Surface Tension of Polymers - MIT

1 June 29, 20051 Surface Tension of PolymersAbhinandan AgrawalHatsopoulos Microfluids LaboratoryDepartment of Mechanical EngineeringMassachusetts Institute of TechnologyJune 29, 20052 Physical origin of Surface Tension / Surface energy Unhappy molecules at the Surface : they aremissing half their attractive interactions Unbalanced forces for the molecules at the Surface lead to additional energy The additional free energy at the Surface is known as surfaceenergy This is the fundamental reason behind liquids adjusting their shapes to expose the smallest possible areaExamples of minimal surfaces spherical shape of dry hair vs.

2 Sticky wet hairJose Bico, Nature, 2004 June 29, 20053 Mechanical definition: as a Surface energy Supply of energy is necessary to create surfacesdWdA = (mJ/m2)specific free energy or Surface Tension =Specific Surface energy of a material is the excess energy per unit area due to the existence of the free surfaceJune 29, 20054 Estimation of Surface Tension based on intermolecular forcesUU/2 Surface Tension is then of order For van derWaalstype interactions, At a temperature of 25 oC, kTis equal to 1/40 eV, which gives = 20 mJ/m222Ua UkT U is the cohesion energy per molecule inside the liquidEnergy shortfall for a molecule sitting at the Surface ~ U/2a is the size of a molecule.

3 A2is the exposed area of a molecule (close to actual value for oils and alcohols)Helium (4 K)EthanolAcetoneGlycerolWaterWater (100oC)Molten ~300485 Surface Tension of a few common liquids in mJ/m2strongly cohesive liquidhydrogen bonding1eVU June 29, 20055 Mechanical definition: as a capillary force Surface Tension ( ) can also be viewed as a force per unit length (mN/mor N/m)The term Surface Tension is tied to the concept that the Surface stays under a tensionExamples where Surface Tension manifests itself as force3) Objects on water2) Capillary adhesionF1) Slider2 Fdxldx =end view of the legWF1F2(F1+F2)cos F1=F2= lJune 29, 20056 ContentsRelationship of Surface Tension with other material propertiesDerivation of Surface Tension theoretically from knowledge of intermolecular forces1) Surface energy of polymer liquids and melts2)

4 Surface energy of solid polymers3)Interfacial Tension between a solid and a liquidJune 29, 200571. Surface energy of liquids and meltsExisting methods for determining the Surface Tension of liquids1) Wilhelmy s method, in which one dips a thin plate or ring in the liquid and measures the capillary force acting on the plate2) The rise of a liquid in a small capillary tube3) The method of drops, in which one characterizesthe shape of dropsFcos()p 2coshgr =is the perimeter of the plate =2(length + width)p rhwaterwashing-liquid Cgz =()()3/21/222111zzzzrCrrr= +++rzJune 29, 20058 Estimation of Surface Tension from related propertiesSince the Surface Tension is a manifestation of intermolecular forces, it may be expected to be related to other properties derived from intermolecular forces, such as work of cohesion internal pressure, and ) Relationship between work of cohesion and Surface Tension (Grunberg 1949)molecular vol.

5 ;AVN=2/3molecules/unit surf. area;ANV = molar vol.;V=1/32/32cohAWNV =2/32/3/ Surface energy per molecule;AVN =surf. energy per unit area; =1/32/3molar surf. energy ;ANV =1/32/32work of cohesion;ANV =2) Relationship between Surface Tension and solubility parameter(Hildebrand 1950)1/32/molar surf. energy //;vVVEV = = (cgsunits)V = is the energy of vaporization; is the solubility parameter;vE 3) Relationship between compressibility and Surface Tension (McGowan 1967) 3 (cgsunits) = June 29, 20059 Introduction to parachorMacleod etal. (Trans. Faraday So.

6 , 1923, 19, 38) is the Surface Tension , Dand dare the density of liquid and vapor at same temperature. Cis a a characteristic constant for a given liquid.()4 CDd = valid for different compounds and at different temperatures1/41/4sMPCMDd == at low temperature, dbecomes smallSugdenS. J. (Chem. Soc., 1924, 125,1177)molecular volume VUnit of Ps (cm3/mol) (erg/cm2)1/4or(m3/mol) (mJ/m2)1/4 Psfor different substances is a comparison of molecular volumes attemperatures at which liquids have the same Surface tensionPsbears an constant ratio to the critical volume, which suggests that it is a true measure of the molecular called parachor(from = by the side of, and = space to signify comparative volumes)

7 June 29, 200510 Useful properties of parachorPsis only a function of chemical composition and it is an additive functionFrom experimental data for Ps, it is found that Pscan be reproduced by adding together two sets of constants, one for the atoms in the molecule, the other for the unsaturation or ring closure. The values for a particular atom is independent of the manner in which it is situated The values for individual element are same from compound to compound. XRCCThe molecular parachor is a useful means of estimating Surface tensionsMis the molecular weight, Vis the molar volume, is the density.

8 If the group contributions of Psand Vare known, results from the above expression4sPV = HR1 OJune 29, 200511 Atomic and structural contributions to the (in esters) of atomic constants: Difference for CH2in paraffins, esters, ethers, and ketoneshas a mean value of nCH2from a series of values for the paraffinsCnH2n+2, values for 2H can be calculatedQuayle Chem. Revs. 53 (1953) 439 June 29, 200512 Example: ethanolOHHUnitContribution to ()321/4 (cm/mol) (erg/cm) ;46 = + + ===== == close to the actual value of 24 mJ/m2 June 29, 200513 Example: poly (ethylene oxide) OHUnitContribution to ()321/4 (cm/mol) (erg/cm).

9 44g/ = + + ===== == close to the actual value of 43 mJ/m2 June 29, 200514 Contact between solids and liquidsSolid/liquid pairpartially wettingnon-wettingwettingdA cos dA ' s sl lairliquidChange in Gibbs free energy dGwhen the drop spreads an infinitesimal amountcosslsldGdAdAdA = +At equilibrium/0cos0slsldGdA = += land are directly measurable; sand slare notwetting behavior dependent on interfacial and solid Surface energy as wellcosssll =June 29, 2005152. Surface Tension of solid surfaces ( s)Methods for determining the Surface Tension of solidsa) By measuring the contact angle between the solid and liquidb) By determining critical Surface Tension ( ) according toZisman (1964), with the assumption that c) By extrapolating Surface Tension data of polymer melts to room temperature (Roe, 1965; Wu, 1969 71)cr crs No direct method available for measurement of Surface Tension ofsolid polymersJune 29, 2005162a.

10 Estimation of solid Surface energy from contact angle()1/321/31/34()slslVVVV =+1/22()slslsl =+ cos0slsl +=Girifalcoand Good (1956)()221cos4sl + Example: PMMA()1/321/31/34( ) ==+ ; == ==2231g/cm;18g/molHOHOM ==68 72o223218cm/mol;72mJ/mHOHOMV ===()2221cos(69) + DBy means of the boxed equation, Surface Tension of solid surfacecan be calculated from measurements of contact angle and Surface Tension of liquidJune 29, 2005172b. Determining solid Surface Tension using Zisman carbonateDimethyl sulfoxideEthylene glycolGlycerolWatercos( ) Surface Tension (mN/m)Toluene238mJ/mcr =Zisman found that cos is usually a monotonic function of l()cos1llcrab = = cris called the critical Surface Tension of a solid and is a characteristic property of any given solid Any liquid with l< crwill wet the surfaceIt is found that critical Surface Tension is close to the solid Surface Tension of polymerscr Zisman plot for PMMA using various testing liquidsJune 29, 2005182c.