Premelting of ice in porous silica glass

Premelting of ice in porous silica glass

j. . . . . . . . ELSEVIER CRYSTAL GROWTH Journal of Crystal Growth 163 (1996)455-460 Premelting of ice in porous silica glass T. Ishizaki a, M. ...

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Journal of Crystal Growth 163 (1996)455-460

Premelting of ice in porous silica glass T. Ishizaki

a, M.

M a r u y a m a b,, , Y. F u r u k a w a

a, J.G.

Dash c

a Institute of Low Temperature Science, Hokkaido University, Sapporo 060, Japan b Department of Physics, Osaka City University, Osaka 558, Japan c Department of Physics, University of Washington, Seattle, Washington 98195, USA

Received 2 August 1995; accepted 27 October 1995


The liquid water thickness at an ice/silica interface in frozen porous silica has been measured with pulsed NMR in a temperature range of - 3 0 to 0°C. The liquid layer exists still at -30°C, ~ 10 ~, thick, grows with temperature, and diverges at a depressed melting point due to the pore curvature. The temperature dependence of the thickness is 90(Tm - T ) - o•60 ~k, which does not follow the standard theory of surface melting for a van der Waals solid. The discrepancy is attributed to the special system of H 2 0 / S i O 2 with a large curvature and a strong interaction.

1. I n t r o d u c t i o n

Since Faraday's pioneering work, numerous experimental and theoretical studies [1] have established that ice begins to melt at its free surfaces well below the melting point Tm = 0°C. The surface melting is driven by a reduction of surface free energies by wetting the solid surface, but the formation of a melted layer is opposed by the increase of volume free energy due to the solid-to-liquid conversion. The equilibrium thickness is determined by the competition between the two effects. For a van der Waals solid with a long range interaction, including ice, the surface melted layer thickens with temperature according to the power law with the - 1 / 3 exponent; d o ct (Tm - T) -1/3. The experimental support is provided by ellipsometry [2,3] for prismatic {1010} faces

* Corresponding author. Fax: +81 6 605 2522; E-mail: [email protected]

above - 2 ° C . The basic mechanisms are not unique to ice, but occurs in common with most solids [1]. Similar premelting mechanisms are also possible for an interface between ice and substrate, and for a boundary between ice grains. Our recent studies have demonstrated the occurrence of interfacial and grain boundary melting: for ice contained within powders such as graphite, talc and polystyrene by neutron scattering [4] and time domain reflectometry [5], and for ice/glass substrates by ellipsometry [3]. These show that the melted-liquid layer is in a quasi-liquid state: the diffusion coefficient is lower than bulk water, and the refractive index is between those of water and ice. The amount of liquid depends on the substrate; the liquid fractions measured for the systems of ice/graphite and ice/polystyrene give good agreement with the above theory corrected by curvature, but the liquid thickness for ice/planar glass does not follow it. In this paper, we report a further investigation of premelting of ice in a porous silica glass, for which

0022-0248/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0022-0248(95)00990-6


T. lshizaki et al./Journal of Crystal Growth 163 (1996) 455-460

several studies [6-8] suggest the existence of a nono freezing water layer of ~ 10 A, highly bound to the silica surface of the pores even at -170°C. The detailed measurements of the thickness, however, have not been made until now. We show that pulsed NMR can provide accurate measurements of the melted-liquid thickness on ice in the porous silica. It is very useful for the detection of H 2 0 molecules, particularly the liquid water content in a sample. Tice et al. [9] successfully applied the NMR technique in the determination of unfrozen water content in frozen soils; hence it is especially appropriate to this study.

porous s l l l ~ p o r e particle


~i n~t e r s ~ ~titia' 'c"

Time Fig. 1. NMR setup, a sample and a resulting NMR signal.

2. Use of pulsed NMR A proton bears a slight magnetic moment originating from its spin, and acts as a magnet that tends to align along a fixed external magnetic field. The magnetization generated by all the protons in a sample precesses around an applied magnetic field B0 with the Larmor frequency ~'0. Its magnitude is proportional to the number of protons and is inversely proportional to temperature, according to the Curie law for paramagnetic substances. Applying a pulse of radio frequency ~'0 the magnetization can be temporarily oriented to another unstable direction; after the pulse each proton spin emits the absorbed energy to return to the initial equilibrium position through a series of relaxation processes which are measured with the NMR instrument. Fig. 1 outlines our NMR setup. The coil surrounding the sample sends the pulse into it and then detects the voltage induced by the magnetization component perpendicular to the magnetic field. The magnitude of the voltage decreases as the magnetization returns to the stable position along the magnetic field. The voltage decay curve is called a free-induction decay (FID) curve and the shape is associated with the T2 relaxation process of protons in the sample. The initial FID peak value is directly proportional to the number of protons in the sample surrounded by the coil; hence the FID peak measurements can provide a convenient detection of H20 molecules contained in the sample. The pulsed NMR instrument employed in this study is a PRAXIS II tuned for hydrogen protons

and operated in the 90 ° pulse and 5 s clock mode. The applied magnetic field is B 0 = 2.5 kG, the radio frequency is ~'0 = 10.7 MHz, and the pulse width is 12 /xs. We have chosen the 5 s clock mode because the hydrogen atoms in the liquid state could be detected by the mode. The FID signal resulting from solid ice rapidly decreases due to a very short T2, whose magnitude is on the order of 5/zs. Therefore, the signal due to the ice disappears within the dead time of the instrument. Thus the observed FID curve depends only on liquid water in the sample.

3. Experimental procedure

3.1. Samples Porous silica glass, so-called Vycor glass, forms a network of interconnected, cylindrical pores with a uniform diameter. The porous silicas we used are powders composed of porous particles of four different qualities, shown in Table 1. The mean particle diameters of the powders were estimated by electron microscopy; the mean pore diameters, the specific pore volumes and the specific surface areas were determined by nitrogen adsorption for 40 and 100 .~ silicas, and by mercury intrusion for 300 and 500 .~ silicas. We filled distilled deionized water only in the particle pores, except for one sample, in the following manner. Some amount of water less than the total pore volume of the dry powder was added to the


T. lshizaki et al. / Journal of Crystal Growth 163 (1996) 455-460

Table 1 Characteristics of the porous silica powders and samples prepared Nominal pore diameter (~,)





Mean particle diameter (p~m) Mean pore diameter (,~) Specific pore volume (cm3/g) Specific surface area (m2/g) Water content (g H 20/g SiO2) Volumetric water content (g H 20/cm 3) Dry powder density (g/cm 3) Water-filling fraction in pore (%)

200 40 0.222 222 0.222 0.176 0.792 100

20 119 0.877 295 0.991, 0.694, 0.700 0.288, 0.286, 0.306 0.291, 0.412, 0.437 100 a, 79, 80

20 309 0.796 103 0.581 0.203 0.350 73

20 495 0.747 56 0.610 0.230 0.377 82

a More than 13% amount of water is contained in interstices between silica particles.

powder. After mixing, the mixture was compacted in a Teflon tube for N M R measurements and sealed off with a rubber stopper to prevent water evaporation. In order to facilitate water filling into the pores, the tube with the mixture was vibrated and warmed up for a few hours with an ultrasonic wave. Then it was kept at room temperature for 24 h to achieve a complete filling of water in the pores. Table 1 presents the details o f six samples, one containing extra water in the interstitial spaces between the particles. Later we checked each sample for the amount of water contained in pores and in interstices by analyzing resultant N M R signals.

4. Results and discussion 4.1. N M R signal intensity

Fig. 2 presents the N M R signal intensity (i.e. FID peak value) per gram of silica, which was transformed by dividing the raw signal intensity per unit volume by the dry powder density. The intensity above 0°C depends on the temperature and water content of the sample. W e can confirm the linear relationship between the intensity at a temperature -20


3.2. M e a s u r e m e n t s

._o 100A:


The tubes with the samples were immersed in a temperature controlled bath containing an ethylene g l y c o l - w a t e r mixture as a coolant and allowed to reach a specified temperature. To measure the sample temperature, not the coolant temperature, a platinum resistance thermometer was inserted in a soil packed in the same Teflon tube placed next to our sample tubes. After an equilibrium temperature was reached, a sample tube was removed from the bath, wiped dry, and inserted in the N M R probe to observe the FID curve. Following the recording o f an FID peak value, the tube was reimmersed in the bath. The time elapsed in this procedure was only 1 min. W e neglect the temperature change of the sample during the procedure, because the room temperature was regulated at 5°C during N M R measurements and a heavy Teflon tube was employed instead of a usual glass tube.





300A: f-I

~ ~ ~.

500A: O





i ~ , v ~ . - ~-A---- ~ . ~ .


nZ I







Temperature (~) Fig. 2. NMR signal intensity (FID peak value) for six samples with the pore diameters shown. Solid symbols designate the cooling run starting from 20°C. The other symbols indicate the warming runs starting after a complete freezing of water at the liquid nitrogen temperature. The solid line at top is a fit to liquid data for a 100 A sample.


T. lshizaki et al. /Journal of Crystal Growth 163 (1996) 455-460

and the water content, since each sample contains a different amount of water; the ratio of the measured signal intensity° at 9°C to water content is 19.9/0.222 = 90 for 40 A pore, 86.6/0.991 = 87, 64.0/0.694 = 92, 63.0/0.700 = 90 for 100 A pore, 50.7/0.581 -- 87 for 300 A pore and 54.0/0.610 = 89 for 500 A pore. Different temperatures above 0°C also give the different constant ratios, indicating the validity of utilizing the FID method for measuring the amount of liquid water contained in the sample. It can be seen from the cooling run that the intensity increases gradually with decreasing temperature but falls suddenly at some temperature below 0°C depending on sample; the smaller the pore size, the lower the temperature. This means that water freezes spontaneously at that temperature. Thus a reduction in the signal intensity corresponds to the amount of ice just frozen. When the samples are wanned up after complete freezing at liquid nitrogen temperature, the intensity coincides with that on cooling, then they become separate and again overlap at a temperature where the pore ice melts completely. A 100 ,~ sample at top behaves differently from the others; a shoulder due to a small change in intensity, corresponding to 14% of the total, exists just below 0°C. The shoulder is attributed to extra water outside the pores that only this sample contains. The value of 14% agrees fairly well with the amount of water prepared in interstices prior to NMR measurements. This interstitial H 2 0 freezes at higher temperature than the pore water, due to the much larger sizes of interstices. The other samples do not have such distinct shoulders, hence indicating the absence of interstitial H20, consistent with the preparation of these samples. The top sample in Fig. 2 includes a fit to the liquid signal above 0°C, which extends to a lower temperature range. The fit, not a straight line, is inversely proportional to temperature. It corresponds to a temperature-correction factor of the NMR signal intensity according to the Curie law for paramagnetism. We also obtained the other samples' liquid signal fits for determining the liquid fraction in frozen pores. To check the reproducibility, the NMR measurements are made twice between the liquid nitrogen temperature and 0°C except for two 100 A samples

( + and ×). The data of two warming runs are plotted alternately at intermediate temperatures of each other, showing only a slight scatter on a smooth curve.

4.2. Liquid fraction Liquid water in our samples contributes to the observed NMR signal, while solid ice does not. The liquid fraction x is calculated as the ratio of the measured NMR signal intensity to the value on the liquid signal curve at a corresponding temperature; the solid fraction is 1 - x. Fig. 3 gives the liquid fraction obtained from the data of warming runs, compared to model calculations described later. The measured one shows that pore ice melts partly even at - 3 0 ° C with the melted fraction strongly depending on pore size; the 40 ~, pore ice melts linearly with temperature and completely at - 1 5 ° C , while the others' melting is accelerated with temperature, ending in an abrupt transition at -4.99°C for 100 A pore,at - 0.19°C for 300 ,~ pore and at - 0.07°C for 500 A pore. This demonstrates that pore size plays an important role in melting. We consider that the premelting in the pores can be ascribed to melting point depression and interfacial melting with the enhancement due to curvature, and in the following we analyze the detailed behavior based on the curvature effect. The complete melting, well below the melting -30 I'

-20 '


- 10 ' _.m,._ . ~ .

0 ~,


g e-


I I~









Temperature (~2) Fig. 3. Liquid fraction calculated from the NMR signal intensity in Fig. 2, comparedwith model calculations.

T. lshizaki et al./ Journal of Crystal Growth 163 (1996)455-460 point, is explained as a result of the melting-point depression due to curvature. The shift of the melting temperature to T" for a cylindrical solid of radius r is known as the G i b b s - T h o m s o n effect:

3`rm Tm -- l " = psqr,


where 3' is the solid-liquid interfacial free energy, Ps is the solid density and q is the latent heat of melting. With experimental values 7 = 29 e r g / c m 2 [10], Ps = 0.917 g / c m 3 and q = 3.33 × 109 e r g / g , we obtain Tm - T" = 2 5 9 / r where r is measured in A; hence the calculated depressions in our pores are 13.0°C for 40 ,~ pore, 4.32°C for 100 ~, pore, 1.68°C for 300 ,~ pore and 1.04°C for 500 ,~ pore. These values are roughly consistent with the complete melting temperatures obtained previously. The discrepancy may be due to the size distribution of pores around the mean diameter; that is, the pores with a little different size contribute to a little different depressed melting temperature, resulting in the appearance of a very small shoulder at a stage of complete melting, which we can see on the curves of 100, 300 and 500 A pores in Fig. 3. We note that the calculations only give the highest complete melting temperatures, because ice in pores shrinks gradually with temperature due to interfacial melting, as analyzed below. To quantify the melting process, we apply a theory of surface melting on a cylindrical solid. We assume that the basic phenomenon is interfacial melting at ice/silica boundaries, controlled by van der Waals forces with the temperature dependence of liquid thickness on a planar surface d o ( T ) = L0(Tm T ) - 1/3. Detailed measurements of interfacial melting of ice around wires support the assumption, which verified the relation [1,11]. The liquid thickness d+(T) on a convex surface of a cylindrical solid is enhanced above do(T) due to curvature [12] and is given for the range d o << r by o


Here, Pl is the liquid density. If the solid in a cylindrical pore of radius r o undergoes surface melting at the interface, the core solid will have a radius r = r 0 - d ÷, and the melted fraction in the pore will be x = 1 - ( r / r o ) z. In Fig. 3 we show calculations according to these relations for three pores. L 0 = 35 A K 1/3 is from measurements of wire regelation [11]. We see the acceleration of melting with temperature. Although the trend is consistent with measurements, they are not in good agreement, particularly for samples of 300 and 500 A pores.

4.3. Liquid film thickness When ice exists only in the pores, the thickness of melted liquid film is given by d ÷ = r 0 [ 1 - ( 1 x)1/2]. Fig. 4 shows the thickness d + for measurements and calculations. In sharp contrast to liquid fraction, all measured d ÷, ranging between 10 and 200 A, fall on the same line. But on careful inspection, we notice that each sample, except 500 A pores, shows the acceleration of melting as supercooling approaches to zero, in qualitative accordance with the calculations. We note that the calculations go well beyond the range of validity of Eq. (2) close to melting temperature, so that the computed curves shown in Figs. 3 and 4 can only give a trend of enhanced interfacial melting due to curvature. o


~:~ u) I/) 0 C






N U. "-I "'-i


d+ ( T ) = d o ( T ) [ l + f ( T ) ],



soaA: ...... 300,A:


IOOA: 40A:

+ x ~


"-%,% '~--".~~ 0 "-'-"~:LIL~.~'" - ~ e , ~Z

(2) 0.1



Supomooling AT (~2)


3`rm f ( T ) = 3 p / q ( T m _ T) "


Fig. 4. Thickness of liquid film at an ice/silica interface in the pores, calculated from the liquid fraction in Fig. 3. AT = Tm- - T. The straight line do is a fit to the experimental values; do = 90(AT) -0"6° ,~.


T. lshizaki et aL / Journal of Crystal Growth 163 (1996) 455-460

In fitting the data that are on a straight line, the slopes are calculated: - 0 . 6 4 for 100 A pore, - 0 . 6 1 for 300 ,~ pore and - 0 . 4 7 for 500 ,~ pore. All the data, excluding the data of the accelerated melting, can be fitted to d o = 90(AT) -°6° ~,, shown in Fig. 4. All the power-law exponents are nearly the double of - 1 / 3 expected from the standard theory of surface melting for the van der Waals solid. However, the larger the pore size is, the closer the exponent is to - 1/3, suggesting size effects. A calorimetric study [8] indicated that a liquid layer exists at ice/silica interfaces in silica pores with a mean diameter 60 ~, even at -170°C, attributed to a strong adhesion between water and silica surfaces. We have also observed NMR signal intensities at - 80°C for 40 and 100 ~, pore samples, showing the liquid fraction 0.40 and 0.093, corresponding to a liquid thickness of 4.5 and 2.9 ,~, respectively. However, 300 and 500 ,~, pore samples gave no signal at - 8 0 ° C ; i.e. no liquid. A recent ellipsometric study [13] demonstrated that at an ice/planar glass interface, the melted layer is not observed on a smooth glass surface, but appears on a roughened surface above - 5 ° C ; the roughness-induced interfacial melting is consistent with our observations in similar experiments [3]. The surface roughness is considered due to surface curvature. All the results suggest that curvature effects play an essential role in the premelting of ice in pores.

5. Conclusions We have confirmed the validity of utilizing the pulsed NMR technique to measure the liquid water content in a sample, and applied it in obtaining the unfrozen water thickness on ice in frozen porous silica. The resulting temperature dependence of the liquid thickness did not show van der Waals interfacial melting with the enhancement due to pore curvature. One reason for the discrepancy is a strong interaction between H 2 0 and SiO 2 molecules: non-van der Waals forces control interfacial melting at ice/silica

boundaries. Another is due to the large curvatures of pores we used, which produce the grain boundaries and unfavorable facets that are forced on the ice crystals because of their enclosure in very small spaces. This raises the energy of the ice close to the substrate, so that the liquid phase is relatively favorable; thus causing premelting [14]. But the detailed mechanisms are still unknown to date, remaining to be explored in future studies.

Acknowledgements We wish to thank Mr. T. Uematsu of Catalysis Research Center, Hokkaido University for conducting pore size analysis. This work was supported by Grant-in-Aid Nos. 07680597, 05680353, 06640452 and 05211203 from the Japanese Ministry of Education, Science and Culture, and by U.S. National Science Foundation grant DMR-9220729.

References [1] J.G. Dash, H. Fu and J.S. Wettlaufer, Rep. Progr. Phys. 58 (1995) 115, and references therein. [2] Y. Furukawa, M. Yamamoto and T. Kuroda, J. Crystal Growth 82 (1987) 655. [3] Y. Furukawa and I. lshikawa, J. Crystal Growth 128 (1993) 1137.

[4] M. Maruyama, M. Bienfait, J.G. Dash and G. Coddens, J. Crystal Growth 118 (1992) 33. [5] J.W. Cahn, J.G. Dash and H. Fu, J. Crystal Growth 123 (1992) 101. [6] J.R. Blachere and J.E. Young, J. Am. Ceram. Soc. 55 (1972) 306. [7] J.F. Quinson, J. Dumas and J. Serughetti, J. Non-Cryst. Solids 79 (1986) 397. [8] J.C. van Miltenburg and J.P. van der Eerden, J. Crystal Growth 128 (1993) 1143. [9] A.R. Tice, J.L. Oliphant, Y. Nakano and T.F. Jenkins, CRREL Report 82-15 (1982). [10] S.C. Hardy, Philos. Mag. 35 (1977) 471. [11] R.R. Gilpin, J. Colloid Interface Sci. 77 (1980) 435. [12] M.B. Baker and J.G. Dash, J. Crystal Growth 97 (1989) 770. [13] D. Beaglehole and P. Wilson, J. Phys. Chem. 98 (1994) 8096. [14] J.G. Dash, J. Low Temp. Phys. 89 (1992) 277.