Harkins equation

The Harkins equation for the spreading of one liquid (e.g. oil) on another liquid (e.g. water) is also valid for the spreading of a liquid on a solid surface. 

The phase morphology of immiscible ternary polymer blends was the object of a review of Shokohooi et al. [12], According to the generalized Harkins equation, in a ternary A/B/C blend, the spreading coefficient, Aqb, is defined as the parameter showing the tendency of component C to encapsulate component B in a matrix of component A and is related to the interfacial tension of the components in the following manner ... 

Ellison and Zisman screened various compounds for surface activity in organic liquids by using a Langmuir film balance. The compound was spread on an organic liquid and the surface film pressure measured as a function of surface area [85]. The results indicated that the surface activity of fluorinated compounds in organic liquids can be predicted approximately from the Harkins equation for the spreading coefficient ... 

Equation 17.23 has the form of an adsorption isotherm since it relates the amount adsorbed to the corresponding pressure. This is known as the Gibbs Adsorption Isotherm. For it to be useful, an expression is required for T. Assuming an analogy between adsorbed and liquid films, Harkins and Jura(15) have proposed that ... 

Equation 17.26, derived by Harkins and Jura(15) may be plotted as In (P/To) against I / V2 to give a straight line. The slope is proportional to A2. The constant of proportionality may be found by using the same adsorbate on a solid of known surface area. Since the equation was derived for mobile layers and makes no provision for capillary condensation, it is most likely to fit data in the intermediate range of relative pressures. 

In the following table are given the limiting values of A calculated from Milner s and v. Szyszkowski s equations by Langmuir and Harkins. 

According to equation (7.7a), the Harkins-Jura equation, a plot of In P/Pq ) versus l/W should give a straight line with a slope equal to — fi and an intercept equal to A. The surface area is then calculated as... 

The term K in equation (7.9) is the Harkins-Jura (HJ) constant and is assumed to be independent of the adsorbent and dependent only on the adsorbate. 

Although it may give satisfactory values for Asp, the Harkins-Jura equation leaves something to be desired at the molecular level. For example, the linear 7r versus o equation of state —the starting point of the derivation of the Harkins-Jura isotherm —represents the relatively incompressible state of the surface phase (i.e., 6 = 0.7 in Fig. 9.6b). (This equation is obtained in analogy with the approximately linear ir versus a equation for insoluble mono-layers discussed in Chapter 7.) However, in most instances of physical adsorption, no satura-... 

This technique is based on the determination of the shape of a pendant drop that is formed at the tip of a capillary. The classical form of the Young and Laplace equation relates the pressure drop (Ap) across an interface at a given point to the two principal radii of curvature, r( and r2, and the interfacial tension (Freud and Harkins, 1929) ... 

The correction factor /3 allows for the non-vertical direction of the tension forces and for the complex shape of the liquid supported by the ring at the point of detachment hence, it depends on the dimensions of the ring and the nature of the interface. Values of / have been tabulated by Harkins and Jordan145, they can also be calculated from the equation of Zuidema and Waters146. 

The prediction of the MWD of emulsion polymers proved to be a relatively intractable problem even after the advent of the Harkins-Smith-Ewart theory. Perhaps the most successful early attack on the problem was that of Katz, Shinnar and Saidel (2). They considered only two microscopic events entry and bimolecular termination by combination. Their theory resulted in a set of partial integrodifferential equations, whose numerical solution provided the lower moments of the molecular weight distribution function. Other attempts to predict the MWD of emulsion polymers include those of Parts and Wat ter son (3 ), Sundberg and Eliassen (4), Min and Ray (5) and Gardon (6). 

Mention should be made of an important relation first brought out by Jura and Harkins (1944). It is simply that the adsorption isotherm is closely represented by the equation... 

The surface tension may be quickly calculated from the weight of a falling drop, formed with the precautions described below, by the following equation and table, which embody the results of Harkins and Brown s measurements. The weight and volume or density of a number of drops are measured, and the radius of the tip from which the drop falls. F is... 

Some doubt has been indicated as to the proper choice of a value for the cross-sectional area of the nitrogen molecule involved in the calculation of the surface area from the B.E.T. plot. The data were replotted according to the following equation rerived from an analysis of Harkins and Jura (119). 

The second method, that described by Harkins and Jura (14), applies the semiempirical equation... 

The above equations are all based on the internal energy. Similar equations can be written with the enthalpy since the surface excess enthalpy and energy are identical in the Gibbs representation when 1 =0 (Harkins and Boyd, 1942). Therefore the various energies of immersion defined by Equations (5.6)—(5.8) are all virtually equal to the corresponding enthalpies of immersion, i.e. (A inmH°, AimmHr and Ah 1), thus ... 

If the nucleation process in this polymerization system is controlled primarily by the Harkins-Smith-Ewart mechanism, the following equation should apply. 

Equation (5) or (5b) is the highly important deduction of Harkins-Smith-Ewart theory. Its validity has been fully confirmed for many cases of polymerization (19). Furthermore, although it is difficult to determine the nvimber of particles, Np, accurately (19) this simple relationship has been used to determine the absolute value of the rate constant, kp, satisfactorily for the polymerization of butadiene and isoprene by Smith (20) and by Morton et al.(21). Conditions where the rate of polymerization is not proportional to the number of particles are where Trommsdorff s effect (22-24) or Gordon s unsteady state (25) principles apply. However, the existence of linear portions of the conversion-time plots proves the absence of these principles in this system. 

It is due to Harkins and Jura and was derived on the basis of an empirical two-dimensional equation of state. Here, A and B are constants. 

Whilst the use of the Kelvin equation can be questioned in the case of smaller mesopores, this is not the case in the present case where, on the contrary, the pores are situated in the upper mesopore range. However, use of the BJH method implies the use of a t-curve. On commercial adsorption equipment, the software proposes the use of several equations to fit the t-curve. In the present case, the Harkins and Jura equation or Halsey equation is proposed. Unfortunately neither of these fit the original t-curve data of de Boer very well. 

An inaccurate form of this equation is given, without mention of Harkins, by Eucken, Lehrbuch der chemischen Physik, 1930, 191. 

Properties of Matter, 1903, 161 Harkins, Nature, 1926,117,690 Moloduyj and Pavlov, Bull. Acad. Sci. Russe., 1920, 14, 241, found this equation true if is the diameter of the neck of the drop just before separation. 

Hagen-Poiseuille law, 72 Hagenbach coefficient, 74 correction, 73, 75 hanging drop, 183, 189 level viscometer, 80 Hare s apparatus, 12 Harkins s equation, 155 heat capacity of electrolyte solution, 225 content of electrolyte and non-electrolyte solutions, 225-6 content of vapour, 348 Heilborn s specific heat formula, 218 Henning s latent heat formula, 307 Herwig s method for density of saturated vapour, 325... 

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