EVALUATION OF THE INFLUENCE OF CAPILLARY FORCES ON THE FORMATION OF PORE STRUCTURE OF DISPERSED MATERIALS Y.G.

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1 EVALUATION OF THE INFLUENCE OF CAPILLARY FORCES ON THE FORMATION OF PORE STRUCTURE OF DISPERSED MATERIALS Y.G. Tselishchev, V.A. Valtsifer, I.I. Lebedeva Institute of Technical Chemistry of UB RAS, Perm, Russia The influence of capillary forces between the particles of dispersion components of a porous aluminum oxide material on the formation of the pore structure of this material is evaluated. The estimates obtained from the results of the adsorption studies on the materials, which are the precursors of porous aluminum oxide, have demonstrated that capillary forces substantially affect pore structure formation. Based on the calculated dependences, which have an experimental confirmation, we have developed a model for investigating the influence of particle size and shape, liquid interlayer volume, surface tension and interlayer wetting angle on the value and behavior of capillary forces and its components. The model also allows one to study the capillary forces acting between the particles of the dispersion components of a porous alumina material and to evaluate their contribution to the formation and evolution of the structure of these materials. Introduction The most significant forces acting between the particles of dispersed components of porous materials with liquid components are capillary forces. These forces arise in the interlayers consisting of liquid components of dispersed materials at the places where particles come into contact with each other, i.e. in the narrow pores and capillaries of porous materials at the stages of their preparation and modification, during their storage and use in the medium containing vapors of moisture and other liquid components. Capillary forces have a significant impact on the formation and evolution of the structure of porous materials. The value of forces depends in this case on different particle parameters, the volume and properties of a liquid interlayer and the environment. Immediate measurement of capillary forces between microdispersed particles and determination of particle parameters and liquid interlayer characteristics affecting the value and behavior of these forces are difficult to perform due to the small dimensions of the examined objects and the low values of forces. The first theoretical studies on the capillary forces acting between 199

2 the model spherical particles of ideal soil were carried out by Haines W B. and Fisher R.A. in the early 20 th century [1-3]. The results of more comprehensive theoretical and experimental studies on these capillary forces obtained by other researchers can be found in [4-7]. Even though last results in this field of research are generally recognized as considerable, they are often incomplete and sometimes even contradictory, which can be attributed to the fact that the analysis of different parameters of particles and liquid interlayers presents essential difficulties. Furthermore, in some cases there arises a need for modeling processes taking place in capillary liquid interlayers. A key advantage of porous aluminum oxide materials is that they have a highly organized structure formed by the particles of micro- and nanodispersed components of a porous matrix characterized by a large surface area of mesopores, their ordered structure and significant volume. Owing to these properties, mesoporous alumina materials have found wide application in different fields, including sorption, extraction and catalysis. The objective of this study is to assess the influence of capillary forces acting between particles on the formation of the pore structure of dispersed materials. For this purpose, we have performed experimental and computational studies to investigate the influence of capillary forces between the particles of the dispersion components of mesoporous aluminum oxide materials on the formation of the pore structure of these materials. Experimental part Mesoporous alumina oxide composites were prepared using the method of hydrothermal template synthesis (HTS). The mesoporous material was synthesized by the sol-gel method of HTS with subsequent heat treatment stages of precursor materials. The pore structure parameters of synthesized composites were determined in the adsorption studies performed at low temperatures (- 196 о С) on the surface area ASAP-2020 by means of different methods (BET, BJH, t-plot, Dubinin-Astakhov, and Horvat-Kavazoe techniques). The structure of porous materials was analyzed using optical (OLIMPUS), electron (Evex HR-3000) and atomic-force (SMENA Solver) microscopes. 200

3 The influence of the capillary forces acting between the particles of dispersion components on the formation and evolution of the initially formed porous structure of the materials precursors of porous composites was investigated in the early stages of their drying and heat treatment. Using the experimentally determined temperature-time regimes for obtaining material-precursors, including the freezing of their structure at low temperatures during some preparatory stages, we determined the pore structure parameters of these materials before and after the capillary forces between particles were applied (Fig. 1, Table 1). The following parameters were analyzed: specific surface area S BET, total volume V tot, pore dimension D p, surface area S m, micropore volume V m (tplot technique), and micropore volume and dimension (Dubinin- Astakhov and Horvat-Kavazoe techniques). Pore structure parameters of the aluminum oxide material Table 1 S Sample /g nm BET, V tot, S m, V m 10 3, D p, m²/g cm³/g m²/g cm 1 * 2 * ** * - pore structure parameters of the material before ( 1 ) and after ( 2 ) the capillary forces between particles were applied; ** «-» - characteristics insignificant in value (S m and V m). The numbering of the samples from 1 to 5 used in the above Table was determined by the main parameters of mesoporous materials and the synthesis conditions for these materials. 201

4 Fig. 1. Adsorption-desorption isotherms (A) and size pore distribution (dv/dd, B) in aluminum oxide sample 4 Adsorption-desorption isotherms (Fig. 1A) and size pore distribution (Fig. 1B) are plotted for aluminum oxide sample 4 before (curve 1) and after (curve 2) the capillary forces were applied. It is seen that capillary forces have a significant effect on the behavior of the adsorption-desorption isotherms and size pore distribution and, respectively on the formation of the porous structure of the material. This conclusion is supported by the data summarized in Table 1, which indicate that after the capillary forces are applied the area of the material with meso- and micropores increases, and the mean size of pores decreases. Calculation part Due to the experimental difficulties encountered in the determination of small in value capillary forces between the microparticles of porous materials, we have performed computational simulations for assessing capillary force effects. 202

5 A variety of dependences and methods are known for determination of capillary forces between particles, which are generally treated as identical spherical particles, [1-6, 8-12]. Capillary interactions between the particles of different sizes, shapes and contact types, which are peculiar to real powders, are much more rarely investigated [13-16]. The above-mentioned problem is one of the reasons for the lack of a method for calculating capillary forces. This method should take into account the combined influence of various parameters of dispersion components and the properties of the liquid layer and the environment and can be used to investigate a wide class of dispersed materials. It also must have an adequate experimental confirmation. As a calculation cell for modeling capillary forces, we have considered the interaction of particles of different shapes (sphere, wedge, plane) and sizes with a liquid interlayer between them, which is illustrated by the example of interacting spherical particles (Figs 2 B, C). Fig. 2. Liquid interlayers between the particles of the dispersion component (A) and the model particles of the calculation cell (B, C). Due to the interaction of liquid molecules between themselves and dispersive particles, the surface of the liquid interlayer is bent. 203

6 Microscopic investigations have shown that the shape of a liquid interlayer between the particles is adequately described by the circumferences O 1 and O 2 with radii r 1 and r 2 (insert А-А in Fig. 2А) [17, 18]. We consider a liquid interlayer of different nature, which is formed from the liquid components of a dispersion composition and from the vapors of moisture and other liquids absorbed and capillary-condensed by the porous material from the environment. By analyzing the obtained results, we have developed equations and dependences, which are based on our experimental measurements for capillary forces performed on the model spherical large-sized particle-segments. A good coincidence between the experimental and calculated values of capillary forces allowed us to use the proposed dependences in further investigations. The value of the capillary force during the interaction of spherical particles of equal and different sizes depends on two components [8, 13, 17]. The action of the first component is determined by the surface tension of the liquid along the wetted perimeter at the interface (F c1). The action of the second component is due to the occurrence of either depression or pressure described by the Laplace equation (P) and is caused by the curvature of the interlayer surface (F c2). The dependence used to determine the value of capillary forces is written as 1 1 Fc Fc 1 Fc 2 R1 sin1 2sin 1 R1 sin1 r l, (1) where R 1 is the radius of the particle (small-sized); is the coefficient of the surface tension of the liquid; 1 is the half filling angle of the interlayer (determined using the parameters of small-sized particles); is the wetting angle between a liquid and particles; r and l are the radii of curvature of the liquid interlayer. The curvature radii r and l are determined as cos 1 R2 1 cos 2 cos cos R1 1 h r, (2)

7 l R1 sin1 r 1 sin 1, (3) where α 2 is the half filling angle of the interlayer determined using the parameters of small-sized particles. The dependence obtained for determining the value of capillary forces through the use of large-sized particle parameters (with R 2 and 2) is not given because equation (1) with small-sized particle parameters meets the requirements of our investigation. By approximating the meniscus of the liquid interlayer as a circular arc (Fig. 2A), we determined the interlayer volume. The equations and dependences proposed in our study were used for developing the computational model realized in the Lazarus programming environment. Results and discussion The dependencies of capillary forces on the relative volume of the liquid interlayer ( = V l/v p ratio of interlayer volume to particle volume) obtained for different surface tension coefficients, wetting angles and particles sizes are shown in Figs. 3, 4, 5. They were determined using the developed computational model. The size (diameter) of particles was D p1, [p2]=10 µm, the gap between particles - h=2 nm, and the environmental temperature affecting the surface tension coefficient σ - Т=20 С. It is seen that significant changes in the value of the capillary force F c and its component F c2 under capillary pressure in the interlayer are observed at high and mean volumes of the liquid interlayer, and the highest value of the force F c is achieved at mean and small volumes of the liquid interlayer. It has been found that a decrease in the surface tension coefficient at the interface from 72.8 mn/m (water, 20 С) to 22.8 mn/m (ethanol, 20 С) is accompanied by a decrease in the capillary force F c and its component F c2. Consideration of water, ethanol and their mixtures as the liquids forming an interlayer between the particles is based on their use in the synthesis of mesoporous aluminum oxide materials. Drying and thermal treatment of the precursor materials during the preparation of mesoporous composite is accompanied by the removal of water and ethanol and a change in the surface tension of the liquid mixture in the range [~ 72.8 ~ 22.8 mn/m. Correspondingly, the patterns reflecting F c 205

8 (F c2) vs. for water and alcohol mixtures lie between curves 1, 2 (3, 4 for F c2). Fig. 3. Dependence of the force F c and its component F c2 (3, 4) on the volume at variations in the coefficient σ (А) and the wetting angle (B). The coefficient σ (mн/m), B: 1-3, А: 1, ; 2, Angle (), А: 1-4 0; B: 1 0; 2 50; Analysis of the obtained dependencies has revealed that the worse wetting of the surface of particle observed when the wetting angle increases from 0 to 80 reduces significantly capillary forces (Fig. 3B). 206

9 Capillary forces decrease in this case more markedly compared to surface tension changes (Fig. 3A). The choice of the possible values of the wetting angle is based on the results of experimental measurements of the angles of wetting of compressed mesoporous silica samples with water and water-alcohol mixtures. The obtained angle varies from ~ 15 to ~ 70. At a wetting angle equal to or greater than 90, the material is characterized as hydrophobic, and the capillary attraction forces of the particles are replaced by the repulsive forces due to the change in the shape of the liquid interlayer and capillary pressure in it, as well as due to a significant reduction in the contact area between the interlayer and the particles. These changes are caused by a higher increase in the forces of interaction of liquid molecules with each other compared to the forces of their interaction with particles. Particle hydrophobicity is accompanied by their repulsion and structure and pore formation instability. Based on the above results, the wetting angle variation range required for studying its effect on the capillary forces acting between particles is assumed to be equal to [0 90]. It is also assumed that the particles in the calculation cell are characterized by the same nature and the same angle of their wetting with the liquid mixture. Also, we have investigated the influence of particle and liquid interlayer parameters on capillary pressure that specifies the component F c2 and the factors responsible for the changes in theses parameters. Simulations have revealed the existence of such volumes of the liquid interlayer within which capillary pressure equals zero (Fig. 4A). Pressure P < 1 shown in the diagrams is characterized by depression in the liquid interlayer and, correspondingly, by the attractive forces between particles. As one can see, the curves Р=0 form the area under the curve with capillary depression [Р < 1, F c=f(f c1, F c2)= + ], characterized by the combined action of both components of the capillary force and by its maximum value. 207

10 Fig. 4. Dependence of the liquid interlayer volume ж on the wetting angle at zero Laplace pressure (A) and on the distance h at F c=0 (B). A - change in h (% от D p): 1 5 nm (0.05); 2 10 nm (0.1); µm (1); 4 1 µm (10). D p1, [p2]=10 µm. B - change in the wetting angle (): 1 0, 2 50, 3 80, D p1, [p2]=5 µm. It is shown that the separation of particles and the increase of the gap between them (curves 1 4 in Fig. 4А) results in a substantial decrease of this area. For the area above the curve Р=0, the capillary force is determined by the component F c1. The worsening of wetting (increase in the angle ) is also accompanied by a decrease (less significant) of this area. Further studies have shown the existence of such volumes of the liquid interlayer within which the capillary force equals zero (Fig. 4B). The area above the curves F c=0 is characterized by the positive value of the capillary force and, correspondingly, correspondingly, by the presence 208

11 of attractive forces between the spherical particles, and the total force is determined by the component F c1. For the area under the curves F c=0, the influence of the component F c1 decreases, and the influence of the component F c2 increases. Under the action of capillary forces, the particles of dispersion components frequently form particle agglomerates, and the sizes of such agglomerates can be essentially larger than the sizes of particles. The influence of particle size (undamaged agglomerates formed by these particles) on the value of capillary forces. The obtained dependence is given in Fig. 5. The value of the coefficient is 72.8 mn/m, distance h - 2 nm, and the wetting angle θ=0. Fig. 5. Dependence of lg F c on the interlayer volume at varying dimensions of spherical particles D p1, [p2] (µm): 1 100; 2 10; 3 1. It is seen that the size of particles (agglomerates) substantially affects the value of capillary force. Application of the developed computational model made it possible to study the influence of particle size and shape and liquid interlayer volume and properties on the value of capillary forces between the particles of dispersion components of porous silicon dioxide materials. The behavior of the interacting particles and the liquid interlayer was investigated using the wetting angle parameters and the surface tension coefficient of liquids at the interface. Simulation results have shown a qualitative coincidence between the calculated and experimental coefficients reflecting the influence of capillary forces on the behavior of the porous structure of synthesized materials. 209

12 Conclusion We have investigated the behavior of the porous aluminum oxide material during its preparation. The obtained results have demonstrated that that the capillary forces have a significant effect on the formation of the porous structure of this material. The proposed model allowed us to study the influence of particle size and shape, liquid interlayer volume, surface tension and wetting angle on the value and behavior of capillary forces and its components. The model can also be used to explore the influence of capillary forces acting between the particles of dispersion components of porous materials and to evaluate the contribution of forces to the formation and evolution of the structure of these materials. Acknowledgements This work was financially supported by Russian Foundation for Basic Research (grants Nr _a). References 1. Haines W B. Studies on the physical properties of soils: Ⅱ. A note on the cohesion developed by capillary forces in an ideal soil. J. Agric Sci, 1925, 15, Fisher R.A. On the capillary forces in an ideal soil; correction of formulae given by W. B. Heines. J. Agric. Sci., 1926, 16, Haines W B. A Further contribution to the Theory of Capillary Phenomena in Soils. J. Agric Sci, 1927, 17, Pietsch W., Rumpf. H. Haftkraft, Kapillardruck, Flüssigkeitsvolumen und Grenz-winkel einer Flüssigkeitsbrücke zwischen zwei Kugeln. Chem. Ing. Tech., 1967, 15, Picknett R.G. Letters to the editors. J. of Colloid and Interface Sci, 1969, 29, (1), Adams M.J., Perchard V. The cohesive forces between particles with interstitial liquid. Symp. Particle Technology, Birmingham, Muguruma Y., Tanaka T., Kawatake S., Tsuji Y. Numerical simulation of particu-late flow with liquid bridge between particles (simulation of a centrifugal tumbling granulator). World Congress on Particle Technology 3, Brighton, UK, CD-ROM published,

13 8. Zimon A. D. Adhesion of Dust and Powder (Second Edition). Springer US. New York, Pietsch W.B. Tensile strength of granular materials. Nature. 1968, 217, Weigert T, Ripperger S., Liquid bridge adhesion force and shear stress at filter cake discharge. World Congress on Particle Technology 3, Brighton, UK, CD-ROM published, Xu B.Y., Yu A.B., Chew S.J., Zulli P. A Study of the Effect of Liquid - Induced Forces on Gas-Solid Flow by a Combined Continuum and Discrete Model. Second Internatiol Conference on CFD in the Minerals and Process CSIRO, Melburn, Australia, Muguruma Y., Tanaka T., Kawatake S., Tsuji Y. Numerical simulation of particulate flow with liquid bridge between particles (simulation of a centrifugal tumbling granulator). World Congress on Particle Technology 3, Brighton, UK, CD-ROM published, Gogelein C., Brinkmann M., Schroter M., Herminghaus S. Controlling the Formation of Capillary Bridges in Binary Liquid Mixtures. Langmuir. 2010, 26 (22), Smolej V., Pejovnik S. Some remarks on the driving force for liquidphase sintering. Zeitschrift fur Metallkunde , (9), Fairbrother R.J., Simons S.J.R. The rupture energy of liquid bridges between spheres; the effect of contact angle and separation distance on liquid bridge geometries. World Congress on Particle Technology 3. Brighton, UK, CD-ROM published, P.A. Kralchevsky and K. Nagayama. Particles at Fluid Interfaces and Membranes. Chapter 11. Capillary Bridges and Capillary- Bridge Forces. Amsterdam, 2001, Tselishchev Yu. G., Val'tsifer V. A. Influence of the Type of Contact between Particles Joined by a Liquid Bridge on the Capillary Cohesive Forces. Colloid Journal, 2003, 65, (3), Tselishchev Yu. G. Evaluation of the Capillary Pressure in a Liquid Interlayer between the Particles of a Dispersed Phase. Colloid Journal, 2007, 69, (4),