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Encyclopedia of Surface and Colloid Science, Third Edition

P. Somasundaran, Namita Deo, Raymond Farinato, Vicki Grassian, Max Lu, Martin Malmsten, K.L. Mittal, Ramanathan Nagarajan, Patra Partha, Gleb Sukhorukov, Darsh Wasan

Acid–Base Behavior of Clay Surfaces in Aqueous Media

Publication details https://www.routledgehandbooks.com/doi/10.1081/E-ESCS3-120028031 Marcelo J. Avena Published online on: 27 Aug 2015

How to cite :- Marcelo J. Avena. 27 Aug 2015, Acid–Base Behavior of Clay Surfaces in Aqueous Media from: Encyclopedia of Surface and Colloid Science, Third Edition CRC Press Accessed on: 23 Sep 2021 https://www.routledgehandbooks.com/doi/10.1081/E-ESCS3-120028031

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Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 nylpdao ufc n oli Science, Colloid Copyright and Surface of Encyclopedia INTRODUCTION Italy Trento, Trento, of University Engineering, Materials of Department Siboni Stefano Volpe Della Claudio Theory Surfaces: (Polymer) of Behavior Acid–Base ufc hsclceity vntdyi scmo to common is it terms today a the experimental even find is and ; cultural paradigm physical of surface acid–base series the long a reasons, the to Due and istry. applications the theory. acid–base of of importance development incredible the to of correlated strongly theory. concept Drago, bases, (MO) the orbital and by molecular acids proposed developed soft who and were hard Klopman, strength factorization and basic the Sec- Pearson, on and the based acid After approaches of reactions. War, electron redox World of the ond limit including the of to and eliminating concept tried pairs by Usanovich the it pairs. generalize using electron further bases, donating and or acids accepting upgraded of Lewis definition mechanics, the quantum of Br introduction the the became solution, over- development. to chemistry able the to was due paradigm crises this cultural introduction. all century its come a before than with chemistry more imagines, For of chemist bulk state a the that difficulty, appli- general and so importance are its cations and chemistry in concept brated a hrce fasrae ntecontrary, the on surface; a of character cal h iuto sdfeeti h il fsraechem- surface of field the in different is situation The an to corresponded paradigms new these cases, all In water in only valid concept, Arrhenius original The cele- most the probably, is, paradigm acid–base The nyteceitcntl,adntawy the always not fluids compounding and from tell, solids. result or will can what chemist chemist, the Only 05b alr&Facs l ihsreserved. rights All Francis. & Taylor by 2015 hoyadteai–aeter,te oe otemteaia ae fteapoc fGVOC further of for approach application the of forces examples of interaction several bases the providing mathematical of surfaces, the overview to of concepts. to due historical key properties crises moves of acid–base cultural a illustration then all before the with theory, overcome chemistry to to begins acid–base of theory able the state entry was the and paradigm This difficulty, this theory and with development. century importance imagines, a chemistry its chemist than and the bulk more chemistry, a For in that introduction. concept its celebrated general most so the are probably, applications is, paradigm acid–base The Abstract “ polar ” — or da .Masters, L. Edgar “ se–or eiiin after definition; nsted–Lowry nonpolar ” hr dto O:10.1081/E-ESCS3-120000910 DOI: Edition Third eiigtechemi- the defining “ young “ po River Spoon h reader the ” n in one ” motneo cdbs neatosa nefcs nthe in interfaces, at section interactions acid–base of importance rte yS ui 1982, in Wu S. How- by theory. written acid–base the the even by ever, 1990s in substituted was components, icsin nti ujc ytelt rf oks by recommended. Fowkes, lively highly Prof. are The al. late role. et the Good minor by by or very Berg subject a this only on plays discussions force, of kind ie ofitn oa ilsta iiiedipole term minimize the by dominated that is forces phase intermolecular condensed of fields in language pro- the if local neighbors Even nearest interactions. of conflicting com- (as number high gases) vides the dilute phases, to condensed in pared that, is point The sur- of context substantially the chemistry are in physical importance) terms face reduced these of (or, that flawed convinced be should eeoe nteclua oano hsc n of and physics “ of domain cultural subject this respectively. the chemistry, on view in of points developed different the on dependent to theoretical attempts inadequate numerous approaches. using the interactions with surface correlated analyze well is tence, aeo h adjective the of case interactions. their and surfaces oxide of kinds different eea qaint xrs h neato potential interaction the and a express 1921 write Between to to between able 1873. equation were in London general and Waals initially Debye, der Keesom, gases, 1930, van in forces by attractive made the of understanding parallel hsi h esnteprdg fthe of paradigm the reason the is This tfrtgac,i a peraprl eia problem. lexical purely a appear can it glance, first At h eeomn fteai–aeter a been has theory acid–base the of development The a have problems These osm xet h s fipoe em,a nthe in as terms, improper of use the extent, some To “ ” oi odn tInterfaces, at Bonding Ionic “ ota farmral civmn nthe in achievement remarkable a of that to pairs ” hc a xrml omnutl1980s, until common extremely was which ” “ bible of ” “ “ polar . ionic fteplrcmoet theory, components polar the of ” ” “ [5] cultural ie ntepeiu sen- previous the in cited oeue.Tewr of work The . niae h potential the indicated ” ” eiae othe to dedicated rgn probably origin, “ polar, [1-4] “ ” polar this 75

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Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption 76 1805 1887 1928 1941 1939 1930 1923 1921–1922 1920–1921 1903–1908 1872–1873 1869 Year theory acid–base 1 Table 1937 oehsoia oe nsraeitrcin n on and interactions surface on notes historical Some . ○ ○ . ○ ○ ○ . . ○ ○ ○ F oaee bases donate and accept acids Lewis: H accept Br H water bases in and acids theory: Arrhenius oaee bases donate and accept acids Usanovich: F F fmolecules of between forces dipole ocsaddul ae ocsin stability forces colloidal layer double and forces Dupre equation Young esm emnn dipole-permanent permanent Keesom: dipole dipole-induced permanent Debye: w Gru and Mie (+ gases pressure real the of on term correction the explain to forces intermolecular hypothesized Waals der van ejgi,Lna:DV hoy vdW theory; DLVO Landau: Derjaguin, D between forces integrating systems between macroscopic interaction of energy Hamaker: an dipole dipole-induced induced London: w potential 6–12 or Lennard–Jones the potential; intermolecular of component repulsive Dent: Lennard–Jones, G il Keesom lj London ij Debye ð ð r r “ se,Lwy cd oae bases donate, acids Lowry: nsted, 12 Þ¼ Þ¼ additive 1 = (1) equation + ¼ needn pairs independent ○ ¼ ¼ ndfeetsolvents different in pairs + r r A A Physics/ 12 n ¨ ” n OH and A neisen: hoyintegrating theory 12 a needn pairs independent 3 2 a 4 3 W g /12 i / µ µ a sv v r adh B kT j 2 r 2 i 2 m B i p ) . = 6 a µ 1 þ j 2 = Chemistry 2 j g 2 I lv i g 2 a lv cos þ I r j 1 i + µ ij 6 I fmolecules of j i 2 g I q j sv + r ( g 1 Continued ij 6 r sl 1 g ij 6 sl ) 1953 1957 1964 1962–1968 1955 1978 1969 1965 1963 Year theory acid–base on and actions ( 1 Table 1985 1966 Continued cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base . . ○ . ○ ...... eaaiiyo .adL forces L. and D. K of on separability based components different tension in surface of division Fowkes: bases and acids soft and hard theory: HSAB Pearson: forces repulsive equation for Hamaker of correction Good: attack electrophylic or for nucleophylic density electron frontier Fukui: hoyo solids of acid–base theory Chaudury: Oss, van Good, solids of theory acid–base Mostafs: Fowkes, interactions dispersive acid–base of and terms forces in oxides solid liquids and of interactions Michaels: Bolger, 1978) in numbers (revised acceptor and donor Gootman: (1991) water of case the evaluates solid phases, of liquid case and the in are important forces not dipole that concludes Good: polarizability of role the Drago: indices. similar reactivity and HSAB of features qualitative the reproduces equation perturbation the reactivity; of chemical treatment general a Klopman: W W ovn medium in solvent interactions to ionization applicable single potential a than more a , with for gases expression dilute general of more case the vdW for of forces theory generalized a McLachlan: problem additivity the avoiding phases condensed to applicable interactions molecular of vdW theory general a Lifshitz: ) D adh adh H oehsoia oe nsraeinter- surface on notes historical Some AB ¼ ¼ = ○ þ E þ 2 2 Physics/ A  q E q fN q B g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g ffiffiffiffiffiffiffiffiffiffiffi + lv LW ð g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lv þ E lv LW C g g A D sv . A sv LW E C g G Chemistry sv LW B B 12 þ 1 = (1) þ p C g ffiffiffiffiffiffiffiffiffiffiffi lv A C g A ( sv þ B Continued 12  Þ /16 p 1 2 ) Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 bouetmeaue I temperature; absolute ewe w molecules two between et nteohrcssrfrt hseccoei rapyia chemis- the physical in a or defined g encyclopedia this precisely to more textbook. refer try cases are other quantities the in these text; of Many results. epce etok eiae osraescience, surface to dedicated called textbooks and respected systems special few lcrsai rsf rpryo A; of property soft or electrostatic the of moment dipole inptnilbtentomolecules two between potential tion odninteractions; London al,aii n ai opnn fsraefe energy. free surface of component basic and superscript acidic Waals, the and A; of Theory Surfaces: (Polymer) of Behavior Acid–Base 1991 e al constants; Waals der ewe w oeue safnto fterdsac;A con- = B A, distance; their of function Mie–Gru the a of as stants molecules two between otc angle; contact cdbs neato,tehdoe od rteforma- the or Lewis bond, of the hydrogen tion as the such interaction, base, rep- acid–base mechanical to quantum possible explicit not an is it forces impor- reduced, the Waals the is resent der forces where those speaking however, van of phases, the directly tance condensed to sense, in refers wide only); dispersive a of term in treatment the forces the London to and of well kind pretty each corresponds potential interac- acid–base not that important. did and very systems were phases tions macroscopic condensed config- for of the hold energy of computation free the urational for assumption the additivity particularly, pairwise results, and, of of Lifshitz’s ideas contribution some on the that based that showed mainly 1960s coworkers, the late this of and in limits Good only internal generalized was the It of theory. McLachlan some showing and also approach Lifshitz, Hamaker, and Year theory acid–base on and actions ( 1 Table safnto fterdsac 1; distance their of function a as 2 et fpyia hmsr n fteter of theory the of field. and surface ele- the chemistry in bedrock even are reactions, physical chemical molecules of elec- the and ments of electron-acceptor abilities the of tron-donor treatment absent. general even the is or covered inter- well surface not to is applied either as actions theory acid–base to reference h cdbs neato nhlybtenlqisAadB; and A liquids between enthalpy interaction acid–base the ij omnorigin; common : nefca nrya h onaybetween boundary the at energy interfacial = hs neatosaeotncniee pcfct a to specific considered often are interactions These ti o ut elacpe htteLennard–Jones the that accepted well quite now is It ntecnrr,teLwsai–aeitrcinand interaction acid–base Lewis the contrary, the On D G 12 “ l h trcieeeg w aallbde fpae and 1 phases of bodies parallel two energy attractive the = (l) adduct Continued “ short-range W “ adh dispersive ” . h oko dein n ftetrevan three the of one = a adhesion; of work the = ¨ compounds. . riiilymdfe surfaces modified on artificially angle contact Whitesides: edno enr–oe potential; Lennard–Jones or neiden v i a anyceia results; chemical mainly : ) h oueo h gas; the of volume the , i molecule i oiaineeg fthe of energy ionization = oaiaiiyo the of polarizability = i oehsoia oe nsraeinter- surface on notes historical Some LW and ” ,and +, , ” neatosta r one on founded are that interactions ○ oc vndrWas Keesom, Waals, der (van force j ; i ; Physics/ C w k A h otmn constant; Boltzmann the , A i ( aae coefficient; Hamaker = h oaeto adproperty hard or covalent the = r and h nryo interaction of energy the = ) “ ee oteLfht–a der Lifshitz–van the to refer hydrophilic . j Chemistry o ey,Keo and Keesom Debye, for i r and i ○ or molecule; anyphysical mainly : i j molecule; r [8] phases; ij ” h distance the , F ocs in forces; ij [6,7] interac- = E µ D T A q i H the = the = the = the = D AB any G 12 = faui ufc ewe hs n hs S. phase and L phase between surface unit formation–disruption a of of process thermodynamic well-defined a 1 Fig. tt hi eut ntrso reeege renthalpies, or surface energies per free of quantities terms thermodynamic surfaces) in interaction results (or their of particles state depend terms two which in between energies, expressed or commonly potentials is view eaaeti ujc rmtegnrlter finter- of to theory possible general not the solid is from forces. to molecular it subject theory this that acid–base separate considering main of the science, the application show surface to completeness, the opportunity of historical an results only of general; is claim in section present science any strongly of and without complex development so, is the science with surface connected of history The Theory Forces Interaction The OVERVIEW HISTORICAL AN in analyzing interactions. not possible without is numerous problem It the all this forces. detail interaction confront chal- of to greatest description possible the the for represent lenge flexibility, structural mous interactions. surface of understanding an for necessary if the work and physics adequately can it but used. rigorous, correctly entirely not is energy, potential of a details and dynamic initial the the not process. the between state, difference thermodynamic final the considering by per sakn of kind a as quantum appears quantum intrinsically explicit an is description. imposes mechanical therefore acid–base nature the and of mechanical whose complexity great the interaction, of because likely ti ot fntn htwietepyiitpitof point physicist the while that noting of worth is It mn ois h oyes hnst hi enor- their to thanks polymers, the solids, of Among approach rigorous more the that opinion our is It of terms in interaction acid–base the of description A si ayohrcss the cases, other many in As h eiiino h oko deincrepnsto corresponds adhesion of work the of definition The - ntbssadprann oagoa system global a to pertaining and basis unit “ heuristic w “ ( heuristic r ,de o xs.Ti smost is This exist. not does ), ” xrse naprml or mole per a on expressed blt fceityaeboth are chemistry of ability ” “ chemical prah oeie it sometimes approach; hmssusually chemists , ntedistance the on ” on fview of point 77

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Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption n12,LnadJnsadDent symbols. and of Lennard-Jones meaning the 1928, explains caption In the and tions 78 ytecretapiaino rsn theories. present solved of are precisely application problems be correct will those the will and by of quantity true many our this partially, however, is when least measured; it only at in solids; controlled be, problems can be of open this energy the that free all opinion surface solve the can quantity interpreting this of measure- tion angle contact research. open by is is explored state point this those chemical ments; and as taken physical same has whose adsorption the surfaces that prove on to place some published. is but difficulty been main zero, have The from results different zero experimental is to contradictory angle close contact considered the is when it commonly side; right-hand ae hs rai nt a esmaie ntefol- the in W summarized be can unit, equation: is lowing area whose face, constant respectively. at phase, solid 1 a Fig. and liquid in the a shown of process variation the the pressure, in to energy corresponds it free adhesion; show of to manner. work linear is a aim in its work chem- not and and does indicative science physics purely that between is 1 results Table istry the in division The W Young the and equation this Dupre equation, Using phases. different the don. eei oeta fteform the of potential generic osdrdtecs ftefre cigbtenpairs between acting forces the the of obtaining case potential, the considered the of famous component repulsive intr ntepesr fara a (+ gas real correc- a of the pressure for the account on term to tion equation; famous his proposed n10,G Mie G. molecules. 1903, between In forces attractive of existence the sized in ewe emnn n/ridcddplswas dipoles Debye, induced by and/or permanent developed between tions forces. these for account to ftegspaet h oi hs sngetd hsfac- this term neglected; is the phase by solid adsorption the expressed eventual to the tor, phase of gas effect the the of equations, these In Warning hr the where adh adh n17–83 a e Waals, der van 1872–1873, In introduc- the that hypothesized repeatedly been has It h okncsayt eto h oi–iudinter- solid–liquid the destroy to necessary work The the is refer to easiest is it which to quantity The 1. Table in defined are here defined not concepts The ni 90 e feutosdfnn h interac- the defining equations of set a 1930, Until [16] ¼ ¼ al hw htteeatfr fteeequa- these of form exact the that shows 1 Table “ 6–12 g g P g lv lv n temperature, and , ij þ þ ybl r h nefca nrybetween energy interfacial the are symbols ” oeta.I l hs ae h theory the cases these all In potential. a bet hwthat show to able was g g [10] sv sv n hnE Gru E. then and [12,13] g g sl sl ¼ p T e Keesom, hudb de othe to added be should , Indexes . w g lv ( r [9] ð )=( 1 tdigra gases, real studying [17] þ ¨ neisen A [14,15] a / cos )/( L v nrdcdthe introduced 2 and r ,h hypothe- he ), n q [11] ) Þð n Lon- and S rt a wrote ( ee to refer B )/( ð r 2 1 m Þ Þ ) a h is tep ocluaeteitrcin between interactions phases. the calculate condensed to theory attempt Hamaker first the the was systems; study the condensed to macroscopic molecules of of pairs independent among forces main the than weaker equation, something Deybe terms. in the however, from resulting, calculated be can interactions h lcrncod fitrcigmlclswl oscil- will molecule. molecules the interacting synchronously. of of late clouds energy The approximation the the from used calculated London oscillations the field. accidental that polarized electrical external be the the can by of cloud by ways polarized electron different be the in can field; that electrical cloud the electron an has however, inwl ieteefc vrgdoe ieadconsid- energy. and molecular time of over distribution the averaged Boltzmann equa- the effect on Keesom ering the depend The give molecules. will will the tion interaction of effective orientation mutual the the and of field oscillations and and direction rotations in the time electrical molecule. to with the vary due of will intensity, distribution field This nonuniform charge. the to owing on depends forces dipole. nonpolar; Keesom constant or a and polar of Debye that molecules, of of existence kinds the all among exist of iiain eentflyrcgie ni 1955. until recognized fully these not Unfortunately, were phases. limitations condensed in different ously by made are approximation pairs independent as method considered molecules, general between same interactions, the calculating even of and potentials described il hoyadti aei ifcl oudrtn the understand to researchers mathematical difficult other quantum it until The on made results based this new phases. widely and sus- was theory electric two Lifshitz field the by of the of used as method frequency function well of complex as the a numbers ceptibilities where is quantum way, clouds the electron of general the a of oscillation in constant Hamaker written the calculated is e.g., is properties, interaction macroscopic are con- their bodies from to and macroscopic continua applicable the as but theory, considered his London, In of phases. that densed to related ment, ipe prahs nrdcda idof kind a as introduced approaches, simpler et,adoecm h rbespoue ythe by produced problems the approximation. overcome bimolecular and ments, approach, additivity igeidpnetmolecules independent single n13,Hmkrapidtecneto interacting of concept the applied Hamaker 1937, In possible A ahmlcl,psesn osatdipole constant a possessing molecule, Each this with interact will molecules dipolar other All molecule any around exist will field electrical An nta er Lifshitz, year, that In the call can we which method, This “ aua frequency natural cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base a eue hnteitrcigmedia interacting the when used be can , “ iuegases, dilute “ rs term cross [18] ” ol rvd h aeachieve- same the provide could aae sdtepreviously the used Hamaker [19-21] umn ptefre acting forces the up summing ” ” ” fti silto a be can oscillation this of ewe hs w main two these between u h iuto sobvi- is situation the but h odnfre can forces London The . eeoe e treat- new a developed [19-21] a hw that shown had bimolecular “ modified rnot or . , Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 a rpsdfcoiigtesraefe nryof energy free surface the factorizing proposed had 2 Fig. Theory Surfaces: (Polymer) of Behavior Acid–Base eo h au siae ytebiomolecular the by estimated that value consequence is boundary important approximation the phase the nearest a All below across to the account. energy into lead and dipole–dipole taken facts be molecule should these the dipoles, of an of geo- approach in like structure dipoles elements, of other metrical orientations some Moreover, the are way. dipole randomize effects effective to the thermal energy the able If their strong, not patterns. appreciably rotating; complex are freely moments to not correspond are minima dipoles the phase omnt s h euto h ae hoyo McLach- of theory later the of result lan, the use to and common greatly, approximation. is bimolecular interaction consequence, the dipole by a enhanced the as wrongly, cal- of to minimum; importance able energy the is correct energy pairs the The dipole culate only minimum. the considers energy that to the second approach the in pertains in dipoles three pair, is both minimum a of (A) pair considered of state dipole if case state energy no the lowest lowest in the dipoles in (B); the two are in and of shown state is (A) energy dipoles in lowest shown the 2; is Fig. in shown ufc eso n oaot2 Nmo oa a der Fowkes van earlier, total years of total three mN/m the 22 Only of about interactions. mN/m mN/m to 72.8 Waals 1.4 of and only value tension of total surface value the a to obtained respect very with he was water interactions For dipole–dipole small. purely in of McLachlan relevance that of conclude equation complete to more the and approach fmlclsi solvent. interactions a the in handle absorption molecules to different of possibility the the of and role frequencies the London, by proposed u ftemlcl ar ntescn,teeeg minimum energy mini- the second, energy certain the a the in to pair; to pertains molecule corresponds the of position mum indicated the case, ahpi snti t nrymnmm fcniee sapair. a as considered if minimum, energy its in not is pair each nfc,oesol osdrta ntecondensed the in that consider should one fact, In ntecrettetet fLfht hoy tis it theory, Lifshitz of treatments current the In is difference this understand to example qualitative A n16,Go tal. et Good 1966, In [22-24] w ( Two h nrdcd ntetobd interaction two-body the in introduced, who A . n he ( three and ) “ structure “ polar [3,4] B ” neatn ioe;i h first the in dipoles; interacting ) ” “ faltemlcls nwhich in molecules, the all of global sdamdfe Lifshitz modified a used oeue iewtrthe water like molecules ” tutr n no and structure well [25] ntelt 90,teai–aeter a greatly was theory, theory Arrhenius acid–base original 1887 in the the introduced to respect 1960s, with late developed the In Lewis Theory the Acid–Base to The attributed was remaining mN/m the 51 interactions. acid–base that about proposed of quota Good phases. condensed Br hre svr ifcl ooti npatclcases, practical in electrical obtain of to difficult excess very significant of is a complementarity electrical charges of the However, complementarity and sense the base charges. recalls certain a bases with a and interact acids In to needs versa. molecule vice a acid, an as plementarity DMSO). (e.g., its acids being the versa; from strength. to vice excluded acid–base respect its and on with base; depends base base stronger or a a acid conjugate and being of the acid to acid weaker respect conjugate with a acid of an base is It sense: lowing ue oitrc ihawtrmlcl ybekn it breaking by molecule (H water a protons with into interact to cules a eie sasbtneal odnt rtnand it. proton accept to a A able donate substance to a able as acid substance base an a a solvents; as nonaqueous defined to was concept this broadened tneis, stance respectively). acid, certain a to (or measured base certain be a can basicity) substance the certain (or a acidity the of that fact the 4. to Eq. be corresponds for This possible cannot is 3 this contrary, the Eq. on measured; of directly constant equilibrium the Unfortunately, Warning equilibrium express to corresponding way natural titative the easily the becomes be this can constants; reactions introducing of kind base1 applied, each consider- becomes to thermodynamic acid1 pertaining The base2; ations acid2. to becomes acid1 base2 transfers the and which from reaction, proton corresponding a the from acid or not has A phase way following liquid the in in written the protons so now free proven; until been of today; existence different slightly the is chemistry, modern acid acid udmna dai cdbs hoyi the is theory are acid–base protons in have idea fundamental not A do that materials those Only ti motn ont hti Lter ahsub- each theory BL in that note to important is It base conjugate a into transformed is base or acid Each of part a is which concept, this of language The nsted 1 , þ eain mn ifrn cd n bases. and acids different among relations [27] contemporarily H B base proton þ fteaii n ai rpris owork To properties. basic and acidic the of n,te neednl,Lowry independently, then and, 2 + , rhdoy os(OH hydroxyl or ) þ [26] effective B A base n ae nteaiiyo mole- of ability the on based and acid nai n aei h fol- the in base a and acid an , 2 þ cdbs ecin a be can reactions acid–base B base 1 only ihrsetto respect with .I 1921, In ). [28] quan- com- (BL) ð ð 4 3 79 Þ Þ

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Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption spootoa otecsn fteavnigcnatageof angle contact advancing the of cos cosine water, the to proportional is hnei ofrainof conformation in change odnt rtn aeteefc flvln h strength the leveling of effect the have protons donate to the stron- electron. the that free and a thinking proton base free by conceivable a cor- gest enhanced is This acid bases. further conceivable and strongest be acids for can easier relation much is it although PE-CO of derivatives acid aminobenzoic 3 Fig. 80 ie fplehln.Tesldcrei h contact-angle the PE-CO is from curve obtained solid deriva- curve The non-titratable polyethylene. but analogous of several the tives the of represent in lines angles inter- variability horizontal the contact polymer The represents the measurements. symbols angle and the contact of liquid size contacting The the phase. of interaction of cos equation, ipytecnatangle contact the simply on rmlwt ihpH. high Source: to low from going eti ovns iewtr htaeal oacp or accept to able are that water, like solvents, Certain ( rmWteie tal. et Withesides From A ersnaiep irto uvsfranme of number a for curves titration pH Representative ) q a (H q 2 sdrcl rprinlt h e reenergy free net the to proportional directly is ) nteesrae.Ti esr,adnot and measure, This surfaces. these on O), q a sue eas,fo Young’s from because, used is , “ polyethylene-anthranilamide [31] 2 .( H. 2 .Tevria axis vertical The H. B Hypothesized ) ” on faisadbss h reai rsn na aqueous an in present acid true H the of bases; solution and acids of otmoaywt h eouinr rpsl by proposals revolutionary the Lewis. with contemporary h oko ogradMichaels and Bolger of work the H hyfudta tdfeetp-ifrn rusare low at groups instance, pH-different For environment. different water (CA), pH the at angle to that contact exposed found and (XPS) they of electron quantity significant a containing chro- thus by — and oxidized acid polymer surfaces contacting of mic (PE) changes the Polyethylene conformational of the surfaces. pH observe under the to with drop surfaces angle contact the advancing of density simple to the able electron is consideration. is that ions the What is hydroxil polymers. and/or modify description hydronium many this of for adsorption in true interesting be The very to basicity. or appears acidity metal of same the layer degrees of different thin properties induce a different with The interact molecules. which water strongly layer, of to hydroxilated of able a layer intrinsically as oxide is considered the acid–base view, be of can and be metals point can dispersive this liquid of a From combination and interactions. oxide a solid by a modeled of surface the between ihhg otc nlsi ae.I otat thigher at contrast, In of surface, water. existence in the the angles pH of environment, contact character external high dispersive the with strongly to a exposed not inducing are and bonds hr oecag fpooshpes u which following:BF the but is reactions. equation happens, acid–base famous of most protons characteristics the Probably the of the of reactions many overcome exchange those have to treating no in able theories where previous was the ideas he of 1923) limits mechanics, (in new quantum the accepting of bases; and acids about qiiru qain eerdt h ecin described reactions the Israelachvili, by the to of referred use the equations through equilibrium passes phenomena these of B. analysis and 3A Figs. angle in contact shown interaction advancing as low strong water, a in a and molecules with water polymer, with the of conformation n h rpsdcnatagettain yWhitesides by titrations angle co-workers contact and proposed the and nwihawl-nw ae moi,rat ihan with reacts ammonia, base, acid. well-known aprotic a which in 2 OHttaal ruswr analyzed. were groups titratable COOH n h da rpsdb Br by proposed ideas The hskn fai–aeapoc seteeyuseful; extremely is approach acid–base of kind This ycmaigterslsotie yXryphoto- X-ray by obtained results the comparing By the of variation the used co-workers and Whitesides interactions the that proposed Michaels and Bolger h ocp a ebodyueu.Tequantitative The useful. broadly be can concept The 3 +1 — þ O [32] OHgop edt omitra acid–base internal form to tend groups COOH n + ). NH ei opeeycagdceit ideas chemist, changed completely Lewis 3 2 cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base () SO [30,31] [6] 4 ihaltelmt led considered. already limits the all with rHli culyH actually is HCl or F 3 — B r ae nterapproach. their on based are COO NH rusidcsadifferent a induces groups 3 se n or were Lowry and nsted [29] noiesurfaces oxide on 3 O + o,generally, (or, ð 5 Þ Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 ny1 er ae Pearson later years 10 Only Theory Surfaces: (Polymer) of Behavior Acid–Base ei cd h ia euto hsai–aerato is reaction acid–base this of a result is called final substance The second donating this acid. of it; Lewis accepting capable of substance capable stance, a is defini- density base this electron Lewis changed A slightly have paradigm tion. dominant chemistry) the modern is which in theory, covalent MO of the (like kind ture peculiar a is forming as which it, known acid, bond, the accept molecule, to another able to electrons of pair ilassre) ea os hc r ei acids, Lewis are which ions, Irving– different so-called Metal (the of series). ions complexes metal Williams with of first transition or was stability with it property ligands the with new This confused with itself. be correlated basicity or not or acid should acidity the it the of and strength base, the the from different completely ity bases. and acids soft and hard of oss h hmclfntosal ogv hmLewis them give (PVF) properties. or to basic polyvinylfluoride able or quartz functions acidic or as chemical (PA), the such polyamide possess solids bonds as common hydrogen exceptional four glass, Also form an molecule. to becomes able per is water it inter- again, because acid–base example, Lewis once of should So, able case bond molecule action. common hydrogen the a a all considered and the are be bonding, bases for hydrogen and form candidates to acids can Natural Lewis of octet. boron with role electron whose pair an molecule, electron ammo- complete trifluoride the nonbonding 5, boron its Eq. the In shares bases. molecule and nia acids Lewis con- of not example theory. is BL this the in and as base strength, Lewis acid–base its a with and/or nected acid Lewis a be h il fai–aeter,wspooe n1953. he in proposed which was in theory, used for acid–base commonly Fukui is of density, the today field that and the electron prize noting Nobel worth frontier the received is connections of It the theory. concept through MO mainly the with theory, of acid–base properties the help and to structures ability proposed its correlate ever is substances. to numerous definition base chemist a a wide to the and so or acid of electrons, to advantage an or able of substance anions tion any furnish elec- cations. as to or with base combine anions acids, a accept with defined to react he and and cations, trons; furnish to acid–base base, many by of blocked example but useful, one “ very is potentially it generalizations, success; great cultural loi hscs,temdr hoiso lcrnstruc- electron of theories modern the case, this in Also a donate to able is base a that is definition Lewis’s h adeso oteso nai rbs saqual- a is base or acid an of softness or hardness The h ocp eie yUsanovich by defined concept The good as considered be can molecules of kinds Many fe h eodWrdWr ayatosextended authors many War, World Second the After a react to able substance any as acid an defined He adduct ” reasons. ti ot oigta ahmlcl can molecule each that noting worth is It . hc ilb hrdwt eodsub- second a with shared be will which , “ dative hsi rbbytewds defini- widest the probably is This ” bond. [36] nrdcdteconcept the introduced [33,34] ee a a had never h real The . [35] n eiso tblt eedefined. were stability of series metal ent B class B. of metal pattern and A same A class the of ions. exhibit called pattern acids first same soft and the classes, follow two acid Hard into divided were . . . . al 2 Table where ntne h eiiino otadhr cd n bases and acids hard and Pearson to soft according of definition the instance, is basicity and acidity acid with an correlation of clear. the not softness but energies and base, hardness a LUMO or to and related HOMO certainly are different. slightly appear and electron, HOMO affinity. the of tial uniaieoeainldfnto fhrns and h hardness for of used definition been have operational softness: orbital, quantitative LUMO unoccupied a so-called high- lowest the the the i.e., and one, (HOMO) orbitals, orbital frontier appli- occupied the wider est a theory; to MO thanks of changed, cation slightly is softness and similar more of something idea by old case the this to the in that substituted Note is versa. rule vice and acids or nTbe2. Table in adai o OOHg UOLarge Small Large Small LUMO High LUMO Low HOMO Low HOMO HOMO Low High HOMO acid High Hard LUMO High acid Soft LUMO Low base Hard base Soft h eiiin fPearson of definitions The differ- two atoms, donor different with complexes For hsapasvr vdn fw opr,for compare, we if evident very appears This definitions common most two the Unfortunately, nti ae oee,temdr dao hardness of idea modern the however, case, this In bases hard with associate to prefer excited bases or easily acids Hard several has and Polarizable. outer electrons. size, outer excited large easily charge, acids several Soft has and electrons; size, small acids Hard with orbitals; associated low-lying empty and oxidized easily electronegativity, inaccessible; hence and bases with energy Soft high associated of and orbital reduce empty to hard electronegativity, bases Hard ¼ I h steaslt hardness, absolute the is otadhr cd n bases and acids hard and Soft 2 A oo tmi fhg oaiaiiy low polarizability, high of is atom donor : h cetrao so o positive low of is atom acceptor the : ero Fleming Pearson cetrao so o oiiecharge, positive low of is atom acceptor : oo tmi flwplrzblt,high polarizability, low of is atom donor : “ iii similibus. similia [36,37] n Fleming, and [36,37] A I eetefollowing: the were ” h oiainpoten- ionization the h UOelectron LUMO the “ complementarity [38] (LUMO–HOMO) sillustrated as D E 81 ”

Absorption—Acid

Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption opeeydsesv oeue ol npicpebe principle in could as defined molecules dispersive completely widely appli- the paradigms. by incorrect produced but is simpler bond of cation orbital–one one of lence molecule more the the or case, one structure. the of molecular in input the the of compromise, along stability since seriously density sites, could electron bond electrons large the a near with or LUMOs to applied properties. basic effective the to only spond if density Thus, completely highest region. changes their have situation orbital HOMOs molecular the the struc- imply; of molecular depletion would electronic the the of that because reorganization ture prohibited bond among too-strong even interspaces or the the inhibited smallest of near be (the could density atoms) molecules the electron the large of sites a with HOMOs account. some into by taken be played should be which presumably factors, could other role important an while properties. acid–base molecule, significant dispersive has glycol completely ethylene a behavior: is acid–base HOMO-LUMO Hexadecane different similar completely very a but have properties, 4A–D, Figs. angles in shown contact in ethylene used 3). and Table commonly (see hexadecane measurements liquids instance, two LUMO proper- for glycol, and acid–base consider, different HOMO ties; significantly similar explain show can very This energies with orbitals. molecules molecular empty why of and pairs iudHM,e UO V(I eV LUMO, eV HOMO, Hexadecane glycol Ethylene Liquid 3 Table 82 nomto rvddb OOadLM energy LUMO the to and gross related the HOMO mainly on but by values, independent provided essentially are information molecule a of from arises basicity a or classifications. energies. to above acidity the HOMO of related definition and as univocal softness LUMO No of between LUMO- that difference large and small a gap iden- with energy the associated HOMO concerns as accordance hardness only of tification the and different be hs adesadsfns emt eproperties be to seem softness and hardness Thus, to pertains orbital molecular a that here Remember be principle in could considerations same The from electrons of removal possible the instance, For molecule, a of behavior acid–base the determining In molecules, these of orbitals LUMO and HOMO The hs n a xetta h cdbs properties acid–base the that expect may one Thus, to out turn definitions two the suprisingly, Quite “ independent OOadLM fehln lcladhexadecane and glycol ethylene of LUMO and HOMO “ hard sauiayobject unitary a as ” or 165305 7.3450 6.8770 3.0650 2.9340 11.625 10.820 ” “ “ soft. nonbonding faiiyadbsct;ee quite even basicity; and acidity of ” ” availability n htteequiva- the that and , OO a corre- can HOMOs “ out ” ftebond the of felectron of )2= A)/2 h n a osdrtesatn on fthe of point starting the consider can One SITUATION MODERN THE xeiet aeb okswspbihdi the famous in most published the was of Fowkes One works by 1980s. other role. made some However, important experiments 1966. an in Good played by or 1964 age . . . rg equation well, Drago quite work data. they of simply, sets wide for relations; correlating of exists kinds explanation and these theoretical direct convincing No compounds. definitely aromatic parasubstituted and epn ut elt h atto between partition the and to well quite respond t anbssi h rgeso unu ehnc.In mechanics. quantum of has book progress however, famous the which, a in view, bases of main point its modern a of 5). opment (Fig. and broken adhesion was film strong the complementary a peeling had the produced during surfaces casting two the postchlorinated the properties, and when PMMA Only by properties, PVC. casted: acidic acidified and were different basic was respectively, these with on polymers basic, solution; sodium–calcic two acidic supports, prevalently diluted common a in a is immersion supports: which basic glass, and acidic iutstremjrfre,oeaigwe w mole- two when indi- operating Fleming collide: forces, mechanics, cules major quantum three of view viduates of point the hrce faisadbases. and acids of character aeai–aetere;i oe rmteoiia work original the energy from Hammet comes of it free theories; acid–base linear face the or use to relationships. connectivity, scale, common solvatochromic very incredible the molecular is the like it to treatments, argument, semiempirical due the in field, correlations of this many complexity of In base reactivity. the chemical are basicity and acidity defini- the in the contained of term tion repulsive the with theories, mn h otfmu fteerltosi the is relations these of famous most the Among soecnesl ovneoeefteefre cor- forces these oneself convince easily can LUMOs one and As HOMOs molecules. interacting the the of the respectively, between orbitals, of attraction charges the opposite finally and the the molecules; different between of attraction orbitals the occupied the molecules; two between repulsion the uha lgn xeietcnrbtdt h devel- the to contributed experiment elegant an Such hsls ramn a oiebeipc nsur- on impact noticeable a had treatment last This Lewis and softness and hardness hand, other the On ” “ ntesraedmi ob h okb oksin Fowkes by work the be to domain surface the in acid–base [39] “ okscmae h deinbetween adhesion the compared Fowkes [40] dispersive cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base [38] ” [41,42] oepanteratvt rn fmeta- of trend reactivity the explain to neatosue nsraefe energy free surface in used interactions nceia eciiy nlzdfrom analyzed reactivity, chemical on ” o h lcrsai n covalent and electrostatic the for interaction. “ dispersive “ acid–base ” Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 oaeeeto est a opeeydsrytemolecule. the destroy completely can density electron donate donating or accepting with not interact portions strongly possess can not which do atoms, orbitals of both hexadexane, pairs of between case centered the not In portions density. wide electron contain orbitals the col, 4 Fig. Theory Surfaces: (Polymer) of Behavior Acid–Base oo n cetrnmes umn ugse that suggested Gutmann numbers. acceptor and donor Tecoefficients (The n e e parameters, new effects: introduc- transfer few steric by a charges, the electrical ing strongly surface for with of in proposed systems been important consideration interacting has particularly correction the A be phenomena. in can interact- which strongly and effects, many for systems fails the ing also an it of essentially However, aspect is cases. substance limiting each most that acid The is treatment material. Drago the quantity the of and ness hardness the the with between the lated complementarity the that no to and is properties pertain enthalpy there materials i.e., of property, different terms of in coefficients written is indexes equation the and and respectively, components, covalent D D h rg qainhsteform the has equation Drago The esol lomninteGutmann the mention also should We H H B or AB AB oteitrcigmtras;nt htteDrago the that note materials); interacting the to ae hc shr oacp nmn common many in accept to hard is which base, a h ( The ¼ ¼ E E E A and A A E E , [41,42] B B B OOad( and HOMO ) E C þ þ nE.6 h quantity the 6a Eq. In . and C C A A C C C B B ee oteeetottcand electrostatic the to refer þ T oacutfrelectron for account to , C T A , T D B UOmlclrobtl fehln lcladhxdcn.I h aeo tyeegly- ethylene of case the In hexadecane. and glycol ethylene of orbitals LUMO-molecular ) C [43] ihtesoft- the with E ocp of concept scorre- is same ð ð 6b 6a A Þ Þ h cdbs nhlyo dutfraincnbe can formation quantities, two adduct of product of the as enthalpy expressed acid–base the fe h ls srne ihHl h PVcnb peeled be can CPCV the HCl, However, PMMA. off. Source: with the peeled rinsed not but be is off, films cannot glass cast CPCV the but polymer off, after peeled acidic easily the are of glass (basic) ordinary onto 5 Fig. hr h oo number, donor the where n;ti prahi neetn ihrsett the to respect with differ- truly interesting Drago it the is make of scale approach form the this simplified of details a ent; this the as view but of seen point model, be certain a can From theory material. the of acidity h eaieo h nhlyfraino h adduct the of formation enthalpy SbC1 the the between of negative the D H AB im ftebscplmrPM atfo solution from cast PMMA polymer basic the of Films rmFowkes. From ¼ DN 100 B “ entrapped AN 5 A [39] n h base the and ” ewe tmpis oacp or accept to pairs; atom between DN B B = ; AN D H A (SbCl xrse the expresses 5 B,is -B), 83

Absorption—Acid

Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption component, the where oaiaiiyand polarizability ecie h hs yrgnbn cdt and acidity hydrogen-bond term phase The acidity. the hydrogen-bond solute describes the for stands technique. through (IGC) made gas acidity–basicity inverse the surface of measurement 84 h ae fgscnesdpaeadcnesdphase– to condensed (LSER) experiments: and condensed-phase relationships gas–condensed-phase of energy cases solvation the linear of tion W ability, oueecs oa refraction; molar excess solute oitrc through interact interac- to acid base–solvent respectively; solute tions, solute-condensed solute and dipole–dipole, base, specific dispersion, acid–solvent i.e., represents interactions, more- phase (or side phase fixed right-hand a in solutes of phases), log series a variable of dependent property the which in sapidt nefca rbeshdbe,substantially, been, organic had physical problems a interfacial theory of to acid–base field applied The as kinetics. the chemical in of and proposed chemistry those struc- interaction mathematical of acid–base same ture the the have express systems interfacial to for chemists by posed following the in analyzed fully section. be case.) will complex or which most phases, properties, the is condensed this are so two condensed, are and three gaseous all is one erally, basicity, hydrogen-bond solute the ae o,euvlnl,teitrailsolid–liquid interfacial equation the sur- two an equivalently, of cases; adhesion energy, of (or, both work the in faces for proposed theory; been acid–base and has all the at of science. surprising in traced not be is can examples fact similar many this However, lation. in that angles note contact should of reader case (The a differ-the phases. reflect the within will between constants processes ences various the For phase separate coefficient. condensed to partition or and between gas–liquid series, distinguish homologous any to in phase homologues the of ability log “ adh baa tal. et Abraham Fowkes o tde o emsrneta h qain pro- equations the that strange seem not does it Now mathematical same the share formulations these All hr r tlattodfeetapoce nterms in approaches different two least at are There rediscovered ¼ SP ¼ c a g c þ s1 2 stepaehdoe-odbsct,while basicity, hydrogen-bond phase the is [1] ). q saftigcntn,adec rdc nthe on product each and constant, fitting a is rR f LW g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi writes lv LW 2 saprmtr eeal hsna 1, as chosen generally parameter, a is ” þ g hoy vni ooentdti corre- this noted one no if even theory, p [44,45] sv LW uesrp niae h dispersive the indicates superscript 2 H r p s eoe h ouedipolarity–polariz- solute the denotes p esrstetnec ftephase the of tendency the measures -and þ 2 H aecerydfndteapplica- the defined clearly have þ fN three ð n a eeto ar and pairs -electron a D 2 H s H hssceit n,gen- and, coexist, phases stepaedipolarity– phase the is þ AB l Þð isameasureofthe b SP b 2 H eest some to refers þ L stesolute the is l log R 2 b L 2 H sa is 8a ð a 7 is 2 H b Þ Þ h nefca cdbs od novd(nmol/m (in involved bonds acid–base interfacial the xrsigterl fteetoi opnn and energies, component inter- free acid–base entropic interfacial into the of action enthalpies of convert to role able the expressing adesadsfns.I per oeintriguing more collected angles contact to appears of reference set It a explicit only requires any softness. it because contain and not hardness does conse- GvOC and it components the basic quently and that acidic of the combinations Note chooses respectively. approach properties, basic W function: parameters six the instead have we h rg hoy(hc rnstettlnme of number W total the brings 8): (which to theory parameters Drago the qiaec ftesur ot ftesraefree surface the of coefficients reveals the roots 7 and square the and components that the energy note 9a rule of also Eqs. combination should equivalence same reader between The the case correspondence well. the constant quite in Hamaker that holds noting the worth of is it However, spe- arguments. different to pertaining cies quantities the of mean of geometric details the in strength. differ acid–base of that scales and identical stantially g that hypothesis further the is there theory ntecs fGo–a s–huhr (GvOC), Oss–Chaudhury Good–van of case the In h ukmtras atclryi em facid–base models of for terms used in currently particularly those theory. materials, to in bulk described similar be the quantities to interactions of the terms allow fol- variables the of in ber introduced fully be will 9a section. Eq. lowing of side hand g and xrsino h oko dein h ufc free surface The component adhesion. the the for of of equations work these energy the with of associated expression is general species no pure however, is, there fact this agreement. on even LFER; i Tot i AB adh adh h uesrps+and + superscripts The soecnse ti omncoc ouethe use to choice common a is it see, can one As hr xss oee,anme fsihl different slightly of number a however, exists, There num- high the and equations these of complexity The right- the entering parameters the of definition The e fepesosfrtesraefe nrisof energies free surface the for expressions of set A nbt ae;mroe,i h aeo h GvOC the of case the in moreover, cases; both in , hscoc sntflyjsiidb theoretical by justified fully not is choice This . ¼ D ¼ ¼ [46-48] H g AB 2 2 i LW q  q g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tnsfrteetap acltdby calculated enthalpy the for stands þ cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base hs ahmtclfruaini sub- is formulation mathematical whose lv LW g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lv LW 2 g q sv LW g sv LW g ffiffiffiffiffiffiffiffiffiffiffi i þ þ g þ i “ fN complementary q ð i N E g ffiffiffiffiffiffiffiffiffiffiffi switnas written is A lv þ E g eoe h ubrof number the denotes niaeteaii and acidic the indicate B sv þ þ C p A ” g ffiffiffiffiffiffiffiffiffiffiffi C a lv B 2 H uefrthe for rule g g Þð sv þ i Tot and  = [3,4,46-48] b g i LW 2 H ð ð 9b 8b 9a the 2 of ), + Þ Þ Þ Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 . . . . . not one, is this previous com- Unfortunately basic case. the surface. the and analyzed like the acidic, equations of dispersive, ponent three linear the three obtaining solve collect to finally of to 2) and set 1) typi- diiodomethane a liquids, acid–base and is different glycerol, the water, three surface cally in evaluate solid angles contact to a advancing order of in parameters needs apparently one. linear a gels, into in problem encased nonlinear the liquids com- by transforming on of obtained set measurements liquids, a common experimental furnished some authors for the ponents temperature; one at Theory Surfaces: (Polymer) of Behavior Acid–Base nti ujc yLei 1996, in Lee paper by first subject the After this approach. on mathematical correct a by praho vCTer oteAi–aeProperties Acid–Base the Surfaces. to of Theory GvOC illustrated of section is Approach the approach in This obtained. briefly been have clusion ae;ti hnmnncnas orsodt a to correspond also can or with phenomenon acidic strongly large very this very interact a the would water; with to that solid liquid component a the mag- basic is of the adhesion example than of An less energy solid. free strongly free cohesive be the the of may of nitude liquid magnitude the the the of that as energy fact interpreted interfacial the is of that this result values; allows negative theory assume acid–base energy GvOC the ries, ntems omncss htasraechemist surface a what cases, common most the In hnaii;tepooe idea proposed the acidic; than l hs ifcliscnb,a es atal,solved partially, least at be, can difficulties the these All have angles receding relevance. the scientific same that many acceptance to so-called mon used in the angles are contact components controlled “ the acid–base papers the been of compute majority not the In have complex laboratories. the they are liquids evaluate test and to the values, of adopted components negative acid–base methods have experimental in to interpret. The and out to difficult turn components appears which they energy common cases surface the practice, some of most in roots are, the calculations square the of probably unknowns theory. The the is to raised measurements; criticism sol- angle variability the contact of the this choice for the employed on vents depend strongly results The surfaces the so the one, of acidic compo- the basic majority than a greater have systematically to nent appear surfaces analyzed The nipratnt sta,dfeetfo te theo- other from different that, is note important An pnst nvra rpryo oi ufcs a surfaces, solid of property universal of kind a to sponds invr ifcl oacp n ofitn ihthe with conflicting techniques. and other accept of findings to difficult very sion static ” ravnigage,atog hr scom- is there although angles, advancing or “ ” nvra aiiycatastrophe, basicity universal “ h ahmtclBsso the of Bases Mathematical The [52-58] “ seem [59] [49-51] ” oecmo con- common some uhmr basic more much htti corre- this that ” saconclu- a is “ direct ” ie aeilo aysrae,btti snta not is this but surfaces, oxi- of many layers thin on oxygen of the of material formation at percentage easy high dized live a the we with induces ocean that really gas fact a of the bottom findings; conflicting some pairs electron nonbonding atoms. of oxygen derivatives, number their of high its the and to thanks (PMMA) polymethylmetacylate or at themselves material. obtained maintain the to of able surface are the surface using which the made agents, of commonly that active is is typical PVC explanation of angles possible polymerization contact A polymer, has molecules. this poly- dispersive really problem; of acidic, case a acidic The potentially remains density. of (PVC) electron presence accept vinylchloride of the to induce substitution able can the sites, atoms while reasons, halogen inert, disper- some same strongly completely the molecule, a sive for is Exactly (PTFE) is the polytetrafluoroethylene molecule. tetrachloroethane is contrary, dispersive as the partial, a on is chloroform; halogenation in their case if only molecules molecules. at these to shown way concepts easy relatively The of polymers. end organic the basic by given the be increases this strongly in percentage glass; component. common metals of O for of layer line presence true the a is however, properties. case, situation create acid–base similar quartz to gives A This molecules Si-OH. water silanols, with strongly (PS). polystyrene abil- by its shared its to is donate thanks partially basic to slightly ity really but hydrophobic, elimi- through angle informations methods. contact obtaining CA zero common of the a possibility have the metals liquids introduce nates common clean necessarily that very fact that on the layers and the oxide interactions, avoiding acid–base an in difficulties of experimental presence More- are acidic–basic. there significantly if interpreted over, or be clear dispersive can not mainly molecules they is as water theories; it with but interaction acid–base of surfaces, their of interpretation high-energy terms the generally are on in agreement properties general metals no is There Examples metastable Some solid of the existence liquid. induce the the would in solve to situation to equilibrium due an measure is to states; angle possibility contact the which a in situation metastable h rsneo atal xdzdlyr a explain can layers oxidized partially of presence The (PEO) polyethyleneoxide are polymers basic Strongly acidic strong potentially are molecules Halogenated can properties acid–base of examples commonest The react to able is that surface a of example an is Quartz apparently material, a of example good a is Graphite “ h oenSituation Modern The p eetos iia property similar A -electrons. — ” osdet h alka- the to due ions a eapidi a in applied be can 85

Absorption—Acid

Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption H reaction: by self-dissociation produced spontaneous hydroxilions the common and hydrogenions most the of between appears case used. water is the and caution is 6 no to This if 5.5 water solution. but minutes, bidistilled 7, acid few not a an is in as water obtained acid. of and be pH weak can dissolves the a it acid, but easily equilibrium, carbonic nitrogen, At producing water or with oxygen reacts the with than contact higher simple modifications. the many can but induce expensive it, can distiller atmosphere produce multiple An air to quartz-made manage. used a and liquid be or a produce device is to Milli-Q water Ultrapure difficult confront. very can one and problems dispersive this environment. of the and with result tertiary an interaction the its acid–base being of is and structure conforma- bond protein quaternary the on each hydrogen of interaction, equilibrium properties, based; acid–base tional Lewis is acid–base of role example and their dispersive whom of mixture necessarily materials oxidized the are basic. nor rule, general 86 ae snto Br a of not is accepts water a it partially to fact, pair which be electron in pair. atom, an this also interaction; hydrogen donate can acid–base neighboring partially extended bond to an an corresponds hydrogen as its of A water interpreted gives formation properties. really the which peculiar bonds in hydrogen in temper- of involved room two network at much is 1/3 about a about molecules, ature, molecules, contrary, of the of number On number greater molecules. total 500,000,000 the every of age qa ei cdadbsccmoet fwtri a is of water theory of however, GvOC components is, original basic the and it purely acid of view the Lewis in choice of equal confronted the point be that this will clear From problem basicity section. Lewis This its next versa. whether than ask stronger vice to is or legitimate acidity is Lewis it is answer; water simple no is there the on however, measured base; is are a material a as it scales. of and different strengths reasons acid basic and an stoichiometric its acidic as of strong for constant equally equilibrium processes; the by reaction measured is strength 2 O hr sasocimti odto fequality of condition stoichiometric a is There times 30 constant Henry a has which dioxide, Carbon the of example significant particularly a is Water complex a have polymers natural important Many saBr in a interaction As acid–base the of aspect main the Thus, percent- low very a involves however, reaction, This saLwsai rbs h iuto sdfeetand different is situation the base or acid Lewis a As þ conventional H 2 O se cdo ae ae swa n its and weak is water base, or acid nsted ¼ H 3 matter. se ye u faLwsone. Lewis a of but type, nsted O þ þ OH ð 10 Þ g yE.1 ne iertasomtoso h form the of transformations of linear revealed problem under properties 13 invariant The Eq. the matrix. by of a because arises of scales transposition the denotes etldt,E.1 ilnthl xcl.W shall We exactly. hold D experi- not of differences will the inaccuracy 12 that the however, Eq. assume, to and data, approximate model the mental the to of Owing experimentally. validity known be to D o e of set a For for hr ufc tensions, surface where angles, g X notation the of use make GvOC we that 13 interface hypothesis Eq. of In the energies. representation in free satisfactory a possible, provides as theory small as are g form the take then theory GvOC deino iudo oi ytefrua9a. added: formula be liquid must the solid the the by of of energy solid tension of free surface a surface work the the on and the for liquid equations expresses a Further theory of acid–base adhesion GvOC The Scales of Multiplicity SURFACES OF THE PROPERTIES TO ACID–BASE THEORY GVOC OF THE APPROACH OF BASES MATHEMATICAL THE g R l l s l i ij l ; ; ; ; i i ¼ i j ð ¼ ¼ ¼ 1 i ¼ ¼ ¼ ¼ =1,2, 2 g þ hi @ B B 0 @ B B B B B 0 X l LW g q X q g l LW i ij T s LW ; i cos 010 001 100 q T i ; p q the of , RY g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j RX þ l LW g ffiffiffiffiffiffiffiffi ; … g ffiffiffiffiffiffi g ffiffiffiffiffiffi i þ j l LW q þ ; l l þ i cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base i ; ; g L i i i 2 , ; j s LW q Þ 2 ; A C C C C C 1 L 2 j iud and liquids q q 2 1 g ffiffiffiffiffiffiffiffiffiffiffi i A C C 1 n ,2, 1, = j and g hlqi nthe on liquid th þ l þ g ffiffiffiffiffiffiffiffiffiffiffi ð l g ffiffiffiffiffiffiffiffiffiffiffiffiffi ; Y l þ 1 g i s þ ; i ; j l g j q g þ l ; ¼ s i ; g ffiffiffiffiffiffiffiffiffiffiffiffi j g l þ D cos ; g s i @ B B B B B 0 g s l,i ; s j ¼ ; flqisadcontact and liquids of , S 8 q q j p q 8 ¼ i ij … ois h qain of equations the solids, þ j g ffiffiffiffiffiffiffiffi Þ g g ffiffiffiffiffiffi g ffiffiffiffiffiffi ¼ g s LW s LW s s þ , ; Y ¼ l ; ; j ; j j j q i j S T hsldaeassumed are solid th A C C C C C 1 1 h superscript The . RY 1 þ g ffiffiffiffiffiffiffiffiffiffiffiffi ; 2 ; l ; j i 2 ; g 2 ... ; s þ p ... ; j ; g ffiffiffiffiffiffiffiffiffiffiffi g 8 L ; s þ s S i ; g ; j j s ð ð ð 11 14 13 ð 12 T Þ Þ Þ Þ Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 C matrix dition nonsingular the that provided .Adrc oprsno cdcadbsccomponents basic and acidic of comparison direct A 2. unsatisfactory is scales possible of multiplicity The 1. implications: important avoided. be by cannot properties introduced basic symmetries The the exist. solutions infinite X Theory Surfaces: (Polymer) of Behavior Acid–Base e,bcueterpout anantesm values. same the maintain term products The their because set, etr o hc h differences the which for vectors iud,oecnawy utpyalteaii compo- acidic constant, the nonzero all arbitrary an multiply by always nents can one liquids, if matrices CX q 3tk oeacpal ml aus hnthe then values, small acceptably some take “ 13 Eq. oisfral swl stefrtoe hrfr tpro- parameters it therefore new one; first of new the a as set vides well as such the formally of solids Any properties acid–base 13 the 15. Eqs. describes of the Eq. property of invariance values through the same to the owing with differences, equations same the satisfies h ai opnnsb h ae bann e set, new a obtaining same, the k by components basic the aemteaia om nohrwrs foehsa has one of the if set theory the words, by GvOC other constituted In with a solution form. share not mathematical free relationship which same is linear energy all models, solvation scales affects linear (LSER) infinite also and but (LFER) of theory, energy GvOC occurrence of the feature that able rpeinfinity triple g T i + X RC h ahmtclsrcueo vCeutoshas equations GvOC of structure mathematical The culy he-aaee group three-parameter a Actually, ! i , ; i feeto cetrdnrbhvo o hc such the which scale for unless other behavior sense, some acceptor–donor with no electron correlated of makes is material scale acid–base same the conventional of completely a conditions in way; additional priori formal a these and invariance fixed 13; be the Eq. can of removes additional properties whose completely some components, acid–base specifying to introduction scale. the to order on determined equivalent requirements in removed. uniquely is and established be This particular be should a must select and criterion purposes Some practical for , “ g opeetrt rule complementarity i j XY CX i =1,2, / ¼ k hc ilaanb ouino h equation the of solution a be again will which , C ¼ k R xss hc byE.1.Ti en that means This 16. Eq. obey which exists, 1 “ sa rirr oiieqatt n thus and quantity positive arbitrary an is ; … ” scale 2 fparameters of ; , ... L ! ” , ; Y fai–aebhvo.I snotice- is It behavior. acid–base of L CY j , ; j =1,2, CY ” j ai o ohaii and acidic both for valid ; … j g , ¼ i + D S , C l,i sasto column of set a is g G 1 , j aife h con- the satisfies K ; 3 D o oisand solids for , 2 L n iieall divide and , ; s,j fra 3 real of ... iud and liquids and , ; S D ð ð ð ij 15 16 17 in 3 S Þ Þ Þ f2. Nmfrtedsesv opnn fpure of component dispersive the a value assuming for accepted and water usually mN/m the 21.8 maintaining of by found be can opnnso nabtaiychosen arbitrarily an of components aesrnt,sc stoeo Taft of those as an such fix strength, to base to necessary material. reference be order second should In a it of invariant. component scale, acid–base material unique compo- reference a the select the leaves of which nents exists, transformations linear ic h ubro oa iiasestypically seems help may minima function, guesses reasonable local merit physically the of but determina- of large, number actual very minimum the the absolute Numeri- from since the accuracy. arise of same) known may tion the are difficulties test possibly data of cal angle a (and sets contact pri- good large of whose a with quite solids components fixed requires and be calculation the liquids a should squared scales, Such water) the ori. due (e.g., of all ambiguity material of the multiplicity reference avoid sum the to the order mate- to is In the choice above. of differences natural components acid–base A the rials. to respect with ag e fts iud n ois eiigamerit a defining solids, conveniently and a differences for liquids the 12 test of determina- Eq. function of of the solution set in best-fit large consists a method of tion rigorous most The method best-fit compo- Nonlinear acid–base applied. of be can determination strategies two practical nents, the For Solids Components for Acid–Base GvOC suitably of Calculation the answer by available. certain yet force–distance surface No is device. question liquid of this AFM to or an evaluation of solid tip the functionalized the meas- of with with curves frontier or or of solid, levels or urements, liquid energy the the suggestions of qualitative, with orbitals Pos- purely correlations defined. moment be be to the could considered still at is be is but it must latter sible, scale the since probably, absolute open, more which is and, all problem at clear the not strength, acid–base of 6.5. to 5.5 and 3 between liquid, vni htcs eti muto neemnc is that indeterminacy and of way amount certain arbitrary a available. almost case still an that in in even assigned be can h tutr ftegroup the of structure The esnbecreain ihohrsae facid– of scales other with correlations Reasonable sfrtepsil orltoswt bouescales absolute with correlations possible the for As odfrsae orltdwt bouesae of scales absolute with strength. basic correlated must and acidic this scales particular, for In meaningful. hold is comparison a [46-48] ute n-aaee ru of group one-parameter further A g + / g ai,frtesm reference same the for ratio, D G l,i , 3 D mle htteGvOC the that implies ij n iiiigit minimizing and , ‘ [44] reference rAbraham or ’ material [45] 87

Absorption—Acid

Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption Source: prahi aall hto rg n ahLFER suggested each method and this Drago this of liquids; that the parallels method. of meas- components is experimentally tension approach and surface directly the to ure necessity the appro- nate of solids. definition and liquids after a devoted for databases, at mainly standards of determined be priate creation are should the solids method compo- to and the the liquids Therefore, solids; the time. and all liquids of of nents number large ciently V 300 . 9100 0.88 0.22 0.23 2.23 0 0.06 0.02 8.25 7.3 11.2 0.01 39.1 0 38.2 34.1 27.8 48.5 37.4 50.8 3.5 1.1 35.0 2.3 26.2 9.5–022.4 0.04 0 57.4 sort 0.64 25.5 a 0 from 0 suffers procedure statisti- this Although of correct, solutions. more best-fit and cally meaningful Oss, 43 van find Good, by to proposed was 3.92 0 scale original 35 The 42 molecules. 25.5 39–43 water for used values elsewhere. the used by been defined has are scale different strength a acid–base Chaudury; of scales two The 50.8 34 PVC 21.8 PMMA PVF PS Iodide Methylene Glycerol Water mN/m in expressed are components The 4 Table 88 aot2.5m/)ta h sal accepted usually the the and than mN/m larger 21.8 significantly of value mN/m) is Fowkes’ 26.25 water of (about component dispersive osdrda eaieoeadaslt compari- attention. absolute ba great and and with considered one acidic to relative between important or a sons tim is community) as such it science considered until theory, of surface that, improve product confirm the new probably (the all a will scale expecting of new scale, work loss a the the established by Anticipating previously induced continue. uncertainty, the of of phase this tions; the 4). of (Table optimal, scale explanation being catastrophe from reasonable basicity far by a although proposed scale, the provides originally a of calculation Such that the GvOC. than for realistic parameters more acid–base be could 4.35 at rprisi obde;tecmaio fcorresponding allowed. of is comparison properties the complementary forbidden; of is comparison properties the scale acidity-basicity ueia siae fai–aecmoet by components acid–base of estimates Numerical elimi- to possible is it method this through that Note sagnrlrl nti context: this in rule general a As sugges- several offered have authors of number A “ redundancy aafo el op Siboni & Volpe Della from Data oprsno h ufc reeeg opnnsfrsm iud n oisotie sn ifrn eeec scales. reference different using obtained solids and liquids some for components energy free surface the of Comparison ” eas tcnwr nyfrasuffi- a for only work can it because ” ” htafcsteoiia GvOC original the affects that g [46-48] LW i rprissol be should properties sic ,ec cl hudbe should scale each e, htasaeweethe where scale a that [46] n a Oss. van and “ rgnlsaeDfeetscale Different scale Original nanonabsolute a On g + / [46–48] g g + ai holds ratio [50] “ hssaei ueyidctv ftedfeetrslsotial ihadfeetscale. different a with obtainable results different the of indicative purely is scale This universal g oi,whereas solid, yuigtecnatagedt on in data solution angle the the contact the for using by required the liquids also method. is probe the three of of application three, num- is number the components Since minimum on unknown parameters. solid known of the as ber algebraic of liquids of data set probe angle linear the a contact a of with containing solution of known equations the components be from acid–base to stems supposed the solid are and liquids accuracy, components three sufficient acid–base least GvOC at the of approach, linear the In methods Linear nhvn eoe with denoted having on b aelqi ntesld epciey wn othe to Owing respectively. solid, the on liquid same the i n h cdbs opnnso the of components acid–base the and A where Ax equations =1, 2, ¼ h aclto fai–aecmoet fasolid a of components acid–base of calculation The ¼ i ¼ hlqi n h qiiru otc nl fthe of angle contact equilibrium the and liquid th @ B B B B 0 @ B B B B B 0 b … g g g ffiffiffiffiffiffi ffiffiffiffiffiffip ffiffiffiffiffiffi p p L 2 1 ð ð ð , g ffiffiffiffiffiffiffiffi g ffiffiffiffiffiffiffiffi g ffiffiffiffiffiffiffiffi 1 1 1 L LW 2 LW l LW L cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base n with and , þ þ þ x g cos cos cos i p p p ftelna e fteahso work adhesion the of set linear the of g and LW g g g q q q L þ 2 þ l þ L 2 1 Þ Þ Þ = = = q p p p g 2 2 2 i g i LW g ffiffiffiffiffiffi g ffiffiffiffiffiffi g ffiffiffiffiffiffi S A C C C C 1 LW r h ufc eso of tension surface the are L 2 l , , A C C C C C 1 g g i + x S + and , and , ¼ L g ‡ + @ B B 0 g iud implies liquids 3 g i p p p S h dispersive the g ffiffiffiffiffiffiffiffi g ffiffiffiffiffiffi g ffiffiffiffiffiffi hs fthe of those S LW S S þ i hliquid, th A C C 1 ð ð 19 18 g Þ Þ Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 MO rmfr,Proe+Ipoe rpe 210.82 triplet Improper 161.93 triplet Improper 193.27 triplet Improper 612.22 699.19 689.17 658.90 474.04 matrices choices data these and 35.999 both of liquids ratio angles, the chemical contact of ill-condi- The acquires the parameters equations. more 34.746 set in the of potentially net set in a the 119.84 180.04 corresponding to errors liquids, the 161.93 opportune correspond experimental in Adding number present forbidden. condition is is the ill-conditioning calculation of of 133.07 the values text. degree which higher the lower in column; in 33.179 a situations 118.30 analyzed second so 0.0000 to is B, and correspond Section condition, values lower in Zero 0.0000 a defined equations. are of s set 6.2996 tioned and iodide 1 Methylene norms The 0.0000 5.6486 and Water + s Pyrrole Hexadecane norm Bromoform, from DMSO, Cn DMSO and Water + Hexadecane Formamide, 6.2821 Glycerol, 0.0000 iodide Pyrrole Methylene a + glycol Formamide 0.0000 Ethylene DMSO Glycerol, Water, 1 Formamide norm from Cn Formamide Quintuplet Hexadecane 0.0000 Formamide glycol Ethylene glycol glycol Ethylene Ethylene Glycerol Glycerol Glycerol 3 Liquid Hexadecane Glycerol glycol Ethylene Hexadecane Glycerol Formamide iodide Methylene Water Hexadecane Glycerol Water Water iodide Methylene 2 Liquid Water iodide DMSO Methylene Water Pyrrole Water Iodide Methylene iodide Methylene Glycerol Glycerol 1 Liquid components 5 Table Theory Surfaces: (Polymer) of Behavior Acid–Base eie stepouto h norm the of product the the results. is as defined the analysis this of number for sign dition tool negative mathematical possible main sets may the The different which and using results liquids solutions, of of the variability the on both uncertainties explain known unavoidable large gives are to ill-conditioning data accuracy, rise of experimental high variation the a large if with a Even yields solutions. equations the the of the coefficients 18. concerns the Eq. set of problem linear roots the The of square ill-conditioning some obtained. the possible in and, of are same used values components liquids the negative of for even triplet cases, the estimated on components depend that solid the provided method, solution, But unique GvOC singular. a shows linear 18 the Eq. of tion Method. Linear Three-Liquids reflected is which uncertainty, solution of the amount in certain a tain Booahhln n yrl orce unult38.2 quintuplet Corrected pyrrole and -Bromonaphthalene l-odtoigmasta lgtcag nthe in change slight a that means Ill-conditioning .Sm odto ubr fdfeetqitpes bandb digpoe iud oipoe iudtriplets liquid improper to liquids proper adding by obtained quintuplets, different of numbers condition Some B. h odto ubr fsm omntilt flqisue o h aclto fai–aesraefe energy free surface acid–base of calculation the for used liquids of triplets common some of numbers condition The a a Booahhln orce unult40.3 quintuplet Corrected 39.7 quintuplet Corrected -Bromonaphthalene -Bromonaphthalene falna e fequations of set linear a of x . .Cniinnmesfrdfeettilt flqiscluae rmtodfeetnorms different two from calculated liquids of triplets different for numbers Condition A. a Booahhln MO703 33.599 7.0033 DMSO -Bromonaphthalene nteuulapplica- usual the In k A L k n h set the and 3 = ftematrix the of Ax A = and A b a a a cond(), , Booahhln 7.9695.56 36.243 175.69 -Bromonaphthalene 0.0000 6.1337 -Bromonaphthalene 0.0000 -Bromonaphthalene snon- is b con- con- A n h norm the and k k ilsaresidual a yields k n fteerr in defined errors ability the if and pnigsbriae arxnr wihsatisfies (which norm matrix k subordinated sponding where netit fteslto a eetmtdas estimated be can solution the of uncertainty odtoigo q 8cnb eue oapoet of property a to reduced be can 18 matrix Eq. of conditioning fi stecs,ecue rmcnatagemeasure- angle contact components. solid from of excluded and, calculations detected subsequent case, priori and the a ments be is can it liquids related of if equations triplet certain GvOC a the to of ill-conditioning possible k k D D A Ax x x x x k k k k k 1 k £ ovn h set the Solving . k k A . k k A ny needn of independent only, cond tnsfrbt h etrnr n h corre- the and norm vector the both for stands A kk kk x ð “ A A k small k .Ntc ht codn oE.2,the 20, Eq. to according that, Notice ). Þ r A  1 = k k A 1 k k k D Ax ” k A b r A k and k matrices k fisivre cond( inverse: its of k Ax þ b b h eaieerrin error relative the , = k r xrse ytesuit- the by expressed are k b D b b sacneune the consequence, a As . D b k A k yapoeuethat procedure a by and nfo om1 norm from Cn D b h relative the , A )= x ð ð k 20 21 is A 89 k Þ Þ

Absorption—Acid

Acid —

Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption 90 ai hrce.I otat od)tkssalrvalues or smaller acidic takes cond() dispersive, contrast, for prevalently of In three same character. or basic the two ill- where share of liquids, feature them probe typical of a sets generally equilibrated is ill-conditioning that n h plcto fetmt q 1t q 2 for- 22, bound Eq. the to to 21 leads 18, Eq. Eq. estimate to similar of mally application the and x therefore is solution the As n h te rvlnl ai ncaatri better a condition of is lower result A character polarity. the same in is the number basic of acidic liquids prevalently prevalently two one complementary than other with and the liquids opposite of and pair with A liquids character: to directed liquids. acidic/basic prevalently evaluate two and to dispersive difficult lently more is it the because results, worst the unknowns). two with equation sufficient one not of is case the only liquid determine polar chemically to sounds one this because matrix; obvious singular a to corresponds for rationale chemical the extract results. are to these is interesting liquids more acidic/basic essentially included. and dispersive A to squares. necessary least solution of then best-fit sense is the It in Whenever solutions solution. best-fit for no search allow to expected rectangular mrv h ult fterslsb nraigthe increasing the by that sense. remains provided results liquids and of employed the set liquids probe of of quality number the improve Method. Best-Fit scale. Linear different a in change can or situation unlike the but sufficiently choices. scale GvOC, appear reference chemical best glycerol the the “ the on and that depends water of liquids is used; one the warning iodide of is character important methylene (G) an (W), glycerol However, water and triplet (MI), used commonly complementary T ¼ð h aclto fcn( o ifrn rpesshows triplets different for cond() of calculation The h hieo h w cdcbsclqissol be should liquids acidic/basic two the of choice The gives this liquids, dispersive any use not does one If and allowed not is liquids dispersive two of use is The What B. and 5A Tables in shown are results Some hntenme flqisis liquids of number the When Ax A LW “ T well-equilibrated A A ¼ opnn.Atiltms oti n preva- one contain must triplet A component. T sapstvl eie 3 defined positively a is A A A Þ T L b two 1 a h ags ak3 h es squares least the 3, rank largest the has A ” x T arxadE.1 sgenerally is 18 Eq. and matrix 3 b cdbs opnns(hsresembles (this components acid–base suiu n satisfies and unique is nteabtaysaecoe ythe by chosen scale arbitrary the in ” “ well-equilibrated rpes where triplets, “ complementary npicpe ti osbeto possible is it principle, In L ymti matrix, symmetric 3 > ” 3. both nteprevious the in ” A hie The choice. eoe a becomes essentially ð ð 23 22 Þ Þ k lhuhwt oelmttos oeaut h equili- cos equation: the following the evaluate from to angle contact limitations, brium some with although aaerr a epromduls otc nl data angle ( contact unless available performed liquids are be test can the errors of data angles solid, contact the the on to related is vector W theory hardness-softness the as view adhesion. of of point his define a endescribed free been lowest common has its on in effectively state is energy that meniscus a obtaining the as angle angle; contact advancing the sensitivity. aaeesads ti ae nawd e fdata. of set wide a Drago on the based through is softness it so and and hardness parameters the to ence otc nl ntecluain fsraefe energies. free surface advancing of the calculations exclusively the is in almost there angle use consequence, contact to free a reason highest as no the surface; really to the of related portion often energy are angles receding that “ reeeg fsld rmtemaueet fcontact of measurements surface the the from evaluate solids angles. to of correct energy not completely free was the was it of he that father however, convinced the adhesion; as of known theory been modern has Fowkes M. Frederic APPROACH FOWKES THE signif- of are values polymers the commom all underestimated. the that icantly of be energy would free this surface to corollary easy An hr h eaieuncertainty relative the where setal eedn on dependent essentially for case the nonsingular and the in 3 introduced conditioning of xlcty u otedenominator the to Due explicitly. k A equilibrium D x adh T x h qainpooe yFwe is Fowkes by proposed equation The to correct more probably is it shown, previously As nte motn rbe stesseai s of use systematic the is problem important Another nfc,Fwe’ prahcnan nepii refer- explicit an contains approach Fowkes’s fact, In oevr thsbe eetdyproposed, repeatedly been has it Moreover, k A q k arcsi omr plcbei rprsense proper a in applicable more no is matrices 3 equ rvdsol ata nomto bu this about information partial a only provides ) ” ¼ [60] hsaie rmteeprmna ifclyin difficulty experimental the from arises this ¼ “ 2 cond sensitivity q 0 ” eoecnatagemaueet,cond measurements, angle contact Before . g ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi omaigu siaeo h estvt to sensitivity the of estimate meaningful no : cdBs eairo Plmr ufcs Theory Surfaces: (Polymer) of Behavior Acid–Base cos 5 lv LW ttso h eicssraesse and system meniscus-surface the of states ð A g T sv LW A [54] q ” Þ adv  þ odt rosms etknas taken be must errors data to k hti svr ifcl oobtain to difficult very is it that D þ k fN ð A both A “ T ð 0 non-Young-like T E A : A cos 5 A k k Þk E A D B b and k þk q k þ / “ rec k A qiiru contact equilibrium b T C k b A b ic h data the Since . A k osntappear not does T C h definition the , k ” B k Þð k A ufcs It surfaces. 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ð H ¼ 1 AB A g ffiffiffiffiffiffi R X D þ AD X i q 2i aiyptit arxform matrix into put easily is 12 Eq. , sasial ymti rhgnlmatrix. orthogonal symmetric suitable a is A say2 any is ¼ i (respectively, T cos RX A ¼ D i q A T  h same the ij D Þ g C E D B g s Tot A ; A l Tot B j ; i !ð ¼ elnniglrmti.I is It matrix. nonsingular real 2 ¼ and Y j Y fcomponents of ) X A j T o oh ntecontrary, the On both. for D i T RY RY B 1 Þ j T ¼ j D B  C E B B “ surface A p n ( and g ffiffiffiffiffiffiffiffi LW ” , practi- A p ð ð ð 1 27 29 28 g ffiffiffiffiffiffi ) þ 91 T Þ Þ Þ , ,

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Downloaded By: 10.3.98.104 At: 09:41 23 Sep 2021; For: 9781351252386, entry3, 10.1081/E-ESCS3-120028031 Absorption REFERENCES ie,astsatr prxmto fteconfidence of the number of large solution the approximation a singularity for interval satisfactory procedure no a the that times, iterating provided of by solved, set occurs. be resulting the can and equations interval confidence appropriate om r lokona om1adnr ,respec- s, norm and 1 norm for as stands known (s tively, also are norms be two not in that will vectors however, and remember, real and to for known useful norms well is usual defini- be subordi- It These to here. and repeatedly. given assumed norms used are vector are tions norms text, matrix the nated Throughout (A) Terms Mathematical Some About Note A 92 k o n vector any for where g pnigsbriae arxnrso any of norms matrix subordinated sponding jj matrix anyi h aa nta fthe of instead data, the uncer- experimental in the well-condition- of or tainty because ill- of essentially of arises problem solution ing The numerical and sets. the truncation equation by the the introduced than larger ones much round-off typically are errors al taeya natraieapoc.Aspecific as A such parameter, approach. experimental alternative each an Monte- of a as value using strategy suggests Carlo This computations. numerical .Br,JC oeo cdbs neatosi etn and wetting in interactions acid-base of Role J.C. 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