Adsorption, NMR, and Thermally Stimulated Depolarization Current

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Langmuir 2007, 23, 3184-3192

Adsorption, NMR, and Thermally Stimulated Depolarization Current Methods for Comparative Analysis of Heterogeneous Solid and Soft Materials V. M. Gun’ko,*,† V. V. Turov,† R. Leboda,‡ V. I. Zarko,† J. Skubiszewska-Zie¸ ba,‡ and B. Charmas‡ Institute of Surface Chemistry, 17 General NaumoV Street, 03164 KieV, Ukraine, and Department of Chemical Physics, Maria Curie-Sklodowska UniVersity, 20-031 Lublin, Poland ReceiVed September 10, 2006. In Final Form: December 13, 2006 Structural characterization of different silicas (ordered mesoporous silicas MCM-41, MCM-48, and SBA-15, amorphous silica gels Si-40, Si-60, and Si-100, and initial and wetted-dried fumed silica A-300) and bio-objects (fibrinogen solution, yeast cells, wheat seeds, and bone tissues) has been done using two versions of cryoporometry based on integral Gibbs-Thomson (IGT) equation for freezing point depression of pore liquids measured by 1H NMR spectroscopy (180-200 < T < 273 K) and thermally stimulated depolarization current (TSDC) method (90 < T < 273 K). The IGT equation was solved using a self-consisting regularization procedure including the maximum entropy principle applied to the distribution function of pore size (PSD). Comparison of the PSDs calculated by using the cryoporometry and nitrogen adsorption methods for the mentioned silicas demonstrates that IGT equation provides satisfactory fit which is better than that obtained with nonintegral Gibbs-Thomson (GT) equation (based on the GT equation) proposed by Aksnes and Kimtys. The NMR- and TSDC-cryoporometry methods applied to probe biosystems give clear pictures of changes in the structural characteristics caused, e.g., by hydration and swelling of wheat seeds and yeast cells, coagulation and interaction of fibrinogen with solid nanoparticles in the aqueous media, and human bone tissue disease.

Introduction There is a problem of structural characterization of soft materials and native bio-objects, such as cells, tissues, seeds, and others because pretreatment (e.g., heating, degassing, and dehydration) typically used on investigations with standard adsorption methods can strongly change the structure of soft materials. Removal of structured intramolecular and endocellular water can lead to denaturation and damage of tender bio-objects. On the other hand, the structure of these materials can be described in the terms related to intramolecular and endocellular water1,2 studied without its removal and, therefore, without structural changes in the materials on the use of nondestructive cryoporometry methods. The behavior of structured water can be studied by 1H NMR spectroscopy (giving temperature dependences of transverse relaxation time and chemical shift of the proton resonance),1,2 XRD (freezing/melting behavior and ice crystalline structure),1,3 measurements of thermally stimulated depolarization current (TSDC) related to relaxation phenomena in structured water depending on temperature and the confined space structure,2,4 FTIR and Raman spectroscopies giving the characteristics of adsorption sites and water binding, and other methods.1 There are several nondestructive methods which can be used for estimation of the pore * To whom correspondence should be addressed. Fax: +38044-4243567. E-mail: [email protected]. † Institute of Surface Chemistry. ‡ Maria Curie-Sklodowska University. (1) Chaplin, M. Water Structure and BehaViour, http://www.lsbu.ac.uk/water/. (2) Gun’ko, V. M.; Turov, V. V.; Bogatyrev, V. M.; Zarko, V. I.; Leboda, R.; Goncharuk, E. V.; Novza, A. A.; Turov, A. V.; Chuiko, A. A. AdV. Colloid Interface Sci. 2005, 118, 125. (3) Morishige, K.; Iwasaki, H. Langmuir 2003, 19, 2808. (4) Gun’ko, V. M.; Zarko, V. I.; Goncharuk, E. V.; Andriyko, L. S.; Turov, V. V.; Nychiporuk, Y. M.; Leboda, R.; Skubiszewska-Zie¸ ba, J.; Gabchak, A. L.; Osovskii, V. D.; Ptushinskii, Y. G.; Yurchenko, G. R.; Mishchuk, O. A.; Gorbik, P. P.; Pissis, P.; Blitz, J. P. AdV. Colloid Interface Sci. In press.

size distributions (PSDs) based on the specific behavior of pore liquids: (i) cryoporometry with the NMR measurements and the Gibbs-Thomson (GT) melting point depression of confined liquids;5-7 (ii) relaxometry using the enhanced relaxation of molecules at a pore surface and assuming rapid exchange between molecules at the surface and in the pores;8 (iii) thermoporometry as a calorimetric method based on the melting or freezing point depression of a liquid confined in pores by reason of the added contribution of surface curvature to the phase-transition free energy;9 and cryoporometry/relaxometry with the TSDC measurements (90 < T < 273 K) of dipolar and direct current (dc) relaxations of pore liquids dependent on the structural characteristics of pores.2,3 The aim of this work is (i) to derive the integral GibbsThomson (IGT) equation for calculations of the distribution functions of pore size on the basis of the 1H NMR spectroscopy and TSDC data for solid adsorbents, soft biomaterials, and native bio-objects and (ii) to develop a calculation procedure for determination not only of the PSDs but also of the specific surface area and the pore volume total and of micropores, mesopores, and macropores. Experimental Section Materials. To test the modified cryoporometry techniques such systems as solid adsorbents with (i) silica gels Si-40 (SBET ) 623 m2/g determined with the N2 molecule occupation area of 0.137 nm2, which is also used for all other silicas here, (SDFT ) 614 m2/g, Vp ) 0.59 cm3/g), Si-60 (SBET ) 314 (316) m2/g, Vp ) 0.82 cm3/g), (5) Strange, J. H.; Rahman, M.; Smith, E. G. Phys. ReV. Lett. 1993, 71, 3589. (6) Strange, J. H.; Mitchell, J.; Webber, J. B. W. Magn. Reson. Imaging 2003, 21, 221. (7) Aksnes, D. W.; Kimtys, L. Solid State Nucl. Magn. Reson. 2004, 25, 146. (8) Gallegos, D. P.; Munn, K.; Smith, D. M.; Stermer, D. L. J. Colloid Interface Sci. 1986, 119, 127. (9) Landry, M. R. Thermochim. Acta 2005, 433, 27.

10.1021/la062648g CCC: $37.00 © 2007 American Chemical Society Published on Web 01/30/2007

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and Si-100 (SBET ) 299 (293) m2/g, Vp ) 1.06 cm3/g) (Merck) described in details elsewhere;10-13 (ii) ordered mesoporous silicas MCM-41 (SBET ) 1019 m2/g (SDFT ) 1025 m2/g), Vp ) 0.7 cm3/g), MCM-48 (SBET ) 1158 (1095) m2/g, Vp ) 1.17 cm3/g), and SBA-15 (SBET ) 832 (852) m2/g, Vp ) 1.33 cm3/g);14 and (iii) fumed silica A-300 initial dry powder (SBET ) 278 m2/g, Vp ) 0.57 cm3/g) and wetted-dried sample (SBET ) 236 m2/g, Vp ) 1.46 cm3/g);15 and bio-objects: (iv) human plasma fibrinogen (HPF);16 (v) yeast cells;2,17 (vi) wheat seeds;2 and (vii) human bone tissues2,18,19 were studied. The silicas were investigated by both cryoporometry and standard adsorption methods. 1H NMR. The 1H NMR spectra of structured water were recorded using a Varian 400 Mercury spectrometer and a Bruker WP-100 SY spectrometer of high resolution with the probing 90o or 40o pulses at duration of 4-5 µs. The temperature was controlled by means of a Bruker VT-1000 device. Relative mean errors were (10% for 1H NMR signal intensity and (1 K for temperature. To prevent supercooling of the studied systems, the measurements of the amounts of unfrozen water were carried out on heating of samples preliminarily cooled to 170-200 K and equilibrated for 5-7 min for each temperature. The 1H NMR spectra recorded here include the signals only of nonfreezable mobile water molecules. The signals of water molecules from ice, as well as protons from the materials, do not contribute the 1H NMR spectra because of features of the measurement technique and the short duration (∼10-6 s) of transverse relaxation of protons in immobile structures2 which is shorter by several orders than that of mobile water. Water or other liquids can be frozen in narrower pores at lower temperatures that can be described by the GT relation for the freezing point depression 2σslTm,∞ k )∆Tm ) Tm(R) - Tm,∞ ) ∆HfFR R

(1)

where Tm(R) is the melting temperature of a frozen liquid in pores of radius R, Tm,∞ the bulk melting temperature, F the density of the solid, σsl the energy of solid-liquid interaction, ∆Hf the bulk enthalpy of fusion, and k is a constant.5-7 Equation 1 can be transformed into differential equation assuming that dVuw(R)/dR ) dCuw/dR, and using eq 1 dTm(R)/dR ) k/R2 ) (Tm(R) - Tm,∞)2/k gives dVuw(R) A dCuw(T) ) (Tm(R) - Tm,∞)2 dR k dT

(2)

where Vuw(R) is the volume of unfrozen water in pores of radius R, Cuw is the amount of unfrozen water per gram of adsorbent as a function of temperature,14 and A is a constant. Equations 1 and 2 can be transformed into an integral equation on replacing dVuw(R)/ dR by fV(R), converting dCuw/dT to dCuw/dR as dT ) dT/dR dR and (10) Gun’ko, V. M.; Leboda, R.; Skubiszewska-Zie¸ ba, J.; Turov, V. V.; Kowalczyk, P. Langmuir 2001, 17, 3148. (11) Gun’ko, V. M.; Dyachenko, A. G.; Borysenko, M. V.; SkubiszewskaZie¸ ba, J.; Leboda, R. Adsorption 2002, 8, 59. (12) Gun’ko, V. M.; Skubiszewska-Zieba, J.; Leboda, R.; Turov, V. V. Colloids Surf. A 2004, 235, 101. (13) Turov, V. V.; Gun’ko, V. M.; Tsapko, M. D.; Bogatyrev, V. M.; Skubiszewska- Zie¸ ba, J.; Leboda, R.; Riczkowski, J. Appl. Surf. Sci. 2004, 229, 197. (14) Gun’ko, V. M.; Turov, V. V.; Turov, A. V.; Zarko, V. I.; Gerda, V. I.; Yanishpolskii, V. V.; Berezovska, I. S.; Tertykh, V. A. Cent. Eur. J. Chem., in press. (15) Gun’ko, V. M.; Mironyuk, I. F.; Zarko, V. I.; Voronin, E. F.; Turov, V. V.; Pakhlov, E. M.; Goncharuk, E. V.; Nychiporuk, Yu. M.; Kulik, T. V.; Palyanytsya, B. B.; Pakhovchishin, S. V.; Vlasova, N. N.; Gorbik, P. P.; Mishchuk, O. A.; Chuiko, A. A.; Skubiszewska-Zie¸ ba, J.; Janusz, W.; Turov, A. V.; Leboda, R. J. Colloid Interface Sci. 2005, 289, 427. (16) Rugal, A. A.; Gun’ko, V. M.; Barvinchenko, V. N.; Turov, V. V.; Semeshkina, T. V.; Zarko, V. I. Cent. Eur. J. Chem. In press. (17) Turov, V. V.; Gun’ko, V. M.; Bogatyrev, V. M.; Zarko, V. I.; Gorbik, S. P.; Pakhlov, E. M.; Leboda, R.; Shulga, O. V.; Chuiko, A. A. J. Colloid Interface Sci. 2005, 283, 329. (18) Turov, V. V.; Gun’ko, V. M.; Zarko, V. I.; Leboda, R.; Jabłon´ski, M.; Gorzelak, M.; Jagiełło-Wojtowicz, E. Colloids Surf. B 2006, 48, 167. (19) Gun’ko, V. M.; Turov, V. V.; Shpilko, A. P.; Leboda, R.; Jabłon´ski, M.; Gorzelak, M.; Jagiello-Wojtowicz, E. Colloids Surf. B 2006, 53, 29.

integrating by R, Cuw(Tm) ) A′

∫

(

)

2 k f (R) dR (Tm,∞ - Tm(R))R V

Rmax

Rmin

(3)

where Rmax and Rmin are the maximal and minimal pore radii (or sizes of unfrozen liquid structures), respectively, and A′ is a normalization factor depending on the values of units used in eq 3.14 Notice that eq 3 was obtained from eq 1 with simple mathematical procedures and only one assumption that the volume of pores corresponds to the volume of unfrozen water and the density of this water is equal to 1 g/cm3 without any additional assumption or simplification. Solution of eq 3 is a well-known ill-posed problem due to the impact of noise on measured data, which does not allow one to utilize exact inversion formulas or iterative algorithms. Therefore, eq 3 (as well as other integral equations used here) can be solved using a regularization procedure based on the CONTIN algorithm20 under nonnegativity condition (f(R) g 0 at any R) and an fixed or unfixed value of the regularization parameter (R) determined on the basis of the F-test and confidence regions using the parsimony principle. Aksnes and Kimtys7 proposed to calculate the distribution function of the pore size f(R) as follows f(R) )

103k

I0,i

N

∑σ

x2π(RTm,∞ - k)2 i)1

[(

i

)]

103R - Xci(RTm,∞ - k)

exp -

x2σi(RTm,∞ - k)

2

(4)

where X ) 103/T, Xci is the normalized inverse transition temperature of phase i, I0,i and σi the intensity and the width of the temperature distribution curve of phase i. To more accurately calculate the distribution function on the basis of the IGT equation, an additional regularizer was derived using the maximum entropy principle21 applied to fV(R) written as N-dimension vector (N is the number of the grid points for f)

(

VAR + R2 1 -

)

S(p b(B)) f f min Smax

(5)

where VAR is the regularizer, R the regularization parameter, S is the entropy, b p 0(B) f ) B, f pi1(B) f ) fi+1 - fi + (fmax - fmin ); pi2(fh) ) fi+1 - 2fi + fi-1 + 2(fmax - fmin ), N

S(B) f )-

∑s

k

ln(sk),

sk )

fk N

∑f

k)1

,

i ) 1, ..., N - 1 i ) 2, ..., N - 1

and Smax ) -ln

() 1

N

k

k)1

The b pj(fB) vector corresponds to the maximum entropy principle of the j-order.21 This procedure was used to modify the CONTIN algorithm20 (CONTIN/MEM-j where j denotes the order of b pj(fB)). A self-consisting regularization procedure (starting calculations were done without application of MEM) with an unfixed regularization parameter (for better fitting) was used on CONTIN/MEM-j calculations. This procedure was also applied to the nitrogen adsorption data with the overall adsorption equations described below. The fV(R) function can be converted into the distribution function fS(R) with respect to the specific surface area fS(R) )

(

)

V(R) w fV(R) R R

(6)

(20) Provencher, S. W. Comp. Phys. Comm. 1982, 27, 213. (21) Muniz, W. B.; Ramos, F. M.; de Campos Velho, H. F. Comput. Math. Applic. 2000, 40, 1071.

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where w ) 1, 2, and 1.36 for slit-shaped, cylindrical pores, and voids between spherical particles packed in the cubic lattice, respectively. Integration of the fS(R) function determined with eq 6 on the basis of the IGT equation gives the specific surface area (SIGT) of the studied materials in contact with structured water (SIGT values are shown in figure legends). Integration of the fV(R) and fS(R) functions at R < 1 nm, 1 < R < 25 nm, and R > 25 nm gives the volume and the specific surface area of micro-, meso-, and macropores. Thermally Stimulated Depolarization Current (TSDC). The tablets (diameter 30 mm, thickness ∼1 mm) with frozen studied materials differently hydrated were polarized by the electrostatic field at the intensity Fp ) 200-300 kV/m at 260 K then cooled to 90 K with the field still applied and heated without the field at a heating rate β ) 0.05 K/s. The current evolving due to sample depolarization4 was recorded by an electrometer over the 10-1510-7 A range. Relative mean errors for measured TSD current were δI ) (5%, δT ) (2 K for temperature, δβ ) (5% for the temperature change rate. Modified eqs 1 and 3 with k as a linear function of temperature k(T) ) 40 + 5/6 (T - 90) (K nm) at T between 90 and 270 K obtained on the basis of the calibration curves for silica gels Si-40 and Si-604 were used to estimate the PSDs on the basis of the TSDC data.2,4,14 Nitrogen Adsorption. Low-temperature (77.4 K) adsorption/ desorption isotherms of nitrogen were measured for silicas using a Micromeritics ASAP 2405N adsorption analyzer. The specific surface area SBET was calculated according to the standard BET method22 but using different pressure ranges p/p0 (where p and p0 denote the equilibrium and saturation pressures of nitrogen, respectively) depending on the studied materials p/p0 ) 0.05-0.17 for MCM-41, 0.05-0.2 (MCM-48), and 0.05-0.23 (SBA-15, silica gels, and fumed silica) to avoid overestimation of the SBET values because of the beginning of the formation of the second layer with adsorbed nitrogen in narrow mesopores. The occupation area of a nitrogen molecule equal to 0.137 nm2 was used instead of 0.162 nm2 typically used for carbon materials.23 The pore volume Vp was estimated at p/p0 ≈ 0.98-0.99 converting the adsorbed amount a0.98 (in cm3 STP of gaseous nitrogen per gram of the adsorbent) to the liquid adsorbate Vp ≈ 0.0015468a0.98. Pore size distributions (PSD, differential fV(R) and fS(R) with respect to the pore volume and the specific surface area, respectively) were calculated using an overall isotherm equation based on the equation proposed by Nguyen and Do (ND method) for carbon adsorbents with slitlike pores24 and modified for cylindrical pores10-14 and voids between spherical particles15 using appropriate LJ potentials (modified ND (MND) method). The integral equation related to the MND method was solved using a regularization procedure based on the CONTIN algorithm20 as described elsewhere.10-15 The differential PSDs fV(R) were converted to incremental PSDs (IPSD). The fV(R) and fS(R) functions were used to calculate contributions of micropores (S*mic, Vmic) at R < 1 nm, mesopores (S*mes, Vmes) at 1 < R < 25 nm, and macropores (S*mac, Vmac) at 25 < R < 100 nm to the specific surface area and the total porosity. Additionally, fS(R) was used to estimate the deviation (∆w) of the pore shape from the model using a self-consisting (to calculate the distribution function of particle size φ(a) and to better fit the nitrogen adsorption isotherms) regularization in the case of the use of a complex model of the pore shape10-15 ∆w )

SBET

∫

Rmax

Rmin

-1

(7)

fS(R) dR

where Rmax and Rmin are the maximal and minimal pore radii, respectively. The S*mic, S*mes, and S*mac values were corrected by multiplication by (∆w + 1) that gives S*(∆w + 1) ) Ssum ) Smic + Smes + Smac ) SBET. The effective w value (wef) can be estimated (22) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982. (23) Thommes, M.; Ko¨hn, R.; Fro¨ba, M. Appl. Surf. Sci. 2002, 196, 239. (24) Nguyen, C.; Do, D. D. Langmuir 1999, 15, 3608; 2000, 16, 7218.

with equation

∫ ∫

Rmax

SBET wef ) Vp

Rmin

RfV(R) dR

Rmax

Rmin

(8) fV(R) dR

The specific surface area (Sφ) of materials composed of spherical nanoparticles characterized by the particle size distribution φ(a) (calculated using the self-consisting regularization for fV(R) and φ(a) (normalized to 1) with the model of voids between spherical particles) can be calculated with equation Sφ )

∫

amax

amin

[

( )xA - a -

3 a 2(a + t)2 + Nrm arcsin 3 A 2a F

N(a + t)

2

(

2

)]

arm + t φ(a) da (9) A

where A ) a + t + rm, a is the particle radius, F the density of material, N the average coordination number of nanoparticles in aggregates, t the thickness of an adsorbed nitrogen layer, and rm is the meniscus radius determined at 0.05 < p/p0 < 0.2 corresponding to the effective radius R of voids between spherical particles. The kernel in eq 9 was described elsewhere.22 Condition Sφ ) SBET can be used to estimate the N value in eq 9. The PSDs were also calculated using overall equation (with the framework of density functional theory, DFT)25 W(p) ) VM

[∫

rk(p)

σss/2

Ff(R)f(R)dR +

∫

]

t F (R)f(R) dR R - σss/2 M (10)

Rmax

rk(p)

where W is the adsorption, where VM the liquid molar volume, Ff the fluid density in occupied pores, Fm the density of the multilayered adsorbate in pores, rk the radius of pores occupied at the pressure p, σss is the collision diameter of the surface atoms. To calculate the density of a gaseous adsorbate (nitrogen) at a given pressure p, the Bender equation26,27 was used in the generalized form p ) FT[Rg + BF + CF2 + DF3 + EF4 + FF5 + (G + HF2)F2 exp(-a20F2)] (11) where B ) a1 - a2/T - a3/T2 - a4/T3 - a5/T4; C ) a6 + a7/T + a8/T2; D ) a9 + a10/T; E ) a11 + a12/T; F ) a13/T; G ) a14/T3 + a15/T4 + a16/T5; H ) a17/T3 + a18/T4 + a19/T5; a20 ) F-2 c ; ai are constants, and Rg is the gas constant. Transition from gas (subscript g) to liquid (l) or fluid in the form of multilayered adsorbate in pores (m) can be linked to the corresponding fugacity, f ln

f(T, F) p(T, F) 1 ) -1+ RgTF RgTF RgT

∫

F

0

[p(T,F) - RgTF]

dF (12) F2

and

( )

fl,m ) fg exp

Ei,m RT

(13)

where E is the interaction energy of an adsorbate molecule with the pore walls and neighboring molecules calculated with the LJ potentials. The CONTIN/MEM procedure was applied to solve eq 10. There are certain limitations of the use of eq 11 described elsewhere;26,27 therefore, the minimal pressure used with eq 11 corresponds to the condition p/p0 > 0.01. (25) Do, D. D.; Nguyen, C.; Do, H. D. Colloids Surf. A 2001, 187-188, 51. (26) Platzer, B.; Maurer, G. Fluid Phase Equilib. 1989, 51, 223. (27) Platzer, B.; Maurer, G. Fluid Phase Equilib. 1993, 84, 79.

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Figure 1. PSDs calculated on the basis of the nitrogen adsorption data and NMR spectra of unfrozen water partially filling pore volume of (a) MCM-41 (h ) 5.2 grams of water per gram of dry material, Cuw|273K ) 0.48 g/g, SIGT ) 507 m2/g, MCM-48 (h ) 0.2 g/g, SIGT ) 242 m2/g) and SBA-15 (h ) 0.16 g/g; SIGT ) 76 m2/g), and (b) PSDs for MCM-48 calculated with different equations and normalized to h ) 0.2 g/g.

Results and Discussion At low hydration (h , VpFuw assuming Fuw ) 1 g/cm3) of a solid adsorbent, water can occupy a certain portion of pores and/or form a thin film covering a pore surface if this surface is hydrophilic or form clusters at adsorption surface sites such as hydroxyl groups. In the case of partially hydrophobic surface (e.g., because of residual fragments of the organic template remaining in pores after calcination of silicas), water can occupy large pores to reduce contact area with the hydrophobic surface patches and air bubbles can remain in pores. For instance, water occupies ∼69% of the pore volume of MCM-41 (having residual CH functionalities) at high hydration h ) 5.2 g/g . VpFuw. However, a water/benzene mixture occupies the total pore volume of this adsorbent at the total volume of water and benzene slightly larger than Vp because benzene can effectively interact with surface hydrophobic patches.14 On incomplete hydration (MCM48 and SBA-15) or incomplete occupation of pores (MCM-41), the PSDs calculated on the basis of the 1H NMR spectra of unfrozen water, i.e., Cuw(T), (PSDuw) are lower than the PSDs calculated with the nitrogen adsorption data (PSDN) (Figure 1a), as well as the SIGT values being smaller than SBET. However, the positions of the peaks of the PSDs of both types are the same for the same material. Observed broadening of the PSDsuw can be caused by several factors: (i) the presence of pores of a larger size than that of the main mesopores;14 (ii) strong effects of noise because a small number of the experimental points (about 10) in the Cuw(T) curves was used to extrapolate the curves with an increase in the point numbers to 150-250 that can cause the broadening of the distribution functions.28 Comparison of the PSDs for MCM-48 calculated using different equations (Figure 1b) shows that there is some difference between the PSDs calculated on the basis of eq 1 (differential PSD) and the IGT equation (incremental PSDs which are closer to incremental PSDs calculated on the basis of the initrogen isotherms). Therefore, PSDs for other materials are shown below as incremental ones obtained using the IGT equation. Notice that eq 4 gives a more smoothed graph in comparison with that obtained with eq 1 (i.e., eq 2). Correction of the SIGT values with consideration for the adsorbed water volume gives smaller values (by 200-280 m2/g) than SBET for MCM-41 and SBA-15 but a larger one (by 250 m2/g) for MCM-48. These results can be explained by a different location

of water in pores of these adsorbents. In the case of MCM-48, water can occupy the narrowest pores and form a thin film at the pore walls in larger pores; therefore, corrected SIGT is larger than SBET. In the case of MCM-41 and SBA-15 residual organic functionalities of the template (CH stretching vibrations are observed in the FTIR spectra)14,29 can inhibit occupation of the narrowest pores and the formation of a continuous thin film at the pore walls; therefore, corrected SIGT < SBET. This is confirmed by the PSDuw shape, especially for SBA-15 because the PSDuw (with both NMR/IGT and TSDC/IGT) is close to zero at R < 2 nm in contrast to the PSDN (Figures 1 and 2). Notice that the wef value calculated with eq 8 can be equal to the model w value (w ) 2 for cylindrical pores) for ‘ideal’ adsorbents with a monomodal PSD and smooth pore walls. However, for real adsorbents with a polymodal PSD and rough pore walls wef > w. For instance, wef ) 2.28, 2.18, and 2.44 (DFT) for MCM-41, MCM-48, and SBA-15, respectively, that suggest certain nonuniformity (imperfection) of these silicas. Clearly this nonuniformity can reflect in the characteristics of pore water, e.g., in broadening of the corresponding PSDsuw. The use of the TSDC/IGT approach gives slightly broader PSDsuw than the PSDsN (Figure 2) and sometimes an additional

(28) Gun’ko, V. M.; Klyueva, A. V.; Levchuk, Yu, N.; Leboda, R. AdV. Colloid Interface Sci. 2003, 105, 201.

(29) Lind, A.; du Fresne von Hohenesche, C.; Smatt, J.-H.; Linden, M.; Unger, K. K. Micropor. Mesopor. Mater. 2003, 66, 219.

Figure 2. PSDs calculated on the basis of nitrogen adsorption (DFT/ MEM-0) and TSDC with the integral Gibbs-Thomson equation.

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Figure 3. PSDs of (a) Si-40 (SIGT ) 607 m2/g, h ) 0.58 g/g), (b) Si-60 (SIGT ) 351 m2/g, h ) 1.09 g/g), and (c) Si-100 (SIGT ) 261 m2/g, h ) 0.59 g/g) calculated from the nitrogen desorption data (MND and DFT/MEM-0) and Gibbs-Thomson relation (GT) and integral GT (IGT) on the basis of the NMR spectra of structured pore water; MND is the modified Nguyen-Do method, and MEM-0 is the maximum entropy method of zero order.

Figure 4. (a) Size distributions of voids filled by unfrozen water in aqueous suspensions of A-300 (NMR, IGT, SIGT ) 200, 249, and 281 m2/g at CSiO2 ) 4.7, 7.0, and 9.0 wt %, respectively) and the PSD calculated on the basis of the nitrogen adsorption isotherm (with the model of voids between spherical particles with the CONTIN/MEM-0 regularization) for initial (278 m2/g) and wetted-dried (236 m2/g) A-300; and (b) particle size distributions for initial A-300 and wetted-dried sample.

peak appears at small R values. The last result is due to the complexity of the dipolar relaxation of water (ice) in mesopores observed by the TSDC method.4 For instance, a portion of the

water clusters of sizes smaller than the pore size can relax at lower temperatures than larger clusters do in the same pores,4 and this affects the calculated PSDs.

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Figure 5. Size distributions of pores filled by unfrozen water for (a) 0.15 mol NaCl or HPF solution at 1.25 and 2.5 wt % and (b) HPF/A-300 at different concentrations of protein and silica (CONTIN/MEM-0 regularization applied to the IGT equation)

Figure 6. PSDs of dry (h ) 0.07 g/g, SIGT ) 122 m2/g) and wetted (h ) 0.52 g/g, SIGT ) 990 m2/g) yeast cells calculated on the basis of the 1H NMR spectra of unfrozen water and the IGT equation (MEM-0).

Integrally the cryoporometry results for silica gels (Figure 3) are similar to that for ordered mesoporous silicas (Figures 1 and 2): the positions of the main mesopore peaks in the PSDsuw (GT and IGT/MEM-0) and the PSDsN (MND and DFT/MEM-0) are close. The SIGT and SBET values are close despite different hydration of the samples (complete for Si-40 and Si-60 and ∼50% for Si-100). This can be explained by the fact that silica gels have totally hydrophilic surface in contrast to the MCM and SBA samples. Therefore, water can totally cover the silica gel surface by a thin film (Si-100) or completely occupy all pores (Si-40 and Si-60). Notice that silica gels are nonuniform as wef ) 2.27, 2.31, and 2.19 (DFT) for Si-40, Si-60, and Si-100, respectively. The PSDsuw for silica gels are broader than the PSDsN. This is due to the difference in the relaxation processes (TSDC) and the molecular mobility (NMR) nearly the pore walls and far from them especially in relatively broad mesopores observed in silica gels. In other words, conditions of freezing/thawing of structured pore water (1H NMR spectra were recorded at T higher than the glass-transition temperature, Tg, for interfacial water) and dipolar relaxation of pore ice (TSDC at T < Tg) depend not only on the pore size but also on the distance from the pore walls especially in broad mesopores or macropores. Fumed oxides characterized by the textural porosity (provided by voids between spherical nanoparticles in their aggregates and agglomerates of aggregates which, however, can be instable in the aqueous media15) have very different PSDs for dry,15 wetted-

Figure 7. PSDs (IGT) of voids filled by unfrozen water in wheat seed alone (initial (h ) 0.072 g/g, SIGT ) 77 m2/g) and wetted for 1 day (h ) 0.42 g/g, SIGT ) 410 m2/g) and 2 days (h ) 0.88 g/g, SIGT ) 806 m2/g) and with the presence of fumed silica A-300 (aqueous suspension at CSiO2 ) 1 wt.%) wetted for 1 day (h ) 0.28 g/g, SIGT ) 170 m2/g) and 2 days (h ) 0.45 g/g, SIGT ) 194 m2/g).

dried,30 or ball-milled powders31 and dispersions in the aqueous suspensions (colloidal solutions with nanoparticles).2,4 Wetteddried nanosilica A-300 is characterized by a greater pore volume (Vp ) 1.46 cm3/g) and a smaller specific surface area (SBET ) 236 m2/g) than that of the initial dry powder (Vp ) 0.57 cm3/g and SBET ) 278 m2/g) that causes the difference in the PSDN values (Figure 4). However, the PSDsN for these samples are close at R < 3 nm and the positions of the main peaks at R > 20 nm are nearly the same. The mentioned similarities and differences can be due to an increase in the parking density of primary particles in aggregates and aggregates in agglomerates (the bulk density of the initial powder is ∼0.06 g/cm3, and it increases to 0.23 g/cm3 for the treated A-300 sample) but without strong changes in the structure of aggregates (bulk density up to 0.7 g/cm3) responsible for the mentioned narrow pores. Notice that eq 9 gives the Sφ values close to the SBET values calculated at the occupation area of N2 molecule of 0.137 nm2. For instance, for dry A-300, Sφ ) 271 m2/g (at N ) 3, t and rm calculated at (30) Gun’ko, V. M.; Zarko, V. I.; Voronin, E. F.; Turov, V. V.; Mironyuk, I. F.; Gerashchenko, I. I.; Goncharuk, E. V.; Pakhlov, E. M.; Guzenko, N. V.; Leboda, R.; Skubiszewska-Zie¸ ba, J.; Janusz, W.; Chibowski, S.; Levchuk, Yu.N.; Klyueva, A. V. Langmuir 2002, 18, 581. (31) Gun’ko, V. M.; Voronin, E. F.; Mironyuk, I. F.; Leboda, R.; SkubiszewskaZie¸ ba, J.; Pakhlov, E. M.; Guzenko, N. V.; Chuiko, A. A. Colloids Surf. A 2003, 218, 125.

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Figure 8. PSDs of (a) dry (h ) 0.07 gram of water per gram of dry material) and wetted (h ) 0.75 g/g) yeast cells, and (b) dry (h ) 0.07 g/g) and wetted (h ) 0.47 g/g) wheat seeds calculated with the TSDC data and the IGT equation.

0.05 < p/p0 < 0.2) and 238 m2/g (N ) 4) for wetted-dried nanosilica at SBET ) 278 and 236 m2/g, respectively. Consequently, the packing density of primary particles in aggregates of the treated sample increases because the average coordination number (N) of primary particles grows from 3 to 4 (at the same position at 5.3 nm of the maximum of the φ(a) distributions for both samples (Figure 4b)) and the specific surface area decreases by 15%. The φ(a) distribution for the treated sample is slightly broader than that for the initial A-300 powder (Figure 4b). This can be due to mass transfer and particle-particle adhesion on the silica treatment leading to both real and apparent growth of primary particles.32 Thus, the textural porosity of treated fumed silica increases because of changes in the structure of aggregates and agglomerates accompanied by certain changes in the morphology of primary particles. The PSDsuw of nanosilica dispersions are characterized by much greater contribution of ‘pores’ (filled by structured water) at R < 10 nm than that for the PSDsN. This is due to rearrangement of secondary particles in the aqueous suspension because in the fresh sonicated concentrated suspensions the primary particles can give up to 99% of the number of particles.15,30,33 The sonicated and concentrated suspensions of nanosilica are more uniform with respect to the size distribution of secondary particles because the polydispersity strongly decreases in comparison with that of nonsonicated and diluted suspensions.33 A greater stability of more concentrated suspensions leads to larger SIGT values for the same silica because of weaker aggregation of primary particles. Relatively fast structurization of secondary particles in the concentrated suspensions affects the dispersion structure depending on aging time. For instance, strong (irreversible) gelation of the suspensions at CSiO2 > 12 wt % occurs for 1-2 days, and the gelation is faster for more concentrated suspensions. The suspensions at CSiO2 < 10 wt % are practically stable with time and strong gelation is absent over the long term. Thus, the NMR- and TSDC-cryoporometry (IGT) methods allow the structural characterization of solid materials with different types of the porosity such as framework-confined (mesoporous silicas) and textural (nanosilica) ones. Therefore, one can assume that these methods can be used to describe the porosity of biosystems in which pores, voids, and pockets are occupied by structured water. Two types of water can be (32) Gun’ko, V. M.; Skubiszewska-Zie¸ ba, J.; Leboda, R.; Khomenko, K. N.; Kazakova, O. A.; Povazhnyak, M. O.; Mironyuk, I. F. J. Colloid Interface Sci. 2004, 269, 403. (33) Gun’ko, V. M.; Zarko, V. I.; Leboda, R.; Chibowski, E. AdV. Colloid Interface Sci. 2001, 91, 1.

distinguished there: (i) water structured inner macromolecules (analogous to water in framework-confined pores) and (ii) extramolecular water locating between macromolecules, e.g., in cells, seeds, tissues, etc. (analogous to water in the systems with the textural porosity). An increase in concentration of fibrinogen in the buffer solution leads to diminution of both types of water (Figure 5a) structured in narrow pores (i.e., pockets in HPF molecules) and broad ‘pores’ between macromolecules coagulated in a long-distance potential minimum. The surface area in contact with the structured water decreases from SIGT ) 2087 to 639 m2/g. Similar effects are observed for the HPF/nanosilica systems (Figure 5b) because an increase in concentrations of HPF and silica causes stronger coagulation of them that leads to the displacement (pressingout) of the interfacial water layers locating between (and inner) macromolecules themselves and silica nanoparticles. For the most concentrated HPF/silica system the SIGT value is minimal (163 m2/g) and smaller than that for the solutions with the materials alone. This corresponds to formation of hybrid dense clots with strong (irreversible) adsorption of HPF onto nanosilica.16 Notice that nanosilica can be used as a component of tourniquet preparations because of strong interaction with plasma proteins and red blood cells. Wetting of dry yeast cells (Figure 6) or dry wheat seeds (Figure 7) leads to swelling of them because contribution of water locating in both narrow (intramolecular water) and broad (endocellular water) pores strongly increases. The swelling leads to a strong increase in the surface area SIGT (in contact with structured water) nearly by order for yeast cells and more than by order for wheat seeds wetted for 48 h (the SIGT values are shown in figure legends). Wetting of wheat seeds in the aqueous suspension of nanosilica (CSiO2 ) 1 wt %) results in much lower hydration of seeds and smaller SIGT values (Figure 7) in comparison with that of seeds alone. This can be due to coverage of the seed shells by silica nanoparticles blocking channels of water transfer into the seeds. Similar effects of swelling of yeast cells and wheat seeds are observed by using the TSDC-cryoporometry (IGT) (Figure 8) showing an increase in the micro- and mesoporosity of wetted cells and seeds. The structural characteristics of bone tissues (healthy and affected by osteoporosis) (Figure 9) can be estimated using the NMR-cryoporometry (IGT).18,19 The PSDuw graphs clearly demonstrate greater mesoporosity and surface area SIGT of the second bone sample (affected by osteoporosis) that is in agreement with the XRD data.19

Analysis of Heterogeneous Solid and Soft Materials

Figure 9. PSDs of human bone tissues healthy (SIGT ) 878 m2/g) and affected by osteoporosis (SIGT ) 1047 m2/g) calculated on the basis of the NMR spectra (IGT).

Conclusion An integral equation based on the GT relation for the freezing point depression for pore liquids was derived to analyze the 1H NMR spectra and the thermally stimulated depolarization current thermograms of water (ice) structured in porous materials. The IGT equation can be used to study the structural characteristics of biomaterials and bio-objects containing water occupying different pores, voids, and pockets. The TSDC- and NMRcryoporometry methods allow us to determine the pore size distributions, the specific surface area, and the volume of pores of different bio-materials (cells, seeds, bone tissues, and protein solutions) containing structured water freezing at T < 273 K. This is of importance because the structural characterization of bio-objects cannot be done by the standard adsorption methods. The cryoporometry methods clearly show the structural changes in the materials with increasing amounts of pore water (e.g., on hydration of yeast cells and wheat seeds) or increasing their concentrations in the aqueous media (fibrinogen/nanosilica) or on changes in the morphology of the materials (bone tissues healthy and affected by osteoporosis). Therefore, one can assume that the IGT equation solved with the CONTIN/MEM algorithm can be used to characterize any solid, soft and biomaterials or bio-objects containing pore water (or other liquids). Calculations of the particle size distributions φ(a) and the Sφ and N values (as well as SIGT and PSDuw) for materials with the textural porosity give useful information for better understanding of their structural features. The MND/MEM and DFT/MEM methods allow the calculations of the distribution functions more sensitive to structural and morphological changes of materials than that calculated by the same methods but without the use of the MEM. The authors thank Prof. V. A. Tertykh for MCM-41 samples, Dr. V. I. Gerda for MCM-48 and SBA-15 samples, and Prof. M. Jabłon´ski for bone tissue samples. Nomenclature A A′ a0.98 a1, a2, ..., a20 A-300

constant normalization factor nitrogen adsorption at p/p0 ≈ 0.98, cm3 STP/g constants in Bender eq fumed silica

Langmuir, Vol. 23, No. 6, 2007 3191 B, C, D, E, F, G, and H CONTIN CSiO2 Cuw dc dCuw/dR dCuw/dT DFT dVuw(R)/ dR E f Fp fS(R)

constants in Bender eq

regularization algorithm concentration of silica, wt % amount of unfrozen water (g) per gram of adsorbent, g/g direct current derivative, g/g/nm derivative, g/g/K density functional theory derivative, cm3/g/nm

interaction energy, kJ/mol fugacity in eq 11, kJ cm3/mol/g intensity of the electrostatic field, kV/m distribution function of pore size with respect to surface area, a.u. FTIR Fourier transform infrared spectroscopy distribution function of pore size with respect to pore fV(R) volume a.u. GT Gibbs-Thomson equation h hydration, g/g HPF human plasma fibrinogen I0,i the intensity of the temperature distribution curve of phase i, a.u. IGT integral Gibbs-Thomson equation IPSD incremental pore size distribution j order of vector b pj(fB) k constant, K nm k(T) function of temperature in GT and IGT eqs based on TSDC data, K nm LJ Lennard-Jones potential MCM-41 ordered mesoporous silica MCM-48 ordered mesoporous silica MEM-j maximum entropy method of the j order MND modified Nguyen-Do method N number of the grid points for f in eq 5 N average coordination number of nanoparticles in aggregates in eq 9 NMR nuclear magnetic resonance p equilibrium pressure of nitrogen, Torr saturation pressure of nitrogen, Torr p0 vector in MEM b pj(fB) PSD pore size distribution, a.u. PSDuw pore size distribution determined from the Cuw values, a.u. R radius of pores, nm gas constant, J/K/mol Rg rk radius of pores occupied at the pressure p, nm meniscus radius, nm rm Rmax maximal pore radius on integration, nm Rmin minimal pore radius on integration, nm S entropy, kJ/mol/K SBA-15 ordered mesoporous silica specific surface area by the Brunauer-Emmett-Teller SBET method, m2/g specific surface area by the DFT method, m2/g SDFT SIGT specific surface area determined with IGT eq, m2/g corrected specific surface area of macropores, m2/g Smac * S mac noncorrected specific surface area of macropores, m2/g Smes corrected specific surface area of mesopores, m2/g noncorrected specific surface area of mesopores, m2/g S*mes Smic corrected specific surface area of micropores, m2/g

3192 Langmuir, Vol. 23, No. 6, 2007 S*mic Si-40 Si-60 Si-100 Ssum Sφ t T Tg Tm,∞ Tm(R) TSDC VAR VM Vmac Vmes Vmic Vp Vuw(R)

noncorrected specific surface area of micropores, m2/g silica gel silica gel silica gel corrected total specific surface area, m2/g specific surface area, m2/g thickness of an adsorbed nitrogen layer, nm temperature, K glass-transition temperature, K bulk melting temperature, K melting temperature of a frozen liquid in pores of radius R, K thermally stimulated depolarization current, A regularizator liquid molar volume, cm3/mol volume of macropores, cm3/g volume of mesopores, cm3/g volume of micropores, cm3/g total pore volume, cm3/g volume of unfrozen water in pores of radius R, cm3/g

Gun’ko et al. W w wef X Xci XRD R β ∆Hf ∆w F Ff Fm σi σsl σss φ(a)

adsorption, cm3 STP/g parameter in Kelvin equation, a.u. effective parameter in Kelvin equation, a.u. the normalized inverse transition temperature, 1/K the normalized inverse transition temperature of phase i, 1/K X-ray diffraction regularization parameter, a.u. heating rate, K/s bulk enthalpy of fusion, kJ/mol relative deviation from the pore model, a.u. density, g/cm3 fluid density in occupied pores, g/cm3 density of the multilayered adsorbate in pores, g/cm3 the width of the temperature distribution curve of phase I, a.u. energy of solid-liquid interaction, kJ/mol collision diameter of the surface atoms, nm2 primary particle size distribution, a.u. LA062648G