T H E SURFACE ENERGY OF SOLIDS I Surface Energy of BaSOa BY B. BRUZS
The equation of the Phase Rule F = C - P + 2 (1) is restricted to systems of three degrees of variance (P,V,T). As soon as a new degree of variance is considered the last member of the above equation must be increased by one. Every two-phase system has a boundary between the two phases which is the seat of surface energy. The latter varies with the extension and character of the interface. Consequently a system for example of one component (C) in two phases (P) has one degree of variance (F) only when the interface is defined, in other words when the surface energy has a fixed value. It is customary to neglect the definition of the surface of a system and still to consider equation ( I ) correct in all cases when the interface is small. This is due to the fact that the intensity factor ( u ) of the surface energythe surface tension-is so small for all investigated systems (it is for liquids on the average about IOO ergs/cm2) that the surface energy uo remains negligible unless the surface (0) assumes very large values. For a particle size as fine as 11.1 0 is about 1 0 6 cm.? and the total surface energy approximately 2 cal./mole. When the interface assumes very large values (particle size below 11.1)we call the resulting systems colloidal or disperse and treat them with special consideration of the surface energy phenomena. It is clear however that the neglect of surface energy in all common cases is justified only under the assumption that for all substances in all states of aggregation u remains below about 1 0 3 ergs/cm.* Unfortunately in the case of solids, which present special difficulties to the determination of their surface tension,' we are confined to indirect methods and have as yet very uncertain information. The indirect methods of determination of u are: I. Theoretical determination with the aid of lattice theories. According to Born and Stern2for a KaC1 lattice: e2 4030 r3 V where e is the elementary charge and V the molecular volume. The assumptions involved in the derivation permit of an approximate calculation only. 2. Calorimetric determination of the surface energy and calculation of u from parallel surface determination is a very promising method but has = 0.933 - = -
Wien-Harms: Handbuch der Experimentalphysik, 6, 255 (1928); Antonoff: Nature, 121, 93 (1928);Arzybishev: 2. Physik, 48, 286 (1928). Wien-Harms: 268 (1928). Handbuch der Experimentalphysik, 6, 268; 7, 412 (1928).
622
B. BRUZS
as yet been used very seldom. Lipsett Johnson and Maass’ determined the surface tension of NaCl from the difference in the heat of solution of NaCl in different states of subdivision. They obtain a value of 386 ergs/cm.2 3. Determination of u from measurements of vapour pressure change (AP) with grain size (radius r) by application of Thomson’s formula: u = ERTAlnP
2m is fairly unsafe on account of experimental difficulties and many assumptions involved in the derivation of the formula. Centnerszwer and Krustinsons2 find by this method surface tensions for different solids of the order of magnitude of 104 to 105 ergs/cm. These values which give for a powder of ~p grain size surface energies above 1000 cal/mole are exceptionally high and at any rate indicate the urgent necessity of more reliable material on the surface tensions of solids. Regarding the high values obtained by Centnerszwer and Krustinsons we want to suggest the following explanation. Apart from the faults inherent in the derivation of the Thomson formula3 we want to stress a special point concerning its application to crystals. First of all surface tension must change with different density of the lattice elements on different surfaces and further on it can be expected that on account of the special position of edges and corners (small radius of curvature) the surface energy will be concentrated on these spots in close analogy to static electricity. Since kinetic measurements on solid-gas reactions4 indicate that the vapour pressure is connected primarily with the edges and corners of the solid phase we suggest that for r in equation (3) one should use a value much smaller than the one obtained from microscopic determination. The high values of Centnerszwer and Krustinsons represent in this case the surface tension of the edges and corners. The vectorial characteristics of surface energy in connection with their manifestation in heterogeneous kinetics might have a special significance for problems of colloid chemistry. With decreasing grain size we obtain systems with increasing vapour pressure, i.e. with increasing free energy. Consequently all colloidal systems are unstable and represent solely stationary states. These states are subject to two kinetic phenomena: the number of nuclei increases (grain size decreases) with increasing concentration of the reagents, the heat of activation, which governs the velocity of recrystallization, increases with grain size. The final equilibrium for all systems will be attained when the grain size will be at a maximum, but for stationary states (limited time) we find that the grain size has a maximum for certain concentration^.^ The aim of the present investigation was the determination of surface energies by the calorimetric method. JVP made use of the above-mentioned l J. Am. Chem. SOC., 49, 925, 1940 (1927);50, 2701 (1928). 2 Z . physik. Chem., 130 (Cohen Festband), 187 (1927), 132, 1 8 j (1928). Bigelow and Trimble: J. Phys. Chem., 31, 1798 (1927). Bruzs: Z. physik. Chem., B3, 427 (1929). 6P. P. von ITeimarn: “Zur Lehre von den Zustanden der Naterie” (1914).
THE SCRFACE ENERGY OF SOLIDS
623
fact that, beginning with a certain concentration of the reagents, the grain size of the precipitate in a metathesis reaction decreases with concentration and we expected to find continually decreasing heats of formation on account of the smaller stability of the precipitates of small grain size. Scheme of the Reaction for the Determination of the Surface Energy of BaS04
+
The following set of reactions was selected: a BaClznaq y [XnS04jH20xaq] = BaS04 n I)HzO [hlnSO45H20] (xy
+
+b +c
BaC12
+ naq
?*lnS045H20
+ +
=
hInC124HzO(y-1)
BaCLnaq
+ (y-
+
+
I)
[hInS045H20]xyaq = y [h1nSO45H~0xaq]
- d
MnC124H40 (y-I) [MnSO45H2O]xyaq
- e
?vInC124H20(y-~) [MnSO4jH20]xyac (y- I) [hlnSOijHzO] (xy n I ) aq
[MnSO45H20]xyaq
=
hInCl24Hz0 (y-I)
+ (n + 1)aq = RInC124H20
+ +
+
+ H20 A H
BaC12 + MnS045H20 = BaS04 MnCl24H20 A H = AH, AHb AH, - AHd - AH,
+
+
AH. is the heat of t,he metathesis reaction. AH, is the integral heat of solution of BaC12 and is constant for all reactions conducted. AH, and AHd are differential heats of solution of hlnS04jH2 and MnC124Hz resp. in a solution of hlnS04 and finally AHd is the heat of dilution of the resulting solution of llnC12 in MnSOa by the water of the disappearing BaCl? solution. Considering that x 18;s~ n 2 300 and y 2 5oo+so one easily sees that AHd plays the role of a second order correction factor only and can conseAH,quently be neglected in the calculation. The resulting A H = AH, AHd const should be a constant independent of the concentration of the reagents if the energy content of BaS04 is independent of the conditions of precipitation. On the other hand a change in the value of A H would represent the change in surface energy. The experimental procedure adopted Tvas the following: Electrical calibration of the calorimeter containing about 100 cm3. I. of an m molar ?rlnS04solution t o which about 4 gr XZnC1?4H20were initially added. Determination of A H , by introduction of approximately I gr. of pure 2. recrystallized hInSO45Ha0(one and the same material throughout). 3 . Determination of AHd by introduction of approximately I gr of LlnC124HZO (one and the same material throughout).
+
4.
of a
0.2
+
Determination of A H , by introduction of approximately 1.5 cm3. molar solution of BaCL
624
B. BRUZS
Apparatus The differential calorimeter used is shown schematically on Fig. I. The calorimeter is made of Durang glass. A battery of 700 thermoelements Cu-Constantan (0.1 mm) (A) divides the calorimeter in two equivalent parts. The thermoelements are isolated by rubber strips and the battery is imbedded in shellack. The surface is polished and the ends of the thermoelements are covered with a thin layer of Durofix entirely waterproof and
FIG.1
isolating. With the aid of a cork rim B the battery is tightly placed in the middle of the cylinder and made air tight along the boundaries of the cork by Picein. The terminals of the battery lead through a glass piece C to a Hartmann and Braun galvanometer. D serves for introduction of the substance and E is a calibrating heater of 0 . 2 mm Constantan enamelled wire bifilarly wound on a quadrangular glass support. Its resistance is 109.70. The ground ends of the cylinder are closed by glass windows F attached with Picein. The calorimeter was put into a shaking apparatus constructed for this purpose. The change in temperature caused by current or reaction was read off every half minute and evaluated by the usual graphic methods. Surface Energy of Bas04 Table I gives the results of the first determinations. The last column shows that with increase in concentration of the MnSOl solution from I molar to 3 molar the surface energy of BaSO4 increases by as much as 2 , 2 0 0 cal/mole. This effect is about 18 times larger than the caloric effect obtained by Lipsett, Johnson and Maass for NaCl and will
625
THE S U R F A C E E S E R G Y O F SOLIDS
TABLE I h = weight of ?YlnS04.gH20 i = galvanometer reading in mm. j = AH, in Jouleslmole k = om3 of 0.2 molar BaCl? 1 = galvanometer reading in cm m = AH, in Joules/mole n = AH. AH,- AHd in cal/mole
molarity of the M n S 0 4 solution current in milliamperes galvanometer reading per 3 0 secs. = heat capacity in Joules j m m = weight of YfnC12.~Hz0 = galvanometer reading in mm = AHd in Joules/mole
a b c d e f g
= = =
b
a
+
e
d
C
f
g
128.2
52.0
128.8
53.0
0.80
+ +
1.j
130.0
54.0
0.94
- 3.0
54.0
2.0
130.0 129.8
0.93
-
0.90
-10.0
2220
1.00
-17.5
3700
51.0
0.90
-18.0
4220
jI.0
0.93
-27.0
6000
0.84
-26.0
6400
1.0
0.81 I ,032
2.0
-500
2.0
-510
h
0.96 1.12
650
1.13
1940
1.16
I ,030
55.0
9.0
1.011
2.5
129.5 128.5
54.5 51.0
1.04
I ,065
3.0
128.3 127.2
1.01
1.043
127.0 i
a I
.o
1.5
2
.o
2 . 5
3.0
- 3.0 - 3.5 - 5.5 - 8.0 -11 . o
-1j.o
51.0
k
1
780
1'54
2.20
-73800
780
1.79 1.62 1.65 1.95 1.73 1.60
2.60
-75000
2.15
-68400 -68600 -64700 -64700 -63200 -62700 -61500 -61700
j
I210
1680 2720
3730
2.20 2.50
2.20
1.90 .oo
I .70
2
1.57
1.85 1.75
1.48
m
n
-17470 -16250 -15510
-15330 -15270
probably be mostly due t o the smaller gain size obtained in our experiment. We believe that for BaS04 the value of u = 3 1 0ergsjcm? given by the lattice theory1 is sufficiently correct for the present status of our knowledge about surface tension of solids.
'
Neglectin change in the Madelun potential and putting the charge Z = z we uee the Born and [tern equation for the Na8l lattice.
626
B. BRUZS
An incomplete set of measurements in the region of small concentrations is given in Table 11. The metathesis reaction Ba(CNS)2aq
+ MnSOlaq
=
BaS04
+ Mn(CT\;S)2aq
was investigated. Unfortunately difficulties in the preparation of Mn(CNS) 2 for the determination of the differential heat of solution prevented temTABLE
Molarity of MnS04 Heatofreactionin Joules/cm3. Successive portions
1.00
1
J
14.9 14.8 15 . 9
11
0.75 14.9 15.5
15 . 2
0.50
14.4 14.6
0.25
13.2 13.6 13.9 13.9
0.125
12.5 12.6 13.2 13.6
0.02
11.9 12.1
porarily the complete evaluation of the data, but from the results of Table I and measurements on the differential heat of solution of M n S 0 4 show that the differential heats play only the role of correction factors and we get an insight into the process by investigation of the heat of the metathesis reaction only. Table I1 shows that in the region of concentrations below 0.75 molar the heat of reaction gradually decreases. The maximum difference is 3 Joules/cm3 of the Ba(CT\;S)*solution between I molar and 0.02 molar solutions. The solution contained 0.06j8 of Ba per cm3 and consequently a surface energy difference is 1490 cal./mole. This result is in accord with the above mentioned observation about a maximum grain size for certain concentrations. The increasing values of AH on further addition of reagent clearly show that BaS04 precipitates on the nuclei already present and the grain size grows (surface energy decreases). An investigation on the combinations ZnSOl-BaC103, SrC1O3, CaC103, PbC103 is now in progress. We hope to determine grain size as well and obtain directly u
summary Methods of determinatjon of the surface tension of solids are discussed. The calorimetric method is applied to the determination of the sur2. face tension of BaSOl and the order of magnitude of the theoretic value of u = 310 ergs/cm2 is confirmed. 3. Surface energies as large as 2,200 cal./mole have been determined. 4. The existence of a region of maximum grain size for certain concentrations of the reagents in a metathesis reaction has been proved calorimetrically. I.
Phys. Chem. Lab. Universzty of L a h a , Riga, Lntaa.
