J. Phys. Chem. 1996, 100, 2195-2200
2195
Low-Temperature Phase Transition of Water Confined in Mesopores Probed by NMR. Influence on Pore Size Distribution Eddy Walther Hansen,* Michael Sto1 cker, and Ralf Schmidt SINTEF Oslo, P.O. Box 124, Blindern, N-0314 Oslo, Norway ReceiVed: June 27, 1995; In Final Form: October 20, 1995X
The NMR signal intensity vs temperature (IT curve) of water confined in mesoporous materials (pore radius lager than 10 Å) reveals one or more “high-temperature” transitions above 222 K, which are dependent on pore size, and an additional transition temperature below 209 K, which is independent of pore dimension. This latter transition shows no hysteresis effect or discontinuity and contributes to more than 65% of the total water content of the porous materials investigated and is explained as interfacial water in contact with the surface of the matrix and the solid ice phase. The thickness of this interface water is estimated to be 5.4 ( 1.0 Å (cylindrical pores). It is shown that the observed NMR intensity of water associated with the “hightemperature” transition phases has to be corrected in order to present the actual amount of water within these phases. It is further demonstrated that these intensity corrections must be implemented in the pore size distribution functions to give quantitative results. The significance of the correction factors increases with decreasing pore radius.
Introduction co-workers1-4
al.5
and Overloop et have recently Hansen and reported on a series of 1H NMR experiments of water confined in mesoporous materials showing that both the spin-lattice relaxation rate (1/T1 at -10 °C) and the freezing point of the confined water can be linearly correlated with the inverse pore radius of such materials. It should be emphasized, however, that Resing et al.6,7 were the first to report on relaxation time vs temperature measurements of water confined in porous materials (high surface area charcoal) some 30 years ago. The freezing point, or more correctly the transition temperature, is determined by model fits to the observed intensity vs temperature curves (IT curves). These experiments have enabled pore size distribution curves to be estimated which are in good agreement with N2 adsorption data. When deriving pore size distributions from these NMR measurements, the low-temperature transition, which has always been evident from the IT curve, has been successfully removed or excluded from these calculations. In this work we concentrate on the origin of this low-temperature transition and show that this transition enables one to determine correction factors which must be applied to the observed high-temperature transition intensities in order to derive “true” pore size distributions. We show that these correction factors might have a significant impact on the calculation of relative intensity distribution of pore sizes, i.e., they become increasingly more important with decreasing pore size. Experimental Section Procedures concerning the synthesis of MCM-41 materials and their characterization have been extensively outlined in previous articles1,3,8 and will not be discussed further in this work. However, a few comments will be given on the preparation of the two composite materials. Composite I was made by mixing silica sol (Ludox LS) with as-synthesized MCM-41 with an ultrastirrer for 10-15 s. Composite II was made correspondingly by manually mixing 6.25 g of as* To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-2195$12.00/0
synthesized MCM-41 with 2.5 g of USY before adding 58.3 g of the silica sol (Ludox LS) and stirring for 10-15 s. The moisture in the slurries was then evaporated on a Rotavap at 100 °C , and the products were dried in a heating cupboard at 100 °C overnight. The sample denoted “matrix” in this work represents a dried silica sol (Ludox LS), and the FCC catalyst is a commercial sample from Grace GmbH. The water-saturated samples were studied by 1H NMR at subzero temperature (T < 273 K) using a Varian VXR 300 S NMR spectrometer, operating at 300 MHz proton resonance frequency. The accuracy of the temperature determination was within (0.5 K. A bandwidth of 100 kHz and an acquisition time of 0.10 s were applied with a repetition time of 10 s between radio-frequency pulses. The long interpulse timing was dictated by the long spin-lattice relaxation time of the silanol protons, which exhibited spin-lattice relaxation times of approximately 3 s.2 Using a repetition time of 10 s (3T1) rather than 15 s (5T1) makes a quantitative error of the measured peak integrals less than 4%. The inherent uncertainty in determining the area of an NMR peak is between 2 and 5%. All measurements were performed with a 90° pulse of 15 µs, and each spectrum was composed of 16 transients. The free induction decay (fid) was sampled after blanking the receiver for 20 µs, thus enabling the signal from the solid ice phase to be ignored because of its very short spin-spin relaxation rate of the order of a few microseconds. Moreover, due to the extremely long spin-lattice relaxation time (T1) of the water protons of solid ice at the applied magnetic field strength (T1 ≈ 900 s at 263 K and 7.05 T),9,10 any residual signal from the solid ice phase would be significantly reduced when taking into account the relatively short pulse repetition time of 10 s used in this work. The temperature was changed in steps of 2 K, resulting in more than 40 spectra (40 different temperatures) for each run. In order to minimize the total time needed to complete an experiment of this kind, the minimum time required to reach an equilibrium temperature was estimated. A porous powder (Y-zeolite) containing methanol in a capillary tube (NMR thermometer)11 was inserted into the NMR magnet, and the temperature was recorded vs time. A typical result is depicted in Figure 1 showing the time needed to reach © 1996 American Chemical Society
2196 J. Phys. Chem., Vol. 100, No. 6, 1996
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A
Figure 1. Temperature vs time within a Y-zeolite containing methanol in a capillary, placed inside the NMR spectrometer, during a sudden decrease in temperature from 223 to 203 K. The solid line represents an exponential fit (eq 1) to the observed data.
B
TABLE 1: Time Constant (k) Characterizing the Time Needed to Reach Temperature Equilibrium of a Y-Zeolite Powder Sample after an Abrupt Temperature Change from Ti (Initial Temperature) to Ts; T∞ Represents the Equilibrium Temperature Ti (K)
T∞ (K)
k (min)
Ts (K)
283 263 243 223 203
265.2 241.2 221.6 200.2 179.1
0.36 ( 0.03 0.57 ( 0.07 0.79 ( 0.05 0.64 ( 0.04 0.81 ( 0.07
263 243 223 203 183
temperature equilibrium when cooled from 223 to 203 K. The solid line represents an exponential model fit to the data of the form
T - T∞ ) (Ti - T∞) exp(-t/k)
(1)
where T is the actual temperature at time t, Ti is the initial temperature, T∞ is the final temperature, and k defines the time constant. The results obtained when cooling the sample from one initial temperature (Ti) to a new setting temperature Ts are shown in Table 1. The equilibrium temperature (T∞) and the setting temperature (Ts) are also tabulated and were used to establish a temperature calibration curve. Only the data from the cooling experiments are presented in this work. As can be seen from Figure 1 and the data summarized in Table 1, the temperature has, after 3 min of temperature equilibration, reached a level near the equilibrium temperature within 3% of the initial difference in temperature. In the experiments reported in this work the temperature across the sample was changed by only 2 K, and the time between each temperature change was set to 4.5 min. Results and Discussion Five different samples (FCC catalyst, Y-zeolite, MCM-41, composite I, and matrix) were saturated with water, and the intensity vs temperature (IT curve) was recorded. The results are shown in Figure 2. The solid lines represent model fits (eq 2)1-3 to the observed data N
I(X) ) ∑ i)1
I0i
xπ
(X-Xci)/x2∆i
∫
exp(-u2) du
(2)
0
where I0i, Xci, and ∆i represent the intensity, the inverse transition temperature (Xci ) 1000/Tci), and the width of the temperature distribution curve of phase i, respectively. Tci is measured in kelvin. As can be seen from the analytical form of eq 2, the temperature distribution curve (dI/dX) is a simple sum of
Figure 2. Proton NMR intensity vs temperature curves (IT curves) of water-saturated (A) Y-zeolite and FCC catalyst and (B) MCM-41, matrix, and a composite I material. The solid lines represent model fits, eq 2.
Gaussian functions centered at Xci with half-width ∆i. The numerical data are summarized in Table 2 together with some data taken from previous publications.1-3 The pore size Ri was determined from eq 3,3
∆T ) Kf/(Ri - tf)
(3)
with Kf ) 494.8 ( 19.6 K Å-1 and tf ) 3.49 ( 0.36 Å. Equation 3 represents a modified Kelvin equation. The composite I material (Table 2) was synthesized from a mixture of 30% MCM-41 and 70% Ludox LS, as described in the Experimental Section. Figure 3 shows the calculated IT curve (solid line) of the composite I material if a pure mechanical mixture of the two components is assumed, i.e., a linear combination of two IT curves, originating from the two “pure” components, with weighting factors 0.3 and 0.7, respectively. The observed IT curve (dotted line) deviates somewhat from the calculated IT curve, in particular at higher temperatures, suggesting that the pore size is somewhat modified during the synthesis procedure as compared to the pore size of the pure components. However, the transition temperature of the MCM41 material is easily recognized although it seems to be broadened compared to pure MCM-41. Keeping in mind the uncertainty in the observed intensity (I0i) and the transition temperature (Tci), the change in pore size of the composite material during the synthesis procedure might be less than anticipated from Figure 3. Note in particular the single and broad temperature transition observed for the Y-zeolite (Figure 2A, Table 2) and the VPI-5 sample (Table 2), suggesting a broad distribution of molecular correlation times of the mobile water.2 As pointed out in a previous work,3 eq 3 does not predict the true pore size of microporous materials (R < 10 Å, like for VPI-5 and Y-zeolite). This result will be addressed later in this work, although additional experimental work on similar microporous materials is needed to understand this behavior fully.
Water Confined in Mesopores
J. Phys. Chem., Vol. 100, No. 6, 1996 2197
TABLE 2: Numerical Values of the Parameters Xc (d1000/Tc) I0i, and ∆i (Eq 2); ∆Tci Represents the Freezing Point Depression and R the Pore Radius (Eq 3) sample
Xci (d1000/Tci)
I0i (%)
∆i (K)
∆Tci (K)
R (Å)
FCC Grace GmbH
4.188 ( 0.021 4.458 ( 0.040 4.981 ( 0.017 4.177 ( 4.865 ( 0.007 4.083 ( 0.245 4.171 ( 0.017 4.835 ( 0.019 4.034 ( 0.004 4.789 ( 0.022 5.241 ( 0.010 4.433 ( 0.002 4.848 ( 0.013 4.495 ( 0.008 4.860 ( 0.017 4.410 ( 0.007 4.839 ( 0.026 5.068 ( 0.13 5.182 ( 0.010 5.320 ( 0.004
10.2 ( 1.6 4.7 ( 2.7 85.1 ( 2.9 13.1 ( 1.1 86.9 ( 1.5 9.0 ( 8.6 15.6 ( 8.6 75.4 ( 3.7 37.9 ( 1.7 62.1 ( 1.9 100 27.9 ( 1.1 72.1 ( 0.7 14.8 ( 2.0 85.2 ( 3.1 24.1 ( 3.4 75.9 ( 4.1 20.5 ( 14 79.5 ( 14 100
6.4 ( 3.1 4.0 ( 5.7 24.9 ( 1.3 0.3 ( 20.4 ( 0.8 23.2 ( 32 5.2 ( 3.1 20.3 ( 1.5 4.3 ( 0.6 36.5 ( 2.2 20.7 ( 0.7 2.0 ( 0.2 32.5 ( 1.2 3.5 ( 1.2 30.2 ( 1.4 3.8 ( 1.0 25.9 ( 2.0 28.2 ( 6.9 12.1 ( 1.2 15.6 ( 0.4
34.4 ( 0.2 48.8 ( 0.4 72.4 ( 0.2 33.7 67.6 ( 0.1 28.3 ( 1.7 33.4 ( 0.1 66.3 ( 0.3 25.3 ( 0.03 64.3 ( 0.3 82.3 ( 0.2 47.6 ( 0.02 66.9 ( 0.2 50.7 ( 0.09 67.4 ( 0.2 46.4 ( 0.07 66.5 ( 0.36 75.8 ( 1.9 80.2 ( 0.15 85.2 ( 0.06
17.9 ( 0.1 13.6 ( 0.1 10.3 ( 0.03 18.2 ( 10.8 ( 0.01 21.0 ( 1.3 18.3 ( 0.07 10.9 ( 0.05 23.1 ( 0.03 11.2 ( 0.05 9.5 ( 0.02 13.9 ( 0.01 10.9 ( 0.03 13.3 ( 0.02 10.8 ( 3.1 14.2 ( 0.02 10.9 ( 0.06 10.0 ( 0.26 9.7 ( 0.02 9.3 ( 0.01
MCM-41 composite Ia dried Ludox LS Y-zeolite MCM-41b MCM-41c MCM-41d MCM-41e VPI-5f
a This material is made from 30% MCM-41 and 70% matrix. b Identical to sample A of ref 2 (R ) 13.9 Å). c Identical to sample B of ref 2 (R ) 13.2 Å). d Identical to sample B of ref 1 (R ) 14.2 Å). e Identical to sample C of ref 1 (R ) 10.0 Å). f See ref 3.
Figure 3. Proton NMR intensity vs temperature curve (IT curve) of a water-saturated composite material (A). This material was synthesized from a mixture of 30% matrix and 70% MCM-41. The solid line is calculated from a superposition of the IT curves of a pure matrix sample (30%) and a pure MCM-41 sample (70%), respectively. The dotted line represents a fitted model curve (eq 2) of the composite. Part B shows an expanded view of the initial part of the IT curve.
A general trend of the IT curves of these materials is the observed low-temperature transition between 200 and 207 K observed for the mesoporous materials and the somewhat lower transition temperature seen in the microporous materials at 191 K for the Y-zeolite and at 188 K for the VPI-5 material, respectively. These low-temperature transitions are rather different from what is expected from a macroscopic freezing of bulk water in that no hysteresis effects are observed during a cooling-heating cycle.1,3-5 As illustrated by the temperature distribution curves of the five materials investigated in this work
(Figure 4), the fraction of water responsible for the lowtemperature transitions is very large. The numerical data tabulated in Table 2 show that more than 60% of the total amount of water in these materials can be ascribed to these lowtemperature transitions. From eq 3, this would correspond to the existence of more than 60% of the pore volume to be related to micropores (R < 10 Å). However, this is indeed not possible, because the MCM-41 materials used in this work have been shown, by N2 adsorption and t plot analysis,3,4 to contain no, or at least an insignificant, amount of micropores. This observation suggests that the low-temperature transition must have another origin than simply describing the freezing of water from micropores. We believe this low-temperature water phase to be located within the pore and coexisting with the small fraction of solidified water (ice)salready formed during the higher transition temperaturessas predicted by the modified Kelvin equation (eq 3). The information collected from the present experiments suggests that eq 3 predicts rather well the transition temperature (Tci) at which water confined in a pore of dimension Ri will start to freeze out. However, the equation does not give any information regarding the amount of water which will freeze out at the specified temperature. A general behavior of the line width vs temperature curve of the water resonance peak is illustrated in Figure 5 for a mesoporous MC-41 sample. The line width increases only barely toward the first transition temperature at 240 K, after which it increases dramatically with decreasing temperature below 235 K. We believe this broadening of the water peak with decreasing temperature below the first transition temperature to originate from a combination of susceptibility effects and reduced molecular motion. The residual “nonfreezing” water of the pore is assumed to be “trapped” in an annulus between the solid matrix and the solid ice formed during this first temperature transition. This residual water phase is assumed to be located close to the surface of the pore, and its NMR line width will be affected by the difference in magnetic susceptibilities between the solid matrix and the solid ice, respectively. The continuous freezing out of this interfacial water with decreasing temperature, which is characterized by a broad distribution of correlation times,1,2 reduces the thickness and the molecular mobility of the interface water and makes it increasingly more influenced by magnetic susceptibility differ-
2198 J. Phys. Chem., Vol. 100, No. 6, 1996
Hansen et al.
A
D
B
E
C
Figure 4. Temperature distribution curves, dI/dX vs X ()1000/T), for the five materials investigated in this work: (A) matrix, (B) FCC catalyst, (C) MCM-41, (D) Y-zeolite, and (E) composite I material. See eq 3.
the solid ice phase by assuming the interface water to have a thickness D:
VL )
Figure 5. Intensity vs temperature (IT curve) and line width vs temperature of water confined in a mesoporous MCM-41 powder sample.
ences, as manifested by the severe line broadening of the NMR resonance peak with decreasing temperature. According to the assumption that the low-temperature transition water is located between the pore wall and the solid ice (which has already frozen out at a higher transition temperature), the volume of this water (VL) can be related to the volume of
[( ) ] Ri Ri - D
R
- 1 V0i
(4a)
where R ) 2 for cylindrical pores and R ) 3 for spherical pores of radius Ri. V0i is the amount of water frozen out at the transition temperature Tci (Xci ) 1000/Tci) as predicted by the modified Kelvin equation (eq 3). Assuming the densities of the different phases to be identical and independent of temperature, the volumes VL and V0i can be replaced by the NMR intensities IL and I0i, respectively, since there is a direct proportionality between these parameters. If the sample contains a finite number (N - 1) of pore sizes, eq 4a can be easily generalized to give N-1
I0N )
∑ i)1
[( ) ] Ri
Ri - D
R
- 1 I0i
(4b)
where I0N represents the total NMR intensity of the lowtemperature transition water and I0i the NMR intensity of phase “i” water. Equation 4b has been used to estimate the D value
Water Confined in Mesopores
J. Phys. Chem., Vol. 100, No. 6, 1996 2199
TABLE 3: Numerical Values of the Parameter D (Interface Water Thickness) As Determined from Eq 4b sample
Dcylindrical (Å)
Dspherical (Å)
sample
FCC Grace GmbH MCM-41 composite Ia dried Ludox LS MCM-41b MCM-41c MCM-41d MCM-41e
7.4 ( 1.1 9.0 ( 0.3 7.2 ( 2.9 6.4 ( 0.3 4.8 ( 0.1 6.3 ( 0.3 5.4 ( 0.4 4.1 ( 1.5
9.5 ( 1.1 11.6 ( 0.3 9.6 ( 3.3 8.9 ( 0.3 6.6 ( 0.2 8.2 ( 0.5 7.2 ( 0.3 5.5 ( 1.7
FCC MCM-41 MCM-41a MCM-41b matrix composite Ic composite IId Y-zeolite
a This material is made from 30% MCM-41 and 70% matrix. Identical to sample A of ref 2 (R ) 13.9 Å). c Identical to sample B of ref 2 (R ) 13.2 Å). d Identical to sample B of ref 1 (R ) 14.2 Å). e Identical to sample C of ref 1 (R ) 10.0 Å). b
for all the samples presented in this work (Table 2). The results are summarized in Table 3. All samples revealing a single hightemperature transition (N ) 2) showswithin experimental uncertaintysa value of D which is independent of pore dimension and equal to 5.4 ( 1.0 Å for cylindrical pore geometry and 7.3 ( 1.3 Å for spherical pore geometry (Table 3). Since the geometry of the mesopores (MCM-41 materials) are typically cylindrical, it is worth noting that the thickness of the interfacial water has a dimension comparable to the tf value of 3.5 ( 0.4 Å (eq 3), which was interpreted as the thickness of a nonfreezing water layer at the pore surface.3 We have also calculated the thickness D of the low-temperature transition water for the FCC catalyst (Grace GmbH) and the composite I material using eq 4b with N ) 3. The results are DFCC ) 7.4 ( 1.1 Å and Dcomposite I ) 7.2 ( 2.9 Å, when assuming cylindrical pore geometry. These results are somewhat larger (approximately 26%) than the corresponding D value derived for the mesoporous materials (N ) 2). However, since the former materials do not have a well-characterized pore geometry, i.e., they are neither cylindrical nor spherical, the D value cannot be uniquely defined. Keeping in mind the larger uncertainty in the D value estimated for the two samples, together with the approximations and assumptions involved in these calculations, the parameter D is assumed to be constant and independent of pore size and to have a value between 3 and 8 Å, based on a 95% confidence interval. It is worth noting that pores with size as large as 50 Å in diameter will havesaccording to eq 4asa low-temperature transition phase contributing to more than 20% of the total water content of the pore. An interesting observation is that the thickness, D, of the interfacial water has the same size as the dimension of micropores, i.e., 0-10 Å. The lack of any observable hysteresis effects upon freezing/melting of these small size water domains suggests that this length scale (e10 Å) defines a lower limit for the applicability of a macroscopic or thermodynamic model for explaining these low-temperature transitions. Fortunately, the temperature of this low-temperature transition, as observed in all the mesoporous materials, seems to be somewhat higher than the temperature transition of water confined in micropores (VPI-5 and Y-zeolite), suggesting that the present NMR technique can be used to differentiates quantitativelysbetween the amount of micropores and mesopores within a porous material. Another important consequence of the analysis presented in this work concerns the derivation of pore size distributions, dI/ dR vs R, from NMR IT curves as stated in a recent publication3
dI dR
TABLE 4: Number of Silanol Groups per Gram of Sample (Ns); Gain ) 30, Attenuation ) 16 dB
N-1
)
∑ i)1
I0i
[ ( )]
(XT0 - 10 ) exp -
103Kf∆ix2π
3 2
X - Xci
x2∆i
2
(5a)
where I0i is identified with the amount of water freezing out at
NMR intensity (au)a mD2O (g) msample (g) 11 200 26 400 32 000 26 400 26 400 21 400 18 800 19 000
0.1420 0.1535 0.1298 0.0999 0.1535 0.1679 0.1531 0.16239
0.0669 0.0211 0.0144 0.0181 0.0211 0.0241 0.0353 0.0310
Nsb 9.56 × 1019 1.04 × 1021 2.02 × 1021 1.33 × 1021 1.04 × 1020 6.71 × 1020 3.96 × 1020 4.48 × 1020
a The uncertainty in the intensity measurements is approximately 2-3%. b The uncertainty in this parameter is estimated from eq 7 and amounts to 2-3%. c This material is made from 30% MCM-41 and 70% matrix (Ludox LS). d This material is made from 10% Y-zeolite, 20% MCM-41, and 70% matrix (Ludox LS).
the temperature transition Tci. As shown in this work, I0i should be replaced by Ii as given by eq 5b:
Ii )
( )
Ri 2 I Ri - D 0i
(5b)
This modification of eq 5a will have no influence on the actual pore size determination; however, it will affect the shape of the distribution curve, in particular if the pore size is close to the limiting value given by the thickness (D) of the lowtransition temperature phase. Its effect will only be marginal if R . D. An important question to be answered is whether the chemical composition of the porous materials will have an impact on the estimate of D. In this respect, the concentration of surface silanol groups of the materials reported in this work was estimated using a very simple NMR technique. The samples were preheated to 200 or 400 °C (depending on the sample under investigation) for 3 h and then saturated with D2O. Assuming a fast equilibration between the surface silanol protons and the deuterated water and that all silanols are accessible and exchangeable,
D2O + Si-OH S Si-OD + HOD
(6)
the number of silanol groups can be determined by simply measuring the intensity of the proton NMR signal by conventional high-resolution NMR. The number of silanol groups per gram of sample (Ns) was determined from a calibration curve relating the signal intensity to the amount of water protons. The empirical equation used is
Igain Ns ) 3.91 × 1015(10(12-gain)/20.11) msample 1.96 × 1019
mD2O msample
(7)
where Igain is the intensity observed at a specific gain (Table 4), msample is the amount of porous material, and m(D2O) is the amount of deuterated water added to the sample. The second term represents the correction term due to residual undeuterated protons in the D2O solvent. The results are summarized in Table 4 and show that the MCM-41 materials contain 2-3 times more silanol groups per gram of sample than the composite material and more than 10 times the FCC catalyst and the matrix material. The amounts of silanol groups of the two composite materials containing MCM-41:matrix:Y-zeolite in the rato 0.3:0.7:0 (composite I) and 0.2:0.7:0.1 (composite II) as determined by this simple NMR technique are well described by the
2200 J. Phys. Chem., Vol. 100, No. 6, 1996 weighted sum of the amount of silanol groups of their respective constituents, which are 6.78 × 1020 and 4.77 × 1020, respectively. These results seem to indicate that the amount of silanol groups does not influence the estimate of D. However, keeping in mind that the specific surface area of the MCM-41 materials is 4-5 times larger than the FCC and matrix materials, the number of silanol groups per surface area would not be much different. Thus, from the measurements presented in this work, no conclusive evidence regarding the influence of silanol groups at the pore surface on the estimate of D can be ascertained. In order to resolve this question, a better approach would be to vary the Si-OH concentration, i.e., through controlled calcination of one sample and see its effect on D. Conclusion The onset of freezing of water confined in mesopores (R > 10 Å) is predicted by a modified Kelvin equation. However, only a fraction [(R - D)/R]2 of the water within the pore of radius R freezes out at this temperature, where D is a constant and equal to 5.5 ( 0.4 Å if cylindrical pore geometry is assumed. For pores with pore dimension R which are close to D, the fraction of water that freezes out within the pore will be very small. This has to be taken into account if quantitative distribution of pore sizes is to be derived from NMR signal intensity vs temperature measurements. The remaining part of the water undergoes a phase transition at a lower temperature,
Hansen et al. within the range 200-207 K. This latter phase transition is not a normal thermodynamic bulk water transition, in the sense that no hysteresis effects are observed. The transition temperature for water confined in micropores is significantly lower than the low-temperature transition observed in mesopores, suggesting that the relative amount of these type of pores can be estimated from NMR measurements. References and Notes (1) Akporiaye, D.; Hansen, E. W.; Schmidt, R.; Sto¨cker, M. J. Phys. Chem. 1994, 98, 1926. (2) Hansen, E. W.; Schmidt, R.; Sto¨cker, M.; Akporiaye, D. J. Phys. Chem. 1995, 99, 4148. (3) Schmidt, R.; Hansen, E. W.; Sto¨cker, M.; Akporiaye, D.; Ellestad, O. H. J. Am. Chem. Soc. 1995, 117, 4049. (4) Schmidt, R.; Sto¨cker, M.; Hansen, E. W.; Akporiaye, D.; Ellestad, O. H. Microporous Mater. 1995, 3, 443. (5) Overloop, K.; Van Gerven, L. J. Magn. Reson., Ser. A 1993, 101, 179. (6) Resing, H. A.; Thompson, J. K.; Krebs, J. J. J. Chem. Phys. 1964, 7, 1621. (7) Resing, H. A. J. Chem. Phys. 1965, 43, 669. (8) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-U.; Olsen, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (9) Barnaal, D. E.; Lowe, I. J. J. Chem. Phys. 1967, 48, 4614. (10) Barnaal, D. E.; Kopp, M.; Lowe, I. J. J. Chem. Phys. 1976, 65, 5495. (11) Hansen, E. W. Anal. Chem. 1985, 57, 2993.
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