicted from the theory of London-van der Waals forces (see Table 8.3). 

Adsorbed layers of stabilising agent may cause a significant lowering of the effective Hamaker constant and, therefore, a weakening of the interparticle van der Waals attraction. This effect has been considered by Void207 and by Vincent and co-workers208 in terms of the Hamaker microscopic treatment of dispersion forces. 

The van der Waals forces between surfaces covered with adsorbed layers can be calculated using the effective Hamaker constant A given by (18)... 

Since three media are involved in these van der Waals interactions, the effective Hamaker constant can become negative. For the water/air interface, A12=A23=0, and hence ... 

If the Hamaker constant between ion and water A13 (in vacuum) is larger than that between water and water A33, the effective Hamaker constant is negative and the ions are repelled by the interface. On the other hand, if A13 < A33, the ions are attracted by the interface. 

Using this substitution and accounting for retardation effects, the effective Hamaker constant is given by [7]... 

The effective Hamaker constants are calculated for many materials. A list of calculated effective Hamaker constants, A h = 0), for oxides, metals, solvents, and polymers is given in Table 10.2. 

By altering the value of the effective Hamaker constant, which means modifying the inherent attractive forces. 

A final interesting observation is the existence of a frequency scale, 3x10 see in Eq. (2-39). This is the frequency at which the electronic cloud around an atom fluctuates it is therefore the rate at which the spontaneous dipoles fluctuate. Since the electromagnetic field created by these dipoles propagates at the speed of light c = 3 x lO cm/sec, only a finite distance c/v 100 nm is traversed before the dipole has shifted. Since the dispersion interaction is only operative when these dipoles are correlated with each other, and this correlation is dismpted by the time lag between the fluctuation and the effect it produces a distance r away, the dispersion interaction actually falls off more steeply than r when molecules or surfaces become widely separated. This effect is called the retardation of the van der Waals force. The effective Hamaker constant is therefore distance dependent at separations greater than 5-10 nm or so. 

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