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Boiling-point elevation of water confined in mesoporous MCM-41 materials probed by 1H NMR
H. Chon, S.-K. Ihm and Y.S. Uh (Editors) Progress in Zeolite and Microporous Materials Studies in Surface Science and Catalysis, Vol. 105 9 1997 Elsevier Science B.V. All rights reserved.
Boiling-point elevation of water materials probed by 1H NMR
543
confined
in
mesoporous
MCM-41
Eddy W. Hansen, Ralf Schmidt and Michael St5cker SINTEF Applied Chemistry, P.O. Box 124 Blindern, N-0314 Oslo, Norway Dedicated to Professor Dr. Klau., K. Unger on the occasion of his 60th birthday. Characterization of water saturated mesoporous MCM-41 materials with narrow pore-size distributions by 1H NMR revealed two temperature transitions above 373 K. The first transition temperature (373 -391 K) was assigned to the boiling point of "free" water within the pores, while the second transition temperature (408 - 413 K) was associated with desorption of less mobile "surface" water. The boiling point, T b, of the "free" water increased with decreasing pore diameter, D (A), according to: T b =a0+a,.i D-l+a2 D-2with a 0 = (373+ 1) K, a 1 = ( 7 0 + 5 9 ) KA. and a 2 = (5.7+ 1.2). 10L~K.,A,~. 1. INTRODUCTION Understanding of pore structure and how it affects physical properties is an important challenge in many aspects of science and technology [1]. Such understanding may lead to development of new materials with improved performance and broaden the range of their applicability. Porous media typically contain interconnected three-dimensional network of channels of non-uniform size and shape. The distribution of pore sizes is therefore an important characteristic of such materials. The techniques most commonly used to characterise pore structure include adsorption or desorption methods and mercury intrusion porosimetry [2]. NMR spectroscopy is another technique used to characterise pore geometry including spin-spin relaxation time (T2), spin-lattice relaxation time (T 1), and diffusion measurements [3-7]. Reliability as well as analysis of relaxation curves to give pore size distribution is a continuous and active area of research. It is well known that physical properties of a liquid confined within small pores can be radically different from those of bulk materials. For instance, the freezing point of a confined liquid is depressed [8]. The relation between the freezing point depression (ATf) and pore radius (r) was originally developed by Gibbs and Thompson (Lord Kelvin) [9] and takes the form: ATf = -2yMT0/rpAH f where y, M, p, T O and AHf are the surface tension, the molecular weight, the density, the freezing point and the molar heat of fusion of the bulk fluid, respectively, and will be referred to as the "Kelvin" equation.
.544 The freezing point depression phenomenon has recently been studied by NMR [1016] to provide a new method of determination of pore size. In this work, a mathematical model will be applied, enabling the boiling point of a liquid (containing protons) confined in a porous material to be determined from 1H NMR signal intensity vs temperature measurements (IT-curve) with the highest possible precision. Such measurements facilitate an empirical correlation between the boiling point and the pore size of the host material to be established. Three sizes of mesoporous MCM-41 materials, with pore diameters of 20, 24 and 40 A, respectively, will be used to demonstrate the method.
2. EXPERIMENTAL The MCM-41 materials were prepared according to synthesis procedures similar to those reported by Beck et al. [17]. The three mesoporous powder materials, denoted by the letters A, B, and C, were saturated with water under vacuum and loaded into 5 mm NMR tubes. The diameter (D) of the materials were 20 A (A), 24 A (B) and 40 A (C), respectively. The structure of the MCM-41 samples was maintained during the temperature treatment (checked by XRD). A Varian Gemini spectrometer, operating at 300 MHz proton resonance frequency was used. A bandwidth of 50 kHz and an acquisition time of 0.030 s were applied with a repetition time of 15 s between pulses. A longer acquisition time was not necessary due to the rather broad spectral lines with half widths of more than 300 Hz. The long interpulse timing of 15 s was imposed by the long spin-lattice relaxation time of the silanol protons of approximately 2 - 4 s [16, 18]. All measurements were performed with a 900 if-pulse of 8 its, on resonance. Each spectrum was composed of 4 transients. Less than 50 mg of material was used which filled the NMR tube to a height of less than 2.5 mm. The temperature of the powder sample was determined with an accuracy of + 1 K. The intensity or area (I) of the resonance peak was determined by numerical integration and corrected for temperature (T) according to an empirical equation, which was determined using a glycerol sample. This temperature correction deviated somewhat from the expected Curie law (I = l/T) [16, 19, 20] and was attributed to the probe design. The same glycerol sample was used to calibrate the temperature. The temperature was increased with a rate of 1.5 K/minute, if not otherwise stated in the text. The NMR spectra were sampled periodically with time, corresponding to a temperature interval of 1.5 K between each NMR cycle of 4 transients. A cotton wool was inserted into the NMR tube, above the detection coil, to prevent condensed liquid water to re-enter the coil area.
2.1. Methodology and underlying theory The 1H NMR signal intensity (I) vs the absolute temperature (T) of water confined in a porous material, denoted as IT-curve, can be expressed by equation 1, where the parameters z~H and AB represent the motional activation enthalpy of the water molecules and the width of the log-normal distribution of correlation times imposed
545 on the water molecules, respectively. T c represents the transition temperature.
,o[
A.
(1)
I(T) - --~ . 1 + erf ( R . AB
The symbol "eft" is the accepted short hand notation of the error function, defined by equation 2, where u is an integration variable
(2)
erf(y) = ~Xo exp(-u2)du If more than one transition temperature exists, equation 1 can be generalised;
- ZN , ~
,:,
AH
I ( T ) - ~ I,(T)- ,:1YL +
;]
1
( g.
(3)
))
where 10i is the intensity contribution of water from phase "i". More details concerning the derivation of equations 1 and 3 are shown in the appendix. 3. RESULTS AND DISCUSSION
Figure 1 shows the 1H NMR signal intensities vs temperature of water confined in samples A and C and demonstrates the decrease in intensity with increasing time due to phase transition of the pore confined water which evaporates and leaves the pore. Since the heating rate is constant (1.5 K/min) in the two experiments, the phase transition of sample A shows up at a higher temperature compared to sample C.
l
1
1
l
1
1
s
c
,
0
,
|
|
i
5
,
,
,
,
,
10
,
,
,
,
I
15
.
.
.
.
I
'
"
20
25
TIM E ( m i n u r e s )
Figure 1.1H NMR signal intensities vs time of samples A and C. Heating rate 1.5 K/minute. The experimental data presented in Figure 1 are in qualitative agreement with
546
equation 4: A ~ = 2yMT~ .]-pA/-I~, r
(4)
which predicts a higher boiling point temperature of water confined in smaller pores (smaller pore radius r) when all other parameters in equation 4 are constant. Equation 4 represents an analogous version of the modified "Kelvin" equation presented earlier in this work, which has been shown to be valid for the freezing of pore confined water [ 10,14-16,18]. The temperature-corrected intensity (area) of the NMR peaks in Figure 1 are plotted against the inverse absolute temperature (ITcurve) shown in Figure 2. The dotted line represents the IT-curve of bulk water, while the solid lines represent non-linear least squares model-fits of equation 3 to the experimental IT-data. The observed decrease in signal intensity at approximately 373 K (Table 1) is found to be independent of pore radius (Table 1) and is caused by evaporation of residual bulk water located between the crystallites of the powder materials. This transition temperature is equivalent to the boiling point of bulk water (~373 K; dotted line) and serves as a 0seful temperature calibration point. The second temperature transition observed in the IT-curve (Figure 2, Table 1) represents the main transition, i.e., the temperature at which most of the mobile water evaporates and is provisionally interpreted as the boiling point of "free" water confined in capillary pores of radius r, as predicted by equation 4. Table 1 The average (Tci) and the standard deviation (RABi/AHi) of the transition temperature of samples A(D=20A), B(D=24A) and C(D=40A). Heating rate 1.5 K/min.
SAMPLE
Tci (K)
,~Bi/AH i (K-1)
Corr. coeff.
A(i=l) A(i=2) A(i=3)
373.5 + 0.9 391.3 + 0.3 416.3 + 5.9
1.4 + 1.5 5.3 + 0.7 15.6 + 8.4
0.9988
B(i=2) B(i=3)
385.7 + 0.3 412.1 + 1.3
7.9 + 0.4 11.4 + 6.1
0.9984
C(i=l) C(i=2)
371.5 378.8 + 0.1
0.3 1.7 + 0.2
0.9973
The two samples containing the smaller pores, samples A and B, reveal a third transition temperature at approximately T = 414 K which is tentatively assumed to represent desorption of the more strongly bounded surface water. Another point of
547
interest is the width or standard deviation (R~B/AH) of the second temperature transition, as can be inferred from the observed IT-curves (Figure 2, Table 1). This width is significantly smaller for sample C, which contains the larger pores, compared to samples A and B. From equation 1 this might be rationalised according to a decrease in the enthalpy of motion (AH) of the water molecules or an increasing spread (AB) of molecular correlation times with decreasing pore radius. The latter seems intuitively reasonable. However, the profile of the IT-curve might also depend on typical external parameters, as for instance the heating rate. A large heating rate might cause a broadening of the IT-curve due to the time needed for heat transfer, evaporation and mass transport between sample and surrounding. However, reducing the heating rate from 1.5 K/min to 0.2 K/min had no significant effect on the shape of the IT-curve, i.e., neither the transition temperature nor the width of the temperature transition changed.
o
zu.l
8O
Z
.
60
Z
|
4O
rv
N
2O
Z -r - - - - - - m - -
'-
0
o
2.26
m
m
m
m
--
n
--
--
m
I
I
I
I
2.36
2.46
2.56
2.66
1000/T (K- 1) Figure 2.1H-NMR IT-curves of samples A, B, C and D (bulk water). Heating rate was 1.5 K/min. Figure 3 shows the observed boiling point temperature (Tb) of the second temperature transition vs inverse pore diameter (D 1 ) of the samples investigated. The boiling point of bulk water corresponds to water within a pore of infinite size (D -1 = 0). The curve is not straight but has a positive curvature towards smaller pore diameters. Referring to equation 4, this might originate from a temperature dependence of one or all of the three parameters, density (p), surface tension (lr), or molar heat of evaporation (AHb). The change in density of liquid water within the actual temperature range (373-390 K) is probably small. The surface tension is
548
known to increase with temperature, however, the increase is probably not more than 10 % within the actual temperature range studied [21]. Thus, we are left with the temperature dependence of the heat of evaporation (AHb), which might be an indirect function of pore radius. We have not been able to find any published correlation between AH b and pore radius, however, Jackson et al. [8] have shown experimentally that the heat of fusion (AHf) of a number of organic liquids confined in pores decreases with decreasing pore radius below approximately 100 A. The existence of a similar relation between pore size and heat of evaporation of pore confined water, might thus explain the shape of the curve displayed in Figure 3. 395
LU
r
A 390 UJ
13_ 385
LU
Z
v
0a _ (.b
380
Z
375
_J
o 370
I
0
0.01
I
I
0.02
0.03
I
0.04
0.05
I/D (,i,-11 Figure 3. Boiling point temperature of the second temperature transition vs inverse pore diameter (D-l) of samples A, B and C. Hansen et al. [16] and co-workers [14,15] have recently presented experimental NMR results on the freezing of water confined in mesoporous materials. For instance, they found [16] that sample A froze at a temperature of 193 K, corresponding to a freezing point depression ATf = 80 K. Combining equation 4 and the equivalent expression relating the freezing point depression to pore radius, the boiling point elevation, AT b, can be expressed by equation 5; = T+
(5)
where Tob and Tof are the boiling point and the freezing point of bulk water, respectively. The density and surface tension are assumed to be temperature independent. The enthalpies of fusion and of evaporation of bulk water are AHf = 1.44 kcal/mol and AH b = 9.82 kcal/mol, respectively. Inserting these values into equation 5 predicts a boiling point elevation of water confined in sample C of approximately 20 K, which is in good agreement with the observed value of 18.2 + 0.4 K. It is clear from the results presented in this work that the boiling point elevation
549
is less sensitive to pore size than the corresponding freezing point depression of water within capillary pores [14-16]. However, one disadvantage when performing cooling experiments below the freezing point of pore confined water is the potential destruction of pore structure upon phase transformation from liquid water to solid ice. It should be emphasised, however, that the sensitivity regarding the boiling point elevation vs pore size depends on the molar heat of evaporation, equation 4. Replacing water with another liquid, having a smaller molar heat of evaporation, might thus improve the sensitivity.
4. APPENDIX
Equations 1 and 3 can be derived using the following arguments. Since the motion of fluid molecules are restricted by the pore walls, a distribution of correlation times is expected. A number of available distribution functions exist, among which the lognormal distribution of correlation times seems to be the most commonly accepted model for describing the molecular motion in solids and liquids, and takes the form:
P('c)d'c- AB-f~ 1 exp(- 5
)dZ
with
Z - ln(-z-z.) r z - x* exp(Z)
(A1)
1;
where I:* represents the average correlation time, defined by the median of the distribution function, and AB characterises the width of the distribution function. Moreover, we will assume that a critical correlation time "rc exists, above which the fluid molecules are transformed into gas phase molecules and escape from the sample and out of the NMR receiver coil area. Identifying this critical correlation time ('rc) with a corresponding critical temperature, T c and assuming 'r* and 'rc to be related to temperature by an Arrhenius type function, we obtain: AH
I;* - 1;o exp(--Z~ )
and
/(1
"r,c -
tu~
"r,oexp(-z-z-)
(A2)
where AH represents the activation enthalpy of the restricted motional freedom of the water molecules. I:0 is a constant. The NMR signal intensity of the liquid water molecules within the pores at a temperature T can thus be calculated;
I(T)-
2 9IP('r.)d'r,~ ~(~,r) 1 exp(_~B2)dZ_ I AB.J--~ 0
0
~(-~-~) ~l
j'exp(-u=),tu
(A3)
-oo
5. CONCLUSION The pore radius of mesoporous MCM-41 materials are shown to be obtainable from
550
1H NMR IT-data above the normal boiling point of bulk water. An improved estimate of the boiling point is obtained by a model fit to the observed IT-data. The boiling point, T b, of the free water increased with decreasing pore diameter. However, the sensitivity is significantly less than what can be obtained from similar NMR experiments at sub-zero temperature ("freeze" - NMR). However, use of another liquid having a lower molar heat of evaporation, might improve the sensitivity of the present NMR technique. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
F.A.L. Dullien, Porous Media, Academic Press, New York, 1979, Chap.1. P.L.Pratt, Materials and Structure, 21 (1988) 106. W.P.Halperin, F.D'Orazio, S.Bhattacharija and J.C.Tarczon, Molecular Dynamics in Restricted Geometries, edited by K.Klafter and J.M.Drake, John Wiley and Sons, New York, 1989. G.C.Borgia, A.Brancolini, R.J.S.Brown, P.Fantazzini and G.Ragazzini, J.Magn.Res. Imaging, 12 (1994) 191. R.L.Kleinberg, W.E.Kenyon and P.P.Mitra, J.Magn.Res., Ser.A, 108, (1994) 206. L.L.Latour, R.L.Kleinberg, P.P.Mitra and C.H.Sotak, J.Magn.Res., Ser.A, 112 (1994) 83. P.T.Callaghan, A.Coy, D.MacGowan and K.J.Packer, J.Mol.Liq., 54 (1992) 239. C.J.Jackson and G.B.McKenna, J.Chem.Phys. 93 (1990) 9002. B.J.Mason, The Physics of Clouds, Clarendon Press, Oxford, Second Edition (1971)2. K. Overloop and L.Van Gerven, J.Magn.Res.,Ser. A, 101 (1993) 179. J.H.Strange and M.Rahman, Phys.Rev.Lett., 71 (1993) 3589. S.M.Alnaimi, J.H.Strange and E.G.Smith, Magn.Res.lmaging, 98 (1994) 1926. W.L.Earl, Y-W. Kim, E.G.Smith, IUPAC Symp. Marseille, France, (1993) 21. D.Akporiaye, E.W.Hansen, R.Schmidt and M.StScker, J.Phys.Chem., 98 (1994) 1926. R.Schmidt, E.W.Hansen, M.StScker, D.Akporiaye and O.H.Ellestad, J.Am.Chem.Soc., 117 (1995) 4049. E.W.Hansen, R.Schmidt, M.St5cker and D.Akporiaye,J.Phys.Chem., 99 (1995) 4148. J.S.Beck, J.C.Vartuli, W.J.Roth, M.E.Leonowicz, C.T.Kresge, K.D.Schmitt, C.TW. Chu, D.H.Olson, E.W.Sheppard, S.B.McCullen, J.B.Higgins and J.L.Schlenker, J.Am.Chem.Soc., 114 (1992) 10834. K.Overloop and L. Van Gerven, J.Magn.Res., Ser.A, 101 (1993) 147. A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, U.K. (1961)2. D.R. Kinney, I.-S.Chuang, G.E.Maciel, J.Am.Chem.Soc., 115 (1993) 6786. B.R.Puri, L.R.Sharma, M.L.Lakhanpal, J.Phys.Chem., 58 (1954) 289.
Boiling-point elevation of water materials probed by 1H NMR
543
confined
in
mesoporous
MCM-41
Eddy W. Hansen, Ralf Schmidt and Michael St5cker SINTEF Applied Chemistry, P.O. Box 124 Blindern, N-0314 Oslo, Norway Dedicated to Professor Dr. Klau., K. Unger on the occasion of his 60th birthday. Characterization of water saturated mesoporous MCM-41 materials with narrow pore-size distributions by 1H NMR revealed two temperature transitions above 373 K. The first transition temperature (373 -391 K) was assigned to the boiling point of "free" water within the pores, while the second transition temperature (408 - 413 K) was associated with desorption of less mobile "surface" water. The boiling point, T b, of the "free" water increased with decreasing pore diameter, D (A), according to: T b =a0+a,.i D-l+a2 D-2with a 0 = (373+ 1) K, a 1 = ( 7 0 + 5 9 ) KA. and a 2 = (5.7+ 1.2). 10L~K.,A,~. 1. INTRODUCTION Understanding of pore structure and how it affects physical properties is an important challenge in many aspects of science and technology [1]. Such understanding may lead to development of new materials with improved performance and broaden the range of their applicability. Porous media typically contain interconnected three-dimensional network of channels of non-uniform size and shape. The distribution of pore sizes is therefore an important characteristic of such materials. The techniques most commonly used to characterise pore structure include adsorption or desorption methods and mercury intrusion porosimetry [2]. NMR spectroscopy is another technique used to characterise pore geometry including spin-spin relaxation time (T2), spin-lattice relaxation time (T 1), and diffusion measurements [3-7]. Reliability as well as analysis of relaxation curves to give pore size distribution is a continuous and active area of research. It is well known that physical properties of a liquid confined within small pores can be radically different from those of bulk materials. For instance, the freezing point of a confined liquid is depressed [8]. The relation between the freezing point depression (ATf) and pore radius (r) was originally developed by Gibbs and Thompson (Lord Kelvin) [9] and takes the form: ATf = -2yMT0/rpAH f where y, M, p, T O and AHf are the surface tension, the molecular weight, the density, the freezing point and the molar heat of fusion of the bulk fluid, respectively, and will be referred to as the "Kelvin" equation.
.544 The freezing point depression phenomenon has recently been studied by NMR [1016] to provide a new method of determination of pore size. In this work, a mathematical model will be applied, enabling the boiling point of a liquid (containing protons) confined in a porous material to be determined from 1H NMR signal intensity vs temperature measurements (IT-curve) with the highest possible precision. Such measurements facilitate an empirical correlation between the boiling point and the pore size of the host material to be established. Three sizes of mesoporous MCM-41 materials, with pore diameters of 20, 24 and 40 A, respectively, will be used to demonstrate the method.
2. EXPERIMENTAL The MCM-41 materials were prepared according to synthesis procedures similar to those reported by Beck et al. [17]. The three mesoporous powder materials, denoted by the letters A, B, and C, were saturated with water under vacuum and loaded into 5 mm NMR tubes. The diameter (D) of the materials were 20 A (A), 24 A (B) and 40 A (C), respectively. The structure of the MCM-41 samples was maintained during the temperature treatment (checked by XRD). A Varian Gemini spectrometer, operating at 300 MHz proton resonance frequency was used. A bandwidth of 50 kHz and an acquisition time of 0.030 s were applied with a repetition time of 15 s between pulses. A longer acquisition time was not necessary due to the rather broad spectral lines with half widths of more than 300 Hz. The long interpulse timing of 15 s was imposed by the long spin-lattice relaxation time of the silanol protons of approximately 2 - 4 s [16, 18]. All measurements were performed with a 900 if-pulse of 8 its, on resonance. Each spectrum was composed of 4 transients. Less than 50 mg of material was used which filled the NMR tube to a height of less than 2.5 mm. The temperature of the powder sample was determined with an accuracy of + 1 K. The intensity or area (I) of the resonance peak was determined by numerical integration and corrected for temperature (T) according to an empirical equation, which was determined using a glycerol sample. This temperature correction deviated somewhat from the expected Curie law (I = l/T) [16, 19, 20] and was attributed to the probe design. The same glycerol sample was used to calibrate the temperature. The temperature was increased with a rate of 1.5 K/minute, if not otherwise stated in the text. The NMR spectra were sampled periodically with time, corresponding to a temperature interval of 1.5 K between each NMR cycle of 4 transients. A cotton wool was inserted into the NMR tube, above the detection coil, to prevent condensed liquid water to re-enter the coil area.
2.1. Methodology and underlying theory The 1H NMR signal intensity (I) vs the absolute temperature (T) of water confined in a porous material, denoted as IT-curve, can be expressed by equation 1, where the parameters z~H and AB represent the motional activation enthalpy of the water molecules and the width of the log-normal distribution of correlation times imposed
545 on the water molecules, respectively. T c represents the transition temperature.
,o[
A.
(1)
I(T) - --~ . 1 + erf ( R . AB
The symbol "eft" is the accepted short hand notation of the error function, defined by equation 2, where u is an integration variable
(2)
erf(y) = ~Xo exp(-u2)du If more than one transition temperature exists, equation 1 can be generalised;
- ZN , ~
,:,
AH
I ( T ) - ~ I,(T)- ,:1YL +
;]
1
( g.
(3)
))
where 10i is the intensity contribution of water from phase "i". More details concerning the derivation of equations 1 and 3 are shown in the appendix. 3. RESULTS AND DISCUSSION
Figure 1 shows the 1H NMR signal intensities vs temperature of water confined in samples A and C and demonstrates the decrease in intensity with increasing time due to phase transition of the pore confined water which evaporates and leaves the pore. Since the heating rate is constant (1.5 K/min) in the two experiments, the phase transition of sample A shows up at a higher temperature compared to sample C.
l
1
1
l
1
1
s
c
,
0
,
|
|
i
5
,
,
,
,
,
10
,
,
,
,
I
15
.
.
.
.
I
'
"
20
25
TIM E ( m i n u r e s )
Figure 1.1H NMR signal intensities vs time of samples A and C. Heating rate 1.5 K/minute. The experimental data presented in Figure 1 are in qualitative agreement with
546
equation 4: A ~ = 2yMT~ .]-pA/-I~, r
(4)
which predicts a higher boiling point temperature of water confined in smaller pores (smaller pore radius r) when all other parameters in equation 4 are constant. Equation 4 represents an analogous version of the modified "Kelvin" equation presented earlier in this work, which has been shown to be valid for the freezing of pore confined water [ 10,14-16,18]. The temperature-corrected intensity (area) of the NMR peaks in Figure 1 are plotted against the inverse absolute temperature (ITcurve) shown in Figure 2. The dotted line represents the IT-curve of bulk water, while the solid lines represent non-linear least squares model-fits of equation 3 to the experimental IT-data. The observed decrease in signal intensity at approximately 373 K (Table 1) is found to be independent of pore radius (Table 1) and is caused by evaporation of residual bulk water located between the crystallites of the powder materials. This transition temperature is equivalent to the boiling point of bulk water (~373 K; dotted line) and serves as a 0seful temperature calibration point. The second temperature transition observed in the IT-curve (Figure 2, Table 1) represents the main transition, i.e., the temperature at which most of the mobile water evaporates and is provisionally interpreted as the boiling point of "free" water confined in capillary pores of radius r, as predicted by equation 4. Table 1 The average (Tci) and the standard deviation (RABi/AHi) of the transition temperature of samples A(D=20A), B(D=24A) and C(D=40A). Heating rate 1.5 K/min.
SAMPLE
Tci (K)
,~Bi/AH i (K-1)
Corr. coeff.
A(i=l) A(i=2) A(i=3)
373.5 + 0.9 391.3 + 0.3 416.3 + 5.9
1.4 + 1.5 5.3 + 0.7 15.6 + 8.4
0.9988
B(i=2) B(i=3)
385.7 + 0.3 412.1 + 1.3
7.9 + 0.4 11.4 + 6.1
0.9984
C(i=l) C(i=2)
371.5 378.8 + 0.1
0.3 1.7 + 0.2
0.9973
The two samples containing the smaller pores, samples A and B, reveal a third transition temperature at approximately T = 414 K which is tentatively assumed to represent desorption of the more strongly bounded surface water. Another point of
547
interest is the width or standard deviation (R~B/AH) of the second temperature transition, as can be inferred from the observed IT-curves (Figure 2, Table 1). This width is significantly smaller for sample C, which contains the larger pores, compared to samples A and B. From equation 1 this might be rationalised according to a decrease in the enthalpy of motion (AH) of the water molecules or an increasing spread (AB) of molecular correlation times with decreasing pore radius. The latter seems intuitively reasonable. However, the profile of the IT-curve might also depend on typical external parameters, as for instance the heating rate. A large heating rate might cause a broadening of the IT-curve due to the time needed for heat transfer, evaporation and mass transport between sample and surrounding. However, reducing the heating rate from 1.5 K/min to 0.2 K/min had no significant effect on the shape of the IT-curve, i.e., neither the transition temperature nor the width of the temperature transition changed.
o
zu.l
8O
Z
.
60
Z
|
4O
rv
N
2O
Z -r - - - - - - m - -
'-
0
o
2.26
m
m
m
m
--
n
--
--
m
I
I
I
I
2.36
2.46
2.56
2.66
1000/T (K- 1) Figure 2.1H-NMR IT-curves of samples A, B, C and D (bulk water). Heating rate was 1.5 K/min. Figure 3 shows the observed boiling point temperature (Tb) of the second temperature transition vs inverse pore diameter (D 1 ) of the samples investigated. The boiling point of bulk water corresponds to water within a pore of infinite size (D -1 = 0). The curve is not straight but has a positive curvature towards smaller pore diameters. Referring to equation 4, this might originate from a temperature dependence of one or all of the three parameters, density (p), surface tension (lr), or molar heat of evaporation (AHb). The change in density of liquid water within the actual temperature range (373-390 K) is probably small. The surface tension is
548
known to increase with temperature, however, the increase is probably not more than 10 % within the actual temperature range studied [21]. Thus, we are left with the temperature dependence of the heat of evaporation (AHb), which might be an indirect function of pore radius. We have not been able to find any published correlation between AH b and pore radius, however, Jackson et al. [8] have shown experimentally that the heat of fusion (AHf) of a number of organic liquids confined in pores decreases with decreasing pore radius below approximately 100 A. The existence of a similar relation between pore size and heat of evaporation of pore confined water, might thus explain the shape of the curve displayed in Figure 3. 395
LU
r
A 390 UJ
13_ 385
LU
Z
v
0a _ (.b
380
Z
375
_J
o 370
I
0
0.01
I
I
0.02
0.03
I
0.04
0.05
I/D (,i,-11 Figure 3. Boiling point temperature of the second temperature transition vs inverse pore diameter (D-l) of samples A, B and C. Hansen et al. [16] and co-workers [14,15] have recently presented experimental NMR results on the freezing of water confined in mesoporous materials. For instance, they found [16] that sample A froze at a temperature of 193 K, corresponding to a freezing point depression ATf = 80 K. Combining equation 4 and the equivalent expression relating the freezing point depression to pore radius, the boiling point elevation, AT b, can be expressed by equation 5; = T+
(5)
where Tob and Tof are the boiling point and the freezing point of bulk water, respectively. The density and surface tension are assumed to be temperature independent. The enthalpies of fusion and of evaporation of bulk water are AHf = 1.44 kcal/mol and AH b = 9.82 kcal/mol, respectively. Inserting these values into equation 5 predicts a boiling point elevation of water confined in sample C of approximately 20 K, which is in good agreement with the observed value of 18.2 + 0.4 K. It is clear from the results presented in this work that the boiling point elevation
549
is less sensitive to pore size than the corresponding freezing point depression of water within capillary pores [14-16]. However, one disadvantage when performing cooling experiments below the freezing point of pore confined water is the potential destruction of pore structure upon phase transformation from liquid water to solid ice. It should be emphasised, however, that the sensitivity regarding the boiling point elevation vs pore size depends on the molar heat of evaporation, equation 4. Replacing water with another liquid, having a smaller molar heat of evaporation, might thus improve the sensitivity.
4. APPENDIX
Equations 1 and 3 can be derived using the following arguments. Since the motion of fluid molecules are restricted by the pore walls, a distribution of correlation times is expected. A number of available distribution functions exist, among which the lognormal distribution of correlation times seems to be the most commonly accepted model for describing the molecular motion in solids and liquids, and takes the form:
P('c)d'c- AB-f~ 1 exp(- 5
)dZ
with
Z - ln(-z-z.) r z - x* exp(Z)
(A1)
1;
where I:* represents the average correlation time, defined by the median of the distribution function, and AB characterises the width of the distribution function. Moreover, we will assume that a critical correlation time "rc exists, above which the fluid molecules are transformed into gas phase molecules and escape from the sample and out of the NMR receiver coil area. Identifying this critical correlation time ('rc) with a corresponding critical temperature, T c and assuming 'r* and 'rc to be related to temperature by an Arrhenius type function, we obtain: AH
I;* - 1;o exp(--Z~ )
and
/(1
"r,c -
tu~
"r,oexp(-z-z-)
(A2)
where AH represents the activation enthalpy of the restricted motional freedom of the water molecules. I:0 is a constant. The NMR signal intensity of the liquid water molecules within the pores at a temperature T can thus be calculated;
I(T)-
2 9IP('r.)d'r,~ ~(~,r) 1 exp(_~B2)dZ_ I AB.J--~ 0
0
~(-~-~) ~l
j'exp(-u=),tu
(A3)
-oo
5. CONCLUSION The pore radius of mesoporous MCM-41 materials are shown to be obtainable from
550
1H NMR IT-data above the normal boiling point of bulk water. An improved estimate of the boiling point is obtained by a model fit to the observed IT-data. The boiling point, T b, of the free water increased with decreasing pore diameter. However, the sensitivity is significantly less than what can be obtained from similar NMR experiments at sub-zero temperature ("freeze" - NMR). However, use of another liquid having a lower molar heat of evaporation, might improve the sensitivity of the present NMR technique. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
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