The Influence of Poly-Molecular Adsorption on the Rheological Behaviour of Lubricating Oil in a Thin Layer

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1 Te Influence of Poly-Molecular Adsorption on te Reological Beaviour of Lubricating Oil in a Tin Layer Igor Mukcortov Lecturer Sout Ural State University, Celyabinsk Elena Zadoroznaya Professor Sout Ural State University, Celyabinsk Igor Levanov Assistant Professor Sout Ural State University, Celyabinsk Kseniya Pockaylo Engineer Sout Ural State University, Celyabinsk Te explanation and modelling of te impact of anti-wear additives in lubricants at modes and friction caracteristics involves considerable difficulties. Te experimental studies of many researcers suggest te influence of adsorption of lubricants on te parameters of boundary friction and te ydromecanical caracteristics of plain bearings. It is known tat te real relationsip between te friction coefficient and te contact pressure at tese units differs significantly from te teoretical one. Using te example of motor oils, te autors ave establised te mecanism of action of anti-wear additives and proved te poly-molecular nature of te adsorption of lubricants on te friction pair s surfaces. Te autors proposed te reological model of a tin lubricating film on te basis of pysico-cemical concepts about te adsorption mecanism wit te influence of te adsorption layer on te viscosity of lubricant near te solid surface. In tis paper a metod of ydrodynamic calculation of te cranksaft bearings of an internal combustion engine wic takes into account te effect of te adsorption of engine oil was developed. Te proposed model of te reological beaviour of te lubricant in a tin layer is based on objective pysical and cemical laws and leads to significantly better compliance between te calculation results and te experimental data. Moreover, te elucidation of te mecanism of antiwear additives action may be useful in te development of lubricants. Keywords: poly-molecular adsorption, reological beaviour, reological model, tin lubricant layer. 1. INTRODUCTION Te beaviour of lubricants in te friction contact as a great influence on te performance of macine parts and mecanisms. It is now known tat te reological beaviour of lubricating oils in tin layers between te friction surfaces is significantly different from tat of a normal liquid. For example, te properties of tin layers of motor oils strongly affect te tribological parameters of te sliding bearings of internal combustion engines. Te typical dependence of te friction coefficient on contact pressure in te radial sliding bearing or in te similar conformal contact of friction wit te lubricant is presented in Figure 1. An explanation of at least two facts must be given wen we are considering te tribological caracteristics of friction units. Te first is te influence of te presence and amount of anti-wear additives in a region of contact pressure, in wic friction as a ydrodynamic caracter. If te viscosity of te lubricating oil is constant, antiwear additives will significantly increase te value of Received: Marc 015, Accepted: June 015 Correspondence to: Dr Elena Zadoroznaya Sout Ural State University, Lenin av. 76, Celyabinsk, elena-nea@rambler.ru doi: /fmet150318m te contact pressure (P 1, Fig. 1) at wic te minimum friction coefficient is reaced. Te second fact is te relative constancy of te friction coefficient over a wide range of contact pressure (P P 3, Fig. 1). Bot tese facts are well known but cannot be explained witin te framework of te usual ydrodynamic lubrication teory wit te elp of well-known teories of boundary friction. f fr P 3 P P 1 1/Р Figure 1. Te typical dependence of te friction coefficient on contact pressure in te conformal tribo-units To describe te reological beaviour of lubricants in te tribo-unit te cange of te state of te fluid during its interaction wit te solid surface must be Faculty of Mecanical Engineering, Belgrade. All rigts reserved FME Transactions (015) 43, 18-18

2 considered. Suc facts as increased viscosity in liquid layers adjacent to te solid surfaces and te anisotropy of te liquid in tese layers can only be explained by poly-molecular adsorption [1-8]. Building an adequate matematical model of a tin lubricant layer can be performed only on te basis of ideas about te laws of poly-molecular adsorption of ydrocarbon liquids containing surfactants (SAS) wit te defined structure.. THE FEATURES OF THE ADSORPTION COMPONENTS OF LUBRICANTS ON METAL SURFACES Te creation of a teory of te poly-molecular adsorption of liquids on solid surfaces is an extremely difficult task due to te inadequate development of te pysics of fluids. It is generally accepted tat te laws of te poly-molecular adsorption of liquids is a consequence of intermolecular interactions and te original structure of te liquid more tan te binding energy of te molecules of a liquid wit a solid adsorbent [4]. Te adsorption of lubricant containing anti-wear additives is a special case since it is caused te secondary adsorption of ydrocarbon molecules on te surface of te monomolecular layer formed by additive molecules. For understanding te adsorption of lubricants and describing te experimental dependencies te adsorption of surfactants, te adsorption of ydrocarbons and te relationsip between tem sould be considered separately. Te adsorption of te zinc dialkylditiopospates (ZDDP) and oter anti-wear components obeys te usual rules. In particular, te dependence of te mean residence time τ of te surfactant molecules on te metal surface is described by Frenkel's formula: τ = τ Q RT, (1) 0exp ( a ) were: τ 0 is mean residence time of te active center of te molecule on te surface at a temperature T = 0; Q a is te molar eat of adsorption; R is universal gas constant. One of te distinguising features of surfactants used as anti-wear additives is te dependence of Q a on temperature. Tis dependence is due to te degree of dissociation and te significant difference of adsorption eat of dissociated and undissociated molecules. For example, in te case of zinc dialkylditiopospate, te pysical adsorption of initial molecules occurs as well as cemical adsorption of te dialkylditioposporic acid. Values Q a of tese processes differ at several times. It results in distinction of τ on some orders [4]. Concentration of te adsorbed molecules of Θ and adsorption (Γ = Θ/Θ max ) on an adsorbent surface usually poorly depends on temperature [,4] because dependence of a degree of dissociation from te temperature as te exponential form similar to dependence τ (T). If activation energy E a of a cemical reaction of a molecule surfactant wit te active sites on a metal surface is rater ig, a salutatory increase of Γ at acievement of a particular temperature of activation T a corresponding to condition E a = Q a (T) may appen peraps. Te tribological properties of some engine oils wit termally activated additives are caused by te presence of at least two surfactants, one of wic as a low eat of pysical adsorption and T a = C. Te second, more important feature of te monomolecular adsorption layers of anti-wear additives is te impossibility of forming dispersion bonds between te carboydrate portions of te surfactant molecules due to steric indrance [1]. Surfactants aving an effective diameter of te polar group close to te diameter of te ydrocarbon radical (alipatic monocarboxylic acids, alipatic alcools, amines, etc.), form layers, in wic te molecules form ydrocarbon radicals in a packed structure. Te insularity of intermolecular bonds witin te adsorbed layer leads to a low surface energy and te practical absence of secondary adsorption of ydrocarbons or oter components. In contrast, ZDDP and oter anti-wear additives wit te large size of te polar groups constitute te coordinatively unsaturated adsorption layer wereby te ydrocarbon radicals create a dispersion connection wit liquid molecules. For adsorption of gases on te solid surface te specific eat of adsorption q is equal to Q a per unit area of a monomolecular layer and is made presented in te form of two components [4]: q = qa + q x, () were: q a is specific eat due to te energy of association of adsorbate molecules to te surface; q x is specific eat due to te formation of bonds between molecules of adsorbate inside te layer (lateral coesion). Wen fluid is absorbed, a value q x is usually small, because of te energy of intermolecular bonds in te liquid and solid pases wic are close to eac oter. It is obvious tat in te adsorption of te ydrocarbon liquid on a surface covered wit a dialkylditiopospate monolayer, q a and q x are identical. In tis case te maximum possible value Q is equal to te specific eat of crystallization of te fluid. Te real values of te eat of adsorption cannot reac tis value due to te reversibility of te adsorption process and te establisment of an equilibrium rate of mass transfer between te adsorbed layer and te adjacent layer of fluid. Tus, te second layer, wic is adsorbed on te metal surface and consists of ydrocarbon molecules, is caracterized by te lower entropy tan te original oil. Te entropy of ydrocarbons in a liquid pase differs from te entropy of solid ydrocarbons no more tan by 10 %. Energy of dispersion communications can reac from several to ten kj/mol, i.e., is close to warmt of pase cange if a lengt of ydrocarbon cains is equal C 0 C 30 and coordination numbers are equal 4 6. In tis case te surface formed by te second layer also as excess energy. It leads to adsorption of te following layer, and so on. In te formation of eac subsequent layer te entropy jump occurs on te pase boundary, te value of wic decreases for eac subsequent layer. Tus, te multimolecular layer is formed. Te compensation of te entropy reduction is eventually caused by te cemical bonds surfactants-metal. Wen te temperature increases te balance between processes of adsorption and desorption of ydrocarbon FME Transactions VOL. 43, No 3,

3 molecules is displaced towards desorption according to Frenkel's formula (1) because te energy of single intermolecular bonds does not depend on te temperature. Te adsorption of ydrocarbon components is caused by regularities of adsorption and structure surfactant. Its termodynamic description by means of known teories of poly-molecular adsorption becomes extremely difficult [4]. Wit only limited success Polyani's teory can be used by representing te polymolecular layer in te form of sequence of monomolecular layers, eac of wic contains some sare φ i of te ordered crystal or te solid pase. Te entropy of a monomolecular layer can be presented as te sum of te entropy of solid S s and liquid S l of pases as a part of tis layer S S S. (3) j = ϕ s + (1 ϕ) In tis case te usual expression of te potential of a force field of te adsorbent E = RT ln ( vs v l), (4) were: v s and v l are te molar volumes of te crystal and liquid pases of te adsorbed component, can be presented as =Δ ϕ ( Qa +ΔS) l E, (5) were: Δφ is te cange of sare of volume of a crystal pase as a part of te adsorptive layer; ΔS is te entropy difference in te layer directly adjacent to a surface of adsorbent and in liquid on infinite removal from a surface. Te difference in potential of an adsorbent field from te value of a jump of isobaric-isotermal potential ΔG on te interpase border metal-lubricant consists in te dependence of te specific eat of adsorption Q a of te first ydrocarbon layer on te structure of te layer of adsorbed surfactant. Tus, ΔG on te metal-lubricant border can be presented as te sum of jump of te potential compensated by adsorption of a dialkylditiopospates ΔG Sur, and te jump of te potential compensated by adsorption of ydrocarbons ΔG c. It is obvious tat for te formation of a poly-molecular adsorptive layer a necessary condition is ΔG c > (G sol G l ), were (G sol G l ) is te difference of isobaric-isotermal potentials for te liquid and solid pases of tis ydrocarbon liquid at tis temperature. Tis condition explains anti-wear properties of surfactant wic ave ig warmt of adsorption on te metal surface and form monomolecular layers. Hydrocarbon radicals of tese layers form a surface wit a rater ig energy. In tis case we expect a lack of te expressed anti-wear properties at surfactant, similar to an oleic acid. As a rule, te anti-wear additives are used as a surfactant, wic is capable of te cemical adsorption wit activation energy of a emosorption (E ac ). Te activation temperature in tis case lies in te range of working temperatures of te tribo-unit. Stable parameters of a boundary layer of lubricant are possible on condition of a transition from te pysical adsorption of surfactant to cemical adsorption in te range of working temperatures, i.e., on condition of E ac RT W, were T W is te working temperature of te tribo-unit. In tis case te dependence of amount of te adsorbed substance on temperature as te known appearance presented in Figure were: Θ is te concentration of te adsorbed component [mol/m ]; a is te temperature interval of transition from pysical to cemical adsorption; b is an interval of relative stability of te parameters of te dividing lubricant layer in te boundary mode; 1 is process of te pysical adsorption of surfactant, E ac < RT W ; is a cemical desorption of surfactant, E ac > RT W ; 3 is concentration of adsorbed surfactant; 4 is te general concentration of te adsorbed molecules, including ydrocarbon components of oil (it is proportional to concentration of adsorbed surfactant). Θ a b 3 Figure. Dependence of Θ on temperature; 1 concentration of pysical adsorption of surfactant; cemical adsorption of surfactant; 3 total concentration of surfactant; 4 general concentration of components of te poly-molecular layer Te condition E ac RT W is satisfied for a number of te usual anti-wear components: ZDDP and calcium alkylsalicylates (engine and ydraulic oils), tripenilpospate and alkiltriazola (oils for guiding slippage), triarilfosforotionata (some plastic lubricants). 3. RHEOLOGICAL MODEL OF A THIN LUBRICANT LAYER Taking into account te mecanism of formation of a boundary layer, we propose a reological model wic describes te influence of a boundary layer on te range of loadings witin wic te ydrodynamic mode is realized (P 1 value in Fig. 1) [3,5-8]. Te value of viscosity near a surface s is close to te viscosity of solid paraffin. In tis case during removal from te metal surface at distance of i we will write down te dependence of viscosity (), as i = + s exp ( i l ) (6) were: s is te parameter representing te conditional value of viscosity at infinitesimal distance from te limiting surface. In a layer limited by two surfaces, possible distinctions between te adsorptive properties and te structuring influence of various materials need to be 4 1 T 0 VOL. 43, No 3, 015 FME Transactions

4 considered. Tese distinctions are described by parameters l 1, l exp i exp i = + + i s l1 l. (7) Te average (effective) viscosity of te layer and a viscous friction force is expressed as s1 s = + s1 s s i i exp + exp d i ; (8) l1 l s F = V0 + s1 s ( s1 s) exp exp d s i i + i l1 l s1. (9) were: V 0 is te speed of offset of te surfaces; s1, s are tickness of layers of lubricant on surfaces, te sift speed of wic can be considered equal to zero. Calculation of s and l is carried out by numerical metods proceeding from (5): ef = ( 0,, s, l ) F( ef, s ) = Fmin. (10) Te model of te additive interaction of te adsorptive layers (7), (8) and (9) allows us to explain a number of experimental data. It can be also used for an explanation of te dependence of te viscosity of suspensions on te sizes of particles. But tis model does not consider te interaction of te adsorptive layers formed on two surfaces. Terefore, it can be applied only at tickness values of te lubricant layer wic considerably exceed s, i.e. in te presence of a lubricant wit te usual viscosity. At furter increase of loading inevitably tere is an interaction of te adsorptive layers wic caracter we can describe by using te following considerations: Te drop of te termal movement in eac layer at distance i from a surface, te increase of an entalpy of intermolecular communications and te accompanying increase of te viscosity can be eliminated by transmission of a moment of te movement as a result of mecanical impact to molecules of tis layer. Te orderliness of te adsorptive layer can be destroyed by influence of some critical tension of sift. Tis statement is rigt and for ideas of liquid crystal structure of a layer. It is reasonable to assume tat te size of te critical tension of sift depends on te size of an additional entalpy of te layer and terefore on te initial viscosity i of tis layer. As te pressing load increases as a result of rapprocement of surfaces and a fall in te value of s, te increase of te sift tension dv/d will lead to a reduction of s and to preservation in a clearance of some lubricant layer wit te viscosity close to te usual 0, i.e., in some range of loadings s const. A matematical impression of te interaction of te adsorbed layers cannot strictly be gained due to te lack of a description of te liquid condition in te adsorbed layers. Te condition s const cannot be considered as strict because of te obvious dependence of te critical value dv/d on initial (in te absence of slipping) i and, terefore, on i. For simplification, we accept tat s1 = s = s. For an approximate calculation it is necessary to accept a condition tat viscosity in te middle of a clearance (/) = 0. Considering tat at small values (/) te value of i 0, expression (7) we replace wit were: i = 0 + s + s exp l i i exp + exp l l (11) = s exp l is viscosity in a middle part of a layer. At ig values (/) te value of te second part tends to zero and te value i 0. For te average viscosity and te power of liquid friction respectively we will find tat were: = + s d s M i s s1 + s exp l 4. CONCLUSION = + 0 s F V0 s ( s ) d s M i s + s exp l i i M = exp + exp l1 l ; (1), (13) Te main engineering objective of ydrodynamic calculations of units of liquid friction is te determination of load ability and speed of wear. To solve tis problem. FME Transactions VOL. 43, No 3, 015 1

5 efficient algoritms for calculating and adequate reological model of te lubricant are needed. Te proposed model of te reological beaviour of lubricant in a tin layer is based on objective pysical and cemical laws and acieves significantly better correspondence of calculation results wit experimental data. ACKNOWLEDGMENT Tis work was supported by a grant of te Ministry of Education and Science of te n Federation for applied researc, code Te unique identifier for Applied Scientific Researc (project) is RFMEFI57714X010. Agreement No REFERENCES [1] Akmatov, A.S.: Molecular Pysics of Boundary Friction, Nauka, Moscow, [] Adams, R.D. and Wake, W.C.: Structural Adesive Joints in Engineering, Elsevier Applied Science Publisers, London, [3] Muortov, I.V., Usoltsev, N.A., Zadoroznaya, E.A. and Levanov, I.G.: Improved model of reological properties of te boundary layer of lubricant, Friction & Lubrication in Macines and Mecanisms, No. 5, pp. 8-19, 010, (in n). [4] Fridriksberg, D.A.: Course of Colloid Cemistry, Kimiya, Saint Petersburg, 1995, (in n). [5] Zadoroznaya, E.: Te researc of non-newtonian properties and reology of tin lubricant layers in ydrodynamic journal bearings, in: Proceedings of te 68 t STLE Annual Meeting & Exibition, , Detroit (USA), pp [6] Zadoroznaya, E., Levanov, I. and Mukortov, I.: Application non-newtonian models of lubricant fluids at calculation complex-loaded units of friction piston and rotor-type macines, Friction & Lubrication in Macines and Mecanisms, No. 7, pp. -30, 011, (in n). [7] Mukortov, I.V.: Multilayer adsorption lubricants and its inclusion in te teory of fluid friction, Bulletin of te Sout Ural State University, Vol. 18, No. 31 (48), pp. 6-67, 011, (in n). [8] Mukortov, I., Zadoroznaya, E. and Levanov I.: Multimolecular adsorption lubricants and its integration in te teory fluid friction, in: Proceedings of te 68 t STLE Annual Meeting & Exibition, , Detroit (USA), pp УТИЦАЈ ПОЛИМОЛЕКУЛАРНЕ АДСОРПЦИЈЕ НА РЕОЛОШКО ПОНАШАЊЕ ТАНКОГ СЛОЈА УЉА ЗА ПОДМАЗИВАЊЕ Игор Мухортов, Јелена Задорожнаја, Игор Леванов, Ксенија Почкаило Објашњење и приказивање утицаја који адитиви за смањење хабања у мазивима имају на врсту подмазивања и карактеристике трења је доста сложено. Експериментална испитивања многих истраживача указују да постоји утицај адсорпције мазива на параметре трења при граничном подмазивању, односно на хидродинамичке карактеристике клизних лежајева. Познато је да се стварна веза између коефицијента трења и контактног притиска код ових елемената значајно разликује од теоријске. Аутори овог рада су на примеру моторних уља установили механизам деловања адитива за смањење хабања и доказали полимолекуларну природу адсорпције мазива на контактне површине. Предложен је реолошки модел за танак слој мазива на основу физичко-хемијског концепта механизма адсорпције, који подразумева утицај адсорбованог слоја на вискозност мазива у близини површина које се подмазују. Разрађен је и метод хидродинамичког прорачуна лежаја коленастог вратила мотора СУС који узима у обзир ефекат адсорпције моторног уља. Предложени модел реолошког понашања танког слоја мазива је заснован на постојећим хемијским и физичким законима, а даје знатно бољу сагласност између прорачунатих и експерименталних резултата. Поред тога, дато објашњење механизма деловања адитива за смањење хабања може да буде корисно и у развоју нових мазива. VOL. 43, No 3, 015 FME Transactions