- Email: [email protected]
Microstructure of porous media probed by NMR techniques in sub-micrometer length scales
Magnetic Resonance Imaging, Vol. 12, No. 2, pp. 339-343, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0730-725X/94 56.00 + .oO
Pergamon
0 Invited Lecture MICROSTRUCTURE OF POROUS MEDIA PROBED BY NMR TECHNIQUES IN SUB-MICROMETER LENGTH SCALES RAINER KIMMICH,* SIEGFRIEDSTAPF,* PAUL CALLAGHAN,~ AND ANDREW COY? *Sektion Kernresonanzspektroskopie, Universitat Ulm, 89069 Ulm, Germany TDepartment of Physics and Biophysics, Massey University, Palmerston North, New Zealand It is shown that field-cycling NMR relaxation spectroscopy in combination with pulsed-gradient spin-echo diffusion studies especially in the supercon fringe field version are suitable techniques for the investigation of length scales of porous media in the range 10 A to 10 Cm. Data for water adsorbed in fineparticle agglomerates, porous glass and ceramics are reported. An orientational structure factor is introduced permitting the characterization of hydrated surfaces on the basis of reorientations mediated by translational displacements of the adsorbed molecules. Known lengths such as the mean pore or particle size have been reproduced in this way. In length scales beyond these structural elements, the geometry of the internal surfaces can be discussed in terms of wavenumberspace fractals. Keywords: Field-cycling NMR relaxation spectroscopy; Pulsed-gradient spin-echo diffusion measurement; Surface diffusion. INTRODUCTION
fusion experiments have been carried out mainly with field gradients of 9 or 38 T/m of the fringe field of the superconducting magnets available in our laboratory.5 Radiofrequency (RF) pulse sequences suitable for the
Magnetic resonance imaging’ refers to the morphology of an object in length ranges limited by 1 pm < Ax << 1 m. While this technique is extremely useful for rendering of ordered structures or physical properties connected with different sites of those structures, one may ask whether a real space image of a disordered object such as a porous medium is necessary or even desirable for the characterization. In this paper we rather follow the objective to specify the microstructure in terms of distributions of wave numbers. It is shown that fieldcycling NMR relaxation spectroscopy2 providing the frequency dependence of spin-lattice relaxation times, Ti = 7’i(v) , in combination with the pulsed-gradient spin-echo method3 (especially in the supercon fringefield version4) for diffusion measurements is a suitable technique for studies of length scales 10 A to 10 pm. Characteristic lengths such as pore diameters or cluster correlation lengths can be derived on this basis. METHODS
RF 7
Figure 1 shows a typical field cycle used for measurements of the spin-lattice relaxation dispersion. The instrument was home-built. In combination with conventional laboratory and rotating-frame experiments the total frequency range was lo2 < v 5 3 x 108. Dif-
t
Fig. 1. Typical field cycle for a resistivemagnet coil. The high detection field is restricted to the signal acquisition interval in order to keep the average production of Joule’s heat low. 339
340
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
record of relaxation independent diffusion decays of stimulated echoes are shown in Fig. 2. The detailed treatment will be published elsewhere.6 THE LONG-CORRELATION-TIME/ FAST-DIFFUSION DISCREPANCY OF HYDRATION WATER Field-cycling NMR relaxation spectroscopy of hydration layers in diverse porous substances indicate water orientation correlation times up to 7 orders of magnitude larger than in bulk water.7,8 Mean residence times in the surface layers consequently are at least lop5 s. The translational diffusion coefficient on the other hand turns out to be only slightly reduced and are in the same order of magnitude.5q9 The conclusion is that the diffusion of water molecules within the hydration layers, that is, along the surfaces, is only slightly slowed down compared with bulk water. This conclusion is confirmed by the relatively slow transverse relaxation decays of hydration water. Typical transverse relaxation times are in the order of 2-10 ms indicating a significant degree of motional averaging.
VAPOR PHASE CONTRIRUTION TO TRANSLATIONAL DIFFUSION Moreover, there is even a tendency toward faster diffusion than in bulk water if the interstitial volume is only partially filled and if the diffusion time is long enough. This is attributed to a contribution of gas molecules in the vapor phase. ‘O-l2To prove this we have varied the free volume in silica fineparticle samples by compression. Representative results are shown in Fig. 3. With the exception of the sample compressed to 16% of the initial powder volume the echo amplitudes decay faster than in bulk water. Samples with a lower specific surface but a similar water coverage show practically an equivalent behaviour if the compression is led to the same silica density. This again demonstrates that water diffusion is determined by the accessible vapor phase volume. With field-cycling NMR relaxation spectroscopy, on the other hand, only minor effects of compression or variation of the water content were found. Merely a slight variation of the absolute values of the relaxation times was observed, whereas the dispersion essentially
Fig. 2. RF pulse sequences for diffusion experiments with the supercon fringe-field (SFF) technique. Only echoes which are relevant for the measurements and which are acquired are indicated. These are primary spin-echoes (p.e.) and/or stimulated echoes (St. e.). The notation of the intervals 6 and A corresponds to that usually used in context with pulsed gradient spin-echo (PGSE) diffusion studies. (A) Three-pulse sequence: TVis kept fixed, whereas 6 is varied. The relaxation independent decay curves to be evaluated are determined by forming the quotient of amplitudes of the stimulated and primary echoes. (B) Fivepulse sequence: 7, and r2 are kept fixed while varying 6. The attenuation of the amplitude of the stimulated echo is then solely due to diffusion.
Microstructure of porous media l R.
0.1
7
A
16 %
q
25 %
.
341
where gz,, (r)is the correlation function of the surface, D is the curvilinear diffusion coefficient, +(
O. .
KIMMICH ET AL.
m m
S(k) = ?rk -rg(r)&(kr)
“.“A
6
2
0
q2(A - !jj/lOs
remained the same. An explanation is that the correlation time scale is too short for fast liquid/gas exchange of water molecules in contrast to the time scale of the diffusion experiments. The direct signal contribution of the vapor phase, on the other hand, in any case is entirely negligible. STRUCTURE
s
=
gz,,(i)*‘(
s
s-kk) +?-;2,2 1
0
k
dk
1 o-’ w T,.eJp p = 0.67
1o-2
g/cm3
(c=O.6)
1 O-33 102
103
10'
105
10'
10'
10'
!
lo9
6 1 J-1
1
““’
SW
a.u.
1 .o
0.6 0.4 0.2 0.8 : 0.0
10’
k S.1/2D
dLr d=k
9(w) =
=lOnm
= (Yzm’(~(0))Y:-m’(SZ(t)l) =
(2)
is the Bessel function of zeroth order. The spectral density is then
FACTOR
The main relaxation mechanism in the hydration shell is attributed to reorientations mediated by translational displacements (RMTD) along the rugged surfaces.r3 The orientation of a water molecule is given by the polar and azimuthal angles formed by the proton-proton vector or-with quadrupolar interaction - by the electric field gradient and the external magnetic field. That is fi = ( p, 0). Spin-lattice relaxation is characterized by the correlation function of spherical harmonics of second order which can be analyzed as follows: G(t)
.
IO (kr)
mW2s
Fig. 3. Decay curves of the relative stimulated echo amplitude, E/E,, of a 400 m2/g “alfasil” sample containing 38% (b.w.) water. The data were recorded in dependence on q = yG,& where y is the gyromagnetic ratio (of ‘H), G, is the field gradient, and 6 is the width of the gradient pulses. The diffusion time A defined by the separation of the gradient pulses was chosen to be 2 ms. The curves refer to the finepartitle powder in the uncompressed state (100%) and with different degrees of compression. The highest compression achievable with our means was 16% of the uncompressed volume. The solid line represents the decay expected for bulk water, i.e., to a diffusion coefficient of 2.2. lo-’ m2/s. All data were measured at room temperature.
THE ORIENTATIONAL
dr
s0
(1)
-l/Z
Fig. 4. Typical spin-lattice relaxation dispersion of hydrated silica fineparticle agglomerates and analysis in terms of the structure factor S(k) . The mean monomer size is (d >= IO nm corresponding to the /3 peak.
Magnetic Resonance Imaging 0 Volume 12, Number
342
2, 1994
where the “mode” correlation times are given by 7/, = l/(Dk’). A computer program has been written which deconvolutes the orientational structure factor from experimental 7-r dispersion curves. INTERPRETATION OF FIELD-CYCLING EXPERIMENTS Figures 4-6 show the experimental T, and T,,, dispersions of silica fineparticles (Cab-O-W), porous ceramics (CPC), and porous glass (Vycor). The samples are specified by the specific surface (a), the water coverage of the surfaces (w), the water weight fraction (c,), and the density (p). In each case, the numerical evaluation of the orientational structure factors is given (bars). Two processes can be distinguished, which are designated by cyand 0. The structure factor can be represented by the general form
1
+---....,
102
100:
i
10'
.,-.-.,
..““‘I
105
““I’,
108
10'
.d
i lo6
lo9
cd> = 4 nm I
ax.
s
103
,‘--T
E
S(k)
r,nTI,
o-.y
l.O-
"".
Vycor, untreated
0.8-
CPC c,=o.31
O.b0.4-
lo-';
0.2OX&-
0 7
10-2:
. TI,
k S
IO-J """'I """1 """'I T '"'7 "I "109 102 103 10' 105 10" 10' loa
v Hz
-l/Z D-i/z
Fig. 6. Spin-lattice relaxation dispersion of hydrated porous glass and analysis in terms of structure factor S(k). The mean pore diameter is specified as (d) = 4 nm. The corresponding fi peak therefore is expected outside of the experimental window.
cd> = 38 nm
S(k) q-------
d’“.
.oj
CPC
if k > kc,
1
S(k) = (4)
0.8
otherwise
0.60.4 0.2 0.0 i 102
103
105
10' k p
Fig. 5. Spin-lattice relaxation dispersion of hydrated porous ceramics and analysis in terms of the structure factor S(k). The mean pore diameter is specified as (d) = 38 nm in accordance with the 0 peak.
where 6, and ba are weighting factors and k,, represents the cut-off wavenumber responsible for the final low-frequency plateau of the T, dispersions. The solid lines in Figs. 4-6 correspond to this expression modified by replacing the S function by a narrow Gaussian function. The P process is interpreted as RMTD along the elementary unit of the system. This can be a fineparticle monomer or a pore. Interestingly, the known lengths, (d), characterizing these units are reproduced by the structure factor evaluation taking the diffusion coef-
Microstructure
of
porous media 0
ficients typically measured in such systems. With Cab0-Sil and CPC the fl process is within the measuring window, whereas with Vycor (d) = 4 nm is too short. The cr process is characterized by a power law with a cut-off at low wavenumbers. This is attributed to the correlation length of a potentially fractal structure. In Ref. 8 a fractal analogue in the k-space has been suggested by interpreting S ( k) as a “mode density” in k-space corresponding to the mass density of fractals in real space. REFERENCES 1. Mansfield, P.; Morris, P.G. NMR Imaging in Biomedicine. New York: Academic Press, 1982. 2. Noack, F. NMR field-cycling: Principles and applications. Progr. NMR Spectr. 18:171-276; 1986. 3. Karger, J.; Pfeifer, H.; Heink, W. Principles and applications of self-diffusion measurements by nuclear magnetic resonance. Adv. Magn. Reson. 12:1-89; 1988. 4. Kimmich, R.; Unrath, W.; Schnur, G.; Rommel, E. NMR measurement of small self-diffusion coefficients in the fringe field of superconducting magnets. J. Magn. Reson. 91:136-140; 1991. 5. Klammler, F.; Kimmich, R. Geometrical restrictions of incoherent transport of water by diffusion in protein or silica fineparticle systems and by flow in a sponge. A study of anomalous properties using an NMR fieldgradient technique. Croat. Chem. Acta 65:455-470; 1992.
R. KIMMICH ET AL.
343
6. Kimmich, R.; Fischer, E. One- and two-dimensional pulse
sequences for diffusion experiments in the fringe field of superconducting magnets. J. Magn. Reson. A (in press). 7. Kimmich, R.; Nusser, W.; Gneiting, T. Molecular theory for nuclear magnetic relaxation in protein solutions and tissue: Surface diffusion and free-volume analogy. Colloids Surf. 45:283-302; 1990. 8. Stapf, S.; Kimmich, R. Microstructure
of porous media and field-cycling NMR relaxation spectroscopy. J. Appl. Physics (in press). 9. Kimmich, R. Reorientation mediated by translational diffusion as a mechanism for nuclear magnetic relaxation of molecules confined in surface layers. Magn. Reson. Imaging 9:749-751;
1991.
10. Karger, J.; Pfeifer, H.; Riedel, E.; Winkler, H. Selfdiffusion measurements of water adsorbed in NaY zeolites by means of NMR pulsed field gradient techniques. J. CON. Interface Sci. 44:187-188; 1973. 11. D’Orazio, F.; Bhattacharja, S.; Halperin, W.P.; Gerhardt, R. Enhanced self-diffusion of water in restricted geometry. Phys. Rev. Lett. 63:43-46; 1989. 12. Callaghan, P.; Coy, A.; Kimmich, R. Gas-phase enhancement of water diffusion in silica fineparticle aggregates. In: M.U. Palma, M.B. Palma-Vittorelli, F. Parak (Eds). Water-Biomolecule Interactions. Conference Proceedings Series Vol. 43 of Italian Physical Society. Bologna: Editrice Compositori; 1993. 13. Kimmich, R.; Weber, H.W. NMR relaxation and the orientational structure factor. Phys. Rev. B 47: 1178811794; 1993.
Pergamon
0 Invited Lecture MICROSTRUCTURE OF POROUS MEDIA PROBED BY NMR TECHNIQUES IN SUB-MICROMETER LENGTH SCALES RAINER KIMMICH,* SIEGFRIEDSTAPF,* PAUL CALLAGHAN,~ AND ANDREW COY? *Sektion Kernresonanzspektroskopie, Universitat Ulm, 89069 Ulm, Germany TDepartment of Physics and Biophysics, Massey University, Palmerston North, New Zealand It is shown that field-cycling NMR relaxation spectroscopy in combination with pulsed-gradient spin-echo diffusion studies especially in the supercon fringe field version are suitable techniques for the investigation of length scales of porous media in the range 10 A to 10 Cm. Data for water adsorbed in fineparticle agglomerates, porous glass and ceramics are reported. An orientational structure factor is introduced permitting the characterization of hydrated surfaces on the basis of reorientations mediated by translational displacements of the adsorbed molecules. Known lengths such as the mean pore or particle size have been reproduced in this way. In length scales beyond these structural elements, the geometry of the internal surfaces can be discussed in terms of wavenumberspace fractals. Keywords: Field-cycling NMR relaxation spectroscopy; Pulsed-gradient spin-echo diffusion measurement; Surface diffusion. INTRODUCTION
fusion experiments have been carried out mainly with field gradients of 9 or 38 T/m of the fringe field of the superconducting magnets available in our laboratory.5 Radiofrequency (RF) pulse sequences suitable for the
Magnetic resonance imaging’ refers to the morphology of an object in length ranges limited by 1 pm < Ax << 1 m. While this technique is extremely useful for rendering of ordered structures or physical properties connected with different sites of those structures, one may ask whether a real space image of a disordered object such as a porous medium is necessary or even desirable for the characterization. In this paper we rather follow the objective to specify the microstructure in terms of distributions of wave numbers. It is shown that fieldcycling NMR relaxation spectroscopy2 providing the frequency dependence of spin-lattice relaxation times, Ti = 7’i(v) , in combination with the pulsed-gradient spin-echo method3 (especially in the supercon fringefield version4) for diffusion measurements is a suitable technique for studies of length scales 10 A to 10 pm. Characteristic lengths such as pore diameters or cluster correlation lengths can be derived on this basis. METHODS
RF 7
Figure 1 shows a typical field cycle used for measurements of the spin-lattice relaxation dispersion. The instrument was home-built. In combination with conventional laboratory and rotating-frame experiments the total frequency range was lo2 < v 5 3 x 108. Dif-
t
Fig. 1. Typical field cycle for a resistivemagnet coil. The high detection field is restricted to the signal acquisition interval in order to keep the average production of Joule’s heat low. 339
340
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
record of relaxation independent diffusion decays of stimulated echoes are shown in Fig. 2. The detailed treatment will be published elsewhere.6 THE LONG-CORRELATION-TIME/ FAST-DIFFUSION DISCREPANCY OF HYDRATION WATER Field-cycling NMR relaxation spectroscopy of hydration layers in diverse porous substances indicate water orientation correlation times up to 7 orders of magnitude larger than in bulk water.7,8 Mean residence times in the surface layers consequently are at least lop5 s. The translational diffusion coefficient on the other hand turns out to be only slightly reduced and are in the same order of magnitude.5q9 The conclusion is that the diffusion of water molecules within the hydration layers, that is, along the surfaces, is only slightly slowed down compared with bulk water. This conclusion is confirmed by the relatively slow transverse relaxation decays of hydration water. Typical transverse relaxation times are in the order of 2-10 ms indicating a significant degree of motional averaging.
VAPOR PHASE CONTRIRUTION TO TRANSLATIONAL DIFFUSION Moreover, there is even a tendency toward faster diffusion than in bulk water if the interstitial volume is only partially filled and if the diffusion time is long enough. This is attributed to a contribution of gas molecules in the vapor phase. ‘O-l2To prove this we have varied the free volume in silica fineparticle samples by compression. Representative results are shown in Fig. 3. With the exception of the sample compressed to 16% of the initial powder volume the echo amplitudes decay faster than in bulk water. Samples with a lower specific surface but a similar water coverage show practically an equivalent behaviour if the compression is led to the same silica density. This again demonstrates that water diffusion is determined by the accessible vapor phase volume. With field-cycling NMR relaxation spectroscopy, on the other hand, only minor effects of compression or variation of the water content were found. Merely a slight variation of the absolute values of the relaxation times was observed, whereas the dispersion essentially
Fig. 2. RF pulse sequences for diffusion experiments with the supercon fringe-field (SFF) technique. Only echoes which are relevant for the measurements and which are acquired are indicated. These are primary spin-echoes (p.e.) and/or stimulated echoes (St. e.). The notation of the intervals 6 and A corresponds to that usually used in context with pulsed gradient spin-echo (PGSE) diffusion studies. (A) Three-pulse sequence: TVis kept fixed, whereas 6 is varied. The relaxation independent decay curves to be evaluated are determined by forming the quotient of amplitudes of the stimulated and primary echoes. (B) Fivepulse sequence: 7, and r2 are kept fixed while varying 6. The attenuation of the amplitude of the stimulated echo is then solely due to diffusion.
Microstructure of porous media l R.
0.1
7
A
16 %
q
25 %
.
341
where gz,, (r)is the correlation function of the surface, D is the curvilinear diffusion coefficient, +(
O. .
KIMMICH ET AL.
m m
S(k) = ?rk -rg(r)&(kr)
“.“A
6
2
0
q2(A - !jj/lOs
remained the same. An explanation is that the correlation time scale is too short for fast liquid/gas exchange of water molecules in contrast to the time scale of the diffusion experiments. The direct signal contribution of the vapor phase, on the other hand, in any case is entirely negligible. STRUCTURE
s
=
gz,,(i)*‘(
s
s-kk) +?-;2,2 1
0
k
dk
1 o-’ w T,.eJp p = 0.67
1o-2
g/cm3
(c=O.6)
1 O-33 102
103
10'
105
10'
10'
10'
!
lo9
6 1 J-1
1
““’
SW
a.u.
1 .o
0.6 0.4 0.2 0.8 : 0.0
10’
k S.1/2D
dLr d=k
9(w) =
= (Yzm’(~(0))Y:-m’(SZ(t)l) =
(2)
is the Bessel function of zeroth order. The spectral density is then
FACTOR
The main relaxation mechanism in the hydration shell is attributed to reorientations mediated by translational displacements (RMTD) along the rugged surfaces.r3 The orientation of a water molecule is given by the polar and azimuthal angles formed by the proton-proton vector or-with quadrupolar interaction - by the electric field gradient and the external magnetic field. That is fi = ( p, 0). Spin-lattice relaxation is characterized by the correlation function of spherical harmonics of second order which can be analyzed as follows: G(t)
.
IO (kr)
mW2s
Fig. 3. Decay curves of the relative stimulated echo amplitude, E/E,, of a 400 m2/g “alfasil” sample containing 38% (b.w.) water. The data were recorded in dependence on q = yG,& where y is the gyromagnetic ratio (of ‘H), G, is the field gradient, and 6 is the width of the gradient pulses. The diffusion time A defined by the separation of the gradient pulses was chosen to be 2 ms. The curves refer to the finepartitle powder in the uncompressed state (100%) and with different degrees of compression. The highest compression achievable with our means was 16% of the uncompressed volume. The solid line represents the decay expected for bulk water, i.e., to a diffusion coefficient of 2.2. lo-’ m2/s. All data were measured at room temperature.
THE ORIENTATIONAL
dr
s0
(1)
-l/Z
Fig. 4. Typical spin-lattice relaxation dispersion of hydrated silica fineparticle agglomerates and analysis in terms of the structure factor S(k) . The mean monomer size is (d >= IO nm corresponding to the /3 peak.
Magnetic Resonance Imaging 0 Volume 12, Number
342
2, 1994
where the “mode” correlation times are given by 7/, = l/(Dk’). A computer program has been written which deconvolutes the orientational structure factor from experimental 7-r dispersion curves. INTERPRETATION OF FIELD-CYCLING EXPERIMENTS Figures 4-6 show the experimental T, and T,,, dispersions of silica fineparticles (Cab-O-W), porous ceramics (CPC), and porous glass (Vycor). The samples are specified by the specific surface (a), the water coverage of the surfaces (w), the water weight fraction (c,), and the density (p). In each case, the numerical evaluation of the orientational structure factors is given (bars). Two processes can be distinguished, which are designated by cyand 0. The structure factor can be represented by the general form
1
+---....,
102
100:
i
10'
.,-.-.,
..““‘I
105
““I’,
108
10'
.d
i lo6
lo9
cd> = 4 nm I
ax.
s
103
,‘--T
E
S(k)
r,nTI,
o-.y
l.O-
"".
Vycor, untreated
0.8-
CPC c,=o.31
O.b0.4-
lo-';
0.2OX&-
0 7
10-2:
. TI,
k S
IO-J """'I """1 """'I T '"'7 "I "109 102 103 10' 105 10" 10' loa
v Hz
-l/Z D-i/z
Fig. 6. Spin-lattice relaxation dispersion of hydrated porous glass and analysis in terms of structure factor S(k). The mean pore diameter is specified as (d) = 4 nm. The corresponding fi peak therefore is expected outside of the experimental window.
cd> = 38 nm
S(k) q-------
d’“.
.oj
CPC
if k > kc,
1
S(k) = (4)
0.8
otherwise
0.60.4 0.2 0.0 i 102
103
105
10' k p
Fig. 5. Spin-lattice relaxation dispersion of hydrated porous ceramics and analysis in terms of the structure factor S(k). The mean pore diameter is specified as (d) = 38 nm in accordance with the 0 peak.
where 6, and ba are weighting factors and k,, represents the cut-off wavenumber responsible for the final low-frequency plateau of the T, dispersions. The solid lines in Figs. 4-6 correspond to this expression modified by replacing the S function by a narrow Gaussian function. The P process is interpreted as RMTD along the elementary unit of the system. This can be a fineparticle monomer or a pore. Interestingly, the known lengths, (d), characterizing these units are reproduced by the structure factor evaluation taking the diffusion coef-
Microstructure
of
porous media 0
ficients typically measured in such systems. With Cab0-Sil and CPC the fl process is within the measuring window, whereas with Vycor (d) = 4 nm is too short. The cr process is characterized by a power law with a cut-off at low wavenumbers. This is attributed to the correlation length of a potentially fractal structure. In Ref. 8 a fractal analogue in the k-space has been suggested by interpreting S ( k) as a “mode density” in k-space corresponding to the mass density of fractals in real space. REFERENCES 1. Mansfield, P.; Morris, P.G. NMR Imaging in Biomedicine. New York: Academic Press, 1982. 2. Noack, F. NMR field-cycling: Principles and applications. Progr. NMR Spectr. 18:171-276; 1986. 3. Karger, J.; Pfeifer, H.; Heink, W. Principles and applications of self-diffusion measurements by nuclear magnetic resonance. Adv. Magn. Reson. 12:1-89; 1988. 4. Kimmich, R.; Unrath, W.; Schnur, G.; Rommel, E. NMR measurement of small self-diffusion coefficients in the fringe field of superconducting magnets. J. Magn. Reson. 91:136-140; 1991. 5. Klammler, F.; Kimmich, R. Geometrical restrictions of incoherent transport of water by diffusion in protein or silica fineparticle systems and by flow in a sponge. A study of anomalous properties using an NMR fieldgradient technique. Croat. Chem. Acta 65:455-470; 1992.
R. KIMMICH ET AL.
343
6. Kimmich, R.; Fischer, E. One- and two-dimensional pulse
sequences for diffusion experiments in the fringe field of superconducting magnets. J. Magn. Reson. A (in press). 7. Kimmich, R.; Nusser, W.; Gneiting, T. Molecular theory for nuclear magnetic relaxation in protein solutions and tissue: Surface diffusion and free-volume analogy. Colloids Surf. 45:283-302; 1990. 8. Stapf, S.; Kimmich, R. Microstructure
of porous media and field-cycling NMR relaxation spectroscopy. J. Appl. Physics (in press). 9. Kimmich, R. Reorientation mediated by translational diffusion as a mechanism for nuclear magnetic relaxation of molecules confined in surface layers. Magn. Reson. Imaging 9:749-751;
1991.
10. Karger, J.; Pfeifer, H.; Riedel, E.; Winkler, H. Selfdiffusion measurements of water adsorbed in NaY zeolites by means of NMR pulsed field gradient techniques. J. CON. Interface Sci. 44:187-188; 1973. 11. D’Orazio, F.; Bhattacharja, S.; Halperin, W.P.; Gerhardt, R. Enhanced self-diffusion of water in restricted geometry. Phys. Rev. Lett. 63:43-46; 1989. 12. Callaghan, P.; Coy, A.; Kimmich, R. Gas-phase enhancement of water diffusion in silica fineparticle aggregates. In: M.U. Palma, M.B. Palma-Vittorelli, F. Parak (Eds). Water-Biomolecule Interactions. Conference Proceedings Series Vol. 43 of Italian Physical Society. Bologna: Editrice Compositori; 1993. 13. Kimmich, R.; Weber, H.W. NMR relaxation and the orientational structure factor. Phys. Rev. B 47: 1178811794; 1993.