ABSTRACT

In the first section of this book, we have extensively discussed structures having coagulation contacts in which the particle-particle interactions are limited to simple “touching,” either directly or via the equilibrium gaps containing the dispersion medium (Figure 6�1a and b)�Low strength and mechanical reversibility are the main characteristics associated with such structures� Mechanical reversibility implies that such structures are thixotropic, that is, they can be spontaneously restored after undergoing mechanical degradation�

In this chapter, we will address structures with phase contacts in which the particles are bound via short-range cohesive forces acting over an area with dimensions exceeding those of an elementary cell� That is, we will focus on the particle cohesion resulting from at least 102 to 103 interatomic bonds� In this case, the contact surface is similar to the grain boundary in a polycrystalline solid, and the transition from the bulk volume of one particle to the bulk volume of another particle takes place continuously within the same phase (Figure 6�1c), which is where the term “phase contacts” originates from�In this chapter, we will heavily reference a number of early works in the area dealing with phase contacts [1-8]� The primary objects of interest here are silicates and cement (i�e�, mineral binders)� A number of essential publications devoted to these materials are covered in references [9-50]�

The minimum value of the strength of the phase contacts can be estimated as

p e

710 4

10» ( ) ~pe - N

where b is the lattice parameter e is the elementary charge

Accounting for specific types of chemical bonding allows one to come up with more precise estimates suitable for particular materials� Since a phase contact with an area sc ~ (102 – 103)b2 ~ 10−16 m2 can be considered defect-free, such a contact has the theoretical strength of an ideal solid (see Section 7�1)� Using this approach, we conclude that the minimal values p1 ~ Pidsc are on the order of ~10−8 N for fusible low-strength materials, ~10−7 N for ionic crystals and medium-strength metals, and 10−6 N or more for refractory high-strength materials� The strength of the phase contact increases with an increase in the area sc and can reach even higher values that are on the order of 10−4-10−3 N� In the limiting case of a continuous polycrystalline material (e�g�, a metal), we are dealing with the cohesive strength at the grain boundaries�

Estimates of the cohesive strength in structures with phase contacts allow one to conclude that, depending on the degree of dispersion (i�e�, on the number of contacts per unit area) and on the mean strength of an individual contact (i�e�, on the chemical nature of particles and all physical-chemical factors corresponding to the formation of a given structure), the values of Pc ~ χp1 cover a very broad range from about 104 to about 108 N/m2 or higher� In contrast to coagulation contacts, phase contacts undergo irreversible destruction� Since the contacts between the particles are the main carriers of the strength, an investigation of the mechanisms of their formation and rupture under various physical-chemical conditions provides one with the basis for developing effective methods for controlling and tuning the properties of disperse structures and of materials�

In a certain sense, the formation of phase contacts can be viewed as a result of partial coalescence between solid particles� Such coalescence occurs due to an increase in the area of contact between the particles and the transition from point-like contact to cohesive interaction over an area that is substantial relative to atomic dimensions� Such a transition may take place gradually, due to the diffusional transport of substance into the contact zone, as in the course of sintering (Figure 6�2), or due to the isothermal transfer of substance via the menisci of residual fluid� The latter can be frequently observed during the storage of fertilizers, which are known to form hard clumps�

Although gradual transition is possible, the experiments show that in most cases this process is abrupt� This is the case when the formation of phase contacts is associated with the need to overcome the energy barrier defined by the work of formation of a nucleus of a contact, that is, of a primary bridge connecting two particles�

In agreement with the concepts developed by Polak [10], the appearance of a contact nucleus may take place when the new crystalline phase forms in the contact zone between the newly formed crystals in the course of crystallization from metastable solutions� The bridging of crystals results in the formation of fine disperse polycrystalline products, such as those formed during hydration hardening of mineral binders and cements�

Similarly, phase contacts can also form when the new amorphous phase (organic and inorganic) is precipitated out of a metastable solution in sol-gel transitions, which are common in technology and in nature�

The formation and further growth of the primary hydration bridge can be the result of mutual particle deformation taking place at the point of contact due to mechanical stresses that exceed the yield stress of the material making up the particles� This is common in all friction and wear processes�

The processes leading to the formation of phase contacts can be studied experimentally by direct measurement of the cohesive forces between the particles� Such studies were described in studies carried out by Amelina [25-27] and Kontorovich [34-36] and will be discussed in detail further in this chapter� Throughout the book, we have described techniques and instrumentation for measuring small cohesive forces� These measurements also yield the energetic and geometric parameters of the process, such as the size of the critical nucleus of contact and its work of formation�

Typical experiments can be carried out in the following manner: Two crystals are brought into contact in a given medium and are kept under the conditions necessary to form a contact� Such conditions include contact time, compression, solution supersaturation, temperature, and the presence of surfactants� After the contact has been formed, the crystals are forced to separate from each other, and the contact strength, p1, is measured�

The results of such experiments typically fall on a rather broad distribution curve that reflects the formation of microcontacts between geometrically and energetically heterogeneous surfaces of the two particles� For this reason, the results are typically presented as differential distribution histograms, which typically contain two maxima: one corresponding to the “weak” (coagulation)

contacts and the other one corresponding to the “strong” (phase) contacts� The difference between these two types of distributions is characteristic of the barrier-like nature of this transition�

Histograms summarizing the results of cohesive force measurements between two silver chloride crystals are shown in Figure 6�3� The mechanical behavior of these crystals is similar to that of plastic metals� The abscissa shows the logarithm of the contact strength, while the ordinate shows the fraction of contacts, ρ, having a strength in the given interval p1� This figure shows that there are only two types of contacts between the crystals: those with strength p1 around or lower than 10−7 N (coagulation contacts) and those with strength p1 on the order of or higher than 10−6 N (phase contacts)� This barrier-like transition from “weak” coagulation contacts to substantially stronger phase contacts indicates the absence of contacts with an intermediate strength� Changing the conditions of this experiment does not result in a gradual increase of the strength of the coagulation contacts and their gradual transition into phase contacts, as would have been seen on the histogram by a simple

shift of the maximum� Instead, the increase in contact strength follows a barrier-like pattern: the histogram becomes bimodal with the maximum of the second mode being separated from the first one by several orders of magnitude of p1� This second maximum corresponds to the appearance of qualitatively new contacts, the strength of which and the fraction of which increase with an increase in the applied compressive force� At the same time, the data shown in Figure  6�3 illustrate the possibility of preventing cohesion between the surfaces in contact by using surfactants (octadecyl amine in the present case) (Figure 6�4)� This example illustrates the essence of using surfactants for controlling the processes of friction and wear as well as the processes of the mechanical treatment of solids, such as pressing or cutting� We will address the subject of surface damage and protection in detail in Chapter 7�

Similarly, one can also observe the barrier-like nature of the phase contacts in the course of the formation of particles of a new amorphous or crystalline phase in metastable solutions�

It is worth noting here that the case of sintering is principally different: this is a nonbarrier diffusion process, and the histograms of the contact strength have a single maximum that shifts with an increase in temperature as shown in Figure 6�2�

One can thus conclude that any given structure may contain both coagulation (residual) and phase (newly formed) contacts� Depending on the prevailing type of contacts, the structures can be subdivided into two large classes: coagulation structures and structures with phase contacts�

Disperse structures with phase contacts can form in a variety of physical-chemical processes, such as in the sintering of ceramic powders and in the course of pressing powders into pellets� Disperse structures with phase contacts that are formed in the process of generating a new phase in metastable solutions or melts are referred to as condensation structures� If the particles forming structures are crystalline, then the structures are referred to as condensation-crystallization structures� These structures can be viewed as “opposite” to the condensation structures composed of amorphous particles�

Structures with phase contacts represent the foundation for the formation of most materials� The formation of phase contacts can be the principal stage in the formation of continuous bodies or the final stage in the formation of porous bodies�

Indeed, the formation of cast metal is the result of nucleation in a melt, the growth of solid phase nuclei, and further bridging leading to the solid phase, which occupies the entire available volume� Similar processes taking place in the Earth’s crust lead to the formation of mineral deposits� One can also name here numerous materials that are based on sintered particles, such as brick, various types of a cement, porous minerals, and catalysts with crystalline phases� The critical role of condensation-crystallization in the formation of structures in the course of the hardening of mineral binders and cements and in the course of the formation of artificial rocks has been described in a number of studies by Polak et al� [9-11]� Although the structure formation in glasses and organic polymers is beyond the scope of this book, we will discuss one essential example of structure formation in systems with amorphous phases, namely, the formation of silica gels and aluminosilicate gels�

Structures with phase contacts also form in the course of the caking of powdered materials� This is especially pronounced if the materials are hygroscopic� The caking process is in fact a type of recrystallization accompanied by the formation and proliferation of phase contacts between individual particles under variable humidity� Caking is an issue in many processes that are associated with the handling of powders: feeding powdered chemicals, transporting and handling fertilizers, dosing drugs, transporting crude oil with precipitated paraffins, etc�

One can say that in some cases the formation of structures with phase contacts is favorable, as it carries with it an increase in strength, while in other cases it should be either minimized or prevented�

The entire spectrum of natural and technological processes involving the formation of structures with phase contacts is very broad� Some principal publications on this matter are listed in References 11-24� In addition to essential studies conducted by the author [1-8], other significant publications relevant to the subject matter discussed in this chapter are listed in References 25-37�

A reasonably simple and yet “classical” example illustrating the formation of a crystallization disperse structure is the hardening of gypsum plaster upon its reaction with water: CaSO4 × ½H2O + 1½H2O = CaSO4 × 2H2O�

Over a broad temperature range, gypsum dihydrate, CaSO4 × 2H2O, is a thermodynamically more stable substance than calcium sulfate hemihydrate, CaSO4 × ½H2O� At 20°C, the solubility of dihydrate is approximately 2 g/L, while that of hemihydrate is 6-8 g/L, depending on the type of calcium sulfate modification� Because of this, in sufficiently concentrated aqueous suspensions of CaSO4 × ½H2O, the liquid phase is saturated with respect to hemihydrate but supersaturated with respect to dihydrate� Supersaturation results in the formation of a new colloidal disperse phase under these conditions� This new phase consists of crystals of CaSO4 × 2H2O, which, together with the particles of initial mineral binder, that is, CaSO4 × ½H2O, form a primary coagulation structure�

A decrease in supersaturation due to the separation of a new phase is compensated by the dissolution of new portions of hemihydrate� This allows one to maintain a continuous supersaturated condition and hence ensures further growth of dihydrate crystals� The preservation of supersaturation as well as the time during which the supersaturated state is maintained depends on the ratio between the rates at which the dissolution of hemihydrate and crystallization of dihydrate take place� The existence of sufficiently high supersaturation allows for the formation of seed nuclei for crystallization contacts between crystals of gypsum dihydrate at their points of contact�

A rapid increase in the number of primary crystallization bridges and their further growth result in qualitative structural changes� The initially formed plastic, thixotropic, and reversible coagulation structures turn into strong, rigid, and brittle structures that undergo irreversible fracture upon crushing� The formation of the new phase contacts and the expansion of their area results in a further increase in the strength of the formed structure� As the hydration of the gypsum hemihydrate progresses further, the degree of solution supersaturation in the system decreases� Consequently, the probability of the formation of phase contacts becomes lower� For this reason, at later stages of the process, hydration does not result in the formation of new contacts any longer, but leads rather to the slower growth of crystals and to an increase in the strength of previously formed contacts� The formation of a compact solid eventually takes place� If the formed structure is destroyed at later stages, the crystals will not bridge together, resulting in the formation of a reversible coagulation structure�

A typical peculiarity associated with the formation of crystallization disperse structures is the development of internal stresses� These stresses are the result of pressure originated during the directional growth of crystals that are bound to each other via a spatial network� X-ray data reported in References 44-46 have shown that these stresses are on the order of 107 N/m or even higher� If the internal stresses that build up in the structure reach the level of the structure strength, further crystallization in the course of the hydration of the mineral binder results in the development of fractures at the weakest points� This action on the part of the internal stresses may be facilitated as the strength of structure declines in the process of hydration� In the case when the internal stresses are lower than the strength, structure failure resulting in stress relaxation may not necessarily occur� Instead, these stresses remain present inside the material in the form of the elastic deformation of crystals and hence in the form of excessive energy associated with it� Further use of a material with the internal stresses preserved may result in a decrease in strength and durability, especially upon exposure to a surface active medium� This will be discussed in detail in Chapter 7� One therefore needs to decrease the internal stresses in the course of the formation of a disperse structure in order to improve performance characteristics and the reliability of materials� It has been shown in the works of Rehbinder and Mihaylov [49] and Uriev and Potanin [50] that the internal stresses can be effectively lowered at early stages of hydration by using a proper combination of vibration and surfactant additives�

Internal stresses can also be generated in other industrial processes associated with the formation of a structure, that is, in the processes used to pelletize powders�

Crystallization disperse structures can also form in aqueous suspensions of other singlecomponent mineral binders� For instance, the hydration hardening of MgO results in the formation

of a fine disperse structure of Mg(OH)2� This process is used to make catalysts granules of a high strength� The same processes also take place in the hydration hardening of calcium aluminosilicate and of other frequently utilized cements�

Silicates and aluminosilicates, including hydrated and dehydrated silica and aluminosilicate gels, represent other examples of noncrystalline condensation structures� Silica gels form in the course of a sol-gel transition in which the new amorphous phase is formed due to the reaction of sodium silicate with an acid:

Na SiO HCl H O NaCl Si(OH)

(HO) Si OH OH Si (OH)3

2 2+ + ® +

- - + - - ® |

(HO) Si (OSi(OH) O Si OH H O3 2 3 21-- - - - + - |

) ( ) ( )n n

This polycondensation reaction may also involve the participation of aluminum salts� In this reaction, first, a sol of silicic acid or aluminosilicic acid is formed� This sol then undergoes coagulation and forms a gel, which serves as the primary coagulation structure� In the presence of supersaturation, the gel particles undergo bridging with the formation of phase contacts, and the condensation structure develops� This process is the basis for the synthesis of numerous catalysts and adsorbents�

In the past few decades, this so-called sol-gel technology has been widely used� The concept of this technology is the controlled hydrolysis of various metal and nonmetal alcoxides, such as of tetraethyl orthosilicate� In contrast to the polymerization reaction of sodium silicate, hydrolysis of alcoxides yields sols containing essentially monodispersed particles ranging in size from nanometers to micrometers� Monodispersed sols of alumina, zirconia, titania, and of course silica can be obtained by this method [51]� The coagulation and subsequent drying of these sols result in their conversion first into hydrogels and then into xerogels� Catalysts, adsorbents, and ceramics are produced by the thermal treatment of xerogels�

The formation of condensation structures is the main cause for the gelling of solutions of various natural and synthetic polymers� Gel formation may be accompanied by conformational changes of the polymer molecules, as is the case with gelatin and other biopolymers, or by various chemical interactions� Such is the acid-catalyzed synthesis of synthetic leather by the partial acetylation of polyvinyl alcohol with formaldehyde� Under supersaturation conditions, the fibers of the polyvinyl formal form in this system and develop into the network structure of synthetic leather�

The described individual examples of disperse structures and of various materials composed on the basis of these structures indicate the essential role that structured disperse systems play in various areas of our daily life� It is thus imperative to make use of the principles of colloid science and physical-chemical mechanics to find the means to fine-tune the properties (primarily mechanical ones) of various nanostructures� Depending on the particular application, one needs to identify ways to decrease or increase the strength of structures and thus to alter the properties of materials based on such structures�

The dependence P = χp1 of the strength, P, on the number of contacts, χ, and the contact strength, p1, provides a path forward that has led to several means to control the mechanical properties, namely, (1) changing the number of contacts by varying the particle size and the packing density and (2) altering the strength of individual contacts by influencing the conditions under which the contacts form and grow� These principal methods allow one to vary the strength over a very broad range from Pc ~ 104 N/m2 for coarse structures with coagulation contacts to Pc ~ 107-108 N/m2 for fine disperse structures with phase contacts� This indicates that the high strength of the material is primarily achieved by fine dispersion, which is the case in both porous and continuous materials� In the latter case, “fine dispersion” means the absence of large structural nonuniformities (defects)� Simple dispersion methods typically do not yield particles with r < 1 μm� Reducing the size further down is facilitated by the presence of surface active media� Finely dispersed systems with particles on the order of 10−8-10−9 m are formed by condensation methods involving the nucleation and growth of particles of the new phase�

Due to the current high interest in nanomaterials and nanotechnology, it is worthwhile to briefly address here the principles of the formation and the unique properties of ultrafine particles with sizes on the order of single nanometers or tens of nanometers [1,8,14,38-42]� The mechanical milling does not enable one to produce materials with particles that small� This limitation can, on the one hand, be explained by the growth in the specific surface area, which is related to the increase in the number of interparticle contacts that need to be broken, which consumes milling energy� On the other hand, as the particles become smaller, they approach a “defect-free state” and thus become stronger and more resistant to further breakdown� Finely dispersed colloidal particles that have sizes in the nanodomain are formed solely by condensation processes, that is, by the formation of a new phase in a homogeneous system under conditions of high supersaturation�

The governing Gibbs-Volmer principles of condensation leading to the formation of nanoparticles are based on a description of the nucleation process in the presence of a potential barrier�The latter can be overcome when the critical work of nucleus formation can be reached by fluctuations�The work required to form a spherical particle of the new phase, W(r), within the initial phase includes the work needed to create a new surface area, 4πr2σ, and the “work gain” of (4/3)πr3|Δμ|/Vm associated with the phase transition, that is,

W r r

r

V ( ) ( )= -4 4 32

p s p Dm/

where Vm is the molar volume of the new phase� This work is maximal when

d d

W r r r

V / = - =8

4 0

p s p Dm

This indicates that the critical size of the nucleus is rc = 2σVm/|Δμ|� Depending on the particular system, the value of |Δμ| is determined either by the pressure excess (in the case of vapor condensation), by supercooling (in the case of crystallization from a melt), or by the level of supersaturation achieved in the liquid phase� Since in the condensed phase Δμ ~ VmΔp and Δp is the Laplace capillary pressure, pσ, we conclude that the “peculiarity of a nanophase” is simply dictated by the high value of pσ(c) = |Δμ|/Vm = 2σVm / (rcVm) = 2σ/rc� The elevated chemical potential (i�e�, metastability) of the nanoparticles is manifested as a change in solubility, a change in the vapor pressure, or a change in other thermodynamic parameters� That is, the nanophase can be characterized by an elevated activity�

By all means, the most important and at the same time the oldest nanotechnology in the world is the hydration hardening of cements� Of special interest here is the fact that the nucleation taking place in the supersaturated phase controls both the formation of new phase particles and the formation of bridges between these particles�

Another nanotechnology that we have already mentioned, that is, the sol-gel transition taking place in the formation of fine porous aluminosilicates and of finely dispersed oxide powders, is also based on the nucleation concepts of Gibbs and Volmer�

In order to avoid misunderstanding, one needs to say here that the formation of the new phase particles can be facilitated by lowering the work of the process through the introduction of seed particles�

It is also worth mentioning the special role that fine colloidal sols with low concentrations of the disperse phase have played in the development of science� Such sols were utilized by the ancient Greeks to make colored pigments for mosaics�Michael Faraday used the famous red gold sols in his studies, while Svedberg was awarded the Nobel Prize for proving the existence of molecules by observing the motion of particles in such sols�

Supersaturation (metastability) in the mother liquor is the necessary condition for obtaining fine disperse structures in the processes of new phase formation by condensation� Since this excess in the chemical potential is in one way or another transferred into the newly formed phase, the particles

reveal properties that differ from those of a macroscopic phase, such as increased solubility, higher vapor pressure (Ostwald-Kelvin), and thermodynamic parameters� One can say that the “transfer” of chemical potential results in the elevated activity� Some interesting changes may take place in semiconductors, as evidenced by the change in the zone structure� At the same time, fine disperse structures may maintain their nonequilibrium nature in the form of residual internal stresses�

While the fundamental principles that were developed by Gibbs and Volmer, Kaishev, and Stransky are well known, there are a number of aspects that have not been fully reflected in the abundant literature on nanotechnology�

First, there is the formation and preservation of nanosize systems under conditions when kinetic and structural factors prevent the transition of the new phases into a macroscopic phase� This includes the processes of the hydration hardening of various mineral binders�

Second, there is the formation of nanosystems that are preserved in their “nanostate” due to thermodynamic reasons� This is possible because of the strong interatomic bonds between small polyvalent atoms� Examples are the C-C and Si-O-Si bonds, which give special properties to the natural and synthetic materials containing them� The unique features of C-C bonds are manifested in a macroscopic phase, that is, in a diamond, as well as in numerous products of nanotechnology, such as fullerenes, nanotubes, and porous carbon nanofibers� The structures with Si-O-Si bonds are not as unique and are rather abundant� These include colloidal silica and aluminosilicates, as well as crystalline aluminosilicates, that is, zeolites, and quartz and numerous silicate minerals� In these structures, the siloxane bonds play a determining role as the carriers of remarkable strength� Here, it is worth addressing the question of what do the processes of drilling for oil and gas and crude oil cracking have in common� The answer to this question is most remarkable� In drilling, one is interested in breaking siloxane bonds in the rock while preserving them in the diamond bit� Conversely, in the process of crude oil cracking, the breaking of C-C bonds takes place, and the problem that one needs to address is how to minimize the mechanical wear of a catalyst containing siloxane bonds� One therefore faces the need to optimize both processes, primarily by controlling the conditions, such as choosing the proper pH and surface active media� Specific studies along these lines are described further in this chapter�

Following Rehbinder, we will state here one more time that high strength in materials requires that they be composed of small tightly packed particles with the maximal number of strong phase contacts between them� However, in fine disperse systems, the process of achieving tight particle packing becomes complicated, since even relatively weak individual coagulation contacts, when combined, give rise to substantial resistance� This is often encountered in the molding of powders and pastes� The influence of coagulation contacts can be overcome at elevated pressures, but this approach introduces additional difficulties, namely, that high pressure leads to the formation of residual stresses that prevent the formation of phase contacts under optimal conditions and result in a decrease in the strength of materials� This means that, at the preparation stages and during molding itself, the high viscoplastic resistance of the disperse system needs to be overcome by the liquefaction of the system, that is, by lowering ηeff and τ* (see Chapter 3)� However, the simplest approach to increase liquefaction by an excess in the dispersion medium is completely unsuitable in many instances� For example, an excess of water content in cement paste results in poor resistance of the concrete to cold weather: it simply bursts once the water unbound to hydrate freezes� It is thus evident that liquefaction of a system needs to be carried out by selecting an optimum combination of mechanical and physical-chemical factors� In order to achieve the best possible particle packing density (yielding the maximum number of contacts in the structure) and at the same time avoiding the development and accumulation of internal stresses, vibration is often used� At the same time, in order to weaken interparticle cohesion (e�g�, in making dry and moist catalyst and ceramic masses), one would use various surfactants that weaken contacts in coagulation structures due to adsorption and prevent the formation of phase contacts�

In order to control the formation and development of structure in the processes of the hydration hardening of mineral binders, electrolytes are used in addition to surfactants� This allows one to

have directional control over supersaturation as well as change the conditions of crystallization and bridging in newly formed formations, so that control over hardening process can be maintained� In fabric and yarn manufacturing, surfactants are used to prevent strong cohesion between the fibers due to the formation of adsorption layers� Similar problems are encountered in papermaking, where there is a need for the fine control over the adhesion forces acting between the fibers�

The investigation of the physical-chemical means needed to control the structure and the mechanical (rheological) properties of disperse systems and materials by using an optimal combination of mechanical action and physical-chemical conditions at interfaces is thus the main subject of physical-chemical mechanics�

In the next section of this chapter, we will present the results of one essential study on the formation of a fine disperse phase in the course of sol-gel transitions in amorphous system conducted by Kontorovich et al� [34-36]� To a large extent, these works were inspired by the interest to the aluminosilicate systems� These systems serve as catalysts in crude oil cracking when they are promoted with transition metals and filled with zeolites� Elsewhere in this book, we will also address the issues associated with the strength of these catalysts in their granulated form, specifically the difficulties associated with introducing zeolite (poor mechanical strength) into an aluminosilicate matrix� One key feature of the essay that follows is that the size of the globular structures in the solgel transition was measured for the first time by small-angle x-ray scattering (SAXS) in an aqueous dispersion, and not after drying�

A number of works have dealt with studies on structure formation in aluminosilicate hydrogels obtained by coprecipitation� An early basic study carried out by Planck (see in References 1 and 34-36) compared the properties of silica gels and aluminosilicate gels synthesized under the same conditions and concluded that there was a substantial difference in their properties� The same change in the synthesis conditions within the defined interval of parameters (increase in pH, concentration of the hydrogel solid phase, duration of syneresis, etc�) resulted in the opposite trends in the change of the specific surface area of xerogels� In particular, the specific surface area, S1 (m2/g), of the aluminosilicate gels increased, while the specific surface area of the silica gels decreased�

Planck interpreted the increase in the specific surface area of aluminosilicate xerogels in syneresis as the evidence for a decrease in the size of the globules and suggested that the latter was caused by the dispersion of the globules due to the cleavage of the –Si-O-Al═ bonds formed in the process of sol formation�

The idea that the specific surface area of xerogels might be a characteristic of the particle size is rather common� This indeed was confirmed by adsorption and electron microscopy studies, which showed comparable particle sizes obtained by these two different methods� However, this agreement is not universal; there are cases when adsorption and microscopy studies yield different results� One such example is the treatment of silicic acid hydrogel with an acid at pH 1�9� Under these conditions, the adsorption experiments revealed a substantial decrease in the xerogel surface area, while the electron microscopy indicated a decrease in the particle size� Since the observed decrease in the surface area was accompanied by a significant decrease in porosity, the observed discrepancies were explained by the inaccessibility of the surface in the vicinity of particle-particle contact to the adsorbate molecules�

The apparent density (dv, g/cm3) of aluminosilicate gels is typically much higher than the apparent density of silicic acid gels� For gels obtained under comparable experimental conditions, the apparent density of aluminosilicate gels is nearly 1�5 times higher than the apparent density of silica gels� The apparent density of silica gels approaches that of aluminosilicate gels only when the former are treated with a very strong acid (pH = 0�6)� Under these conditions, the apparent density of silica gels was 1�23 g/cm3, which is close to the 1�39 g/cm3 reported for aluminosilicate gels [35]�

Since in this case where there was no correlation between the change of specific surface area and the particle size was observed with a silica gel of high apparent density, dv = 1�3 g/cm3 (porosity of 0�33 cm3/g), one may assume that there is no correlation in the region of high apparent densities� This suggests that the “anomalous” trend in the specific surface area of aluminosilicate gels may not be much related to the differences in the mechanisms by which globules form in the hydrogel, but is due to the inaccessibility of a large fraction of the internal surface of these xerogels to the adsorbate molecules� The latter, obviously, increases with an increase in the particle packing density� To verify this, the change in the size of globules in aluminosilicate gels was studied in hydrogels with varying depths of syneresis� The particle size, R, was assessed from the SAXS, which made it possible to determine the particle size directly without exposing the hydrogel to heat, which might lead to a change in the material morphology and particle size [52]� It is worth pointing out that the analysis of xerogels by SAXS is complicated by the inability to distinguish the size of particles from the size of pores, due to the identical diffraction from the particles and the pores� For this reason, the analysis of xerogels by SAXS is only possible when reference data on particle size obtained by other means are available� In the hydrogels with a very low volume concentration of the solid phase (Pv ~ 2�5% to 3�5%), significantly smaller than that in xerogels, there is no such issue because the size of the pores is six to seven times larger than the size of the particles� For this reason, the particle size of 7-30 Å determined in fine disperse aluminosilicate hydrogels must be related to the size of the particles and not the size of the pores (assuming the opposite would yield an unrealistic particle size of 1-4 Å)� A complete dehydration of the hydrogel yields a decrease in pore radius by about 25%, which corresponds to a decrease in the pore volume by a factor of 2�5, while the volume of the sample itself shrinks by a factor of 10�

In the experiments described, the aluminosilicate hydrogels had a pH of 8�0-8�3, Pv = 3�2%, and a weight ratio of Al2O3:SiO2 = 6� The hydrogel was prepared by mixing cold 0�6 N solution of aluminum sulfate acidified to pH ~ 0�7 using sulfuric acid with a 1�25 N solution of sodium silicate in a ratio of 2�8:1� The syneresis was conducted in the prepared mother liquor for 1, 48, and 96 h at 22°C and for 3, 12, and 27 h at 70°C�After the completion of the syneresis, the gel was thoroughly washed for 2 days at 22°C-25°C in order to remove sodium sulfate� The completeness of the removal was tested qualitatively with the addition of BaCl2 solution (lack of turbidity)�

A rectangular 1 mm thick specimen of hydrogel was used for the SAXS analysis�In order to prevent drying, the specimen was placed into a special cuvette made of a thin film transparent to x-rays� The wash solution from the final stage of the two-day wash cycle was used as a background to correct for scattering from the dispersion medium� The SAXS experiments were conducted in a 4-slit chamber with an ionization detector using 18-20 kV x-ray source� The experimental data were presented as differential distribution curves showing the inhomogeneity dimensions�

The results of the particle size analysis obtained from the SAXS are summarized in Table 6�1, which shows the sizes corresponding to the particle size distribution maxima, Rmax (Figure 6�5), and the two types of mean radii: those obtained from the distribution curves and those calculated using the Hosemann approach [52] Rm and Rm,H, respectively�

TABLE 6.1 Inhomogeneity Sizes Obtained at Various Syneresis Times

The data in Table 6�1 clearly show that the values of Rm, Rm,H, and Rmax do not exceed 30-35 Å� Apparently, these values are related to the size of the globules rather than to the size of the pores, and the change in the particle size only in the range from 7-17 Å to 25-35 Å due to changes in the syneresis conditions is indicative of the change in the size of the hydrogel globules� The interpretation of the microheteregeneities with sizes >40 Å is ambiguous, as these dimensions can be assigned to both particles and pores: in the studied gels (Pv = 3�2) with Rmax = 7 Å, one may anticipate to find a large number of pores with sizes R ~ 50 Å� As seen in Figure 6�5, the differential particle size distribution curves for different syneresis durations at room temperature are nearly identical, which indicates a very low rate of hydrogel ageing under these conditions (Table 6�1)� An increase of the syneresis temperature to 70°C resulted in a sharp increase in globule size: within 3 h at this temperature, the percentage of the smallest globules (7 Å < R < 15 Å) decreased almost twofold (from 50% to 24%), as compared to hydrogels that were aged at room temperature� The mean radius, Rm,H,increased approximately 1�4 times, while Rmax more than doubled� When the

syneresis duration was increased to 12 h at 70°C, the processes that result in the growth in the globules continued to take place: the percentage of the smallest globules (7 Å < R < 15 Å) decreased to 7%, and Rm,H and Rmax increased by a factor of 1�5� Further ageing of the gel resulted in slower growth in the globules-the particle size distribution curve obtained for gel aged at 70°C for 27 h is practically the same as the curve obtained after 12 h of ageing at the same temperature� These data are shown in Figure 6�5b�

The results of this study indicate that the radius of the globules in the course of the ageing of the aluminosilicate hydrogel increases as the hydrogel ages� This behavior is in fact the same as that previously observed for polysilicic acid hydrogel� These results confirm that there is no correlation between the trends in the change in the specific surface area and particle size in the corresponding hydrogels� This is especially well seen in the aluminosilicate hydrogels that underwent acid treatment at pH ~ 3� Ageing in acid resulted in a large decrease in the surface area, while the SAXS data indicated no change in the size of globules� These results indicate that one needs to be extremely careful when using adsorption data in estimating the particle size in dried hydrogels�

Here, we will address the mechanism of the formation of phase contacts in the process of the bridging of amorphous (SiO2) and crystalline (CaSO4 × 2H2O) particles in solutions supersaturated with respect to one or more of the constituents� We will also discuss the results of the x-ray analysis of the internal stresses developing in the hydration products of single-component mineral binders, such as CaSO4 × 0�5H2O, CaO, MgO� These studies allowed one to answer the principal question as to why the bridging takes place� The results discussed are of principal importance both for the understanding of the modern nucleation theory of nanophase and for solving practical problems associated with the improvement in the quality of modern construction materials and the manufacturing of catalysts and adsorbents�

In this section, we will present an overview of essential studies that focus on understanding the mechanisms of particle bridging in the course of the formation of solid structures (rocks) in crystalline and amorphous systems� In this discussion, we would like to emphasize the importance of and acknowledge the principal works by Kontorovich, Amelina, Shchukin, and their coauthors, collaborators, and graduate students [1,25-27,34-37]; we would like to specially acknowledge the contribution by Yusupov, Vaganov, and Lankin [26,27,36]�

The formation of concrete involves the bridging of particles in the course of the hydration hardening of cement and is in fact the oldest nanotechnology in the world: the concrete dome of the Pantheon in Rome has been around for more than 2000 years� This masterpiece of ancient nanotechnology reflects the level of technological perfection that can be achieved� At the same time the answer to the question as to why the hydration hardening yields a stone is a very difficult one� The search for an answer to this principal question has revealed the need to consider a particular combination of supersaturation and ageing duration, along with the mutual mechanical compression of the newly formed solid particles in the analysis of the thermodynamics and kinetics of these processes� While the mechanical compression stipulates particle bridging, it is also associated with the generation of residual stresses in the system� In the works by Rybakova et al� [44-46], the influences of the two opposing factors, the microstresses of the second kind and the dispersity, were separated� This was achieved by the analysis of the line broadening in the x-ray diffraction patterns of these substantially amorphized systems� It has turned out that in certain cases, the internal stresses achieved levels comparable to the material strength� The role of various physical-chemical factors and conditions in the development of these internal stresses and the influence of these factors on their magnitude were thoroughly investigated� This provides a means for controlling the development of the internal stresses and hence for fine-tuning the properties and stability of materials� These studies

have made an essential and critical contribution to the understanding and advancement of the technology of making strong and long-lasting construction materials, as well as of porous adsorbents and catalysts�

The processes of particle bridging and specifically the formation of strong contacts are responsible for the transition from a free-disperse system (i�e�, a sol) to a connected-disperse system, such as a solidifying paste with a particular mechanical strength� Consequently, one needs to achieve complete understanding of the reasons, conditions, and mechanisms of particle bridging (agglutination)� One needs to pay special attention to the origination and development of the internal stresses in the forming structure� We have already pointed out several times that there are two principal types of contacts: weak coagulation contacts with a strength of ~10−9-10−7 N and strong phase contacts with a strength of ~10−6 N and higher� The formation of phase contacts requires the displacement of the dispersion medium from the area exceeding the dimensions of the elementary cell� Phase contacts are mechanically irreversible, and the structures based on such contacts typically exhibit elastic-brittle and elastic-plastic behavior� Nearly all construction materials belong to the class of structures with phase contacts ranging from point like (contacts are small relative to the particle size, such as in catalysts and carriers) to continuous (in the case of a complete bridging of particles, such as in metals, alloys, melts, and various composites)� Many ceramic materials as well as materials obtained by means of various powder processing technologies and the structures obtained in the course of hydration hardening can be viewed as intermediate ones� The strength of the contacts between the particles in heterogeneous systems is the principal factor controlling the strength of the resulting structures and hence the durability and properties of the material� Nevertheless, coagulation contacts play an equally important role at various stages of the formation of materials, stages at which one needs to control the mobility of the system by controlling the adhesion forces�

Let us now discuss the transition from coagulation contacts to phase contacts, that is, from the touching of the particles to their bridging, using two characteristic examples� The first example is the formation of contacts between the crystals of gypsum (calcium sulfate dehydrate) in the supersaturated solution of calcium sulfate, and the second one is the formation of the contacts between the amorphous particles of polysilicic acid (i�e�, silica) in the supersaturated solution of silicic acid� The first case represents the process of bridging taking place in hydration hardening, while the second one corresponds to the formation of a silica xerogel due to particle bridging in the course of a sol-gel transition� These two basic examples are essential for a better understanding of the bridging processes taking place in more complex multicomponent systems�

A comparative study of the conditions under which particle bridging takes place in the individual contacts and the principal laws governing the development of the corresponding macrophase allows one to understand the dependence of these processes on various factors, such as the degree of supersaturation in the starting system, time, the crystallographic orientation of crystals with respect to each other, and the presence of various additives (electrolytes or surfactants)� These studies have also allowed one to emphasize the special role of mechanical factors, such as the mutual compression of particles� The example with gypsum indicates that bridging does not take place without compression� However, in the absence of external forces, the compression can only originate from the action of the internal stresses (crystallization pressure, phase transitions, etc�)� To crystallographers, these are known as stresses of the second kind, or microstresses� These stresses take active part in the processes of particle bridging and in the development of structure strength, but at the same time may manifest themselves as residual stresses that may be the cause of a significant lowering of the strength, especially in an active medium�

All of these processes indicate the need to examine the conditions of particle bridging as they relate to the origination of residual stresses in the products of hydration hardening� This approach is

essential for achieving a more complete understanding of the physical-chemical concepts of hydration hardening and for the optimization of various industrial processes�

The formation of contacts can be studied experimentally using the magnetoelectric galvanometerbased device described in detail earlier in this book (see Chapter 5)� Since there is no need to measure distance, the measuring scheme allows one to measure forces on the order of 10−8 N�

In a typical measurement, two gypsum crystals of size 5 × 5 × 0�5 mm, cleaved from a gypsum single crystal, were mounted in the measuring device-one on the manipulator and the second one attached to the galvanometer arm (Figures 1�28 and 4�15)� The crystals were then brought into contact with their edges normal to each other by varying the crystallographic planes forming these edges� The samples were placed in calcium sulfate solutions supersaturated with respect to gypsum� The supersaturated solutions were prepared by dissolving calcium sulfate hemihydrate, filtering the resulting solutions, and diluting them to the necessary concentration, which was maintained at a constant level (the solubility of hemihydrate and dihydrate in water is 6�2 and 2 g/L, respectively)� In the study, the following parameters were varied: supersaturation, α; crystal contact time, t; compression force f; and the crystallographic orientation of the gypsum crystal contact edges�

The bridging of gypsum crystals with fluorite, calcite, and quartz, as well as the bridging of these crystals with each other in supersaturated calcium sulfate solutions, was also studied� In some cases, the calcium sulfite solutions contained electrolytes and surfactants�

In the studies with silica, it was not possible to use individual particles because the silica globules forming silica sols are very small� For this reason, the bridging in this system was studied using two crossed glass threads coated with silica particles� First, silica sols of pH 7 and containing 0�6% SiO2 by mass were prepared by mixing a solution of sodium silicate with hydrochloric acid [6,31]� The threads were then immersed into these silica sols, which resulted in the deposition of single-silica particles (2-3 nm) and silica particle aggregates (tens and hundreds of nm) on the surface� While the surface of the particle coating was mainly covered with silanol groups, in the bulk of the deposited layer, these groups were converted into the siloxane groups formed by condensation:

- - + - ® - - - - +Si OH OH Si Si O Si H O2 |

The silica-coated threads were oriented perpendicular to each other and were placed into contact in freshly prepared silicic acid sols supersaturated with respect to amorphous silica� The degree of supersaturation, α, was determined as the ratio of the amount of silica dissolved in the dispersion medium of the silica sols to the solubility of silica at a given pH and temperature� The value of the supersaturation was varied by changing the concentration of sodium silicate from 0�06% to 0�012% by mass� The concentration of the dissolved silica decreased with time, and consequently the value of α decreased as well� The sols were used while the change in the value of α was less than 6%� Temperature, pH, α, t, and f were all varied within a broad range, while the temperature was maintained constant at 20-22°C�

The bridging of silica particles with the crystals of quartz, fluorite, periclase, bruscite, white asbestos, anthophyllite, and amorphous quartz (uncoated threads) was also studied� The specimens used in these studies were crystals with size 2 × 5 × 5 mm, which were mounted on the manipulator (Figure 1�28) and were cross-contacted with the silica-coated quartz thread� The area of contact was a plane with the dimensions 2 × 5 mm� The thread was positioned parallel to the short edge of the specimen�

6.2.1.1 Formation of Phase Contacts between Crystals of Gypsum The measurements of the cohesive forces carried out with the individual crystals yielded widely scattered data for contacts measured under the same conditions� This indicates the need to use statistical analysis and to employ suitable distribution functions� The data can be represented in the form of histograms showing the differential distribution function ρ = dn/(n0 d log p1) as a function of

the logarithm of the strength, p1, n as the current measurement number, and n0 as the total number of measurements� To generate each histogram, at least 100 measurements were carried out� The histograms showing the distribution of the strength of edge-to-edge contacts between two gypsum crystals are shown in Figure 6�6�

Results shown in Figure 6�6 indicate that, based on the strength, there are two types of contacts: “weak” coagulation contacts with p1 ~ 10−2 dyn and “strong” phase contacts with p1 ~ 10−1 dyn, corresponding to particle bridging� The “conversion” of weak contacts into strong ones involves a barrier-like process� In Figure 6�6, this is seen as the shift of the second (right) maximum in the histogram to the right from the position of the first maximum by several orders of magnitude� There are no contacts with intermediate strength between 10−2 and 10−1 dyn� This very sharp transition corresponds to bridging and provides one with the possibility of studying the mechanism of the bridging process� For this purpose, the dependence of the probability of bridging, Wb, on various parameters has been studied� The probability of bridging is defined as the ratio of the number of “strong” contacts, wt, to the total number of contacts, w0,that is, Wb = wt/w0. As seen in Table 6�2, the bridging probability increases with an increasing degree of supersaturation and an increasing time of contact�

The dependence of the bridging probability on the contact time and the degree of supersaturation allows one to relate the initial step of bridging to the fluctuation process of the formation of the primary contact nucleus� This process is critical for a given supersaturation� Mathematical analysis of the data in Table 6�2 reveals the exponential dependence of the probability of bridging, Wb, on the time, t:

w

w W Itt b

0 1= = - exp( ) (6�1)

where I is the reciprocal characteristic time, sufficient to cause bridging in 63% of the cases out of the total number of experiments, w0. Consequently, I may be viewed as the “rate of bridging�” In accordance with the fluctuation theory of nucleation [2,6,8-10],

I I A

T = -æ

è ç

ö ø ÷0 exp

k (6�2)

where I0 is a prefactor with the units of reciprocal time, s−1

Ac is the work of formation of the critical nucleus of contact

The magnitude of Ac depends on the degree of supersaturation in the solution, α, and on the value of the specific surface energy, σ, of the interfaces that either form or disappear during the process of the contact nucleus generation� This dependence may be expressed quantitatively, provided that the model describing the geometry of the forming nucleus is specified� For example, one may use a model similar to Polak’s model describing “quasi 2D” nuclei [10], but with one principal difference: the height of the nucleus, h, is a finite value with distinctive upper and lower limits (Figure 6�7a)�

The contact nucleus is assumed to have the shape of a rectangular prism with a square base of dimension a × a formed in a gap of width h� If the bridging crystals have random orientation, we assume that the contact nucleus is cooriented with the crystal lattice of only one of the crystals in contact, as shown in Figure 6�7b�Figure 6�7c corresponds to the case when the contact nucleus is formed between crystals that have a chemical composition different from that of the nucleus�

The energy required to form a nucleus with the volume a2h consists of two portions-the energy of a phase transition, (–a2h kT/V1), where V1 is the molecular volume, and the energy released due to the disappearance of two crystal/solution interfaces (–2a2σ3)� At the same time, free energy equal to 4ahσ1 is spent in the formation of the lateral surface of the contact nucleus, and the energy a2σ2 is spent in the formation of a nucleus-crystal boundary similar to the grain boundary in a polycrystalline material� The terms σ1, σ2, and σ3 are the specific surface free energies of the boundaries between the nucleus and the solution, the nucleus and the crystal, and the crystal and the solution, respectively� The size of the contact critical nucleus is obtained from the expression of the extremum of the free energy:

a

h h T Vc

= +

s a s[( ) ln ]k / * (6�3)

where σ* = 2σ3 − σ2, and, respectively,

A h

h T Vc k =

s a s[( ) ln ]/ * (6�4)

TABLE 6.2 Probabilities of Bridging, Wb, for Gypsum Crystals and Amorphous Silica Particles as a Function of the Contact Time, t, and the Degree of Supersaturation, α

Comparison of the expressions for the work of formation of various nuclei formed in crystallization processes indicates that the contact nucleus is substantially different from both a 2D and 3D nuclei� The work of formation of a contact nucleus in a saturated solution (α = 1) has a finite value� Indeed, the works of formation of a 2D nucleus, A2, and the work of formation of a 3D nucleus, A3, depend on the degree of supersaturation as A2 ~ 1/(ln α) and A3 ~ 1/(ln2 α) [15]� For the contact nucleus, Ac = b/(ln α + c), where b and c are constants independent of the degree of supersaturation: b = 4hs12V1 (kT)2; c = σ*V1/hkT. Consequently, for the case of α = 1, one obtains Ac = b/c. Furthermore, one may expect that there exists critical supersaturation that depends on the sign of σ* (αc > 1 when σ* < 0 and αc ~ 1 when σ3 ~ σ2)� This conclusion is indeed supported by the experimental results indicating that phase contacts also appear in the saturated solution, albeit with a very low probability, not exceeding 6% at t = 1000 s�

The experimental data provide a means for evaluating Ac and establishing the dependence of Ac on α� First, let us rewrite Equation 6�2 as follows:

I I b

c = -

+ é

ë ê

ù

û ú0 exp (ln )a (6�5)

By substituting the experimental values of Wb into Equation 6�1, we obtain the values of I corresponding to various degrees of supersaturation� The values of I may be used to estimate the values of b, c, and I0� The latter can be accomplished by solving a system of equations similar to Equation 6�5 graphically� These results are shown in Table 6�3, which also contains the values for the work of formation of 2D (A2) gypsum nuclei, calculated using Polak’s expression A2 ~ 9 kT/ln α� The data in Table 6�3 indicate that the Ac values are consistent with the predictions of the fluctuation theory of nucleation and that these values are consistently lower than the corresponding A2 values�

Our model implies that the gap has a constant width, h. In order to assess the value of this width rigorously, one would need to analyze the thermodynamic factors, such as the concentration, and the kinetic factors, such as the rate of diffusion in the gap� One can, however, get an estimate of h on the basis of the available experimental data� For a crude estimation, we can neglect particular values of σ2, just assuming that σ1 = σ3 = σ >> σ2� From the expressions for b and c, and V1 = 1�2 × 10−22 cm3, we find σ ~ 20 erg/cm2 for gypsum dehydrate at room temperature� Substitution into the equation for b yields h ~ 1 nm (10 Å)� This value of h may be viewed as the mean width of the gap between the crystals at the point where the contact bridge is most likely to form� Near the contact zone, the surfaces of the crystals may not necessarily be parallel to each other� The values of σ ≈ σ1 at the nucleus/solution interface are in reasonable agreement with the experimental data reported for the nucleation in solutions, particularly for the nuclei of gypsum [16,54]�

The value of the size of the critical nucleus, ac, may be found using Equation 6�3� If h ≈ 1 nm, ac appears to be within the range of values between 0�6 and 0�9 for all achievable supersaturations, α = 1-3� This estimate for ac appears to be reasonable, which supports the hypothesis that the formation of crystallization contacts in the process of the bridging of crystals has a fluctuation nature� It also confirms that the dependence of Ac on α is described by Ac ~ b/(ln α + c).