Technology of Dispersed Systems and Materials

Prikhod’ko XIII 1 Challenges of Technology of Dispersed Composite Materials 1 References 7 2 Structure Formation in Dispersed Systems and Materials 11 2.1 Types of Contacts between Parti

Naum B Uriev

Technology of Dispersed Systems and Materials

Prof Naum B Uriev

Leningradskij Pr., d.35, kv.54

125284 Moscow

Russia

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Preface IX

Foreword by A.Yu Tsivadze XI

Foreword by V.M Prikhod’ko XIII

1 Challenges of Technology of Dispersed Composite Materials 1

References 7

2 Structure Formation in Dispersed Systems and Materials 11

2.1 Types of Contacts between Particles in Dispersed Systems and

Materials 11

2.2 Criteria of Formation of Dispersed Structures 14

2.2.1 Characteristic Critical Particle Size 14

2.2.2 Concentration Factor and Strength of Coagulation Structures 18

2.2.3 Time Factor of Strength of Contacts and Dispersed

Structures 22

References 28

3 Dynamics of Dispersed Systems in Processes of Formation of

Composite Materials 31

3.2 Dynamics of Contact Interactions in Dispersed Systems 36

3.2.1 Nonequilibrium as the Most Important Feature of Dynamics of

Contact Interactions 36

3.2.2 Dynamics of Contact Interactions in Two-Phase Dispersions

Containing a Solid Phase and Liquid Dispersion Phase (S–L

3.2.2.1 Consideration of the Electrostatic Component of Disjoining Pressure

and Slipping of the Dispersion Medium 37

3.2.2.2 Consideration of Particle Shape Factor 39

3.2.2.3 Role of Elastic Properties of Particles and Structural–Mechanical

Barrier Formed by Adsorption Surfactant Layer 41

3.2.3 Elements of Dynamics of Contact Interactions in Highly Dispersed

3.2.4 Dynamics of Contact Interactions in Three-Phase Systems 45

References 48

4 Rheology, Vibrorheology, and Superfluidity of Structured Dispersed

Systems 51

4.1.1 Fundamentals of Rheology and Vibrorheology of Two-Phase S–L

Systems: Pastes and Suspensions 52

4.1.2 Main Methods and Devices for Measurement of Rheological

Properties of S–L Systems 53

4.1.4 Full Rheological Flow Curve of Dispersed Systems 60

4.1.5 Rheology and Vibrorheology of Structured Mineral Suspensions 63

4.1.6 Surfactants in Dynamic Processes 71

4.1.7 Vibrorheology and Structure Formation in Bitumen–Mineral

Compositions 77

4.1.9 Flow and Spreading of Two-Phase S–L Systems over Solid

5.1 Kinetics Structure Formation Process in Three-Phase Dispersed

Systems under Vibration in the Course of Mixing 109

in Compaction Processes 130

References 136

6 Application of Methods of Physicochemical Dynamics in the

Technology of Dispersed Systems and Materials 139

6.2.1 Pipeline Hydrotransport of High-Concentration Suspensions 141

6.2.1.1 Wasteless Technology of Ore Mining with Filling Excavation Cavities

by a Hardening Mixture of Highly Dispersed Dead Rock, Cement,Water, and Surfactant Additives 141

6.2.1.2 Technology of Production and Hydrotransport of

High-Concentration Coal-Water Slurries 141

6.2.1.3 Technology of Production of Multicomponent Highly Dispersed

Aggregation- and Sedimentation-Resistant Dispersions 145

6.2.1.4 Prevention of Consolidation of Hygroscopic Powdered

Materials 147

6.3.1 Dispersed Hydration Hardening Materials 149

6.3.2 Abrasive Materials as an Example of High-Filled Highly Dispersed

6.3.3 New Type of Composition Material for Road Construction: Asphalt

Concrete with Nanodispersed and Polymer Components 155

6.3.4 Effect of Exposure to Vibration of Crystallization Structure, Filled

Polymer Composition, and Fibrous Materials 157

The monograph summarizes the long-term studies of the author in a new field ofphysical chemistry of dispersed systems and surface phenomena: physicochemicaldynamics of dispersed systems and materials The author studied this new trend

in the Laboratory of Highly Concentration Dispersed Systems founded in 1985 atthe Institute of Physical Chemistry of the Academy of Sciences of the USSR

A distinctive feature of the studies of the author and his laboratory presented inthe book is that fundamental projects have been for many years implemented inmany applied fields of engineering and technology Moreover, a whole number offundamental studies ensued and was induced by engineering challenges regardingvarious dispersed systems and materials

The initial stage of studies by the author was related to his long-term work inthe Department of Dispersed Systems headed by academician P.A Rehbinder ofthe Institute of Physical Chemistry of Academy of Sciences of the USSR

The breadth of his scientific interests and the diversity of implementation ofhis results in various fields, including applied projects, served as a good examplefor the author in his research activity At the same time, the author’s long experi-ence of delivering lectures at the Moscow Institute of Road Traffic (State TechnicalUniversity) also promoted the application of fundamental developments in manyfields of engineering and technology

In the opinion of the author, the present, often significant, gap between theresults of fundamental studies and their practical implementation in the tech-nology of dispersed systems and materials is the major obstacle in the way oftransition to a new, qualitatively higher level of solving technological problems

in this field

It is for this purpose that the goal set in this book was to justify the necessityand show the fundamental possibility of eliminating this gap and also formulatingthe ways and methods of solving this problem using the example of technology ofvarious dispersed systems and materials

This book is meant for senior students, Masters students, Ph.D students,and faculty members in higher educational institutions, researchers of researchinstitutes specializing in the field of fundamentals of technology of dispersedsystems, dispersed composite materials, and methods of control of theirstructural–rheological properties in the procedures of their synthesis and

processing It includes lecture notes from the course of “physical chemistry inroad materials science” that the author has been delivering for many years at theMoscow Institute of Road Traffic (State Technical University).

The author’s research was financially supported by the Russian Foundation forBasic Research (project no 12-03-00473)

The author is grateful to his colleagues and his family for their support Specialthanks for support to Flow-iD GmbH (www.flow-id.ch) and especially to Dr BorisOuriev for his editorial work

2016

Foreword by A.Yu Tsivadze

N.B Uriev’s book is the first in the new field of physicochemical dynamics ofdispersed systems and materials developed by the author in the A.N FrumkinInstitute of Physical Chemistry and Electrochemistry of the Russian Academy ofSciences

A significant feature of this new direction in physical chemistry of dispersedsystems and surface phenomena is that the presented results of long-term fun-damental studies of the author are closely related to the solution of problems

of the modern chemical technology of dispersed systems and materials in manyfields

The fundamental regularities of dynamics of contact interactions betweenparticles of dispersed phases established by the author experimentally andtheoretically, a new concept in the field of rheology and vibrorheology ofdispersed systems, including nanodispersed ones, the effect of superfluid-ity of dispersed systems he discovered and development of methods for itsachievement, were implemented in more than 15 fields of engineering andtechnology

This allowed, in many cases, changing fundamentally the conventional theories

in these fields and passing to a qualitatively new level of engineering solutions.These solutions included development of new efficient materials based onmineral binders well introduced into industry and construction, materials based

on organic binders with nanodispersed and polymer components; technology

of pipeline hydrotransport of high-concentration suspensions, techniques ofintensification and optimization of a number of chemical-engineering-fluidizedprocesses, high-velocity processes of mixing multicomponent dispersed systems,microencapsulation, and a whole number of other fields

An unquestionable advantage of these solutions consists in the fact that the damental tasks and problems appearing in the course of their implementationhave been solved and are being successfully solved by N.B Uriev and his teammembers in the Laboratory of Highly Concentration Dispersed Systems in theA.N Frumkin Institute of Physical Chemistry and Electrochemistry of the RussianAcademy of Sciences

fun-The results of these works by the author were given the Award of the Council ofMinisters of the USSR, the Rehbinder Award of the Russian Academy of Sciences,

Vinogradov’s Award, International Award of MAIK Nauka/Interperiodica, and anumber of others.

President of D.I Mendeleev Russian Chemical Society Director of A.N Frumkin Institute of Physical Chemistry and Electrochemistry

Russian Academy of Sciences Academician of Russian Academy of Sciences

A.Yu Tsivadze Russian Academy of Sciences A.N Frumkin Institute of Physical Chemistry and Electrochemistry RAS (IPCE RAS)

Foreword by V.M Prikhod’ko

An academician of the Russian Academy of Natural Sciences, Professor, Doctor

of Chemical Sciences N.B Uriev has for years been successfully teaching in theMoscow Institute of Road Traffic (State Technical University) the new course hehas developed: “Physical Chemistry in Road Materials Science.” An unquestion-able advantage of this course, the same as that of the book offered to the reader, isthat it considers for the first time the most important problems of the technology

of dispersed composite materials as regards the modern fundamental ments in the field of physical and colloid chemistry and the new domain of physicalchemistry of dispersed systems and surface phenomena he has developed: physic-ochemical dynamics of dispersed systems and materials

achieve-This new field of science was the result of the generalization of a complex ofexperimental and theoretical studies in various fields of materials science carriedout by the author It is characteristic of the book of N.B Uriev that these results led

to the development of new types of high-performance materials: asphalt concretewith nanodispersed and polymer components, sand concrete, colloid polymer-cement slurries, and other materials

These materials are characterized by enhanced structural–mechanical ties and long service time

proper-At the same time, the book of N.B Uriev considers new methods of tion and intensification of technological processes occurring under conditions ofimplementation of the principle of maximum fluidity of high-concentration andhighly dispersed systems justified using physical chemistry

optimiza-I believe that the book of N.B Uriev will be very useful for senior students, ters students, Ph.D students, faculty members in higher educational institutions,and researchers in the field of fundamentals of modern materials science

Mas-V.M Prikhod’ko Rector of Moscow Institute of Road Traffic (State Technical University)

Corresponding Member of the Russian Academy of Sciences

Challenges of Technology of Dispersed Composite Materials

This chapter considers the significant features and obstacles hindering thesynthesis of one of the most widespread and widely applied among world-wide dispersed materials: cement and asphaltic concretes with a high level ofstructural–mechanical properties – as a demonstrative example illustrating thenecessity of implementation of the approach substantiated in the Preface and

in the introduction toward solution of problems of technology of dispersedsystems and materials on the basis of physical chemistry of dispersed systemsand physicochemical dynamics

The further chapters also pay a great deal of attention to materials based onmineral binders and bitumens, as these materials are typical representatives ofvarious highly filled solid phases of multicomponent dispersed composites

By now, significant progress has been achieved in the technology of obtainingvarious dispersed composite materials including materials used in construction,for example, in the building of roads, bridges, and airdromes

The increased requirements for these materials and the constructions madeusing them led to an increase in freight traffic density; and, accordingly, values ofstatic, dynamic, temperature, and chemical exposure of constructions and facili-ties, in their turn, impose increased demands toward strength, deformation prop-erties of dispersed composites, and their service life

At the same time, significant importance has been attached to the increasedrequirements for technical and economic indices of materials in the course ofoperation of constructions using them

Progress within the conventional approach to the technology of obtainingvarious dispersed materials, and primarily concretes, based on mineral andorganic binders achieved in the recent years is related chiefly to application ofcements with improved characteristics, new types of plastifiers, and modifyingagents However, transition to a qualitatively new, higher level in compositematerials science under the conditions of such a conventional, and, as pointedout above, to a certain degree empirical, approach is limited by the possibilities

of this conventional technology

What are these limitations and what are the ways of overcoming them? Let usgive several examples to answer these important questions

Technology of Dispersed Systems and Materials: Physicochemical Dynamics of Structure Formation and Rheology,

First Edition Naum B Uriev.

A vivid example illustrating these limitations is the technology of obtainingcement concretes implemented at present In particular, the design of their com-positions according to the existing standards is carried out taking into account theoptions of the available equipment as regards the mixing, transport, casting, for-mation, and compaction of concrete mixtures These parameters determine theplaceability of mixtures as related to these, that is, their rheological properties(viscosity and fluidity) and, accordingly, water–cement ratio and water content.This limitation results in a significant (in some cases, by several times) increase

in the water content of concrete mixtures (up to W/Cem = 0.4–0.5) as compared

to that required for full hydration of cement (W/Cem ≈ 0.2) [1, 2].

At the same time, cement hydration approaching 100% during the standard

28 days of normal concrete hardening is possible only in the cases when the size

of cement particles does not exceed approximately 15 μm [1, 2] The averagegrain size in commercial cements is considerably higher than the stated value

(d≥ 20–25 μm and more) [2] Therefore, the hydration degree of standardPortland cements by the concrete age of 28 days usually does not exceed 50–60%and can reach 80% only in the case of fine quick-hardening cements Herewith,

as the time period since preparation of concrete mixes and start of interactionbetween cement and water until concrete placing and compaction is usually notmore than 1–3 h, the hydration degree of cement during this period does notexceed several percent

One can assume on the basis of the effect of the surface of solid phases on theproperties of thin water layers [3, 4] that the thickness of these layers with changedproperties does not exceed the size of 2–3 molecules of H2O, that is, does notexceed 10 Å (1 nm) Thicker layers of 3–5 water molecules and more correspond

to bulk water by their properties (viscosity, freezing point, etc.)

The amount of water covering grains of cement, sand, and chippings and acterized by its bulk properties does not exceed 1% of the given water content,that is, it is admittedly below the maximum amount required for full hydration.This means that mobility and placeability of concrete mixtures, especially during

char-the first hours after concrete preparation, even at W/Cem ≈ 0.2, would apparently

be necessarily achieved

However, in reality, the minimum W/Cem ratio in concrete mixtures is

usu-ally at least 0.3–0.35 even when plastifier additives are applied And this meansthat excess water content determined by the requirements of placeability causes asignificant increase in residual concrete porosity, decrease in its water imperme-ability and freezing resistance, and increase in shrinkage and creep

Besides, it is necessary to increase cement consumption as a result of increasedwater content to provide the given strength of concrete At the same time,the consequence of increased water content of mixtures predetermined by thenecessity of providing the given mobility (placeability) is the further segregation

of excess water, especially in the course of their transportation to the site of crete placement and also during the first hours after placement and compaction(Figure 1.1a)

con-(a) (b)

1 3 2 3

Figure 1.1 (a) Scheme characterizing water

segregation in concrete mixtures: V0is the

initial volume of the concrete mixture, V1is

the volume of water segregated under static

conditions, V2is the volume of water

segre-gated in the course of transportation to the

site of placement, V tis the final volume of

the concrete mixture after placement and compaction (b) Scheme of formation of a water “lens” under coarse filler grains as a result of sedimentation: (1) grains of chip- pings or gravel, (2) cement solution, and (3) water “lens” under filler grains.

It is this circumstance, particularly due to sedimentation of the binder andwater segregation under coarse grains (Figure 1.1b) that, to a great extent,explains reduced frost resistance and water impermeability of concretes

However, an attempt to pass to harsh mixes with lower water content and bility without allowing for the achievement of the maximum uniformity of mix-tures under mixing and formation and compaction to the required density results

casta-in the fact that the hardness of concrete calculated accordcasta-ing to the conventionaldependencies, for example, according to Equation 1.1, cannot be implemented

when the critical value of given (Cem/W ) is exceeded.

As seen in Figure 1.2, a drastic decrease in strength is observed above this value,though it should grow according to Equation 1.1 [5]:

Rconcr=ARcem(Cem∕W − C) (1.1)

where Rconcris the strength of concrete at the age of 28 days of normal-humidity

storage; Rcem is the activity of cement in mPa; A is a parameter accounting for the shape of filler particles (chippings, gravel) and hardness of mixtures; C is an

empirical correction of ≈0.5

The following questions arise as related to the above material:

1) Why is it necessary, under actual conditions of concrete technology, toincrease the water content of concrete mixtures considerably to reach thespecified fluidity to the detriment of the properties of concrete and itstechnical–economic indicators?

2) What is the mechanism of achieving the required plasticity (placeability)and, ultimately, fluidity of concrete mixtures from the perspective of physicalchemistry that results in such a considerable increase in the required amount

of water?

This problem becomes even more complicated in the case of finely groundquick-setting cements, as the amount of water required for concrete mixturesbased on these cements becomes even greater

Figure 1.2 Dependence of strength of

con-crete on the cement/water ratio Curves 1

and 2 correspond to concretes made on

usual (2) and quick-setting, highly

dis-persed (1) cements (S is the specific surface

area of cements) Curve 3 is the

depen-dence of Rconcreteon Cem/W according to Equation 1.1 Arrows point to the Cem/W

limitation relation to loss of placeability of concrete mixtures.

And, finally, the most significant issue is

3) What are the ways of resolving the contradiction between the necessity

of decreasing water content in the mixtures, that is, increasing Cem/W

and, moreover, advisability of application of finely ground (includingquick-setting) and fully hydratable cements, on the one hand, and, in thisconnection, sharply rising viscosity, problems related to mixing, placing, andcompaction of mixtures and loss of their placeability due to this cause?Similar issues and problems arise in the technology of synthesis of otherdispersed materials: of cement according to the wet method, of silicate materials,asbestos cement, concreting paper, and so on The excessive water content inmany of the above examples is due to the necessity of carrying out the processesrelated to fluidity (e.g., pipeline transport), deformation (particularly, in the mix-ing of mixture components), formation, and compaction This excessive water

is removed in many cases (particularly, by drying or vacuum treatment) in thefollowing technological procedures And this, in its turn, results in considerableenergy losses and complication of the technological procedure But if excessivewater remains (in case of cement concretes), it causes not only formation ofadditional porosity but also layering (Figure 1.1a) and formation of water lensesunder coarse filler grains (Figure 1.1b), which is the main cause of decreasedfreezing resistance, increased water permeability, shrinkage, and creep

A lot of such examples can be provided Whatever their diversity for tation of technological procedures in the initial stages, that is, before the start ofphase and chemical transitions accompanied by the curing of materials, the con-ventional technology solves a single main problem: redistribution of components

implemen-in the course of the miximplemen-ing, further formation, and compaction of mixtures [5],that is, occurrence of the required values of viscosity, fluidity, plasticity, and abil-ity to change the mixture volume and shape under exposure to external forces To

solve this problem, addition of an excess of the dispersion medium (water for many

of the above materials) is in fact an induced, but the simplest, most widespreadmethod of reducing mixture viscosity and increasing their plasticity, though oftenaccompanied by addition of plastifiers in the conventional technology

Let us consider another example characteristic for composites based on anorganic binder, primarily, bitumen concrete

It is commonly known that specific conditions of achieving the requiredplasticity–fluidity of bitumen–concrete mixtures (and mixtures of any com-posites based on a thermofluid binder) are determined by viscosity of bitumen,temperature parameters of mixture preparation and placing, and also bulkcontent, dispersion degree, and particle shape of inorganic components

In all these cases, the so-called thermorheological effect, characterized bysynergism of the temperature factor and required deformation rate during thepreparation, transportation, placement, compaction, and formation of variousthermoplastic mixtures, is observed

As applied to materials based on a bitumen binder (bitumen concretes, nous mastics, etc.), alongside with this effect, the same as in the case of the abovesolutions for cement concrete, the problem of a decrease in viscosity is generallysolved by addition of plasticizing agents and fluidifiers The latter are removed byevaporation when the above materials are used after their placement

bitumi-At the same time, of considerable importance as applied to bitumen concrete

is the thickness of the bituminous film on the surface of inorganic solid-phaseparticles [6, 7], presence and shape of additives of plasticizing agents, and possi-ble polymer and fluidifier additives Also, one cannot but take into account thecharacter of interaction between the organic binder and filler surface, adhesion

to it, that is, ultimately, properties of contacts between particles at the interphase

boundaryof binder–filler (aggregate)

An important element of the process of contact formation at the interphaseboundary of the binder–filler is the wetting of the surface of inorganic componentparticles and spreading of the liquid medium over this surface [8] This process

is determined by the physicochemical properties of solid surfaces (this refers tophysicochemical surface uniformity or nonuniformity), their lyophilic–lyophobicmosaic structure [9].1)

The spreading process of non-Newtonian2)viscous liquids, predominantly ous types of binders (cement pastes, asphalt binders) and paint composites along-side the spreading of low-viscous Newtonian2)liquids over solid surfaces plays animportant role

vari-It should be pointed out that physicochemical literature considers mainly theprocesses of wetting and spreading over solid surfaces of Newtonian liquids1) A surface that is lyophilic toward the liquid is characterized by a wetting angle lower than 90∘; the

wetting angle on a lyophobic surface exceeds 90∘ [8].

2) Newtonian liquids are liquids with viscosity that is independent of the deformation rate in a inary flow; viscosity of non-Newtonian liquids depends on the deformation rate and decreases at its increase or even grows at an increase in the shear rate in the case of the so-called dilatant fluids

lam-[10, 11].

under static conditions [12–14] Meanwhile, the processes of spreading ofboth Newtonian and non-Newtonian viscous liquids under dynamic conditionsassume real significance in the technology of obtaining dispersed composites[15] It is these conditions that are characteristic of the technology of obtainingdispersed composites.

This process, especially in high-filled systems, is preceded and (or) nied by procedures of component mixing, further transportation, formation, andcompaction As a rule, these operations in the technology of synthesis of dispersedmaterials are considered separately, individually, and independently, as sequential,and are determined by different targets and parameters of exposure of dispersedsystems At the same time, according to physicochemical concepts, these proce-

accompa-dures are stages of a single process of structure formation and transition of

three-phase systems (solid three-phase–liquid–gas; i.e., S–L–G systems) at the start of theprocess into two-phase ones (solid phase–liquid; i.e., S–L systems) at its end.Such a physicochemical approach to the process of structure formation and,therefore, properties of usually multicomponent materials in the initial stages of

technology of their synthesis is the first fundamental difference from the tional, so-called step-by-step approach mentioned above.

conven-The second important difference of the modern physicochemical approach inthe technology of obtaining dispersed composites is as follows The conventionalapproach provides for determination of parameters of technological operations

by variation in bulk properties of multicomponent mixtures: their uniformity andviscosity (or fluidity), that is, plasticity and placeability

Here, the most important fact usually not taken into account is that the above

bulk properties are determined by the integral set of interactions between

individ-ual particles, that is, contact interactions between particles forming componentmixtures at all stages of the technology of its synthesis

In fact, formation and failure of these individual contacts in the course of thetechnological process form the basis for the technology of formation of the struc-ture of composites determining their bulk properties

The laws of formation of dispersed structures as a set of individual contact actions between particles forming such structures are described by independentfields of physicochemical science: physical chemistry of dispersed systems and

inter-surface phenomena: physicochemical mechanics of materials developed by P.A Rehbinder and his school [12, 16, 17] and, in recent years, physicochemical dynam-

ics of dispersed systems and materials[18, 19]

Physicochemical mechanics, as already pointed out in the introduction, lishes the functional relationship between strength (or adhesion force) in individ-ual contacts between solid-phase particles and bulk strength and other properties

estab-of dispersed structures and materials and also regularities estab-of their decompositionunder external exposure combined with the effect of surface-active media At thesame time, processes of formation and decomposition of dispersed structures and

solids according to physicochemical mechanics are studied mainly under static

conditions

As already pointed out in the introduction, real diverse logical processes of formation and decomposition of dispersed structuresrelated to contact interactions between the dispersed phases forming themoccur predominantly under dynamic conditions These conditions, as shown

chemicotechno-in [18–20], fundamentally change the character of the relationship of contactinteractions between particles and the most significant bulk (predominantlystructure–rheological) properties of dispersed systems and structures forming

and decomposing in such systems under dynamic conditions This similarly refers

to an important element of the modern technology of dispersed systems andmaterials: the ever wider application of surfactant plastifier additives regulatingthe strength and energy of interparticle contact interactions As shown in furtherChapters, the mechanism of their action under dynamic conditions differssignificantly from static conditions, which must be taken into account in theirchoice

All the above stipulates the necessity of considering chemical technology cesses in dispersed systems and in the technology of obtaining dispersed compos-ite materials on the basis of physicochemical dynamics

pro-The main problem that this new field of physicochemical science and ochemical basics of technology of dispersed systems and materials should solve

physic-consists in establishing the fundamental regularities of achieving the maximum

fluidity of structured dispersed systems combined with achievement of the

maximum degree of uniformity of dispersed structures in high-concentration and

highly dispersed systems and dispersed composite materials forming on theirbasis

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[In Russian].

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monomineral’nykh vuazhushchikh

veshchestv: voprosy teorii (Curing of

Monomineral Binders: Theoretical Issues)

(ed V.B Ratinov), Stroyizdat, Moscow,

208 pp.

3. Tarasevich, Y.I (1984) Study of state

of molecules of water and

hydrocar-bons adsorbed on hydrophilic and

hydrophobic surfaces Collection of

articles, Fiz.-Khim Mekh Liofil’nost

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6. Korolev, I.V (1981) About nous film on mineral grains of bitu-

bitumi-men concrete Avtomob Dorogi., 7,

23.

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Dolgovech-v protsesse ekspluatatsii (Durability

of Asphalt Concrete Road Pavement and Factors Promoting In–Service Destruction of Asphalt Concrete Struc- ture)(eds E.V Kotlyarskii and O.A.

Voeyko), Tekhpoligraftsentr, Moscow,

136 pp.

8. Summ, B.D and Goryunov, Y.V (1976)

Fizikokhimicheskie osnovy smachivaniya

i rastekaniya ( Physico–Chemical

Fun-damentals of Wetting and Spreading),

Khimiya, Moscow, 232 pp.

9. Yakhnin, E.D (1968) O svjazi prochnosti

dispersnoj struktury s silami

vzaimod-ejstvija mezhdu ee jelementami (On

relation between strength of dispersion

structure and interaction forces between

its elements), Dokl Akad Nauk SSSR.,

178(1), JS.I, 152–156.

10. Schramm, G (1994) A Practical

Approach to Rheology and Rheometry,

Gebrueder Haake, Karlsruhe, 292 pp.

11. Uriev, N.B (1980)

Vysokokontsen-trirovannye dispersnye sistemy

( High–Concentration Dispersed Systems),

Khimiya, Moscow, 319 pp.

12. Shchukin, E.D., Pertsov, A.V., and

Amelina, E.A (2006) Kolloidnaya

khimiya ( Colloid Chemistry), Vysshaya

shkola, Moscow, 444 pp.

13. Birdi, K.S (2009) Handbook of Surface

and Colloid Chemistry, CRC Press,

756 pp.

14. Schukin, E.D., Savenko, V.I., and Malkin,

A.I (2015) Lectures on the

Physical-Chemical Mechanics, Nobel Press,

Moscow, 676 pp [In Russian].

15. Uriev, N.B (2006) Kolloidn Zh., 68 (4),

539 [Fluidity and spreading of

struc-tured disperse systems, Colloid J., 2006,

68(4) 494].

16. Rehbinder, P.A (1979) Izbrannye trudy.

Poverkhnostnye yavleniya v dispersnykh

systemakh ( Selected Works Surface

Phenomena in Dispersed Systems.

Physico–Chemical Mechanics), Nauka,

Moscow, 308 pp [In Russian].

17. Rehbinder, P.A (1963) Na

granit-sakh nauk (On the Boundaries of

Sciences), Izd Znanie, Moscow, 31 pp.

[In Russian].

18. (a) Uriev, N.B (2004) Physico–chemical dynamics of dispersed systems and

materials Usp Khim., 73 (1), 39.

[Physicochemical dynamics of disperse

systems, Russ Chem Rev (2004) 73(1)

37].

19. Uriev, N.B (2010) Physico–chemical dynamics of structured nanodispersed systems and nanodispersed compos-

ite materials Fizikokhim Poverkhn Zashch Mater., 46 (1, Pt 1), 3; (3, Pt 2)

227; [Physico chemical dynamics of structured nanodisperse systems and nanodisperses composite materials:

part I, Prot Met Phys Chem Surf.

Moscow, 256 pp.

Further Reading

Birdi, K.S (ed) (2009) Handbook of Surface and Colloid Chemistry, CRC Press, 756 pp.

Schukin, E.D, Savenko, V.I., and Malkin, A.I.

(2015) Lectures on the Physical-Chemical Mechanics, Nobel Press, Moscow, 676 pp.

[in Russian]

4. Explain the concept of contact interactions between particles and their role

in the structure of dispersed composite materials

5. What are the principal and particular characteristics of the physicochemicalapproach toward technology of dispersed composite materials?

dispersed systems and materials

7. What is the role and significance of reaching the maximum fluidity of highlyconcentrated and highly dispersed systems in technology of dispersed com-posites?

Structure Formation in Dispersed Systems and Materials

2.1

Types of Contacts between Particles in Dispersed Systems and Materials

As already pointed out, though dispersed systems are vastly diverse in theirchemical composition and physical properties, most of them, especially nano-and colloid dispersed systems are characterized by a combination of two main

features: presence of a strongly developed interphase surface area S and a highly

dispersed phase concentration in liquid (or gaseous) dispersed media (𝜑) A

consequence of this is the high free interphase energy (F *) Free system energyalways tends to decrease, so that spontaneous processes accompanied by a

decrease in this energy (ΔF *) can occur in dispersed systems [1–5]

Free energy can decrease as a result of appearance of interparticle contacts due

to coagulation, that is, coalescence of particles occurring especially intensively

in lyophobic (see note in Chapter 1), aggregatively unstable dispersed systemsvulnerable to coagulation, that is, particle aggregation [6, 7] When a certain crit-ical concentration of dispersed-phase particles is reached in liquid- or gaseous-dispersed media (𝜑0), this process results in the spontaneous appearance of a 3Dstructural network, the main elements of which are contacts between particlesand the very particles forming 3D cells in the bulk of the dispersed system Here-with, a dispersed system becomes structured, that is, passes from a free-dispersedstate to a connected-dispersed (aggregated) state Thus, reaching𝜑0is in fact thestart of the formation of the structure of dispersed composite materials

Appearance of 3D structures results in a fundamental change of the mainstructural–mechanical properties of such systems Colloid dispersed systems

are formed by particles with a characteristic size of d≤ 1μm; the particle size in

nanodispersed systems is d ≤ 100nm = 0.1μm They lose aggregative stability

completely (i.e., the above transition from a free-dispersed state to a dispersed state occurs) Herewith, dispersed systems acquire sedimentationstability (i.e., stability toward layering and precipitation), as the structuralnetwork confines fixed particles of dispersed phases At the same time, suchsystems lose fluidity and mobility, and their viscosity at the given concentration

connected-of 𝜑 ≥ 𝜑0 grows continuously with the increase in dispersion degree S and

the corresponding decrease in size, and also an increase in concentration𝜑 of Technology of Dispersed Systems and Materials: Physicochemical Dynamics of Structure Formation and Rheology,

First Edition Naum B Uriev.

particles in dispersed media Structured dispersed systems are characterized by

their elasticity modulus and tensile strength P m We point out only the mostcharacteristic parameters of dispersed structures

Two main groups among the majority of factors determining the properties ofstructured dispersed systems that are related to the following fundamental param-

eters can be distinguished: cohesion (interaction) force f c and energy E cin contacts

between particles of dispersed phases; number n of contacts between particles per

When materials based on mineral binders (primarily cements for cement cretes in dry mixtures or in other types of powdered binders (gypsum, lime)) areobtained, type A direct (or atomic) contacts are formed at transportation andstorage in containers and batching; type B coagulation contacts are formed whenwater is introduced into mixtures; type C phase contacts are formed as a result ofcrystallization

Figure 2.1 Main contact types between

particles of dispersed phases according to

Rehbinder [1] and the corresponding

struc-tures formed (see Figure A.1) Contacts: (A)

direct (atomic) in powders ; (B) coagulation

in pastes and suspensions; and (C) phase ones in dispersed material structures.

A similar pattern is observed when ceramic products with type A contacts areobtained under the condition that the raw material is dried clay; structures withtype B contacts are formed when water is added; calcination of the mixture results

in formation of structures with type B calcination phase contacts

Asphalt concrete at different stages of its synthesis is also characterized by thepresence of all these three contact types in Figure 2.1:

• Type A direct (atomic) contacts are formed in the mineral part of asphalt crete, predominantly in mineral powder and also when nanocomponents areintroduced

con-• Type B is typical for the period of asphalt concrete production when liquid men is introduced and in the initial stage of its hardening

bitu-• Type C condensation contacts are characteristic of the formed asphalt concretestructure after its hardening when the oil phase is removed from bitumen

A particular feature of weak structures with the first (A) and second (B) type

contacts is their full reversibility by strength.

Distinguishing separate types of direct (atomic) and coagulation contacts is, to acertain degree, arbitrary, as, for example, full displacement of liquid from the inter-particle gap is possible in coagulation structures in the case of strong lyophobicinteractions and the difference between these contact types disappears [5–7].When outer mechanical exposure of the structure ceases after it is destroyed,type A and type B contacts can be spontaneously restored to their initiallevel This property, denoted as thixotropy [8], is a characteristic of manytypes of powdered and pastelike dispersions Structures with strong phasecontacts are wholly devoid of this feature Such structures, denoted as conden-sation structures (crystallization structures in the case of cement concretes),are formed in dispersed systems with contacts with reversible strength as aresult of phase and chemical transitions, for example, crystallization fromoversaturated solutions or melts (on cooling), polymerization, baking, plasticdeformation on compaction, removal of liquid dispersion medium, and so on(Figure 2.2)

In addition, the scheme of transitions of direct (atomic) and coagulation tacts to strength-irreversible contacts of dispersed materials (Figure 2.2) as a result

con-of chemical and phase transitions should also include cases con-of direct transition,for example, due to compaction of powdered materials with type A contacts orremoval of the liquid medium from dispersions with type B contacts with forma-tion of fiber material structures (paper, cardboard)

The phase contact with the minimum area corresponds to approximately 102

interatomic bonds In fact, such a contact does not differ from the atomic onecharacteristic of highly dispersed powders As the area of such a contact is onlyapproximately 10−16m2, the probability of appearance of such a defect causing adecrease in its strength is also very small, and therefore its strength approachesthe strength of a defect-free ideal solid At an increase in the phase contact area,

the f value in it usually reaches approximately 103N

Disperse Materials

(contacts with

“reversible” strength) Phase and chemical transitions

Atomic “Point” contacts

(in highly dispersed

powders)

Coagulation contacts

(in pastes and suspensions)

Polymerization Crystallization (from oversaturated solutions or melts) Calcination, plastic deformation Removal of dispersion medium (a)

Asphalt concrete, filled polymers, varnishes, paints, cement concrete

Ceramics, Abrasive and other fired materials

Paper, Cardboard (”Interweaving”

contacts) (b)

Dispersed materials (“irreversibly”

destroyed contacts

with f c >> 10 –6 N)

fc ≈ 10–6 N

fc ≈ 10–8 N

Figure 2.2 Scheme illustrating a transition of dispersed systems with (a) reversible-strength

direct and (b) coagulation contacts to structures with irreversibly destroyed contacts in persed materials.

dis-As already pointed out above, mechanical properties of dispersed structuresmanifested at different stages of the structure formation process depend on force

f c per individual contact determined by its nature and also on the number ofsuch contacts per unit volume An important role in formation of properties ofdispersed systems and especially of dispersed materials, of which typical repre-

sentatives are cement concretes and asphalt concretes, is played by coagulation

structuresformed by particles with type B contacts (Figure 2.1) It is with theirformation that synthesis of structured dispersed systems and materials starts

2.2

Criteria of Formation of Dispersed Structures

2.2.1

Characteristic Critical Particle Size

Formation of dispersed structures is possible under two conditions determining

critical size d cof dispersed phase particles and their critical concentration𝜑 cinliquid or gaseous dispersion media

To the first approximation, such conditions can be represented as follows.1) As dependent on the type of contacts, systems have their own characteristic

critical particle size; if d ≤ d c (d cis the characteristic particle size), the

struc-ture can be formed and can exist, while if d ≥ d c, the structure in the field ofthe gravity force becomes unstable, that is, it can be spontaneously destroyedunder exposure of the particles forming it to the gravity force

2) When the critical concentration of particles of dispersed phases is reached inthe dispersion medium, that is, at𝜑 ≥ 𝜑0in the system, as already pointed out

above, a 3D structure characterized by strength P m > 0 can be formed

spon-taneously

Let us consider consistently quantitative values of these criteria

In accordance with the first condition, the criterion of aggregation ability [6]characterizing the possibility of appearance of dispersed structures is based on asimple principle: a structure with type A and type B contacts in dispersed systemscan appear if the adhesion forces between particles become commensurable withthe particle weight (or exceed it in the given dispersion medium):

density), and g is the gravity acceleration.

For structures with direct atomic contacts [6],

According to the DLFO (Deryagin–Landau–Verwey–Overbeck) theory ofintermolecular particle interactions [9], particle fixation in the case of stronglyophobic interactions occurs in the so-called near potential well, at the distance

of hmin, while in the case of weak particle interactions with lyophilic (hydrophilic

in the case of water dispersions) surface, the wetting angle in contact with thesolid phase surface 𝜃 < 90∘ [5, 9] (Figure 2.4) and the most probable mutual

position of two particles is determined by distance h max(Figure 2.3) Accordingly,the interaction energy and force of particles fixed in the near and far potentialwells differ by up to two orders of magnitude and decrease with an increase inthe distance between the particles This follows from the relationship:

f c= A∗r

where A * is the Hamaker constant of intermolecular interactions [4, 5, 9], r is the particle radius, and h is the distance between them.

In the case of dispersions with particle fixation in the near coagulation position

(in the near potential well at h ≈ h1):

Potential interaction of particles

E – energy of interparticle interaction

f c– particle adhesion force

Figure 2.3 Scheme characterizing the

com-bination of dispersion attraction forces and

electrostatic repulsion forces (see Figure A.2):

(a) manifestation of dispersion attraction

forces and electrostatic repulsion forces and

(b) dependence of energy E and interaction force f c on distance h [7, 9].

Figure 2.4 Character of solid-phase surface

wetting in the case of (a) hydrophobic and

(b) lyophilic (hydrophilic toward water)

sur-faces:𝜃 is the wetting angle between the

solid-phase surface and the tangent line to the liquid drop surface at the site of con- tact with the solid surface [1], according to Young’s law [10]: cos𝜃 = 𝜎sg −𝜎sl

𝜎lg

In the case of formation of coagulation structures with particle fixation in the

position of far coagulation (in the far potential well at h ≈ h1):

where B is the Lifshitz constant [9].

An important result obtained in calculation of d c for typical values of A ∼ 10−19

to 10−20J, B ≈ 10−28J m,𝜌 ∼ 2 consists in the fact that d c ≫ 1 μm and can reach

100 μm and even more This exceeds the size of colloid particles by several orders

of magnitude Relationships (2.4)–(2.6) are presented per single contact between

two particles: a hypothetical limiting case characteristic of the initial stage ofaggregate formation from particles.

In fact, the coordination number for a particle in the structure is z≥ 2 Hence,

it follows that the d cvalue for each of the considered structure types can exceedthose calculated according to Equations 2.4–2.6

In the general case, the criterion of aggregation for the solid phase–liquidmedium dispersions can be found under the condition of commensurability ofpotential energy of interaction of contacting particles and energy of the dispersedsystem exposure [6, 11]

When the potential energy of a particle interaction is presented in the form of amodel function consisting of two potential wells with the shape of parabolic curves

with depths of U1and U2, accordingly, the stability (or aggregation) criterion forstatic conditions in the general form is

U i >4

Index i = 2 corresponds to far coagulation, while i = 1 corresponds to near

coag-ulation Relationship (2.7) is an energy criterion of sedimentation stability of thestructure, that is, stability to destruction of the structure and precipitation of par-ticles under the effect of their own weight

If condition (2.7) is united with the condition of stability of the structure toBrownian motion [7, 11], the relationship that determines the range of critical par-ticle sizes capable of forming structures stable under static conditions is obtained:

d i

2 =r i≡

[

U i r

×103kg/m3, we obtain for particles d c/2 ∼ 10−7–10−5m for systems with far

coag-ulation and d c/2 ∼ 5 × 10−5–10−4m for systems with near coagulation The

maxi-mum d c/2 values correspond to aggregability criteria in Equations 2.5 and 2.6.Thus, calculations of the aggregation ability criterion according to

Equations 2.5–2.8 yield similar results The obtained numeric values of d c show that spontaneous formation of coagulation structures is possible in disper-

sions with the particle size of tens and even hundreds of micrometers.This meansthat surface phenomena, contact interactions, and structure formation processeslargely determine the properties and regularities of behavior of most naturaland engineering dispersed systems that are traditionally classified as coarse(for this cause, they have been considered as objects for study in continuummechanics and hydrodynamics) Such systems are diverse powdered materials [6,12], for example, mineral binders (cement, lime, gypsum); fillers for varnishes andpaints, rubbers, polymers, bitumens; dustlike fuels; mineral fertilizers; powdersfor firefighting; and also paste systems and suspensions, including raw slurries

in cement production, asphalt binders; suspensions of cellulose fibers used inproduction of paper and cardboard; suspensions and pastes for production ofporcelain, faience, and ceramics; heterogeneous fuels; dustlike and paste sideproducts and some production waste, in particular, waste from concentration

plants; a variety of natural dispersed systems (subsoils and soils); sediment beds

of rivers, lakes, seas, and oceans

At the same time, particles in these systems (at d≥ 1 μm and all the more so at

d ≥ d c ) cannot participate in heat Brownian motion, as their characteristic size exceeds the size of colloid particles by several orders of magnitude (d≤ 1 μm).Therefore, conditions for development of the dynamic particle state in such sys-tems, that is, their motion required for implementation of various chemical engi-neering (e.g., mass exchange) processes cannot be implemented on the basis ofheat motion It is necessary to supply energy from external sources with acceler-

ation no less than gravitational acceleration g to create the dynamic state similar

to Brownian motion in dilute aggregatively stable (lyophilic) colloids

2.2.2

Concentration Factor and Strength of Coagulation Structures

The criterion determining the possibility of structure formation is the minimumstrength of the structural net capable of retaining particles that form it in the grav-ity field Ultimately, it is the structure strength that determines its stability underdynamic conditions

The modern strength theories suggested in [1, 5, 11, 13] are based on an tive approximation that, in the general form, can be presented by the followingrelationship:

where𝜒 is the number of contacts between particles per unit surface.

In a specific form, Equation 2.9 can be presented as follows:

P m≈𝛼 f c n2∕3=𝛼 f c f (𝜑)

d2

(2.10)where𝛼 is a coefficient close to 1 that characterizes the packing geometry; n is the

number of particles per unit volume; f ( 𝜑) is the function of bulk particle content;

dis the average characteristic particle diameter

Number of contacts n can be determined according to Equation 2.11 for the

so-called globular porous structure model [14]:

n =

[

32

z𝜑

𝜋d2

)3∕2

(2.11)

where z is the coordination number characterizing the number of contacts of the

particle with the neighboring particles; Π is the porosity;𝜑 is the bulk dispersed

phase concentration in the dispersion medium, Equation 2.12 as follows:

𝜑 = Vs.ph.

Vs.ph.+Vl.ph.+Vg.ph.

where Vs.ph.is the solid-phase volume in the dispersed system; Vl.ph.is the

liquid-phase volume; V is the gas-phase (air) volume

(b) (a)

Figure 2.5 Dependence of strength P mof

dispersed structures on the dispersed phase

concentration (porosity)𝜑 in the dispersion

medium (see Figure A.3): (a) the general

dependence and (b) the dependence found using percolation theory [15]; points corre- spond to experimental data [14].

The plot of the dependence of the structure strength on the dispersed phaseconcentration in the dispersion medium according to these concepts is shown inFigure 2.5

One can introduce a number of additional parameters characterizing intensity

of strength growth as dependent on the concentration: tg 𝛼 = d⋅P m /d 𝜑 in the range

of𝜑0< 𝜑 < 𝜑 c and tg 𝛽′in the range of𝜑 > 𝜑 c, where𝜑0is the minimum centration at the start of structure formation and𝜑 cat the start of its dramaticstrengthening, accordingly

con-Let us note in particular that theoretically obtained Equation 2.10 correlates

with empirical Equation 1.1 Indeed, the P mvalue in Equation 2.10 corresponds

to parameter Rconcrin Equation 1.1, f c in Equation 2.10 in the generalized

inte-gral form in Equation 1.1 corresponds to the Rcemvalue, while function f ( 𝜑) in

Equation 2.10 is similar to the Cem/W in Equation 1.1 This analogy allows at the least to perform qualitative analysis of the dependence of Rconcron the parameters

in it with the dependence of P m on f cin Equation 2.10

The character of the dependence of the strength of the dispersed compositestructure can be illustrated using the example of the actual model obtained exper-imentally by baking in contacts of monodispersed spherical polystyrene particles

In each experiment, particles (of similar diameter d, but decreasing by half from

experiment to experiment) were packed to the maximum to the level of the iting hexagonal packing at𝜑 V=0.74 (Figure 2.6) This experiment confirmed to agreat degree of approximation the correctness of the theory of strength of porousmaterials for the cases of a globular model assuming a “regular” nonchaotic posi-tion of particles in a structural network with regularly repeating structure ele-ments [1, 6, 12]

lim-At the same time, as soon as particle size d becomes lower than d c

(Equations 2.3, 2.5, and 2.6), that is, becomes lower than the critical size

1 2 3 4

Figure 2.6 Scheme of the experiment modeling the composite porous structure formed by

monodispersed spherical particles; (1, 2, 3)𝜑 = 0.74.

(aggregability criterion) (Figure 2.6, scheme 4), strong correlation betweenthe particle size, concentration, and strength disappears This is related tospontaneous chaotic particle fixation in the structural network as a result ofmanifestation of forces of intermolecular interaction of particles

In this case, the so-called percolation approach can be used to describe theabove functional dependence between the structure strength, number of contactsper unit volume, and porosity

Assuming an irregular chaotic bulk distribution of particles as opposed to a ular distribution in Equations 2.9 and 2.10 in [11], a more general form of thedependence of strength on dispersed structure porosity that is based on using theconcepts of percolation theory is obtained

reg-Application of the model of a lattice of randomly packed spheres [11] allowedtaking into account the possibility of formation of dispersed structures withdiverse particle distributions in a wide range of coordination values, from 3 to 9

To describe the dependence of the structure on its relative porosity V = 𝜑/𝜑0

by analogy with the dependence of conductivity on porosity of the structure of

conducting balls, parameter C that reflects a certain topological property of the

dispersed system and is determined by the following relationship is introduced[11, 15]:

C = P m(V )

where P m (V ) is the strength of the porous structure at any given value of effective porosity and P m (I′) is the strength of the system at the maximum bulk particleconcentration (𝜑max) in the dispersion medium

The latter relationship allows establishing the dependence of c(V ) on nation number z in the range of its variation from 3 to 9, that is, practically for

coordi-any type of quasi-lattice The following dependence was found on the basis of

Equation 2.10 and also accounting for K values for different z:

monoDependences of strength on porosity of 3D structures formed in highly persed structured systems of clusters and particles and of aggregates of primary

dis-particles in a more general case (at d ≪ d c) were determined on the basis of theconsidered theory

Strength of the structure consisting of aggregates is expressed by the followingdependence:

a 1D linear figure, f = 2 for a 2D one, f = 3 for a 3D one; f ais the fractal dimension

of the cluster (aggregate)

This relationship is implemented at f < 3 In particular, in the case of percolation

aggregates (clusters), f a=1.8 at f = 2.5; then 𝛾 = 8.8; for branched clusters, f a=1.5

at f = 2; then 𝛾 = 4.3.

Thus, Equations 2.15 and 2.16 obtained using the percolation theory alloweddescribing the dependence of strength on porosity for chaotic distribution in thebulk of the structure of particles and aggregates This is the most general casecorresponding to actual conditions and characteristic of the structures of mostdispersed composite materials

Important sequences following from the above equations regarding strength ofdispersed structures and materials (and above all Equation 2.10) consist of thefollowing

The lower the average particle size d, the higher the strength P mof the material

at the same porosity value Herewith, an increase in porosity is inversely

propor-tional to d2(Figure 2.6) This means that highly dispersed materials a priori have

higher porosity In particular, one can compare, for example, natural rock als of volcanic origin: abyssal and extrusive Abyssal dense rocks (granite, etc.) due

materi-to slow lava cooling under high pressure, form a coarse crystalline structure underslow cooling Dense extrusive rocks (e.g., basalt and diabase) are formed under

the conditions of fast cooling Due to melt solidification, their structure is finelycrystalline, as large crystals do not have enough time to grow due to fast growingmelt viscosity Accordingly, strength and life time of these natural rocks consid-erably exceed the corresponding indicators for abyssal rocks of similar mineralcomposition.

2.2.3

Time Factor of Strength of Contacts and Dispersed Structures

Modern theories of contact interactions between particles of dispersed phases[1, 5, 7] and theory of strength of dispersed structures [1, 11, 15] considered inSections 2.1 and 2.2 correspond to static quasi-equilibrium conditions and do nottake into account the fact that mutual relative motions of both individual particlesand aggregates they form generally occur in the course of chemical technologyprocesses related to the processing of dispersed systems and obtaining dispersedcomposite materials

Relative rates of these displacements are largely determined by the intensity oftheir dynamic, primarily mechanic exposure

The role of dynamic exposure of dispersed systems and their parameters will beconsidered in the following chapters

At the same time, in the context of estimation of strength of contacts andstructures they form, it is necessary to take into account that appearance anddisruption of contacts between particles, aggregates of particles, generation,and destruction of dispersed structures, for example, in such processes as dosage

of solid components, mixing them with a liquid matrix, mixture formation,and compaction occurs under nonequilibrium state, non-steady-state dynamicconditions

The nonequilibrium state of these processes and their dependence on the rateand intensity of external exposure cannot fail to affect both strength of contactsand strength of dispersed structures appearing and destroyed in the course ofthese processes In other words, the time factor must probably produce a signif-icant effect on the measured values of these characteristics as regards the values

of strength parameters of contacts and dispersed structures

When solidified composite materials, same as phase and condensation contactsforming their structure, are destroyed, the time factor also affects the measuredstrength values This means that the rate of an increase in the load, and accordingly

of stresses when strength of composites is determined, must be taken into accountboth in determination of strength of composites and in possible failures in thecourse of their operation in structures and facilities

It can be shown that the measured values of strength of contacts of all types,dispersed structures and materials at an increase in the loading rate must becommensurable with the relaxation rate of the appearing stresses on externalexposure

ε θ

Figure 2.7 Kinetics of development and decrease of deformations under stress and

unload-ing of solid structures, where (a) reversible deformation and (b) a combination of elastic and plastic irreversible (residual) deformation, after stress is removed.

As stress relaxation period𝜃 depends on viscosity 𝜂 and elasticity moduli E

according to the general equation1)and elasticity modulus E according to the

par-A clear example of the role of the time factor in appearance of stresses on sure of the composite material to external forces is the behavior of asphalt concrete

expo-at high summer and low winter temperexpo-atures In the first case, predominantlyplastic deformation occurs at low𝜃 due to a decrease in viscosity of bitumen; in the

second case, brittle fracture of the material prevails at reduced fracture resistanceand considerably lower limiting (full) deformation before failure

This well-known example shows that the value of limiting (full) deformation alsobecomes of considerable importance alongside the role of the time factor

It is known that the limiting deformation value𝜀limcomprises elastic𝜀elandplastic (irreversible) deformation (Figure 2.7), that is,𝜀lim=𝜀el+𝜀el1

1) Effective viscosity𝜼 is determined by the ratio of shear stress P to the deformation rate, that is,

𝜂 = P∕ ̇𝜀, where ̇𝜀 = d𝜀∕dt; 𝜺 is the relative deformation; and t is the time.

Figure 2.7 shows kinetics of development and decrease in deformations under

stress and unloading in time If stress P < P k is implemented in the elasticregion, the system is “reversible.” When stress is removed, there is no residual

deformation (Figure 2.7a) At stress P > P k , a combination is observed of elasticand plastic irreversible (residual) deformation remaining after stress is removed(Figure 2.7b) [1]

In the first case, overall deformation time t including the elastic component

(developing at the acoustic speed) and slow one (relaxation) are determined by thetime of reaching the initial (before applying the load) linear size of the deformedsystem

In the second case, this time can be much higher and the system does not return

to the initial state

The deformation pattern characteristic of the behavior of dispersed structuresand dispersed materials reflects the behavior of individual contacts formed

by them

As seen in Figure 2.8, the three main contact types are direct (atomic), tion, and phase contacts in structures of dispersed systems; and hardened mate-rials behave differently under stress

coagula-Schematically, deformation𝜀 under stress 𝜎 of these three types is characterized

in the first case by constant stress value with an increase in𝜀 In the second case,

the region of development of elastic deformation is observed at the beginning ofdeformation until the flow limit is reached (𝜎 ≈ 𝜎 m), after which plastic yield with

a constant value of equilibrium𝜎 svalue is manifested In the third case, the dence of𝜎 on 𝜀 is characteristic for elastic deformation with contact destruction

ε

σ s = f(έ)

Figure 2.8 Character of deformation of dispersed structures under stress with (a) direct, (b)

coagulation, and (c) phase contacts.