Langmuir 1987, 3, 631-634
t'O
Figure 4. Dependence of II= f ( t ) ;(2) nmru = f(t).
and h- on temperature: (1)hdn
structural component of disjoining pressure by an exponential dependence,
II, = noexp (-ah)
(4)
while the total isotherm is approximated by the expression
II = II, exp (-ah)
- Bh-4
(5)
where B is the constant of retarded dispersion interactions. In Figure 3 are presented the isotherms of the structural component of disjoining pressure, measured at 40,50, and 60 "C. The lower limits of the thickness of a wetting nitrobenzene film for each temperature correspond within the limits of experimental errors to the extremum point of the total isotherm of disjoining pressure, (5). On passing
631
through this point, the value of the derivative (dII/dh), becomes positive, and the film breaks up due to its thermodynamic instability. The moment of transition of the wetting nitrobenzene film into its thermodynamically unstable state was ascertained by a considerable increase in the ellipsometric angle \k, as well as by direct examination with an optical microscope. On attaining the nonequilibrium state, a considerable number of microruptures were formed over the whole film surface. The positions of microruptures were statistically varied over the entire film surface, when it formed again (having the same thickness). Yet in the cases where the film instability was caused by lyophobicity of separate areas of a quartz plate, the film rupture spots did not change in the course of repeated experiments. In Figure 4 are represented the minimum film thickness vs. temperature dependences, hminand IImax,calculated with eq 5. For comparison, the ranges of experimental values,,,,II are indicated by vertical lines. As appears from Figure 4, the film is rather unstable at t > 60 "C, and it cannot exist at higher temperatures. The experimental results derived from the examination of wetting nitrobenzene films on a quartz surface, presented in this paper, definitely prove that stability of such films is completely due to the effect of the structural component of disjoining pressure. Moreover, in distinction from the electrostatic and the molecular component of disjoining pressure, the structural component is sensitive to temperature and decreases as the temperature is raised. Registry No. Nitrobenzene, 98-95-3; quartz, 60676-86-0.
Evaluation of the Thickness of Nonfreezing Water Films from the Measurement of Thermocrystallization and Thermocapillary Flowst B. V. Derjaguin, N. V. Churaev,* 0. A. Kiseleva, and V. D. Sobolev The Department of Surface Phenomena, The Institute for Physical Chemistry, USSR Academy of Sciences, Moscow 117915, USSR Received March 10, 1987 The thicknesses h of nonfreezing adsorbed water films on the surface of a quartz capillary between two ice menisci were obtained by measuring the thermocrystallization film flow rate under the effect of a temperature gradient. The values of h decrease from 5-6 nm at -1 "C to 1-1.5 nm at -6 "C. In this temperature range the thermocrystallizationflow rate is much higher than the thermocapillary flow rate of the liquid films. When the pore space of porous bodies is filled but incompletely with ice, the surface of particles, which is not in contact with ice, is coated due to the adsorption of vapor by the polymolecular water films that remain in the liquid, nonfrozen state.lY2 When a temperature gradient is imposed on a frozen, porous body, the moisture is transferred into the cold side due to diffusion of vapor and film flow. In the first series of experiments,lV2it has been established that in capillaries about 10 pm in radius the contribution of the film thermocrystallization flow is commensurable with that of the vapor diffusion. In the present work are given the results of the further experiments carried out within a wider temperature range 'Presented a t the "VIIIth Conference on Surface Forces", Dec 3-5, 1985, Moscow; Professor B. V. Derjaguin, Chairman.
and including research on the same quartz capillaries of both the thermocrystallization and the thermocapillary flow of water films. The films were formed on the capillary walls between two menisci (of ice or water) maintained at different temperatures on a setup enabling a permanent temperature gradient to be preserved for a long period of time.3 As was done earlier,1-3the film transfer rates, V,, were determined as a difference between the measured menisci shift velocity, V, and the vapor diffusion rate, V,, calcu(1) Derjaguin, B. V.; Churaev, N. V.; Sobolev, V. D.; Barer, S. S. J. colloid Interface sei. 1981. 84. 182. (2) Barer, S . S.; Kiseleva, 0.'A.; Sobolev, V. D.; Churaev, N. V. Kolloidn. Zh. 1981, 43, 627. (3),Kiseleva,0. A.; Rabinovich, Ya. I.; Sobolev, V. D.; Churaev, N. V. Kollordn. Zh. 1979, 41, 1074.
0743-7463/87/2403-0631$01.50/0 0 1987 American Chemical Society
632 Langmuir, Vol. 3, No. 5, 1987
Derjaguin et al.
i 17
l2
Figure 1. Chamber for the sealing of capillaries under high gas
pressure.
lated for the given conditions. The accuracy of determining the position of menisci by using the comparator amounted to about f l pm. To enhance the accuracy of measurement of the film transfer rates, a new technique was The technique consists of reducing the vapor diffusion (and hence, increasing the relative contribution of film flow) due to an increase in the pressure of an inert gas filling the capillary space between the menisci. The procedure of preparing a capillary for measurements consisted of the following (Figure 1). Capillaries (1) containing an air bubble about 10-15 mm long inside the liquid column were placed into a chamber (2), where different pressures Pt (up to 50 atm) of nitrogen could be set. The gas was supplied into the chamber from a flask through a reducer and a valve (3). The chamber was at first blown through with nitrogen 5-6 times; then the pressure required was set, and the open ends of the capillaries were sealed by heating a rhenium-tungsten allow wire (4), pressed to these ends. In this case, a 18-20-A current was passed for a short time through the wire. After the capillaries were sealed under pressure, the length of the bubble reduced to about l2 = 0.2-1 mm, which was convenient for carrying out experiments. In Figure 1 to the right is represented the sealed capillary ( 5 ) ,extracted from the chamber. The length 1, of the free part of the capillary was 1 cm. Then the sealed capillaries were arranged in the grooves of a metal plate, whose ends were maintained at a prescribed temperature, ensuring the needed temperature gradient, V T , and a definite mean temperature, t,, of the bubble. Since water in fine capillaries can be strongly supercooled, the plate was subjected to a quick cooling (to about -50 "C) by liquid nitrogen. Thereafter, a thermocontrol system was applied to set definite values of V T and t,.3 At t , = -4 + -5 "C the setup enabled one to create temperature gradients up to about 18-20 deg/cm. Temperature t , was maintained at on accuracy of about f O . l "C. A more precise thermostating cannot be achieved, because of the influence of illuminating the capillary when measuring the shift of menisci. Figure 2 gives as an example the time dependence of the shift X of ice menisci in a capillary ( r = 13.4 pm) at a mean temperature t , = -0.95 "C.Under these conditions, the menisci shift velocity, V = dX/dr, amounted to about 10 pm/h. Lowering of the mean temperature decreases the shift velocity to about 5 Fm/h (at t , = -2 "C)and to
-
(4) Globus, A. M.; Rosenstock, S. K. In Collection of the Proceedings o n Agricultural Physics; 1971; Issue 32, p 31. (5) Globus, A. M . Dokl. Akad. Nauk. SSSR 1972,207, 394.
Figure 2. Shift X of the ice menisci in the quartz capillary under the effect of temperature gradient V T = 12.6 deg/cm. (1) Experimental results; t , = -0.95 O C ; Pt = 10.5 atm; 1 = 0.107 cm; r = 13.4pm. (2) The calculated shift of ice menisci, as caused by the diffusion of vapor.
I 0
0,5
1,s
I,0
'c ,hours
Figure 3. Shift X of the ice menisci in the quartz capillary under the effect of a temperature gradient V T = 12.4 deg/cm. (1) Experimental results; t , = -0.56 "C; Pt = 1.7 atm; 1 = 0.013 cm; r = 2.5 Mm. (2) The calculated shift of ice menisci, as caused by the diffusion of vapor.
around 2 pm/h (at t, = -5.7 "C). This is connected with a decrease in the film thickness as the temperature is lowered. The ice menisci shift velocities increase in finer capillaries, where the thermocrystallization f i flow makes a more noticeable contribution. Thus, for a capillary having the radius r = 2.5 pm and at a mean temperature t , = -0.56 "C, the menisci shift velocity, V, already amounts to about 100 Fm/h (see Figure 3, curve 1). The dashed lines 2 in Figures 2 and 3 indicate the shift of menisci, which should take place in the case where the mass transfer between the menisci would occur only due to the diffusion of vapor. The values of the velocity, V,, of the menisci shift due to vapor diffusion were calculated by the following equation: FD v, = piRT
0381
- Ps2)
1
where D is the coefficient of diffusion of vapor through gas; p is the water mole mass; pi is the ice density; R is the gas constant; psl and ps2are the pressures of vapor over ice at the menisci temperatures TIand T2,respectively; and 1 is the distance between the menisci. The values of the diffusion coefficient, D, were calculated by the known equation:6
(6) Kruger, A. J.; Owens, S. S.; De Vriz, D. A. In Heat and Mass Transfer;Naukova Dumka: Kiev, 1969; Vol. 6, part 2, p 296.
Langmuir, Vol. 3, No. 5, 1987 633
Thickness of Nonfreezing Water Films
where Pa= 1atm, Pt is the pressure of a vapor-gas mixture in a capillary during the experiment, and T , is the corresponding mean temperature (K). The gas pressure, Pt, in the space between the ice menisci was determined as follows. On completing the experiments, the capillary was removed from the thermal gradient chamber, and at room temperature the length of gas bubbles, l1 and 12, was measured (see Figure 1). Then the free end of the capillary was broken off, and the length of the bubble was measured again; lza > 12. Hence, the gas pressure in the capillary is equal to P = Palza/12. The pressure Pt maintained during the experiment was calculated by taking into account the dissolution of gas in water: (3) where l1 and l2 are the lengths of the bubbles prior to the opening up of the capillary; 1',and 1'2 are the mean lengths at room temperature, differing from ll and l2 due to the dissolution of gas in the course of the experiments; lZ8is the bubble length at room temperature T prior to the experiment; and 12, is the mean value of the bubble length in the course of the experiment at the mean temperature
7".
As appears from comparison of the experimental points in Figures 2 and 3 with the dashed straight lines, the film flow makes the main contribution to the thermal transfer of moisture. Subtracting from the experimental values of V those of V,, calculated with eq 1,allows the film thermocrystallization transfer rate to be calculated. This flow is connected, in accordance with Derjaguin and Churaev's theory,' with the water-ice phase transition. The corresponding expression for the thermocrystallization film flow was derived
Vf =
v - v,
2ph3L
= -V T
311rpiT
(4)
where p is the density of water, h is the mean film thickness, L is the heat of the ice-water phase transition, 11 is the viscosity of water in the film, and r is the radius of capillary. Using eq 4, it will be possible to determine the ratio h 3 / ~ from the known values of p , L, r, pi, T , and V T . The calculation of the film thickness requires some additional suppositions to be made on the viscosity of water in thin films. As is known, in fine pores about 15-35 A in radius, the viscosity of water at room temperature increases approximately by a factor of 1.5-1.6."'O Therefore, as a first approximation, it will be possible to assume 7 = 1.5q0, where 7, is the viscosity of bulk water at the mean temperature, t,. The results of these calculations are illustrated by curve 1 in Figure 4, where the abscissa plots mean temperature t,, while the ordinate plots the thickness of the polymolecular films of water, h. The values of h near 0 "C are close to the thicknesses of the polymolecular adsorption a-films of water on a quartz surface at room tempera(7) Derjaguin, B. V.; Churaev, N. V. Kolloidn. Zh. 1980, 42, 842; J . Colloid Interface Sci. 1978, 67, 391; J . Cold Region Sci. Technol. 1986, 12, 57. (8) Lashnev, V. I.; Sobolev, V. D.; Churaev, N. V. Theor. Fundam. Chem. Techn. 1976, 10 (6), 926. (9) Hadahane, N. E.; Sobolev, V. D.; Churaev, N. V. Kolloidn. Zh. 1980, 42, 911. (10) Kiseleva, 0. A.; Sobolev, V. D.; Starov, V. M.; Churaev, N. V. Kolloidn. Zh. 1979, 41, 245.
l
-6
I
I
-4
I
1
-2
I
l
0
t ,oc
Figure 4. Experimentally obtained dependence of the thickness h of the nonfreezingwater film on the surface of quartz capillaries on temperature (curve 1). Temperature dependence of the thickness of the nonfreezing water interlayer between the ice and
the silica surface.14
t~re.'l-'~ Figure 4 shows that the film thickness decreases with temperature, amounting to around 10 A at t , = -6 "C. The qualitative run of the temperature dependence h(t)(curve 1)fits with that obtained earlier by Kvlividze and Kurzaev14 for thin, nonfrozen water interlayers between the ice surface and silica particles (curve 2). It will be of no sense to compare quantitatively curves 1 and 2, because these relate to different systems-the nonfreezing adsorption films on quartz in the first case and the nonfreezing interlayers between silica and ice in the second. A decrease in the film thickness as temperature is lowered (curve 1)is associated with an increase of disjoining pressure, which depends on a difference between the vapor pressure over the supercooled bulk water and that over ice at the same temperature.' The decrease in the thickness of nonfreezing interlayers (curve 2) reflects the melting point depression for thin interlayers.' Thermocrystallization film flow of approximately the same intensity also takes place when one of the menisci is in the liquid state. In this case, the point corresponding to t = 0 "C was found in the middle of a bubble between the menisci. The same capillaries were also used to investigate the thermocapillary flow rate of films between the liquid water menisci. In this case, the velocity of the menisci shift due to the thermocapillary film flow, Vf, is determined with the known equation:15 (5) where 6 is the surface tension. The values of the ratio h2/qwere determined from this equation. For calculating the film thickness, the viscosity values of water films 7 = 1.511, were used as earlier. The film thicknesses, h, ranging from 50 to 100 A, have been obtained for 16 experiments carried out at a mean temperature t , from -1.5 "C (for supercooled water) to +19.5 "C. These values of h are close to those measured in the thermocrystallization experiments (Figure 4). A relatively (11) Derjaguin, B. V.; Zorin, Z. M. Zh. Fiz. Khim. 1955, 29, 1755. (12) Ershova, G. F.; Zorin, Z. M.; Novikova, A. V.; Churaev, N. V. In Surface Forces in Thin Films; Nauka: Moscow, 1979; p 168. (13) Ershova, G. F.; Zorin, 2.M.; Churaev, N. V. Kolloidn. Zh. 1975, 37, 208. (14) Kvlividze, V. I.; Kurzaev, A. B. In Surface Forces in Thin Films; Nauka: Moscow, 1979; p 211. (15) Derjaguin, D. V.; Mel'nikova, M. K. In Collection Dedicated t o the 70th Anniversary of Academician Joffe; AN SSSR Moscow, 1950; p 842.
634 Langmuir, Vol. 3, No. 5, 1987
t
Derjaguin et al. v, c m
".Io3
.*-I 10-6
k10
I
I
20
30 t,OC
Figure 5. Temperature dependencesof the thermocapillary flow rate V , (curve 1) and of the vapor diffusion V, (curve 2) in a capillary r = 0.8 wm and at Pt = 46 atm.
large scatter of the film thicknesses (from 50 to 100 A), obtained by measuring the thermocapillary flow rates, is associated with the influence of the eontact angle hysteresis. As is known, the quartz surface coated by a-films of water is wetted by bulk water but in~ompletely.~~J~ To clarify the scatter of the h values, it will be sufficient to assume that the advancing angle, eA, amounts to about 8-10", while the receding angle, OR, is close to zero, which agrees with the results of direct measurements of 0, and eR.le-18
The influence of thermoosmosis on the thermocrystallization film flow may be neglected, becaase the enthalpy of fusion much exceeds the enthalpy of the boundary water-bulk water transition.' In the case of the thermocapillary experiments the influence of thermoosmosis on film flow could have been noticeably greater,16 but it proved to be difficult to take it into account quantitatively in view of the absence of reliable data on the coefficient of thermoosmosis in water films.lg In Figure 5 (curve 1) is shown the dependence of the thermocapillary film flow rates V,, as calculated with eq 5, on the mean temperature t, in a very fine capillary, r = 0.8 pm. The dashed curve 2 indicates the corresponding (16) Zorin, Z. M.; Sobolev, V. D.; Churaev, N. V. Dokl. Akad. Nauk.
SSSR
1970,193,630.
(17)Berezkin, V. V.; Churaev, N. V. Kolloidn. Zh. 1982, 44, 417. (18)Kornil'ev, I. N.; Zorin, Z. M.; Churaev, N. V. Kolloidn. Zh.1984, 46, 892. (19) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Nauka: Moscow, 1986; p 322.
