4030
J. Phys. Chem. 1903, 87,4030-4034
Kinetics of Ice Nucleation in Aqueous Emulsions D. CIausse,* L. Babin, F. Brolo, M. Aguerd, and M. Clausse Labwatolre de Thermodynamlque, I.U.R.S., 84000 PAU, France (Received: August 23, 1982; I n Final Form: January 31, 1983)
Calorimetric studies of aqueous emulsions during continuous cooling or at constant temperature are reported. Pure water emulsions or water emulsions inseminated with AgI particles have been studied by differential scanning calorimetry. In both cases a S-shapeice crystallization curve has been obtained when the emulsions are maintained at a fixed temperature Tc > T H . The memory effect observed for pure water emulsions after having been frozen at Tc shows points common with the deactivation of the AgI particles dispersed within the water droplets. While ice nucleation during continuous cooling in pure water emulsions is thought to be due to a homogeneous process, it is probable that ice nucleation at a fixed temperature Tc > TH is due to a different process which has much in common with that observed in AgI-inseminated aqueous emulsions.
Introduction When studying the nucleation of undercooled melts, the emulsion technique has been widely used as it is thought that it is the best way to avoid, for the most part, heterogeneous nucleation. Furthermore, a great number of samples can be tested at the same time and the results obtained are therefore more significant. As far as steady cooling experiments are concerned, it is generally believed that the data obtained are closely related to a homogeneous nucleation process, and the homogeneous nucleation temperature T H of the dispersed melt has been determined in this way. Difficulties in interpretation arise when experiments performed on water emulsions maintained a t temperatures well above T H are undertaken.' Unexpected nonzero freezing probability and S-shape ice crystallization curves are found. The same kind of problems are encountered when aqueous LiCl solutions dispersed within emulsions have been studied2well above what is called the unosenof the time-temperature transformation curve. A heterogeneous nucleation process is assumed as the results obtained cannot be explained in terms of a homogeneous process. In this article, true heterogeneous nucleation experiments are reported for aqueous emulsions inseminated with AgI particles. The results obtained will be compared to those obtained by studying pure water emulsions in order to point out the common features. All the results reported were obtained with a PerkinElmer differential scanning calorimeter (DSC). Few details of the use of the calorimeter for making such experiments are given in this article. More informations dealing with the use of the DSC for studying undercooled melts dispersed within emulsions are available Crystallization of Ice During Steady Cooling Emulsions of pure water were made from resin-exchanged water and an oil phase containing 75% (wt/wt) liquid paraffin and 25% (wt/wt) lanolin used as the surfactant. The value of P, the weight fraction of dispersed (1) F. Broto and D. Clausse, J. Phys. C, 9, 4251 (1976). (2) D. R. McFarlane, K. Kadiyala, and C. A. Anaell, to be submitted for publication. (3) C. A. Angel1 and J. C. Tucker, Science, 181, 342 (1973) (4) F. Franks, Cryo-Lett., in press. (5) D. H. Rasmussen and C. R. Loper, Acta Metal., 24, 117 (1976). (6) J. P. Cordiez, G. Grange, and B. Mutaftschiev, J. Colloid Interface Sci., 85, 2, 431 (1982). J. P. Cordiez, These Docteur IngBnieur, Aix Marseille, France, 1981. (7) J. P. Dumas, D. Clausse, and F. Broto, Thermochim. Acta, 13, 261-75 (1975).
water, ranges from 0.10 to 0.40. Electron microscopys of replicas of the emulsions has shown spherical granules whose diameters are less than 1 ym, the most probable diameter D , being around 0.5 Fm. We define the following: No is the total number of droplets, 6N is the number of droplets whose diameters are between D and D 6D, N is the total number of droplets whose diameters are less than D , D, is the most probable diameter, f(D) is the proportion of droplets whose diameters are less than D, and g(D) is the droplet number density: probability density of finding a droplet of diameter D in the system. Then we have
+
f ( D ) = N/No 1 6N g(D) = - No 6D
f ( D )=
1g ( D )
The values of f ( D ) vs. D deduced from the analysis of the photographs obtained from electron microscopy of the emulsion are shown in Figure 1. The theoretical curve f ( D ) has been deduced from the following expressiongof g(D):
As it can be seen in Figure 1,good agreement is obtained between the experimental results and the theoretical curve. Small portions of the emulsion were sealed in aluminum DSC pans whose volumes are around 25 mm3. Figure 2 represents the thermogram corresponding to the breakdown of undercooling of the dispersed water that has been steadily cooled a t the rate of T, = -1.25 K min-'. An analysis' of the thermogram has pointed out that the droplets will freeze in greatest numbers around T* = -39 "C. This temperature at which the nucleation rate J must increase drastically has been taken as the homogeneous nucleation temperature T H of the water droplets. The influence of soluble particles on the homogeneous nucleation of ice has been studied by different authors: the depression A T H of the nucleation temperature has been found to be larger than the depression AT, of the corresponding melting point.loJ1 A linear relation between AT, (8) F. Broto, D. Clausse, L. Babin, and M. Mercier, J . Chim. Phys., 75, 10, 908-10 (1978). (9) G. A. Kozlov and A. A. Ravdel, Kolloid. Zh., 33, 6, 847-53 (1971).
0022-3654/83/2087-4030$01.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983 4031
I c e Nucleation in Aqueous Emulsions
ft
1-
0,5-
,
1
/
,
0,s
0
~
-
~
~
I
~
Dum
I,O
Flgure 1. Polydispersity of the w/o emulsions: (+) experimental data;
(-j theoretical curve.
-
10
1000
100
l 0 Y P
Flgure 3. Pure water emulsions. Proportion x ( t ) of frozen water vs. time for different values of T,: (a) T , = -21 OC;(b) T, = -26.5 OC; (c) T , = -33 O C . !x
I
-37
Figure 2. cooling.
-39
I
-41
-D
T'C
Thermogram of a water emulsion submitted to steady
and AT, has been pointed outlo by studying the ability of aqueous solutions to undercool and an evaluation of the proportional factor K (ATH = KAT,) has given K between 1.75 and 2.0 for low molecular weight solutes.12 By contrast solid AgI particles within dispersed water droplets cause THto rise from -39 to -22 OC.13 A deactivation phenomenon has been observed when the concentration of the AgI particles is less than 0.5 mol L-l. The deactivation is observed when the emulsion is left at room temperature13 or when steady cooling-heating cycles are ~erf0rmed.l~
Isothermal Crystallization of Ice Water emulsions have been maintained at fixed temperatures Tc between the homogeneous nucleation temperature TH and the melting temperature T, = 0 O C . Because of the long observation times involved and the consequent inobservability of the heat released, it was not possible to detect directly the nucleation of the droplets maintained in the calorimeter. The method used is described elsewhere.'J5 (10) D.H.Rasmussen and A. P. MacKenzie in 'Water Structure at the Water-Polymer Interface", H. H. G. Jellinek, Ed., Plenum Press, New York, 1972, p 126. (11) D. Clausse, L. Babin, F. Broto, I. Sifrini, and J. P. Dumans in "Water and Steam. Their Properties and Current Industrial Applications", J. Straub and K. Scheffler, Ed., Pergamon Press, Oxford, 19M.nn fifid-71 -__-, - - - . -. (12) F. Franks, Cryo-Lett., 2,27-31 (1981). (13) M. Aguerd, D.Clausse, and L. Babin, Cryo-Lett., 3,164-71 (1982). (14) M.Aauerd, D. Clausse, and L. Babin, to be submitted for publication. (15) D. Clausse and F. Broto, Colloid Polyym. Sci., 260,641-2 (1982).
0 0
1
2
3
4
5
Figure 4. Water emulsions inseminated with AgI particles. Proportion x ( t ) of frozen water vs. time for T, = -10 O C .
The values of the proportion x ( t ) of frozen water vs. time
t for different values of Tc are given in Figure 3. An onset time to is observed during which no freezing events are detected. Afterward an increase of the crystallization rate is noticed. The S shape of these curves has been also obtained when studying the nucleation of ice within water droplets inseminated with AgI particles. The variations of x vs. time t for Tc = -10 "C for the latter are plotted in Figure 4.
Memory Effect After having been maintained at Tc for a length of time t , the water emulsion was directly melted and then subjected to steady cooling. Two freezing signals whose areas are dependent on the time t at Tc are recorded during the cooling. One corresponds to T H = -39 "C and the other to -34 OC. Figure 5a gives the thermogram corresponding to this phenomenon observed on a water emulsion held at Tc = -26.5 "C for 150 h. As it has been shown1 that it is the drops obtained by melting of the ice globules formed at Tc which crystallize around -34 "C,this phenomenon has been referred to as "the memory effect". Heating and cooling cycles make this effect vanish (Figure 5). The effect is also eliminated by holding the emulsion at room temperature for a long time.
4032
Clausse et ai.
The Journal of Physical Chemlstry, Vol. 87,No. 2 1, 7983
-3;
-
.':--c
7
-
-3:
T
-
- 1 0 T'C
Flgure 5. Memory effect: Cooling thermograms of a water emulsion which has been frozen at T,: (a) first cycle; (b) second cycle; (c) third cycle; (d) fourth cycle; (e) sixth cycle; (f) seventh cycle.
xt
emulsion is previously placed at Tc' = -30 "C for time 7 and then maintained at Tc = -10 "C (curve 1). The corresponding rate of crystallization is even higher than the one observed when the emulsion is directly placed at -30 "C (curve 4). The same conclusions can be done on considering Tc' = -21 "C instead of Tc' = -30 "C (curves 3, 5, and 6). 2. The lower the value of Tc', the higher the rate of crystallization at Tc (curves 1 and 3). 3. An indication of the influence of Tc' upon the rate of crystallization for different values of Tc is obtained by considering curves 1 and 2. Although the rates are not very different (much less different than considering Tc = -21 "C and Tc = -10 "C without passing by Tc' = -30 " C , see curves 5 and 6) it seems that when a precooling step is included, the rates of crystallization vs. the temperature Tc is the opposite of the one observed when the emulsions are directly placed at TC= -10 "C or -21 "C (compare curves 6,5, and 4 and curves 1 and 2). 4. No influence of T on the results has been found for 7 values on the range 5-60 min. For T less than 2 min no precooling effect has been observed.
Analysis of the Supporting Phase
.-
t
Figure 6. Precooling effect: Proportion x ( t ) of frozen water within aqueous emulslons which have been precooled to T', before being maintained at T,. T , < T', < T,. T N 10 minutes: (1) T , = -10 o c , T', = -30 O C ; (2) r, = -21 OC, T', = -30 OC; (3) r, = - i o o c , rf, = -21 OC; (4) r, = -30 OC;(5) rc = -21 OC; (6)rc = - i o "C.
I t has been found that a portion of the emulsion maintained at room temperature during the whole experiment behaves normally during steady cooling. This memory effect is also not systematically observed. Nevertheless it has bee also noticed16for water emulsions made with a different surfactant and supporting phase such as Span 64 (sorbitan tristearate) in the 1:l mixture methylcyclohexane + methylcyclopentane. Aqueous saline solutions dispersed within emulsions and maintained at a fixed temperature Tc > T Halso show this effect with the same features.16
Precooling Effect Before being maintained at Tc the water droplets dispersed within the emulsion were precooled to Tc' (Tc' < Tc) for a short time, T = 10 min, and then the freezing probability x' at Tc is compared with the probability x observed when the droplets are directly placed at either Tc or Tc'. The results obtained are presented in Figure 6 where the values of x and x'vs. time t are plotted. The following remarks can be made. 1. Considering the curves 1,4, and 6 it appears that the highest rate of crystallization is obtained when the (16) I. Sifrini and D. Clausse, to be submitted for publication.
The supporting phase is found to vitrify around T , = -72 "C and devitrify at Td = -70 "C. When it is held at a fixed subzero temperature Tc higher than T , or T d ,a signal is observed during the heating at a temperature which is not very well defined, as it moves from one experiment to another one and sometimes does not exist. This signal could be a manifestation of the devitrification of the material which could have vitrified during the time it was held at Tc. As far as the isothermal crystallization of the dispersed water has always been observed, no matter if this signal exists or does not, it has been concluded, from these first experiments,16 that there is not an obvious correlation between the modification of the supporting phase and the crystallization of the dispersed water vs. time.
Discussion All the experiments reported here dealing with pure water have been performed on emulsion samples which are usually considered to provide a means of avoiding, at least for the most part, heterogeneous nucleation. Nevertheless the results cannot be interpreted simply in terms of a homogeneous nucleation process. At first sight, the S shape of the crystallization curve is not in agreement with what can be deduced when considering a monodisperse system and a homogeneous nucleation process and a stationary value of the nucleation rate J. However, the large polydispersity of the emulsion should be taken into account in any analysis. This analysis has been made for the following conditions: the polydispersity is characterized by the function g(D) see eq 1;the nucleation is homogeneous; the nucleation rate has reached at Tc its stationary value Jo(Tc). We make the following definitions: x ( t ) is the proportion of crystallized water at time t , m(t)is the mass of crystallized water at the same time t , M is the total amount of water dispersed within the emulsion sample, p is the density, and 6Nv and 6Nfv are the number of uncrystallized droplets at t = 0 (6Nv) or t (6N;) and whose volumes are included between V and V + 6V. 6N; is related to 6Nv as follows:
6N; = 6Nv exp[-JoVt]
The Journal of Physical Chemisfry, Vol. 87, No. 21, 1983
Ice Nucleation in Aqueous Emulsions
The expression for x ( t ) in terms of 6N’v and 6Nv are
t
4033
t in h o u r s
or
C6NVV exp (-Jo Vt) x(t)
= 1-
V
C~NVV
(2)
V
From the relation 1,6NVcan be expressed vs. r and 6r and eq 2 can be written as follows:
’-1 0)
I
I
I
0
1
2
3
1
-
1
I
v1-x
Figure 7. Influence of the polydispersity on the ice crystallization times. Verification of the relation x ( f ) = 1 - 1/[1 4- 2ar,3Jof]*.
g’(V), g’’(S), and g(r) are the corresponding droplet number densities. x ( t ) can be written as follows:
or x ( t ) = 1-
1 [l + 2 ~ r , ~ J ~ t ] ~
(4)
Relation 4 can be written in a different manner, such as
t=
1 a ( l - x)1/2
- -1 a
(5)
with a = 2rr,3Jo. The experimental values of t vs. [l/(l
- x)’/~]- 1are plotted in Figure 7. The shape of the curve
obtained is not in agreement with the straight line expeded from relation 5. Then if we assume a homogeneous nucleation process, the rather large polydispersity observed still cannot explain the S shape of the crystallization curve obtained. Consideringthat the water droplet is surrounded by the surfactant,” it can be thought that the nucleation could occur at the droplet surface with a uniform value of the nucleation probability. So that this point can be checked, an analysis has been made by assuming heterogeneous nucleation on the droplet surface and the polydispersity has been taken into account. Then x ( t ) is given by
with
6N’” = 6NV exp[-JoSSt] S represents the droplet surface area and Josthe nucleation rate which gives the number of germs formed by time unit and area unit. The number of droplets whose volumes are between V and V + 6V or surface areas between S and S + 6s or radii between r and 6r is given by CUV = Ng’(V) dV = N,g”(S) d S = N g ( r )dr where d V = 4rr2 dr and d S = 8 r r dr and (17) P.Becher in “Emulsions: Theory and Practice”, 2nd ed, Reinhold, New York, 1965.
A numerical analysis of relation 6 has been made and there is still no agreement between theory and experimental results. Then the hypothesis of a heterogeneous nucleation due to a “special uniform organization” at the surface of the droplet is not supported by the experimental results. Nevertheless some form of heterogeneous nucleation process should be considered since a comparison between the results obtained for isothermal crystallization of ice in the presence and absence of AgI particles shows numerous common features (see Figures 3 and 4). S-shaped curves are obtained in both cases. Also the way the memory effect disappears is very similar to the deactivation phenomenon observed in water emulsions inseminated with AgI solid particles and described briefly in an earlier section. From this it could be concluded that the nucleation of ice at Tc rather than at THis due to a heterogeneous nucleation process very similar to the one observed with nucleating particles. It should be kept in mind that a satisfactory theory of nucleation by foreign particles has not yet been achieved. Two hypotheses18have been proposed. According to the stochastic hypothesis, the effect of foreign particles in the liquid is considered nonspecific, i.e., they are assumed to enhance the efficiency of the random nucleation process but not to disturb its stochastic nature. Under these conditions the theory becomes equivalent to that given for homogeneous nucleation. According to the singular hypothesis, on the other hand, the freezing temperature of a drop is determined by that particle in the drop which has the highest characteristic temperature, and the number of ice germs formed in a drop volume V , during time t at a supercooling T i s given by the number concentration of particles inside
n,(n
(18) The stochastic hypothesis has been proposed and used by numerous scientists. Bigg (1953), Carte (1959), and Dufour and Defay (1963) are the most cited. Levine (1950) and Langham and Mason (1958) are known as having developed the singular hypothesis. Comparisons between the two models have been made by Barklie and Gokhale (1959), Stansbury and Vali (1965), and Vali and Stansbury (1965, 1966). A survey of all these works can be found in H. R. Pruppacher and J. D. Klett in “Microphysics of Clouds and Precipitation”, D. Reidel, Dordrecht, 1978, p 274.
4034
J. Phys. Chem. 1903, 87, 4034-4037
the drop which becomes active as nucleators between 0 "C and T, i.e., n&T) = SotJ(t)dt. The stochastic hypothesis seems to fit best the results obtained.13 But then, the S shape need not necessarily indicate a heterogeneous nucleation process since a homogeneous nucleation process for which the nucleation rate J has not reached its stationary value also gives an Sshaped crystallization curve. In this case it is better to consider the memory and the precooling effects as the distinguishing features of the nucleation process. Precooling experiments on water emulsions inseminated with AgI are therefore now undertaken in order to see if the precooling effect is well correlated with a heterogeneous nucleation process. Considering a heterogeneous nucleation process, the problem which remains to be solved is how this process may occur within the emulsion maintained a t a fixed subzero temperature. It has already been shown that the
behavior described above is not specific to water emulsions. For instance, it has been observed in benzene emulsion^'^ as well and also in molten hydrate salts dispersed within the same carrier as water.20 A better knowledge of the structure of the w/o emulsions is needed, specially about the water-oil-surfactant interface. Some experimental work in this area has already been undertaken6 Acknowledgment. The authors are indebted to C. A. Angell, F. Franks, P. H. E. Meijer, B. Mutaftschiev, and D. H. Rasmussen for profitable discussions. Registry No. Water, 7732-18-5;AgI, 7783-96-2. (19) F. Broto, D. Clausse, and J. P. Dumas, Proceedings of the JournBes de CalorimBtrie et d'Analyse Thermique, Vol. VII, Besangon, May 1976. (20) B. Combes, L. Babin, and D. Clausse, SBminaire "Stockage thermique et sa modBlisation"La Bade, France, 1982. Published in Reu. G6nBrale Thermiq., special issue 254, 209-13 (1983).
Dielectric Study of Dispersed Ice Microcrystals by the Depolarization Thermocurrent Technique P. Pissls,' L. Apekls, C. Chrlstodoulldes, and G. Boudourls NaNonal Technical University, Physics Laboratory A, Zografou Campus, Athens 624, Greece (Received: August 23, 1982; In Final Form: November 30, 1982)
Dispersions of ice microcrystals obtained from the breakdown of water-in-oil emulsions were investigated by means of the depolarization thermocurrent (DTC) technique in the temperature range 85-250 K. Two predominant peaks were observed at temperatures of about 140 and 225 K. The low-temperature DTC peak at 140 K was studied extensively with different kinds of electrodes. Its position and shape were found to change in the course of time. The characteristics of the low-temperature DTC peak in dispersionsof ice microcrystals at advanced states of evolution with time are discussed in relation to those of the low-temperature DTC in macroscopic pure ice. Our results provided more evidence that the low-temperature DTC peak in dispersions of ice microcrystals is due to dipolar absorption in ice.
Introduction This paper deals with depolarization thermocurrent (DTC) measurements on dispersions of ice microcrystals in oil in the tempeature range 85-250 K. When waterin-oil (W/O) emulsions with water globules a few microns in diameter are cooled, the water globules supercool to an extent of about 40 OC.' From the breakdown of supercooling, dispersions of ice microcrystals are obtained, The dielectric study of such dispersions is of interest due to the practical interest in emulsions. On the other hand, the comparison of the dielectric behavior of dispersions of ice microcrystals with that of macroscopic ice samples (of a few mm3 or more) could give us information useful to the understanding of the dielectric behavior of ice a t the molecular level. In a previous paper2 we reported, for the first time, on DTC measurements in dispersions of ice microcrystals in oil in the temperature range 85-250 K. With Au electrodes, two predominant peaks were observed at temperatures of about 140 and 225 K. The low-temperature DTC peak at 140 K was studied extensively. We could show (1) J. Lachaise and M. Clausse, J . Phys. D,8, 1227 (1975). (2) P. Pissis, L. Apekis, C. Christodoulides, and G. Boudouris, Z. Nuturforsch. A , 37, 1000 (1982).
that this peak and the dielectric absorption observed in ice emulsions in the kilohertz frequency range by many investigators3+ using ac methods are due to the same relaxation mechanism. Moreover, based on our own and existing experimental results on ice emulsions, macroscopic pure ice, and macroscopic HF-doped ice and taking into account an explanation given by Johari and Whalley7 for the temperature dependence of the activation energy W of the dielectric absorption in macroscopic pure and HFdoped ice, we could explain for the first time, why, although the observed dielectric absorption in ice emulsions is generally attributed to dipolar absorption in ice, the emulsion activation energy is so much lower than that of macroscopic pure ice a t temperatures higher than about -50 "C: Due to supercooling breakdown the concentration of extrinsic physical defects in ice emulsions is very high, so that extrinsically generated orientational defects dominate over the intrinsically generated ones in the whole temperature range, with the result that the activation (3) I. D. Chapman, J . Phys. Chem., 72, 33 (1968). (4) G. Evrard in "Physics and Chemistry of Ice", Whalley, Jones, and Gold, Ed., Royal Society of Canada, Ottawa, 1973, p 199. (5) B. Lagourette, J . Phys., 37, 945 (1976). (6) C. Boned, B. Lagourette, and M. Clauase, J . Glaciol., 22, 145 (1979). ( 7 ) G. P.Johari and E. Whalley, J . Chem. Phys., 75, 1333 (1981).
0022-3654/83/2087-4034$01.50/00 1983 American Chemical Society
