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A Stray Field Magnetic Resonance Imaging Study of the Drying of Sodium Silicate Films
JOURNAL OF COLLOID AND INTERFACE SCIENCE
177, 208–213 (1996)
Article No. 0022
A Stray Field Magnetic Resonance Imaging Study of the Drying of Sodium Silicate Films P. D. M. HUGHES,* P. J. MC DONALD,* ,1 N. P. RHODES,† J. W. ROCKLIFFE,† E. G. SMITH,†
AND
J. WILLS†
*Department of Physics, University of Surrey, Guildford, Surrey, GU2 5XH United Kingdom; and †Unilever Research Port Sunlight Laboratories, Quarry Road East, Bebington, Wirral, L63 3JW United Kingdom Received February 10, 1995; accepted June 14, 1995
Stray field magnetic resonance imaging (STRAFI) is shown to be highly suited to the study of drying processes in thin films. Sodium silicate films have been chosen as a model system exhibiting many of the properties of film drying in general. Films have been dried, as a function of temperature in the range 22 to 627C, down to water contents of order 28% by weight, at which stage the film is glassy. The experimental results have been quantitatively analyzed by treating the drying film as a colloidal solution. The results suggest that the localized hydrogen spin–spin relaxation time, and hence the mobility of the water in the films is independent of the drying regime and depends primarily on the local water concentration. q 1996 Academic Press, Inc. Key Words: sodium silicate; drying; thin film; nuclear magnetic resonance imaging; STRAFI.
I. INTRODUCTION
Thin film technology is important for many applications such as adhesives, binders, coatings, and paints. There remains, however, a need for a noninvasive, quantitative method of studying the distribution and mobility of constituents within the films. Although nuclear magnetic resonance (NMR) techniques such as relaxation time analysis and high-resolution spectroscopy can be used to study films, these are necessarily confined to studies of the average bulk properties. Unfortunately, these methods are not suitable for studying dynamic processes such as drying or solvent ingress in nonequilibrated samples. In these situations, a gradient of either concentration, or structure, or both exists across the film, and measurement of average properties is insufficient to fully characterize the system. Thus in many instances there is a need also for spatial resolution, which, in principle, magnetic resonance imaging can provide. However, conventional medical imaging techniques cannot cope with the short spin–spin relaxation (T 2 ) times commonly encountered in solids. These short times generally result either from restricted molecular mobility leading to dipolar broadening or 1
To whom correspondence should be addressed.
0021-9797/96 $12.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
/ m4420$3904
11-29-95 17:30:45
from susceptibility broadening whereby spatial inhomogeneity of the magnetic susceptibility causes nuclear spin dephasing. Broad line (short T 2 ) methods have been developed (1), but most suffer from insufficient resolution or the inability to accurately quantify T 2 . Stray field magnetic resonance imaging (STRAFI) (2) is a relatively new technique which uniquely offers the opportunity for high resolution imaging of systems with short T 2 relaxation times. Moreover, STRAFI permits spatially resolved measurement of the relaxation time (3). It successfully overcomes both dipolar and susceptibility broadening. The principle of the method is that the sample is placed in the fringe field of a high field magnet where the field gradient can be as much as 50 T/m. In this high field gradient, a hard 90 7x radiofrequency pulse is used to excite nuclei in only a very thin slice of the sample. A second 90 7y pulse is applied a short time, t, later and stimulates a solid echo at time 2t. The intensity of the echo is recorded as a measure of the signal intensity resulting from that slice. The sample is moved within the field gradient, and the process repeated for the next slice. Thus a profile is built up point by point in the gradient direction. In STRAFI, the pulse length, tp , combined with the gradient strength, g, determines the spatial resolution, dr, according to q
dr Å
[1]
where g is the magnetogyric ratio of the nuclei ( Å2.675 1 10 8 rad/s for protons). Multiple echoes, from which spin– spin relaxation time information is extracted, are accumulated using a train of 90 7y pulses. However, when using multiple echo data, it is necessary, as a first-order correction, to multiply the intensity of the first echo by 1.5 to bring it into line with the other echoes of the series (3). This has been done for all the first echoes discussed in this work. We have previously used STRAFI to study solvent ingress into polymers (4). In this paper, we apply STRAFI to the study of thin films for the first time. In particular, we have
208
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3p , tpgg
AP: Colloid
STRAFI STUDY OF SODIUM SILICATE FILM DRYING
chosen to study the drying of sodium silicate films from aqueous solution with a view to gaining information about the drying process. Sodium silicate films were chosen because they show a strong dependence of T 2 on hydration ranging from tens of microseconds in the glassy state to a few milliseconds in the highly viscous ‘‘rubbery’’ state and because, in many other ways, they display typical properties of films. There is already a considerable body of literature relating to high-resolution nuclear magnetic resonance spectroscopy of silicate glasses (5) and specifically to hydrous silicate glasses (6). However, these studies are necessarily confined to bulk measurements. A previous study of the drying of sodium silicate films has been made by Dent Glasser and Lee (7) using differential thermal analysis and solubility tests, although this study too was necessarily confined to average bulk properties. One objective of this new study was thus to demonstrate that STRAFI could measure water concentration profiles across drying sodium silicate films. A second objective was to determine whether STRAFI could probe spatial variations in water mobility within drying films. If it could, it would then be possible to use STRAFI to determine whether the water mobility at a given location depended on factors other than the local hydration, such as the rate of drying. For instance, the same hydration at a given depth into a film can be achieved either by rapid drying of the film at high temperature or by slow drying at lower temperature. There is no a priori reason, however, for the water to be in the same molecular environment and the same dynamic state as a result of the two drying procedures. II. EXPERIMENTAL
Commercial STRAFI probes offering a full three-dimensional imaging capability are available. However, considerable information can be obtained with simple equipment operating in one dimension only. To this end, we have modified an existing Bruker X nucleus probe equipped with a saddle coil and operating with a Bruker MSL 300 MHz spectrometer. A strong probe support was attached to the leg of the 7-T magnet such that the probe rested on a large screw with a fine thread. Adjusting the screw allowed the probe to be moved vertically through the fringe field of the magnet with a resolution of better than 25 mm. The region of field corresponding to an NMR frequency of 85-MHz protons was used. At this position the gradient was 38 T/ m. A multiple solid echo pulse sequence with a 90 7x 90 7y pulse gap, t, of 50 ms was used to acquire the data. Sixteen echoes were acquired in each echo train, extending the measurement time out to 1600 ms. The pulse length was 10 ms. For the parameters used, dr Å 53 mm. The spatial step, Dr, determined by the screw advance between measurements, should be of a similar order for an optimised experiment. In our case, Dr is 100 mm and was set slightly high because the flatness and error in alignment of the samples did not
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warrant greater spatial resolution. Each of the profiles discussed in this work is the result of 128 averages and typically took between 1 and 2 h to acquire. The primary cause of the long profiling time was the necessity to wait 1 s between each echo train for the nuclei to recover. An automated probe movement system would have permitted interleaving of data acquisition from all the slices so that the overall imaging time would have been substantially reduced. However, with the adopted procedure, the sample was stationary during each data acquisition so that velocity corrections to the data were not required (3). Tests on rubber phantoms were used to verify that the equipment was working satisfactorily and that quantitative T 2 information could be extracted. The resolution was primarily limited by the accuracy with which the sample could be aligned in the simple probe. The films were prepared by placing 30 g of sodium silicate solution with a SiO2 to Na2O mole ratio of 3.41 and total solids of 38.1% (obtained from Crosfield Group, UK) in a plastic petri dish 7.5 cm in diameter. The films were dried in temperature controlled ovens at temperatures ranging from 22 to 627C. The resulting films were typically 1–2 mm thick with a moisture content in the range 28–38% by weight. The high moisture content films remained rubbery and soft whereas the low moisture films were glass-like and brittle. Plastic dishes were used as the films strongly adhere to other materials, and it was necessary to be able to periodically remove pieces of the film for the experiment whilst leaving the remainder intact for continued drying and later study. The samples which were removed were typically 10 mm in diameter. They were weighed and lightly glued (superglue) by the lower surface (which had been in contact with the dish) to a ground glass rod which was then put in a long NMR tube of close fitting diameter. The tube was sealed. The long tube helped ensure that the film remained orthogonal to the magnetic field gradient when placed in the NMR sample coil and magnet while the rod filled the majority of the free volume. After proton density profiling using STRAFI as described above, the bulk proton spin–spin relaxation time of the film was measured using a Bruker Minispec operating at 20 MHz. Both the profiles and bulk T 2 measurements were made at room temperature, and no significant drying occurred during the NMR measurements. Finally, the total water content of the film pieces was determined by thermo gravimetric analysis. III. RESULTS
The bulk T 2 analysis of the films at 20 MHz showed that the high moisture content samples had two T 2 components. The largest in amplitude ( ú90%) had a T 2 of order 5 ms at 38% moisture. The T 2 of this component decreased rapidly with hydration. The smaller component ( õ10%) had a T 2 of less than 20 ms and was attributed to isolated water mole-
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HUGHES ET AL.
at the chosen echo time of 100 ms since it decays in intensity by a factor of order 10 3 – 4 . A shorter echo time can be used but this unduly complicates the analysis. M0 is thus a measure of the more mobile local water concentration. In order to quantify the relationship between M0 and hydration, and therefore to compare the profile intensity from different films, allowance must be made for variations in the cross sectional area of the samples. The magnetization expected from a slice of a film is given by M0 (r) Å kArrhr ,
[3]
where A is the cross-sectional area of the film, rr is the local density, hr is the local hydration, and k is a constant which includes the slice thickness, dr . The cross-sectional area of the films is given by AÅ
FIG. 1. As recorded STRAFI profiles from sodium silicate films dried at 427C for (a) 18 h, (b) 39 h, and (c) 67 h. In each case the first (top trace), fifth, ninth, and thirteenth, (bottom trace) echo profile of a 16 echo series are shown.
M(r, t) Å M0 (r)exp
S D 0t T 2 (r)
.
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rd rw , rw / h( rd 0 rw )
[5]
where rd and rw are the density of fully dehydrated sodium silicate and of water, respectively. At low hydrations, and when rd É rw this expression simplifies to r Å rd 0 h( rd 0 rw ).
[6]
The solid line in Fig. 2 is a fit to the data using this simplified expression with rd Å 2.4 g cm03 and rw Å 1.0 g cm03 . Given the assumptions made, the fit is surprisingly good and
[2]
T 2 and the preexponential factor, M0 , can then be plotted as a function of r to yield T 2 and hydrogen density profiles. The implicit assumption is that the very short and low amplitude T 2 component observed in the bulk studies of the more hydrated films is not observed in even the first echo recorded
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[4]
where ma is the total mass of the sample, s is the thickness and ra is the overall density. Figure 2 shows the results of an experiment to measure the density, r, of the films as a function of hydration, h. Based on the addition of volume fractions, the overall density is expected to be given by rÅ
cules and OH groups. The lowest moisture content sample had a single T 2 component of order 80 ms. Figure 1 shows a representative set of STRAFI profiles of a film dried at 427C. The profiles show the expected behavior, in that moisture is lost preferentially from the uppermost (right hand) surface of the film and that as time proceeds the overall moisture content decreases. Moreover, it is clear that as the film dries it decreases in thickness. Careful inspection of the profiles shows that intensity in later echoes is lost more quickly on the top drying surface (right) than on the underside (left). This indicates that the spin–spin relaxation time is shorter on the drying side. This observation can be quantified by fitting an exponential decay to the echo intensities at each position, r, in the profile as follows (8):
ma sra
coida
FIG. 2. The density of sodium silicate solution as a function of hydration. The solid line is a least-squares fit to the data.
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STRAFI STUDY OF SODIUM SILICATE FILM DRYING
FIG. 3. (a) Calculated spin–spin relaxation time profiles of sodium silicate films dried at 487C for 15 h (circles), 23 h (squares), 45 h (triangles), and 63 h (solid circles). (b) The calculated hydration for the same films as in (a).
is entirely adequate for continued analysis of the STRAFI results. Combining Eqs. [3], [4], and [6] yields M0 (r) Å
kma ( rd 0 hr ( rd 0 rw ))hr . s( rd 0 ha ( rd 0 rw ))
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temperatures, it can be seen that the drying is more uniform at lower temperatures. While this may have been expected, it highlights the use of STRAFI to quantify the drying process. Interestingly, there is evidence in the profile of the film dried at 627C that the film has dried from both sides. When preparing the sample, it was found that this film was particularly poorly adhered to the plastic. It should be noted that, compared to the thermo gravimetric analysis, the fitting procedure has systematically underestimated the hydration of the films. The error increases as the hydration decreases and is by almost a factor of 2 in the driest film. For instance, in Fig. 3 the average hydrations for the four films, measured by thermogravimetric analysis, are 38, 36, 31, and 28%, respectively, and in Fig. 4 they are 37, 36, and 30% respectively. This discrepancy is primarily due to errors in the first echo intensity correction to which the analysis is very sensitive. Multiplication by 1.5, as carried out here, is strictly only sufficient when the pulse gap is much smaller than T 2 (3). It also ignores partial line narrowing effects which are known to occur (9). The omission of more complicated higher order corrections systematically over estimates T 2 and underestimates M0 at short T 2 . Finally, ignoring the very short T 2 components also systematically under estimates M0 . From the profiles presented in Figs. 3 and 4, it is clear that the spin–spin relaxation time is very sensitive to the local moisture content. The T 2 values determined from the profiles range from 200 ms to 6 ms and can range by an
[7]
The magnetization intensities are thus normalized by multiplying by the film thickness and an overall hydration factor, ( rd 0 ha ( rd 0 rw )), and by dividing by the mass of the sample. This has been done for each data set. The film thickness, s, has been measured directly from the profiles. The overall hydration, ha , is available from the thermo gravimetric analysis of the samples. The constant k, which is spectrometer dependent, has been determined from the profile of a film dried at 227C for 48 h. The slow drying provided a film of near uniform hydration in which hr equals ha throughout. Thus it has been possible to deduce, by solving a quadratic equation, the hydration across each of the other films. Figure 3a shows the calculated relaxation time and Fig. 3b shows the calculated hydration as a function of position across films dried at 487C for 15, 23, 45, and 63 h. Figures 4a and 4b show similar results for films dried for 24 { 1 h at 35, 48, and 627C, respectively. Together, Figs. 3 and 4 represent almost half of the profiles recorded and span the full temperature and drying time range examined. Apart from the obvious observation that films dry more quickly at higher
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FIG. 4. (a) Calculated spin spin relaxation time profiles of sodium silicate films dried for 24 { 1 h at 357C (circles), 487C (squares), and 627C (triangles). (b) The calculated hydration for the same films as in (a).
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HUGHES ET AL.
FIG. 5. The correlation between the calculated spin–spin relaxation time and hydration for all the sodium silicate films studied, as well as for the starting solution and water. The solid line is discussed in the text.
order of magnitude across one film. In order to compare how water mobility is affected by the different drying conditions, a master graph of T 2 against calculated hydration has been drawn. This is shown in Fig. 5. The data have been extracted at 300-mm intervals from all of the recorded profiles. Also included in Fig. 5 are data points representing the solution from which the films were dried (h Å 0.62) and bulk water (h Å 1.0). It is striking that the combined data presented in Fig. 5 tend to lie on a single curve. This very strongly supports the contention that the molecular mobility of the water is independent of the drying conditions and depends primarily on the local hydration, thereby answering one of the primary objectives of the study. IV. DISCUSSION
The hydration dependence of the observed liquid spin spin relaxation time, T obs 2 , in porous systems is often explained by a two-site model involving rapid exchange of free and bound liquid molecules (10) in which 1 f bound (1 0 f bound ) Å / , T obs T bound T 2f ree 2 2
[8]
where f bound is the fraction of bound molecules. In many instances, the bound molecules are those attached to solid surface sites. In the limit of fast diffusion and rapid exchange between bulk and surface sites, the relaxation rate is controlled by the pore surface to volume ratio which can be linked to hydration (11). We have been unable to fit our data using a model of this kind. This is for two reasons. First, the model assumes that the surface area of sodium silicate particles comprising the film and accessible to the water is independent of the hydration level. This is not the case in hydrated sodium silicate, where the area can change due to polymerization of silicate anions. Second, in porous glasses and rocks the solid matrix provides a static environment for enhanced relaxation of bound components. This is
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coida
also not the case in sodium silicate solutions, where the water is bound to mobile solid particles. Attempts to vary the basic model to account for these effects, for instance, by varying the available volume for bound water as the hydration is reduced, have been unsuccessful. A better model invokes a critical hydration, hc which is approximately the water required to fill the primary hydration layer around the sodium silicate species. For h õ hc , it is reasonable to assume that the system is a glass and that T 2 is a constant equal to T bound . For h ú hc the system is 2 treated as a colloidal solution in which the spin relaxation is governed by molecular motion and the dipolar interaction such that (12) 1 Å C h, T2
[9]
where h is the viscosity and C is a constant of order ( m20 g 4\ 2 )/(8pb 3kBu ). b is of order an internuclear distance, u is the temperature, and the other symbols have their usual meaning. For b Å 2 1 10 010 m, C Å 108 m kg 01 at room temperature. The viscosity of colloidal solutions has been studied for many years and is usually written in terms of the solid (volume) fraction, f Å 1 0 h, as (13) h Å h1 (1 / a1f / a2f 2 . . .),
[10]
where h1 and ai , i Å 1, 2, 3. . ., are constants. For small f (large hydrations) the sequence is truncated after just two or three terms. An equivalent, but for the current purposes more useful, expression which can be applied more easily over a wider range of hydrations is (14) h Å h0 (h 0 hc ) 0k ,
[11]
where h0 and k are constants and h ú hc . Neglecting density differences and assuming f Å 1 0 h, algebraic manipulation shows that h1 Å h0 (1 0 hc ) 0k , a1 Å k(1 0 hc ) 01 and a2 Å k(k / 1)(1 0 hc ) 02 /2. Thus for h ú hc , T obs Å T bound / 2 2
(h 0 hc ) k . C h0
[12]
The constant term T bound has been added to smoothly interpo2 late between the motionally narrowed regime (h ú hc ) and the rigid lattice regime (h õ hc ). In the latter, the distribution of dipolar magnetic fields, which become dominant as h decreases towards hc , prevent T 2 monotonically decreasing. The possibility of an intermediate slow motion regime has not been considered, but, based on the current data, could not be reliably determined. The solid curve in Fig. 5 is an empirical fit to the data Å 200 ms, C h0 Å 0.625 s 01 , and k Å using hc Å 0.1, T bound 2
AP: Colloid
STRAFI STUDY OF SODIUM SILICATE FILM DRYING
4.5. The value of k is typical of values in the literature for a variety of systems (14). Moreover, using k Å 4.5, the viscosity power law coefficients a1 and a2 , evaluate to 5.0 and 15.3, in reasonable agreement with theoretical predictions of 2.5 and 14.1 for spherocolloids (13). The constant h0 is also of the expected magnitude. With C h0 Å 0.625 s 01 and C Å 108 m kg 01 and setting h Å 1 gives 0.9 1 10 03 m01 kg s 01 for the viscosity of water in good agreement with the accepted value of 1.0 1 10 03 m01 kg s 01 at 20 C (15). The critical hydration, hc Å 0.1, is a factor of 2–3 times smaller than that required for primary hydration of the sodium cations and thus smaller than expected. This is explained by the under estimation of hydration already discussed. Likewise, the value of T bound Å 200 ms is some2 what greater than expected for a glass. V. CONCLUSION
Stray field magnetic resonance imaging has been shown to be applicable to the study of drying processes in thin films. Although the data interpretation and analysis requires refinement, the experiments which have been described on sodium silicate films demonstrate that it is possible to obtain molecular mobility and density information with high spatial resolution in a relatively straightforward manner. This information could clearly be of considerable value in testing models of drying behavior. For instance, Allen-Waggoner and Blum (16) have calculated toluene concentration profiles in drying polystyrene/toluene films using NMR pulsed field gradient diffusion data as input. STRAFI has the potential to directly verify the calculations. Finally, we note that evidence has been obtained that the local water mobility in
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sodium silicate films depends primarily on the local hydration and is independent of the drying conditions. ACKNOWLEDGMENT One of us (PDMH) is grateful to the United Kingdom Engineering and Physical Sciences Research Council for a studentship.
REFERENCES 1. Jezzard, P., Attard, J. J., Carpenter, T. A., and Hall, L. D., Prog. Nucl. Magn. Reson. Spectrosc. 23, 1 (1991). 2. Samoilenko, A. A., Artemov, D. Yu., and Sibel’dina, L. A., JETP Lett. 47, 417 (1988). 3. Benson, T. B., and McDonald, P. J., J. Magn. Reson. A 112, 17 (1995). 4. Perry, K. L., McDonald, P. J., Randall, E. W., and Zick, K., Polymer 35, 2744 (1994). 5. Eckert, H., Prog. Nucl. Magn. Reson. Spectrosc. 24, 159 (1992). 6. Kohn, S. C., Dupree, R., and Smith, M. E., Nature 337, 539 (1989). 7. Dent Glasser, L. S., and Lee, C. K., J. Appl. Chem. Biotechnol. 21, 127 (1971). 8. Callaghan, P. T., ‘‘Principles of Nuclear Magnetic Resonance Microscopy,’’ Chap. 2. Oxford Univ. Press, Oxford, 1991. 9. Mansfield, P., and Ware, D., Phys. Lett. 22, 133 (1966). 10. Zimmerman, J. R., and Brittin, W. E., J. Phys. Chem. 61, 1328 (1957). 11. D’Orazio, F., Bhattacharja, S., Halperin, W. P., Eguchi, K., and Mizusaki, T., Phys. Rev. B 42, 9810 (1990). 12. Abragam, A., ‘‘Principles of Nuclear Magnetism,’’ Chap. 8. Oxford Univ. Press, Oxford, 1961. 13. Guth, A., and Simha, R., Kolloid-Z. 74, 266 (1936). 14. Sahimi, H., ‘‘Applications of percolation theory,’’ Chap. 11, 12. Taylor and Francis, London, 1994. 15. Swindells, J. F., Coe, J. R., and Godfrey, T. B., J. Res. Nat. Bur. Stand. U.S.A. 48, 1 (1952). 16. Allen-Waggoner, R., and Blum, F. D., J. Coatings Technol. 61, 51 (1989).
AP: Colloid
177, 208–213 (1996)
Article No. 0022
A Stray Field Magnetic Resonance Imaging Study of the Drying of Sodium Silicate Films P. D. M. HUGHES,* P. J. MC DONALD,* ,1 N. P. RHODES,† J. W. ROCKLIFFE,† E. G. SMITH,†
AND
J. WILLS†
*Department of Physics, University of Surrey, Guildford, Surrey, GU2 5XH United Kingdom; and †Unilever Research Port Sunlight Laboratories, Quarry Road East, Bebington, Wirral, L63 3JW United Kingdom Received February 10, 1995; accepted June 14, 1995
Stray field magnetic resonance imaging (STRAFI) is shown to be highly suited to the study of drying processes in thin films. Sodium silicate films have been chosen as a model system exhibiting many of the properties of film drying in general. Films have been dried, as a function of temperature in the range 22 to 627C, down to water contents of order 28% by weight, at which stage the film is glassy. The experimental results have been quantitatively analyzed by treating the drying film as a colloidal solution. The results suggest that the localized hydrogen spin–spin relaxation time, and hence the mobility of the water in the films is independent of the drying regime and depends primarily on the local water concentration. q 1996 Academic Press, Inc. Key Words: sodium silicate; drying; thin film; nuclear magnetic resonance imaging; STRAFI.
I. INTRODUCTION
Thin film technology is important for many applications such as adhesives, binders, coatings, and paints. There remains, however, a need for a noninvasive, quantitative method of studying the distribution and mobility of constituents within the films. Although nuclear magnetic resonance (NMR) techniques such as relaxation time analysis and high-resolution spectroscopy can be used to study films, these are necessarily confined to studies of the average bulk properties. Unfortunately, these methods are not suitable for studying dynamic processes such as drying or solvent ingress in nonequilibrated samples. In these situations, a gradient of either concentration, or structure, or both exists across the film, and measurement of average properties is insufficient to fully characterize the system. Thus in many instances there is a need also for spatial resolution, which, in principle, magnetic resonance imaging can provide. However, conventional medical imaging techniques cannot cope with the short spin–spin relaxation (T 2 ) times commonly encountered in solids. These short times generally result either from restricted molecular mobility leading to dipolar broadening or 1
To whom correspondence should be addressed.
0021-9797/96 $12.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
/ m4420$3904
11-29-95 17:30:45
from susceptibility broadening whereby spatial inhomogeneity of the magnetic susceptibility causes nuclear spin dephasing. Broad line (short T 2 ) methods have been developed (1), but most suffer from insufficient resolution or the inability to accurately quantify T 2 . Stray field magnetic resonance imaging (STRAFI) (2) is a relatively new technique which uniquely offers the opportunity for high resolution imaging of systems with short T 2 relaxation times. Moreover, STRAFI permits spatially resolved measurement of the relaxation time (3). It successfully overcomes both dipolar and susceptibility broadening. The principle of the method is that the sample is placed in the fringe field of a high field magnet where the field gradient can be as much as 50 T/m. In this high field gradient, a hard 90 7x radiofrequency pulse is used to excite nuclei in only a very thin slice of the sample. A second 90 7y pulse is applied a short time, t, later and stimulates a solid echo at time 2t. The intensity of the echo is recorded as a measure of the signal intensity resulting from that slice. The sample is moved within the field gradient, and the process repeated for the next slice. Thus a profile is built up point by point in the gradient direction. In STRAFI, the pulse length, tp , combined with the gradient strength, g, determines the spatial resolution, dr, according to q
dr Å
[1]
where g is the magnetogyric ratio of the nuclei ( Å2.675 1 10 8 rad/s for protons). Multiple echoes, from which spin– spin relaxation time information is extracted, are accumulated using a train of 90 7y pulses. However, when using multiple echo data, it is necessary, as a first-order correction, to multiply the intensity of the first echo by 1.5 to bring it into line with the other echoes of the series (3). This has been done for all the first echoes discussed in this work. We have previously used STRAFI to study solvent ingress into polymers (4). In this paper, we apply STRAFI to the study of thin films for the first time. In particular, we have
208
coida
3p , tpgg
AP: Colloid
STRAFI STUDY OF SODIUM SILICATE FILM DRYING
chosen to study the drying of sodium silicate films from aqueous solution with a view to gaining information about the drying process. Sodium silicate films were chosen because they show a strong dependence of T 2 on hydration ranging from tens of microseconds in the glassy state to a few milliseconds in the highly viscous ‘‘rubbery’’ state and because, in many other ways, they display typical properties of films. There is already a considerable body of literature relating to high-resolution nuclear magnetic resonance spectroscopy of silicate glasses (5) and specifically to hydrous silicate glasses (6). However, these studies are necessarily confined to bulk measurements. A previous study of the drying of sodium silicate films has been made by Dent Glasser and Lee (7) using differential thermal analysis and solubility tests, although this study too was necessarily confined to average bulk properties. One objective of this new study was thus to demonstrate that STRAFI could measure water concentration profiles across drying sodium silicate films. A second objective was to determine whether STRAFI could probe spatial variations in water mobility within drying films. If it could, it would then be possible to use STRAFI to determine whether the water mobility at a given location depended on factors other than the local hydration, such as the rate of drying. For instance, the same hydration at a given depth into a film can be achieved either by rapid drying of the film at high temperature or by slow drying at lower temperature. There is no a priori reason, however, for the water to be in the same molecular environment and the same dynamic state as a result of the two drying procedures. II. EXPERIMENTAL
Commercial STRAFI probes offering a full three-dimensional imaging capability are available. However, considerable information can be obtained with simple equipment operating in one dimension only. To this end, we have modified an existing Bruker X nucleus probe equipped with a saddle coil and operating with a Bruker MSL 300 MHz spectrometer. A strong probe support was attached to the leg of the 7-T magnet such that the probe rested on a large screw with a fine thread. Adjusting the screw allowed the probe to be moved vertically through the fringe field of the magnet with a resolution of better than 25 mm. The region of field corresponding to an NMR frequency of 85-MHz protons was used. At this position the gradient was 38 T/ m. A multiple solid echo pulse sequence with a 90 7x 90 7y pulse gap, t, of 50 ms was used to acquire the data. Sixteen echoes were acquired in each echo train, extending the measurement time out to 1600 ms. The pulse length was 10 ms. For the parameters used, dr Å 53 mm. The spatial step, Dr, determined by the screw advance between measurements, should be of a similar order for an optimised experiment. In our case, Dr is 100 mm and was set slightly high because the flatness and error in alignment of the samples did not
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warrant greater spatial resolution. Each of the profiles discussed in this work is the result of 128 averages and typically took between 1 and 2 h to acquire. The primary cause of the long profiling time was the necessity to wait 1 s between each echo train for the nuclei to recover. An automated probe movement system would have permitted interleaving of data acquisition from all the slices so that the overall imaging time would have been substantially reduced. However, with the adopted procedure, the sample was stationary during each data acquisition so that velocity corrections to the data were not required (3). Tests on rubber phantoms were used to verify that the equipment was working satisfactorily and that quantitative T 2 information could be extracted. The resolution was primarily limited by the accuracy with which the sample could be aligned in the simple probe. The films were prepared by placing 30 g of sodium silicate solution with a SiO2 to Na2O mole ratio of 3.41 and total solids of 38.1% (obtained from Crosfield Group, UK) in a plastic petri dish 7.5 cm in diameter. The films were dried in temperature controlled ovens at temperatures ranging from 22 to 627C. The resulting films were typically 1–2 mm thick with a moisture content in the range 28–38% by weight. The high moisture content films remained rubbery and soft whereas the low moisture films were glass-like and brittle. Plastic dishes were used as the films strongly adhere to other materials, and it was necessary to be able to periodically remove pieces of the film for the experiment whilst leaving the remainder intact for continued drying and later study. The samples which were removed were typically 10 mm in diameter. They were weighed and lightly glued (superglue) by the lower surface (which had been in contact with the dish) to a ground glass rod which was then put in a long NMR tube of close fitting diameter. The tube was sealed. The long tube helped ensure that the film remained orthogonal to the magnetic field gradient when placed in the NMR sample coil and magnet while the rod filled the majority of the free volume. After proton density profiling using STRAFI as described above, the bulk proton spin–spin relaxation time of the film was measured using a Bruker Minispec operating at 20 MHz. Both the profiles and bulk T 2 measurements were made at room temperature, and no significant drying occurred during the NMR measurements. Finally, the total water content of the film pieces was determined by thermo gravimetric analysis. III. RESULTS
The bulk T 2 analysis of the films at 20 MHz showed that the high moisture content samples had two T 2 components. The largest in amplitude ( ú90%) had a T 2 of order 5 ms at 38% moisture. The T 2 of this component decreased rapidly with hydration. The smaller component ( õ10%) had a T 2 of less than 20 ms and was attributed to isolated water mole-
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at the chosen echo time of 100 ms since it decays in intensity by a factor of order 10 3 – 4 . A shorter echo time can be used but this unduly complicates the analysis. M0 is thus a measure of the more mobile local water concentration. In order to quantify the relationship between M0 and hydration, and therefore to compare the profile intensity from different films, allowance must be made for variations in the cross sectional area of the samples. The magnetization expected from a slice of a film is given by M0 (r) Å kArrhr ,
[3]
where A is the cross-sectional area of the film, rr is the local density, hr is the local hydration, and k is a constant which includes the slice thickness, dr . The cross-sectional area of the films is given by AÅ
FIG. 1. As recorded STRAFI profiles from sodium silicate films dried at 427C for (a) 18 h, (b) 39 h, and (c) 67 h. In each case the first (top trace), fifth, ninth, and thirteenth, (bottom trace) echo profile of a 16 echo series are shown.
M(r, t) Å M0 (r)exp
S D 0t T 2 (r)
.
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rd rw , rw / h( rd 0 rw )
[5]
where rd and rw are the density of fully dehydrated sodium silicate and of water, respectively. At low hydrations, and when rd É rw this expression simplifies to r Å rd 0 h( rd 0 rw ).
[6]
The solid line in Fig. 2 is a fit to the data using this simplified expression with rd Å 2.4 g cm03 and rw Å 1.0 g cm03 . Given the assumptions made, the fit is surprisingly good and
[2]
T 2 and the preexponential factor, M0 , can then be plotted as a function of r to yield T 2 and hydrogen density profiles. The implicit assumption is that the very short and low amplitude T 2 component observed in the bulk studies of the more hydrated films is not observed in even the first echo recorded
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[4]
where ma is the total mass of the sample, s is the thickness and ra is the overall density. Figure 2 shows the results of an experiment to measure the density, r, of the films as a function of hydration, h. Based on the addition of volume fractions, the overall density is expected to be given by rÅ
cules and OH groups. The lowest moisture content sample had a single T 2 component of order 80 ms. Figure 1 shows a representative set of STRAFI profiles of a film dried at 427C. The profiles show the expected behavior, in that moisture is lost preferentially from the uppermost (right hand) surface of the film and that as time proceeds the overall moisture content decreases. Moreover, it is clear that as the film dries it decreases in thickness. Careful inspection of the profiles shows that intensity in later echoes is lost more quickly on the top drying surface (right) than on the underside (left). This indicates that the spin–spin relaxation time is shorter on the drying side. This observation can be quantified by fitting an exponential decay to the echo intensities at each position, r, in the profile as follows (8):
ma sra
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FIG. 2. The density of sodium silicate solution as a function of hydration. The solid line is a least-squares fit to the data.
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FIG. 3. (a) Calculated spin–spin relaxation time profiles of sodium silicate films dried at 487C for 15 h (circles), 23 h (squares), 45 h (triangles), and 63 h (solid circles). (b) The calculated hydration for the same films as in (a).
is entirely adequate for continued analysis of the STRAFI results. Combining Eqs. [3], [4], and [6] yields M0 (r) Å
kma ( rd 0 hr ( rd 0 rw ))hr . s( rd 0 ha ( rd 0 rw ))
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temperatures, it can be seen that the drying is more uniform at lower temperatures. While this may have been expected, it highlights the use of STRAFI to quantify the drying process. Interestingly, there is evidence in the profile of the film dried at 627C that the film has dried from both sides. When preparing the sample, it was found that this film was particularly poorly adhered to the plastic. It should be noted that, compared to the thermo gravimetric analysis, the fitting procedure has systematically underestimated the hydration of the films. The error increases as the hydration decreases and is by almost a factor of 2 in the driest film. For instance, in Fig. 3 the average hydrations for the four films, measured by thermogravimetric analysis, are 38, 36, 31, and 28%, respectively, and in Fig. 4 they are 37, 36, and 30% respectively. This discrepancy is primarily due to errors in the first echo intensity correction to which the analysis is very sensitive. Multiplication by 1.5, as carried out here, is strictly only sufficient when the pulse gap is much smaller than T 2 (3). It also ignores partial line narrowing effects which are known to occur (9). The omission of more complicated higher order corrections systematically over estimates T 2 and underestimates M0 at short T 2 . Finally, ignoring the very short T 2 components also systematically under estimates M0 . From the profiles presented in Figs. 3 and 4, it is clear that the spin–spin relaxation time is very sensitive to the local moisture content. The T 2 values determined from the profiles range from 200 ms to 6 ms and can range by an
[7]
The magnetization intensities are thus normalized by multiplying by the film thickness and an overall hydration factor, ( rd 0 ha ( rd 0 rw )), and by dividing by the mass of the sample. This has been done for each data set. The film thickness, s, has been measured directly from the profiles. The overall hydration, ha , is available from the thermo gravimetric analysis of the samples. The constant k, which is spectrometer dependent, has been determined from the profile of a film dried at 227C for 48 h. The slow drying provided a film of near uniform hydration in which hr equals ha throughout. Thus it has been possible to deduce, by solving a quadratic equation, the hydration across each of the other films. Figure 3a shows the calculated relaxation time and Fig. 3b shows the calculated hydration as a function of position across films dried at 487C for 15, 23, 45, and 63 h. Figures 4a and 4b show similar results for films dried for 24 { 1 h at 35, 48, and 627C, respectively. Together, Figs. 3 and 4 represent almost half of the profiles recorded and span the full temperature and drying time range examined. Apart from the obvious observation that films dry more quickly at higher
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FIG. 4. (a) Calculated spin spin relaxation time profiles of sodium silicate films dried for 24 { 1 h at 357C (circles), 487C (squares), and 627C (triangles). (b) The calculated hydration for the same films as in (a).
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FIG. 5. The correlation between the calculated spin–spin relaxation time and hydration for all the sodium silicate films studied, as well as for the starting solution and water. The solid line is discussed in the text.
order of magnitude across one film. In order to compare how water mobility is affected by the different drying conditions, a master graph of T 2 against calculated hydration has been drawn. This is shown in Fig. 5. The data have been extracted at 300-mm intervals from all of the recorded profiles. Also included in Fig. 5 are data points representing the solution from which the films were dried (h Å 0.62) and bulk water (h Å 1.0). It is striking that the combined data presented in Fig. 5 tend to lie on a single curve. This very strongly supports the contention that the molecular mobility of the water is independent of the drying conditions and depends primarily on the local hydration, thereby answering one of the primary objectives of the study. IV. DISCUSSION
The hydration dependence of the observed liquid spin spin relaxation time, T obs 2 , in porous systems is often explained by a two-site model involving rapid exchange of free and bound liquid molecules (10) in which 1 f bound (1 0 f bound ) Å / , T obs T bound T 2f ree 2 2
[8]
where f bound is the fraction of bound molecules. In many instances, the bound molecules are those attached to solid surface sites. In the limit of fast diffusion and rapid exchange between bulk and surface sites, the relaxation rate is controlled by the pore surface to volume ratio which can be linked to hydration (11). We have been unable to fit our data using a model of this kind. This is for two reasons. First, the model assumes that the surface area of sodium silicate particles comprising the film and accessible to the water is independent of the hydration level. This is not the case in hydrated sodium silicate, where the area can change due to polymerization of silicate anions. Second, in porous glasses and rocks the solid matrix provides a static environment for enhanced relaxation of bound components. This is
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also not the case in sodium silicate solutions, where the water is bound to mobile solid particles. Attempts to vary the basic model to account for these effects, for instance, by varying the available volume for bound water as the hydration is reduced, have been unsuccessful. A better model invokes a critical hydration, hc which is approximately the water required to fill the primary hydration layer around the sodium silicate species. For h õ hc , it is reasonable to assume that the system is a glass and that T 2 is a constant equal to T bound . For h ú hc the system is 2 treated as a colloidal solution in which the spin relaxation is governed by molecular motion and the dipolar interaction such that (12) 1 Å C h, T2
[9]
where h is the viscosity and C is a constant of order ( m20 g 4\ 2 )/(8pb 3kBu ). b is of order an internuclear distance, u is the temperature, and the other symbols have their usual meaning. For b Å 2 1 10 010 m, C Å 108 m kg 01 at room temperature. The viscosity of colloidal solutions has been studied for many years and is usually written in terms of the solid (volume) fraction, f Å 1 0 h, as (13) h Å h1 (1 / a1f / a2f 2 . . .),
[10]
where h1 and ai , i Å 1, 2, 3. . ., are constants. For small f (large hydrations) the sequence is truncated after just two or three terms. An equivalent, but for the current purposes more useful, expression which can be applied more easily over a wider range of hydrations is (14) h Å h0 (h 0 hc ) 0k ,
[11]
where h0 and k are constants and h ú hc . Neglecting density differences and assuming f Å 1 0 h, algebraic manipulation shows that h1 Å h0 (1 0 hc ) 0k , a1 Å k(1 0 hc ) 01 and a2 Å k(k / 1)(1 0 hc ) 02 /2. Thus for h ú hc , T obs Å T bound / 2 2
(h 0 hc ) k . C h0
[12]
The constant term T bound has been added to smoothly interpo2 late between the motionally narrowed regime (h ú hc ) and the rigid lattice regime (h õ hc ). In the latter, the distribution of dipolar magnetic fields, which become dominant as h decreases towards hc , prevent T 2 monotonically decreasing. The possibility of an intermediate slow motion regime has not been considered, but, based on the current data, could not be reliably determined. The solid curve in Fig. 5 is an empirical fit to the data Å 200 ms, C h0 Å 0.625 s 01 , and k Å using hc Å 0.1, T bound 2
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4.5. The value of k is typical of values in the literature for a variety of systems (14). Moreover, using k Å 4.5, the viscosity power law coefficients a1 and a2 , evaluate to 5.0 and 15.3, in reasonable agreement with theoretical predictions of 2.5 and 14.1 for spherocolloids (13). The constant h0 is also of the expected magnitude. With C h0 Å 0.625 s 01 and C Å 108 m kg 01 and setting h Å 1 gives 0.9 1 10 03 m01 kg s 01 for the viscosity of water in good agreement with the accepted value of 1.0 1 10 03 m01 kg s 01 at 20 C (15). The critical hydration, hc Å 0.1, is a factor of 2–3 times smaller than that required for primary hydration of the sodium cations and thus smaller than expected. This is explained by the under estimation of hydration already discussed. Likewise, the value of T bound Å 200 ms is some2 what greater than expected for a glass. V. CONCLUSION
Stray field magnetic resonance imaging has been shown to be applicable to the study of drying processes in thin films. Although the data interpretation and analysis requires refinement, the experiments which have been described on sodium silicate films demonstrate that it is possible to obtain molecular mobility and density information with high spatial resolution in a relatively straightforward manner. This information could clearly be of considerable value in testing models of drying behavior. For instance, Allen-Waggoner and Blum (16) have calculated toluene concentration profiles in drying polystyrene/toluene films using NMR pulsed field gradient diffusion data as input. STRAFI has the potential to directly verify the calculations. Finally, we note that evidence has been obtained that the local water mobility in
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sodium silicate films depends primarily on the local hydration and is independent of the drying conditions. ACKNOWLEDGMENT One of us (PDMH) is grateful to the United Kingdom Engineering and Physical Sciences Research Council for a studentship.
REFERENCES 1. Jezzard, P., Attard, J. J., Carpenter, T. A., and Hall, L. D., Prog. Nucl. Magn. Reson. Spectrosc. 23, 1 (1991). 2. Samoilenko, A. A., Artemov, D. Yu., and Sibel’dina, L. A., JETP Lett. 47, 417 (1988). 3. Benson, T. B., and McDonald, P. J., J. Magn. Reson. A 112, 17 (1995). 4. Perry, K. L., McDonald, P. J., Randall, E. W., and Zick, K., Polymer 35, 2744 (1994). 5. Eckert, H., Prog. Nucl. Magn. Reson. Spectrosc. 24, 159 (1992). 6. Kohn, S. C., Dupree, R., and Smith, M. E., Nature 337, 539 (1989). 7. Dent Glasser, L. S., and Lee, C. K., J. Appl. Chem. Biotechnol. 21, 127 (1971). 8. Callaghan, P. T., ‘‘Principles of Nuclear Magnetic Resonance Microscopy,’’ Chap. 2. Oxford Univ. Press, Oxford, 1991. 9. Mansfield, P., and Ware, D., Phys. Lett. 22, 133 (1966). 10. Zimmerman, J. R., and Brittin, W. E., J. Phys. Chem. 61, 1328 (1957). 11. D’Orazio, F., Bhattacharja, S., Halperin, W. P., Eguchi, K., and Mizusaki, T., Phys. Rev. B 42, 9810 (1990). 12. Abragam, A., ‘‘Principles of Nuclear Magnetism,’’ Chap. 8. Oxford Univ. Press, Oxford, 1961. 13. Guth, A., and Simha, R., Kolloid-Z. 74, 266 (1936). 14. Sahimi, H., ‘‘Applications of percolation theory,’’ Chap. 11, 12. Taylor and Francis, London, 1994. 15. Swindells, J. F., Coe, J. R., and Godfrey, T. B., J. Res. Nat. Bur. Stand. U.S.A. 48, 1 (1952). 16. Allen-Waggoner, R., and Blum, F. D., J. Coatings Technol. 61, 51 (1989).
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