Applied physical chemistry, Appunti di Chimica Fisica

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APPLIED PHYSICAL CHEMISTRY 45/09 . | INTRAMOLECULAR BINDING FoRrcES he, because or tne differences of eepuimentat. data| © From ideal , Yan de Waals studied +ne influence of infenmolecui on FOnce? 2% ; "ha i when | speak abovt bound, sioni Ne= equilibuum distance — re is the length of the bound forces A—B x ne xe Hiee—h id innamol. int. Da potential eneugy ofa system R(distance) —rorces: shont/l0n9 range, attraciion, reputsion I inst aggregalion urde 2000 Ù nuctedus Que he / Attraction too close FOICES Mie equazioni :FINST mMarhemATCAI fonmutari on Palo ne puasi ve i wir) = ce[[E\ (LI est (ny wm: iniesociion porentiat [(f) (SI x nm (3) ) l£]= = Dispexsion energy [6]= m= Distance at which W(6)=0 : cowision RADIVS n,imone adjustable and define the stepness of repulsion(n) and attiaciion(w) (ennard, Jones potential: most used (special case n=12,m= 6) 12 Jaye ge A= GEGS n:avenage distance betweei Wylr)= de [| fap pr E n Both the Mie and Lennard-Jones potentials are categorized as pair potentials, meaning they only consider interactions between two individual particles. These models are not suitable for describing many-body interactions involving three or more particles directly. Nevertheless, the total potential energy of a multi-particle system can be approximated by summing the contributions from all pairwise interactions: Natoms Via = > wij(r) i#j INTERMO UECULAR INTE RACTI ON i — interaction between moiecutes atthe motecuton Leve : the behavior isthe same in the molewutes but we Focus On this: STR) % } ATTRACTION: Molecutes closer . REPULSION: the etectron ciouo outside the motecute move away each othn H —1(linthecase ofintnamolecuiar Forces this is given by the 2 nuceeous 0F ; atoms. «Ne depends on the phase — re has a certain Lever Fon gas/lig. / sold atimo.ction Fonces 4 : condensed phase shorten Liney dont change, they axe given by the stuuctun ofthe moleute quring its life, +hey change only “with tas seeh in the guaph Li Ì Mavogene Boundi; 'REESON- between dipolan molecutes (lange then Debye) t#h8 smongest VAN DER WAALS L' BERYE - intenaction between polar and no pola? morecutes » NiTtondON * berween non-dipol molecutes charges are unifonmally distubured LI 9” ne Interaction make the etecanons R permanent —+ metnane (non pon) — ofthe non-polovi molecutes to move TAL] dipole far fnom the d° of ware 1 generation of a non-permanent elecmons are Free to move dlipote the behavioa is desuibedl the cennard. Jones Porential - the mi nitude of tnose Foltces can be different because of different elecinons densi ty and eigttrons charges distubute a in tne volume the sTronger the attactio +he higher the interaciion enengy MOLECULES ane NOT foten al O Kellin but they have to be stable at a centain T. rh mansrmmed in kinetic enugy - MOISORIES que free to move With SOME degnees of need om TT= i ù Ni higner the 7 the higher the DOF, and the velocity, rinetic energy ‘ me vowiadion is. high the absolute value of the atmaction enengy is similar to the internal enegy of 4he malecute. ifthene is hign en in atmoaction berween Molecute , they ore not fner To Move (f071 exampie in ®, than methane that have ony “candon forces has much mone DOF) I intraction keep inem closer in acondensed phase, Hey one net fnoten but free t0 more onlY in the volume, keeping it the same n. noeasina 7 they move faster and +hey start occoupy mole space (mone nor] VATTHE BOÎLING POINT ‘THE NOLECVUES ARE FREE TO MOVE ( ATTRACTION” iS_LOWER THEN THE KINETIC ENERGY) | * mese hi Ss one votidi also wiih aggregates of molecutes (when | have intenphase bounding)) Cai ì ex: HYOROCARBON: the intenmolecuton bound Ò apolar ane marimum in water fon H-Bounding? N20 : Sinongest Cause of Hydrogen boundin È iù ua 9° I CioH:2 is stongest Crol2z apolar because in ihe ‘volume + metnane : apolar of tNE molecute it nas a lot of sunface ihat can attnact othea molewdtes: (even if Gporlon) 1 MOLECULES ARE COMPIEX SYSTEMS (©) and also U20 Cio zz _l because of the 1 diffiuut to understand — fact that ne boilin the seal interaciions { easier +0 polonite big point OF Ciolzz ÎS high Molegukt@s A6\09 E (+he dipole is given by the some of / al the one" on thé surface) the bigger the molecutes, the lange the interaction @ 390x — KkT=S80 Cal mol Inmeasing the T | have mone ene: and t 9A e is more space betweèn molecutes l 5 Tekect INTERNAL ENERGY ; at some point molentes oicesn't rel anymoze attraction Where x [D] = [3.336 x 107? C - m] is the permanent dipole moment of the molecule, J k = 1.380649 x 107° cl is the Boltzmann constant, and 7 [K] is the absolute temperature. The total polarizability of a polar molecule can thus be expressed through the Debye-Langevin equation, which combines the electronic contribution with the orientational one: 2 a = 0 + Qorien = 4reoS + 557 Although tabulated values of the atomic volume S for certain simple molecules can be found in the literature, such data are often limited to small or well-characterized species. For more complex molecular systems, an effective approach to approximate the molecular volume consists of summing the contributions of the individual bonds or functional groups that constitute the molecule. This method provides a reasonable estimation of S, particularly when direct experimental or tabulated values are not available. The values of selected group contributions, together with the atomic volumes of some relevant atoms and simple molecules, are summarized in Table 1. Atoms and Molecules He 0.20 (6105) 2.6 Hy 0.81 CH30H 3.2 H30 1.48 Xe 4.0 (Ch 1.60 CH’ = CH, 43 Ar 1.63 CoHe 4.5 co 1.95 Cl 4.6 NH3 23 CHCl3 8.2 CHi 26 CoHs 10.3 HCI 2.6 CC 10.5 Bonds (Aliphatic Molecules) C-C 0.48 O-H 0.73 Cc-0 0.60 C-C1 2.60 c-H 0.65 C-Br 3.75 Bonds (Aromatic Molecules) C.C 107 C=C 1.65 C=0 1.36 N-H 0.74 Molecular Groups C-0-H 1.28 —CH2- 1.84 C-0-C 1.13 Si-0-Si 1.39 C-NH> 2.03 Si-OH 3.75 Table 1: Atomic volumes (5) of some relevant molecules, bonds, and molecular groups. AII values of S are expressed in À* (= 10-?° [m8]) L'EXTERNAL EUECTRIC FIELD: E; (el: Field intensity Quivsveeni= cE= Lei with e= -1,602-10°"° [c] Ù the dipole induced in apolonm molecole, proponti ona to he polanizalion of ine mol. and also ot the cnange and distance (e) DISSIPATION | — guantuM_ MeckaniCAL DISSI PATION I FLUCIVATION of eteemons creates dissipalion Unlike the interactions previously discussed, which arise from electrostatic effects involving both polar and non-polar molecules, dispersion forces (also known as London forces) act universally between all molecules, including those that are electrically neutral and non-polar. Dispersion forces represent a fundamental contribution to the total van der Waals interac- tions, as they are always present, independent of a molecule’s polarity or permanent dipole moment. These forces play a crucial role in a wide range of physical phenomena, including adhe- sion, surface tension, physical adsorption, wetting, gas and liquid properties, thin film behavior, particle flocculation in liquids, and the structural organization of condensed macromolecular systems such as polymers. Dispersion forces originate from quantum mechanical fluctuations in electron density. While their rigorous derivation lies beyond the scope of this course, the first and most aightfor- ward mathematical description of the interaction energy w(r) between two identical atoms or molecules was proposed by London in 1937 and is given by: potential of molecwei Final eg: OLO races — LONDON EQUATION FOR 2 MOLECVUES: wins -3 Aoioj a Iii 2 (uMe o)? ne fitti ]= FIRST IONILATION POTENTIAL OF 4" MOUECULE — ine ovien shell of the elecmon ciouda, iS conati the ong who generate it, because thats the Aoi= POLARIZABILITY OF 1" MOWECUE eneigy 10 remove these electrons, Big molecule — big polarization = big inieracisons MACROMOWECUUES HAVE VERY STRONG INTERACTION (ex. balfpr lene sl Poly prdpylene ) im pornticuan alcane / Kydnocmbons . ._on enzime, that operate dew t0 this interaction. In this expression, /; is the first ionization potential of species î, and ao; is its molecular polarizability. It is noteworthy that the interaction energy varies as > 1/r°, which is the same distance dependence as the attractive term in the Lennard-Jones potential. This emphasizes the underlying connection between dispersion forces and the broader category of van der Waals interactions. Fameaction x i buk Feovomae X da The significance of dispersion forces becomes evident even when comparing molecules with similar chemical compositions, such as alkanes. Small molecules like methane and ethane exist as gases at room temperature, whereas larger molecules such as hexane are liquid under the same conditions. This trend reflects the increasing strength of dispersion forces with molecular size, as larger molecules possess greater polarizability and thus stronger attractive interactions. ‘atintertace the molecute don't stay quiet like in 4ne bulk (withovt any fonce, moving only because of thenmal enegy) but they are instable, ‘cause of a Force: di ine intenface molecutes ane not in 1ngimodinamie equilibuum, they want to “Vump* in the bulk, wnexe they con dectease their Gibbs eneagy (9) 4, this happens : mole cutes at +ne interface “Jump" into the bulk and one replaced by others, which do the same 00, “Tumping®* too. -continous Mass transfu. : POSÌTIVE MASS TRONSFER FROM THE FACE INTO ZIHE BULK they want to reach the steady state, where forces ne balanced ‘gionally, at the molecutes tend to uve the interface. lin liquid, in Solid inis doesn't pen * SYSTEM TRY TO MINIMIYE THE INTERFALE (minimize the extra fonce) ex: ge gnlagioo is sferica to minimite interface at equilibuium) * SURFACE FREE ENERGY = ts" (9) : extra enengy that is the variation of A dA IT Gibbs ene (computed by all the “ work nequireoa to increase Molecute s) the surface of the pnase by Q unit amount tor this Surface) for Uiquid : SURFACE FREE ENERGY = SURFACE TENSION ($s] = -_. Nm, N° :force acting likea unit or length m' mi m ex: Fon watev = Yuzo= Q072.M, => 32m, (milinewtornzimeter) inaeasing the interface : — boro] = this is not Natura, +heAmodinamically I the system inies 10 90 back a payment oraddiciimot a eneagy — put mone molecutes Ys ne fonce that avoid the natura incaease of the surface has this direction: tt | paroutet to the sunfoace |! + +nis Mies to shrunic the inierfaa if | put a moss: => the density tres to put Va if into +hebutk, but to doit | need to open Ù the interface i \ inueasing = _ the suntaces +ension the suntoce tension is not T to balance ma s goes against the Force but — to Follow the theamoodinamie equi Li qriuw li it is against the direction of surface expansiow air Va cioz Tia : the system tres to minimite eve interface tia1 (in solid, there is rhis extna coni, the surface tension, but this is not visible because molecoles"are not able to move in uystals.) Y between 1and 2 ne pae ot g between two phases gepenge apon the mutuou interactions phase 1 and +he mutualintesactions in phase g. « noe phase (air) Y is the highest, because the intermolecutan interactions ‘ey weak Ymox => pure molecutes in contact with air Ya, a => it is defined always between two phases t TA there Que 2 Forces at the intuface. pr if one of the phases is gas: | * interections between “its molecutes oxe Low Y - also density 0F molecutes is IOWeL — neo dW= TAA = — wonkto spend against the eneigy, exatuy the same doing in a piston dy= PaV 4 î] pi l they wak cn the opposite: - piston increase volume when realeased (t0 equali?e P) * surface fendi 10 deueast when_|realease the face (it tes 10 minimite +he surface) Site! — the smamter tne system, the no tuomspou pnenomena face tension igni vi Loca Ni wr a teusion : sunface ten ity cant win i O P also effects mass 199 Y ] È trans) —: highew manspont prenomena Di (bubble same) . . (pipet, smau volume, 50 Ipxess to win the suntace tension) wnen this property is used: 4. DISTILLATION (PACHED COLNNES) La bubble rormation dropiet coalescence . wetling of packing mateuals 2. SPROY DRYERS L Droplet site qopiet bneackt-Up Sur Face wettings 3. ABSORBER- STRIPPERS L -Ug. inteections 9fiim Ranma tion wetting — mass tran sfev G. CYCLONE - SEPA RATORS coalescence of avoplets separation efficiency Wetting ot SUrFaces 5. LIA-UQ EGUILIBRIVM (EXTRACTORS) L dropiets site — transpont phenomena settling rate — mass nansfe eficiency 6. FORM COLUMNS/FRACIIONATORS 7 m cm m cm popular dimensions: È FETEE Fe] * Surface tension — typical values tor liquids (20°C, mN/m) Water 72.8 Benzene 28.9 Acetone 23.7 Acetic acid 27.6 Ethanol 225, n-octanol 27.5 n-hexane 18.4 Mercury 485 * Interfacial tension — often between the surface tensions of the two individual liquids (20°C, mN/m) Liquid 1 Liquid 2 Vi Water Benzene 35.0 Water n-octanol 8.5 Water n-hexane Sii Water Mercury 375 Surface is the key dimension of colloids: 1cm cube + 2-3 molecules out of 10 millions at the surface 1mm cube —+> 1molecule out of 450 at the surface 10 nm cube > 1molecule out of 4 at the surface - 4000 morecutes 1 nm cube + no more molecules in bulk! + system isnot a dpler, mote cutes 25f benave difftuent 20h $ v . È alline molecutes are expedtenving the 2 phase È ® 0 2 1 [.] 1 2 log (dum) mamosecpio - mieroscopic Surface is the key dimension of colloidal dispersions: if Icut: laminar fibrillar corpuscular Mi = Laminar 1cm? into a filmof 10nm >210%cm? —suntace is huge * Fibrillar ‘1cm?intofibersof10nm >4105cm? = Corpuscolar 1cm? into cubes of 10nm > 6 106 cm? * Colloidal dispersions — range of optical resolution * Colloidal behavior exhibited also when not all three dimensions are within the colloidal range (fibers (2D), films (1D)) Specific surfaces are usually considered: 2 2 S,= [| sì s,= [| g cm For spherical particles: __ ad’ 6 p = true (bulk) density pa(d°/6) pd d = diameter w Example: ‘1cm cube divided into 0.1mm cubes surface from 6 cm? to 60 m? (10° factor) when dispersed into 6 cm? of water, the available interface is 8.6 m2/cm3 The finer the subdivision, the larger interface and impact on the final dispersion properties Disperse | continuous phase phase Fog, spray, tobacco smoke, Liquid or solid Liquid or Gas aerosol sprays, flue gases aerosols solid Milk, butter, mayonnaise, Emulsions Liquid Liquid asphalt, cosmetic creams Inorganic colloids (gold, Sols or colloidal Solid Liquid silver iodide, metallic suspensions hydroxides) Clay, mud, toothpaste Slurry Solid Liquid Opal, pearls, colored glass, Solid dispersions Solid Solid pigmented plastics Foam Liquid foams Gas Liquid Foamed plastics Solid foams Gas Solid Class Disperse phase Continuous | phase Macromolecular colloids Jelly, glue Gel Macromolecules Liquid (solvent) Association colloids Soap/detergent in water - Micelles Liquid (solvent) Biocolloids Blood == Cells Liquid (serum) Triphasic colloidal systems Oil-bearing rocks Porous stone Oil Water/stone Mineral flotation Mineral Water Air COLLOIDAL_BEHAVIOR, SURFACE po, 4 VOLUME LENGHT (n) R- o S__® a v I reach 0 COLOIDAL SYSTEM e n * at inis point . rn —— = N removing the ENegy E De, TOTRUYLINSTABWE /” she syÉ. goes back “ igive enegy to incuease ine surface and ueate dluoptets ENULSION TheamodyNamMIC - it goes against celloicat systems i i 20 wswatey becalise of kinetic p effects the smalleu the porticte, the highu, the surface, the hignur the en I need inteufases: no moleculte way to be on the suaface 1 when 2 duoprets one close to each otheu they tenda to mix: CORVESCENCE) : CO — O it 18 tnenmodynamici more stabie “ because th Sunface is Jess. The (iuinetie puocess is associaned +0 the necessary to remove qu #ht oil molecules that one betwem the 2 doptets that try to include) each other 4a iynen the 2 duoplets are approaclung each other +here are these different situations : «these mol .ax£ at the surface and 124 to goin the bulk to have a 5 4oweA eneagy IStability) Al -also these oil'e mol. try to neaclu +he bulk I “7 thisis a piace with lower ene1gy (stable) ‘when the duwpletS are Vv Cose this part ieepsthem apont because it is +he pont of the system roxe stable then +he one neax SUNFACES Line molecutes itself QUE Oueating an eneugetic bamniex +#nok goes ogainst the theamoaynamics ajsteru is characteriteol by thermodynamic stability And Follows the kinetic tI ; P 7 we have to cueate Ne dispersion if | Want +0 neackh inis colloidal SYS.: sometimes Ineed to speed up T:(49) tells who mute enengg need to give to tne system to increase the AAT surface, soit teus Who mutch enexgy In ed to create suspension if 3} =» +he process to become colloidat is easier ( i's necessosy (est energy ) bui, once | creote the. colloidal system, if 51 the enewgy bawuer that goes against the coalescence is Less. va . . it Can prevail thermodynamics, so +he . colloi dat system £ast Less. 1 can Srange. TY inpresence of different phases: * itis difficutt to incmease CAI « lcan decuease lt Knowing that %12 << Ya and Ye, M-0CTANOL AVV 9A _ fon it TiS MUICN quer 1 420 . ? te, dhe mol.are fner 10 moving andit would onient with Ci Pa — inteaFase Oxygen neo water instedol 0Ftne nydrophobic tail DELE Lit keeps mot. in oniented way %, TT +hen wiih ain because of tne N-h° high interection given by the onienzazion Kinetic Stability Dispersions are heterogeneous systems in which fine particles (solid, liquid, or gas) are dis- tributed within a continuous phase. These systems are inherently thermodynamically unstable because the dispersed phase tends to minimize its surface area to reduce interf: “jal energy, leading to aggregation or phase separation over time. However, many dispersions remain ap- parently stable for prolonged periods due to kinetic barriers that prevent or significantly slow down these processes. This phenomenon is referred to as kinetic stability. A dispersion is said to be kinetically stable when the particles do not aggregate or sediment rapidly, even though the system is not at its lowest free energy state. The stability arises from repulsive interactions (such as electrostatic or steric repulsion) that introduce an energy barrier between particles. When this barrier is sufficiently high compared to the average thermal energy of the system (typically on the order of &T°, where & is the Boltzmann constant and T° the temperature), particle aggregation becomes an unlikely event. Thus, the system can remain dispersed for long periods despite the thermodynamic drive toward separation. Brownian motion plays a central role in the kinetic behavior of dispersions. It refers to the random, thermally driven motion of colloidal particles in a fluid, which results from collisions with solvent molecules. This motion keeps the particles in continuous movement, increasing the probability of inter-particle encounters. The collision frequency between particles depends on their concentration, size, and diffusivity, the latter being inversely related to particle size and fluid viscosity. 3. THÎN (MONOMOWECULAR) FilM WITH VENSES (MONOLAYER iN EQUILIBRIVM WITH LENSES ) AR WATER Di na _ this pont OFtne mol. likes wateu, so HYDROPHOBIC L in J OCTANOL CH3- CH3- CH2- CHa = Cp - CH = CH “Cl (OR) — the dispositiono make this pont to stay in contact witn watev to e L E n oily movecute not misuble with water Stabi lite. . + ueates the surface tension * SPREADING COEFFICIENT spreading occuus when the adnesion work is greate +nen ne conesion wonk WA.- We.> 0. S= Wa-We = (Ja + Y8 - Yag) - 2% S= T68- Ya - Fae = Te - (5a + Fas) =» Spueading occurs When s>o => if tnesum of the FREE surface enengies of new surtaces “and of the INTERFACE is Smallev than +he Free enegy of +hé OLD suntace $= tw - (Vow +9) >0 “When | add Vit +0 watety | coud Nave spneading on not Lwhnen surFACES are not FVOR sO they one Kept tne smallest ssible ( s is negative) - it's pretered Wateu with only oluoptets of vil t0 minimite +he surface on the spneading ? it depenas on the y | have if | put a duop of octanol in water, the hydwophobic pants tend 10 create the cuop L Wat@ is in contact with 04 ports SO Yow L and ST the organization tares some time, molecutet aMe fre to diffuse. AIR in this point, A Few graws ot WATER ET è octanoi can'be Solubie ta little) , ness a lig-lig equilibuum SEI 4ne Nyguophobic tails tend to ° Sperti Ebert s 0 i uilibuum- so, the one’ dissolve stay in contact with Qiv n Watev is gonna, enter in contact l . with tne ‘surface wat- dix this is decueasing the suntace tension w-aiw : 4 changes 4 xi the amount 05 molecules that cnange inis % is veuy smolL Cress then 1 nanomettes) ‘To stays the same - Tow and! Yw have to equiibiate — to: Su Sw bio Fowsb wi Vis smallee when at {he intevface there are molecotes that like each other ton with 20) — this changes the value of S xinetio PROTESS © DIFFUSIVIM) OF OCTANOL IN WATER Substance | Spreading Coefficient S |mN/m] | Ethanol | 50.4 Propionic Acid 45.8 Diethyl Ether 455 Acetic Acid 45.2 Acetone 424 Oleic Acid 24.6 Undecylenic Acid 32 Chloroform Benzene Hexane Octane Dibrom Liquid Paraffin ‘hene LI@UID SPREANS bw VAPOR tia. tv IS" soio «when | nave a liquid the duw Qaavity, it is moRe plate at ine 13 89 3.4 0.22 3.19 13.4 OVER SOLID S> Us-(&+ USO) importance oLso for 4he prop es ot a puodtict (es. paint, lubuicants) Ysw= Ist + Tv COSO coso = Isv- Fs LIT) if vapor = air coso = 9s-%s. LIA si Roli a mass And it becomes round, but, because of +he l Vv With solid this doesn't happen ‘ 8ys. not Spneading = : Once | Know the SURFACE tension => NO WETTING 8 > 90° I have a duoptet Der the surFace A with a ditterent snape Da and SM) So Toi $>0 — l have spueadingy | can compute @ (shap® of cuopl2XS) {and not spneading ) - the quavity make the duopeet +0 spread, it 9<90° WETTING = DISPLACEMENT FRON A SOLID OF ONE FWID FROM ANOTHER ONE © by SPREADING © adnesional © immevsionot SPREADING WETTING È © ) p Mit happens unen [ast Vul < lisvl w var. S= Isv- (ttt I [saio _ __] $>0 => spontaneous spreading S<0 => divoptet formation (0 contact angie) tm semina te” di = = cai intevactiohs petweei Ysv = Us + YwC0S0 YOUNG'S' EQUATION sdlid-vapor s>0 => cose >1 Sco =) 0 € 0180” © AoesionaL Wenling 10} initial state K+Is + vap, Li Fou. final state Ts WasWe Foaming Agents Surfactants that promote and stabilize foam formation are called foaming agents. Their effec- tiveness depends largely on their molecular structure and surface activity. In general, surfac- tants with low critical micelle concentrations tend to be more efficient at foam formation, as they more readily saturate the interface and reduce surface tension. A strong foaming agent must form a robust, elastic interfacial film that can resist mechanical stress and thermal fluc- tuations. Molecular features that enhance foam stability include long, linear hydrophobic chains that pack tightly at the gas-liquid interface, forming a cohesive barrier. However, excessively long chains may reduce the surfactant’s mobility and surface activity. foaming surfactants typically possess medium-length alkyl chains, For optimal performance, usually comprising 12 to 14 carbon atoms, which provide a balance between interfacial packing strength and dynamic sur- face activity. The behavior of foaming agents is also influenced by the surrounding medium. In ionic en- vironments, such as saline solutions, non-ionic surfactants generally produce less foam, and the foam tends to be less stable. This is due to their lower surface elasticity and weaker elec- trostatic stabilization compared to ionic surfactants, which benefit from charge repulsion and more rigid interfacial structures. As a result, ioni urfactants are often preferred in applica- tions where persistent and resilient foams are required, such as in cleaning agents or personal care formulations. Pressure Inside Bubbles The pressure inside a bubble is always higher than the pressure outside. This pressure difference arises due to surface tension, which tends to minimize the surface area of the interface and, in doing so, exerts a contracting force on the bubble. The pressure difference across the curved interface is directly related to the curvature of the bubble and the interfacial tension of the liquid phase. In general, the smaller the bubble, the higher the internal pressure, as curvature increases with decreasing radius. For a spherical gas bubble in a liquid, the pressure difference between the inside (gas phase) and the outside (liquid phase) can be derived in two ways: 1. Mechanical Approach: By considering the balance of fore cap of the bubble due to surface tension and pressure, it is poss ‘ting on a hemispherical ole to write: Fin = Vin A e Pin TRO Four = Pour A+ Fsurr = Pour GTR° + YBTR dEsorr = S- dA = Fsver dk => Fsuer= A dA liquid na FT ue Man AEG (aeuivative) tonci | need Fin = Four A4P= 25 to balance RO Pix > Pour ! [appea, that tend to decngase on increase the nadius 0f the bubble that have to the sus. is in equilibuum Just because of Y. (Sunface tension) witnokt +nat bubbles would not erist because #he pressure inside and outside would not balance. the smallea the nadius the higher the sunface , the highee AP of the sys. => /need mae enexgy SURFACE ENERGY APPROACH — what is gonna happen it im inmeasing the radius of the bubble 2. Surface Energy Approach: By evaluating the change in Gibbs free energy due to a virtual increase in the bubble’s surface area and equating it to the mechanical work done by the pressure difference, the same expression is obtained: dWin = Pin dU = Pin 4ITR® dR dWour = Pour dV + Uda eneugg to increase the area Piu GITRAR = Pour GIR'AR + % BITRAR ] dWm = dWovw = eQuiibuium Pin = Pour = SL BTRAR , 2% 4 RI AR R so dp= 2% : enevgy I need toceate the bubble is the surtace tension R Both methods lead to the same result, which is known as the Young-Laplace equation, where YL is the surface tension of the liquid film, and r is the internal radius of the droplet. This fundamental relation describes how the pressure inside a curved interface depends on the mean curvature of the surface and the surface tension if +#ne syg. has difteuent cuwatues (not a perfect sphere) | can generalize : DIFFERENT CURVATURES A4P= (1, È) = 2% Ra Ra Pei) Ri= main curvature raoio ‘ | USE the evonage of different radius fsame as with different WUVaXULES, | have 10 : soap bubbe (Foam)! now thar thee ue 2 gas-liquid intensaces in onde to sunvive, the bubble has a +hickness +hat is negligrble, I nave a A4P= 2% and 4.9= 28. so the Final 4P is: = R Ri: a e (AP= St = because | have 2 intevfaces (this happened Only when Ra ® Ra) Ri R i Ra * uNen I consider the tnickness ot the film, | use the gen eralited equation x APPLICATIONS: @ FORM —— METALLICO —— CATALUTICAL PROCESS — when | condense a lot of bubble EN POLYMERIC — INSULATION . , in most of the case the quealion of of Foam is not wanted |‘cause of a pressure d10p) (cavitation) — this happen any time è. is lower tnen a specific value when Iwant foam |play on lowering dr @ FLOTATION IN MINING — When I have to recorev a now mateuial in the ground we use TTT—T