Heats of immersion

The theory for heat of immersion is due to Harkins [101] and Bangham and Razouk [102-104].  

When a clean solid surface is immersed in or wetted by a liquid, it leads to the disappearance of the solid surface and the formation of a solid-liquid interface. As a result of the disappearance of the solid surface, e total energy of die solid surface is liberated. The formation of the solid-liquid interface leads to an adsorption of energy equtd to the energy of the interface. Thus, from thermodynamic considerations, the heat of immersion (Eimm) is equal to the surface energy of the solid-gas (or vapor) interface (Egy) minus the interfacial energy between the liquid and the solid (Esl), so  

This may be simplified by the use of the adhesion tension relationship of Young and Dupre [cit. 30] 

Finally, substituting equation (5.20) into (5.17) and considering that a liquid which wets a solid has zero contact angle  

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The heat of immersion is measured calorimetrically with finely divided powders as described by several authors [9,11-14] and also in Section XVI-4. Some hi data are given in Table X-1. Polar solids show large heats of immersion in polar liquids and smaller ones in nonpolar liquids. Zetdemoyer [15] noted that for a given solid, hi was essentially a linear function of the dipole moment of the wetting liquid. 

One may obtain the difference between the heat of immersion of a clean surface and one with a preadsorbed film of the same liquid into which immersion is carried... 

A heat of immersion may refer to the immersion of a clean solid surface, qs.imm. or to the immersion of a solid having an adsorbed film on the surface. If the immersion of this last is into liquid adsorbate, we then report qsv.imm if tbe adsorbed film is in equilibrium with the saturated vapor pressure of the adsorbate (i.e., the vapor pressure of the liquid adsorbate P ), we will write It follows from these definitions... 

Fig. X-11. Heats of wetting from 0 ( ) and calorimetric heats of immersion (O) of PTFE in n-alkanes. (From Ref. 67.)...

Knowledge of the temperature coefficient of 0 provides a means of calculating the heat of immersion. Differentiation of Eq. X-18 yields... 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

Calculate the heat of immersion of talc in water around 2S°C. Comment on the value. 

As a quite different and more fundamental approach, the isotherms of Fig. XI-10 allowed a calculation of X as a function of temperature. The plot of In K versus 1 /T gave an enthalpy quantity that should be just the difference between the heats of immersion of the Graphon in benzene and in n-heptane, or 2.6 x 10 cal/m [141]. The experimental heat of immersion difference is 2.4 x 10 cal/m, or probably indistinguishable. The... 

A number of methods have been described in earlier sections whereby the surface free energy or total energy could be estimated. Generally, it was necessary to assume that the surface area was known by some other means conversely, if some estimate of the specific thermodynamic quantity is available, the application may be reversed to give a surface area determination. This is true if the heat of solution of a powder (Section VII-5B), its heat of immersion (Section X-3A), or its solubility increase (Section X-2) are known. 

Two approaches of this type, purporting to give absolute surface areas, might be mentioned. Bartell and Flu [19] proposed that the heat of immersion of a powder in a given liquid... 

The general type of approach, that is, the comparison of an experimental heat of immersion with the expected value per square centimeter, has been discussed and implemented by numerous authors [21,22]. It is possible, for example, to estimate sv - sl from adsorption data or from the so-called isosteric heat of adsorption (see Section XVII-12B). In many cases where approximate relative areas only are desired, as with coals or other natural products, the heat of immersion method has much to recommend it. In the case of microporous adsorbents surface areas from heats of immersion can be larger than those from adsorption studies [23], but the former are the more correct [24]. 

The contact angle for water on single-crystal naphthalene is 87.7° at 35°C, and ddjdT is -0.13 deg/K. Using data from Table III-l as necessary, calculate the heat of immersion of naphthalene in water in cal/g if a sample of powdered naphthalene of 10 m /g is used for the immersion study. (Note Ref. 135.)... 

Bartell and Flu [19] were able to determine the adhesion tension, that is, ysv -7SL. for the water-silica interface to be 82.8 ergs/cm at 20°C and its temperature change to be -0.173 erg cm K . The heat of immersion of the silica sample in water was 15.9 cal/g. Calculate the surface area of the sample in square centimeters per gram. 

Make a numerical estimate, with an explanation of the assumptions involved, of the specific surface area that would be found by (a) a rate of dissolving study, (b) Harkins and Jura, who find that at the adsorption of water vapor is 6.5 cm STP/g (and then proceed with a heat of immersion measurement), and (c) a measurement of the permeability to liquid flow through a compacted plug of the powder. 

The heat of adsorption is an important experimental quantity. The heat evolution with each of successive admissions of adsorbate vapor may be measured directly by means of a calorimeter described by Beebe and co-workers [31]. Alternatively, the heat of immersion in liquid adsorbate of adsorbent having various amounts preadsorbed on it may be determined. The difference between any two values is related to the integral heat of adsorption (see Section X-3A) between the two degrees of coverage. See Refs. 32 and 33 for experimental papers in this area. 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) differential heat of adsorption q may be obtained from the slope of the Qi-n plot, or by measuring the heat evolved as small increments of adsorbate are added [123]. 

Further information as to the width of constrictions can be obtained from measurement of the heat of immersion of the solid in a range of liquids... 

Fig. 4.24 Heat of immersion of a carbon (prepared by pyrolysis of Saran Polymer A) in different liquids at 300 K. The liquids for points 1-6 were (I) methanol (2) benzene (3) n-hexane (4) 3-methyl benzene (5) 2,2-dimethyl butane (6) 2,2,4-trimethyl pentane. The abscissae represent the molar volumes of the liquids. (Redrawn from the original diagram of Barton, Beswick and Harrison. " )...

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

Hydrogen is chemisorbed by diamond at temperatures from 400° upwards as was shown by Barrer (134b). Apparently, surface hydrides are formed as is indicated by the decrease in the capacity for potassium chemisorption (Table XIII). A significant decrease was also measured for the heat of immersion in water after hydrogen treatment at 800° [(55), Table XIV]. Methane is liberated when hydride-covered diamond is heated in a vacuum (153c). 

Wade and Hackerman (302) measured the heats of immersion in water of both anatase and rutile as a function of particle size and outgassing temperature. Apart from the distinct influence of the particle size, a maximum in the heat of immersion was observed after outgassing at 300 to 350°, indicating a rehydroxylation reaction. This is similar to the behavior of silica. Whereas, with silica, the decrease at higher evacuation temperatures is caused by the slowness of the reopening of siloxane bonds (see Section III,A,2), it is very probably caused by a decrease in surface area in the case of TiOj. The maximum in the heat of immersion curves was distinct only with samples of high surface area. Stbber et al. (225) observed a decrease in the surface area of fine particle size anatase already at 450°. 

The terms AHj, L, AH yUnd i used in Fig. 7.1 are all enthalphy changes defined as follows AHi is the heat of immersion of the solid into the liquid, L is the latent heat of condensation, AH yis the heat of adsorption when the solid is equilibrated with saturated vapor, and i is the heat liberated when solid in equilibrium with saturated vapor is immersed into liquid. Using Hess s law of heat summation... 

For powder samples that differ only in their surface area, the heat of immersion will be proportional to the surface area. Thus,... 

E. Utility of Heat-of-Immersion Values for Samples Equilibrated at High... 

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