Surface free energy of sulfur—Revisited: I. Yellow and orange samples solidified against glass surface

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Abstract

Surface free energy of two different samples of solidified sulfur (yellow and orange) was investigated, using several approaches for its determination. It was found that values determined about two decades ago for surface free energy of sulfur were overestimated. From current studies the apparent value of this energy ranges between 30 and 60 mJ/m2, depending on the kind and age of the sulfur samples (up to 1 year old) and/or the probe liquid used for the advancing and receding contact angle measurements. The energy has been calculated from van Oss et al.'s approach (Lifshitz–van der Walls, electron-donor, and electron-acceptor components), the contact angle hysteresis approach proposed by Chibowski, the equation of Owens and Wendt (dispersion and polar components), and Neumann et al.'s equation of state, as well as from equilibrium contact angle using Tadmor's procedure. The lowest values of the energy for 3-day- and 3-month-old samples of sulfur were calculated from the equation of state; they were below the range mentioned above.

Graphical abstract

Surface free energy of two different samples of sulfur was investigated using several approaches for its determination. Thus determined the apparent energy ranges between 30 and 60 mJ/m2.

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Introduction

Sulfur is a naturally hydrophobic solid insoluble in water, whose melting point is 383–392 K (110–119 °C). It appears in several different allotropic modifications, rhombic, monoclinic, polymeric, amorphous, and others. They differ in solubility, specific gravity, crystalline arrangements, and other physical parameters. Moreover, depending on temperature and pressure, various allotropic forms can exist together in equilibrium. Both rhombic and monoclinic crystalline sulfur form puckered-ring structures consisting of eight sulfur atoms. At normal atmospheric pressure and below 95 °C the stable form is rhombic sulfur, while above this temperature and up to the melting point (119 °C) the monoclinic form is more stable. Above 160 °C the sulfur rings break and form long unbranched chains of polymeric sulfur. At suitable high temperatures (above 190 °C), the chains can convert into crystalline patterns of coiled helices [1], [2], [3]. If the rhombic sulfur crystals are melted and then molten sulfur is cooled, first monoclinic crystals are formed, which then transform themselves into orthorhombic structures [4].

Because of the different forms of sulfur that can exist, one can expect that depending on the sample origin, its surface free energy may differ. Moreover, because some changes in the structure of sulfur forms can occur over time, changes in its surface free energy can take place too. Generally, because the sulfur surface is hydrophobic, therefore the dominant interactions are those of a London dispersion nature.

About 20–30 years ago we published several papers dealing with the surface free energy of sulfur [5], [6], [7], [8]. However, probably the most detailed study on sulfur surface free energy was conducted earlier by Janczuk et al. [9]. Some of those results will be recalled later. The interest in sulfur surface properties resulted from some problems emerging from the flotation of its ore, which was applied in Poland at that time. On the other hand, sulfur is a good model solid, which can be easily melted and crystallized against different solid surfaces, for example, smooth glass plates. In those papers the surface free energy of sulfur was determined from the water advancing contact angle, the adsorption isotherm of n-alkane, or even zeta potential measurements, and using the assumption that its surface interacted totally by London dispersion forces. The values of the energy thus determined were scattered, depending on the method used, interpretation of the experimental data, and the sample origin, and they were in a broad range, from ca. 60 up to 165 mJ/m2 [5], [6], [7], [8], [9].

In the meantime, although the problem of experimental determination of surface free energy of solids is still not solved, new theoretical approaches have appeared. One of them is that of Van Oss et al. [10], [11], [12], which distinguishes a Lifshitz–van der Waals component γsLW (actually London dispersion, γsd) and Lewis acid–base γsAB, electron-acceptor γs+, and electron-donor γs components of surface free energy (LWAB approach):γs=γsLW+γsAB=γsLW+2(γs+γs)1/2. Thus the work of adhesion Wa of a liquid to the solid surface can be expressed asWa=γl(1+cosθa)=2(γsLWγlLW)1/2+2(γs+γl)1/2+2(γsγl+)1/2, where subscripts s and l mean solid and liquid, respectively, and θa is the advancing contact angle of a probe liquid [10], [11], [12]. If contact angles are measured for three probe liquids, such as diiodomethane, water, and formamide, for which the surface tension components are known, then Eq. (2) can be solved and the solid surface free energy components can be determined.

Another approach, proposed by Chibowski [13], [14], [15], [16] (the contact angle hysteresis approach, CAH), relates the total apparent surface free energy of a solid γstot to the surface tension of a probe liquid γl and its contact angle hysteresis, which is defined as the difference between the advancing θa and receding θr contact angles:γstot=γl(1+cosθa)2(2+cosθr+cosθa).

Using this approach, the surface free energy of a solid can be evaluated from the contact angles of one probe liquid whose surface tension is known.

Actually, the LWAB approach gives relative values of solid surface free energy because it is based on the assumption that for water γl+=γl=25.5mN/m, which seems to be most reasonable at room temperatures (in the literature there are also considered unequal values of γl+ and γl for water [17], [18]; see Table 1). However, the acid–base component γsAB=2(γs+γs)1/2 can be considered as a true value for the tested surface, but still to some extent its experimental value depends on the three probe liquids used for the contact angle measurements, which are needed to solve simultaneously three equations of Eq. (2) type. So both γsLW and γsAB are apparent values. On the other hand, the values determined from the CAH method are also apparent, because they depend somehow on the probe liquid used. In fact, so far there is no experimental method in which a probe liquid has to be used that allows determination of the absolute value of solid surface free energy.

Some time ago Owens and Wendt's [19], [20] equation was often used (and sometimes at present too [21]) to determine the dispersion γsd and nondispersion (polar) γsp interactions from the advancing contact angles measured for one apolar (e.g., diiodomethane) and one polar (water) probe liquid:γsl=γs+γl2(γsdγld)1/22(γspγlp)1/2. Here the work of adhesion is expressed asWa=γl(1+cosθa)=2(γsdγld)1/2+2(γspγlp)1/2.

If the contact angle has been measured for an apolar probe liquid, then from Eq. (5) one can calculate γsd, because in this equation the last term becomes zero.

The so-called “equation of state” proposed by Neumann and co-workers [22], [23], [24] also allows calculation of solid surface free energy from the contact angle of one probe liquid,γsl=γs+γl2γsγleβ(γlγs)2, which in connection with the Young equation givescosθ=1+2γsγleβ(γlγs)2, where β=0.000125(mJ/m2)−2 is an experimental value (the authors use 0.000116 or 0.000125 for β in some of their papers, but in fact it does not make any essential difference in the calculated values of solid surface free energy). However, numerical solution of Eq. (7) gives two values for the solid surface free energy, one of which is usually much greater, and one has to decide which is more reasonable.

There is also the problem of experimental determination of the equilibrium contact angle θ0 that results from minimum free energy in the investigated solid/liquid drop/air system at T, p=constant. This contact angle is expressed by the well-known Young equation. Its value should lie somewhere between those of the advancing and receding contact angles. The use of advancing contact angles for calculation of surface free energy of solids is, however, a common practice. Lately several attempts have been published to determine equilibrium contact angle experimentally [25], [26], [27], [28], [29], [30], and a theoretical approach to calculate this angle was published by Tadmor [31]. He assumed that, if advancing and receding contact angles result from the surface roughness and heterogeneity being distributed in an isotropic way on the surface, the resistance of the three-phase solid/liquid/air line to the motion out (advancing mode) will equal the resistance of the motion in (receding mode). Based on this assumption, he derived an equation relating the advancing θa, receding θr, and equilibrium θ0 contact angles,θ0=arccos(Γacosθa+ΓrcosθrΓa+Γr), whereΓa(sin3θa(23cosθa+cos3θa))1/3,Γr(sin3θr(23cosθr+cos3θr))1/3.

The equilibrium contact angle in the solid/liquid drop/air system is understood as that when there is no contact angle hysteresis [24], [25], [26], [27], [28], [29], [30], or in other words, the advancing contact angle is equal to the receding one, and both are equal to that of equilibrium, θa=θr=θ0. As a consequence, for the equilibrium contact angle Eq. (3) converts into [32]γstot=(1/2)γl(1+cosθ0).

The purpose of this paper is to revise the surface free energy of sulfur determined in the past with the help of currently used models and using sulfur samples prepared in different ways and after different times of sample storage. The sulfur samples were prepared by casting molten sulfur against glass plates. The advancing and receding contact angles on the sample surfaces were measured for water, formamide, and diiodomethane. In Section 2, the sulfur has been crystallized in air or on different solid surfaces, i.e., gold, silicon, and Teflon.

Section snippets

Experimental

Crushed rhombic mineral specimens of sulfur (>99% purity, from the sulfur mine in Tarnobrzeg, Poland) were slowly melted (at ca. 120 °C) and then cast into rectangular glass boxes (ca. 2×2.5×0.5cm) placed on a large glass plate, which was earlier cleaned with a surfactant solution and Milli-Q water in an ultrasonic bath. In this way yellow samples of sulfur were obtained. From X-ray diffractograms it was found that initially the sulfur was monoclinic. Next, the melted sulfur samples were

Previous evaluations of sulfur surface free energy

Let us recall first investigations of sulfur surface free energy conducted by Janczuk et al. [9], which to our knowledge were the most exhaustive. In their experiments the authors also used mineralogical specimens of sulfur, which were melted and then cast onto glass plates. Those samples were aged for 1 month in a closely fitted vessel and then contact angles of water, or a captive air bubble, decane, and undecane in water were measured. Moreover, using a specially constructed autoclave vessel

Conclusions

Surface free energy of yellow and orange sulfur samples was determined applying different approaches. The obtained results show that previously published values of the energy are overestimated. Obviously, there is no doubt that the sulfur surface is hydrophobic and almost completely interacts by dispersion forces, but some residual polar interactions may also appear, probably as a result of surface chemical processes (e.g., single bondSsingle bondH or single bondSdouble bondO formation).

The surface free energy determined from apolar

Acknowledgment

Financial support from the Polish Ministry of Education and Science, Project No. 3 T09A 04329, is very much appreciated.

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