胶体及界面化学(第6章)-dzx

1、Chapter 6. Surface Tension and Contact Angle6.1 IntroductionSurface tension is a parameter can be used to characterized property of liquid surface (interface) and measured.Contact angle can be used mostly to characterize surface property of a solid and measured.Focus of this Chapter Concerning the e

2、quilibrium behavior of interfaces between “pure” phases; Definitions of surface tension and contact angle and what effects they have on the equilibrium behavior of materials; Laplace equation, the pressure across a curved interface; To use surface tension and contact angle determining wetting phenom

3、ena of solid. 6.2 Surface tension, surface work and surface free energySurface tensionSurface tension() is a force that operates on a surface and acts perpendicular(垂直垂直) and inward from the boundaries of the surface , tending to decrease the area of the interface. =F/2L (1)Characteristics: A contra

4、ctile (收缩收缩) force，tends to shrink (收缩收缩) the surface; A force of per unit length, (N m-1 or dynes cm-1)； A two-dimensional pressure;F（1） Reason for producing surface tensionAssumption of vacant state of surface（表面层表面层空位假说）空位假说）: （Bakker，Davies，Fowkes，Ademson）The molecules in the surface of liquid e

5、xchanges with the molecules of its vapor and the liquid. Based on kinetic molecular theory of gases (气气体分子动力学理论体分子动力学理论) and theory of diffusion in liquids (液体扩散理论液体扩散理论), when temperature is in 20C：Exchange rate of molecules between surface and vapor is: 2.91020 / s.cm2Exchange rate of molecules be

6、tween surface and liquid is: 1.71025/s.cm2In equilibrium the distance between the molecules on the surface is larger than that in liquid, there is “vacant position” on the surface. Due to the distance between the molecules on the surface is larger than that of the molecules in liquid the molecules i

7、nteracted attractively and in the state of tension.Molecules in liquidThe distance between the molecules on surface is larger that predicated by this assumption is agree with the distance calculated by Prigogine and Saraga with statistics method based on a model of surface thermodynamics. 热热力力学学函函数数

8、 无无空空位位 30空空位位 实实验验值值 表表面面自自由由能能（mJ/m2） 9 13.0 13.2 总总自自由由能能（mJ/m2） 25.8 37.3 35.3 表表面面熵熵（e.u.） 0.19 0.27 0.26 Thermodynamic functions of liquefied argon(液氩液氩) (85K)（2）Mechanical model of surface tension(表面张力表面张力的力学模型的力学模型) Based on the assumption of vacant state of surface, surface tension of matte

9、rs is related to the forces between the molecules.Surface tension： (Fowkes)Dispersion force, London force （d）( 色散力色散力);Hydrogen bonding (h) (氢键氢键)Metallic bonding (m) (金属键金属键) Interaction of electrons () (电子相互作用电子相互作用)Interaction of ions (i) (离子相互作用离子相互作用)Surface tension defined by Fowkes： d h m i （

10、6-1）Hydrocarbon liquids（H）： HH d （6-2）Water（W）： w wd w h （6-3）Mercury(汞汞)(Hg)： Hg Hgd Hgm （6-4）Only the dispersion force exist in all matters and the distance of the dispersion force act on is the longest (within few molecules) 。Surface tension of matters状状态态组组成成 作作用用力力 （mN/m） 固固体体 化化学学建建，金金属属键键 数数百

11、百数数千千 水水 氢氢键键 72.8 一一般般液液体体 Van der Waals 力力 数数十十，小小于于 w 气气体体 Van der Waals 力力 很很小小 （3）Surface tension and attractive force Due to surface tension is produced by the attractive forces between molecules, the value of interface tension measures the difference of the attractive force（f） between the mol

12、ecules in liquid or between a gas and liquid. Plane surface surface tension fattractive force (liquid) f - attractive force (gas) f =ff f Surface tension fAttractive force of the molecules on the surface;ftangential force of f;f radial force of f;The value of surface tension is related to f;The tota

13、l of f is the extra force act on the molecule in the surface towards to the center of the liquid drop.Curved surface（4）Direction of surface tension Plane surface ： Parallel to the surface， contractile force，tends to shrink the surface Curved surface ：（5）Surface tension and temperature or pressure an

14、d T T（density of gas，f；distance of molecules in liquid ，f） and PP（some of molecules in gas phase go into liquid，f； density of gas ，f）2surface work(表面功表面功) Surface tension is a contractile force, work can be done by the force under certain conditions. W2LdxdA （6）Surface work：The work done by surface

15、tension with reduction of surface area. （J/m2）or（mJ/m2）When the force F make the wire though dx, the work done on the system, and the work equals to the work required to produce a new surface.FTwo equivalent interpretation of ：Force per unit length of boundary of the surface;Energy per unit area of

16、the surface.3. surface free energy(表面自由能表面自由能) Work done by reducing of surface area predict that the surface have energy and the energy is as surface free energy.Surface free energy： The energy of the molecules on the surface excess in the energy of the molecules in liquids. （mJ/m2）。）。 Surface free

17、 energy is an “excess” energy.From thermodynamics, for a equilibrium system of two phases in the process of equilibrium the work done by the system includes pressure-volume work(膨胀功膨胀功), chemical work(化学功化学功) and surface work, then： dUTdSPdVdA （6-5） iiidnUenergy of the system；Sentropy(熵熵)；Vvolume；Tt

18、emperature；Ppressure；ichemical potential of i component(成分成分)； n amount of substance(物质的量物质的量)； surface free energy； Aarea of surface.Surface free energy is the energy of the system increased by increasing per unit area of the surface when entropy, volume and fractions are constant. , ,()is v nUAFro

19、m eq.(6-5)：Based on definitions of enthalpy(焓焓), free energy and Gibbs free energy: （6-6） （6-7） （6-8）()iiidHd UPVTdSVdPdAdn()iiidFd UTSSdTPdVdAdn ()iiidGd HTSSdTVdPdAdn then： （6-9） （6-10） （6-11）Surface energy is the change of energy, enthalpy, free energy and Gibbs free energy of the system by incre

20、asing per unit area of the surface under certain condition. . .()iS P nHA. .()iT V nFA. .()iT P nGAWhy small drops of liquid always be changed into a large one spontaneously? dGdA，when is constant，AG6.3 Contact angle and wetting(润湿润湿)WettingWetting is the displacement(置换置换) from a surface of one flu

21、id(流体流体) by another.Wetting involves three phases, at least two of which must be fluids.The wetting of a gas (usually air) is displaced by a liquid at the surface of a solid. When a dry substance wet substance the enthalpy(焓焓) of the substance is changed. H imH wetH dry (6-12）H im heat of immersion(

22、浸泡浸泡)H im 0，a process of releasing heatAir is displaced by a liquid at the surface of solid spontaneously, G 90 no wettable 1For a solid surface with roughness factor r, the Young equation is given r（SASL）LA cos （6-17）apparent contact angle，comparing（6-17）with（6-15）gives （6-18）coscosrqqFrom Eq.(6-18

23、) it will beAFor 90，90， ， a rough surface of a solid is less wettable than a smooth surface of the solid.Cmeasurement of is very difficult. ，errors of measurement.5. Advancing (前进前进) and Receding (后退后退) Contact angleAdvancing contact angle ( a a): larger valueReceding contact angle ( r r): smaller v

24、alueBoth advancing and receding contact angles should be measured. (a)- The tilted(倾斜的倾斜的) plate is pushed into the liquid.(r)- The tilted plate is pulled out from the liquid.6.4 Cohesion(内聚内聚), Adhesion(粘附粘附) and Spreading(铺展铺展)1. CohesionNo surface 2A(or B) SurfacesCondition: One unit of surface i

25、s affected by the process. The shape of the affected area is immaterial (非物质的非物质的).Work of cohesion:The work required to pull apart a column of liquid A apart. G=2A =WAA (56)It measures the attraction between the molecules of two portion.Surface tension measures the free energy change involved when

26、molecules from the bulk of a sample are moved to the surface.2. Adhesion1 AB Interface 1A + 1B SurfacesDifference between the final and initial free energies for this process yields G=WAB = A + B - AB (57) WAB is work of adhesion that measures the attraction between the two different phases. The wor

27、k of adhesion between a solid and a liquid phase may be defined WSLLA（1cos） (60，6-16)For 0， WSL2LA = WAAFor 180 ，WSL0，the liquid is tangent to the solid and there is no interaction between the phases. 3. Spreading G= AB + B - A (61) Difference between the final and initial free energies for spreadin

28、g B over A (symbolized B/A) we obtainThe negative of GB/A is called the spreading Coefficient SB/A.For SB/A 0， B spreads freely over A and wets it.By combining Eq.(56), (57) and (61) the spreading coefficient can also be written SB/A = WAB - WBB (62)If WAB WBB the A-B interaction is sufficiently str

29、ong to promote the wetting of A by B.If WAB WBB no wetting occurs. Since the work required to overcome the attraction between two B molecules is not compensated(平衡平衡) by the attraction between A and B.For SB/A P2 .P1P2P11211()PRRThe Laplace Equation（29）Eq. (29) is general and applies equally well to

30、 geometrical bodies with radii of curvature that are constant over the entire surface or to more intricate（复杂的）（复杂的） shapes for which the Ris change from place to place on the surface.（1）For a spherical surface，R1R2R ，2PR（30）（2） For a cylindrical surface，R1， (31) （3）For a planar surface，R1R2， P0 （32

31、） The pressures in both sides of the surface are equal. 2PR （4）R1 and R2 ，P ； （5）For a gas bubble, （6） For a saddle (马鞍马鞍) shaped surface, P0， （7） It may be a liquid or a gas at both sides of the surface. 4PR1211RR The total of f is the extra force act on the surface towards to the concave side of t

32、he interface. Due to the value of P relate to f and relate to f, therefore, can be used for measuring of P 。Why there is a pressure difference operates across a curved interface? PPP or PP PP PP PCondition: The wall of capillary is wettable by a liquid.（1）弯曲液面压差）弯曲液面压差When a capillary is just pushed

33、 into water P1P2P3P4Due to the pressure at point 4 is lower，the liquid flows from point 2 toward point 4 and enter the capillary. At equilibrium: P5P1P2 P62. Capillary RiseRradius of the curved surface； rradius of capillary; For rR cos， then， The difference of pressure across the curved interface pu

34、sh liquid flows into the capillary.562PPPghR 2 coshgrq（6-19）（2） 重力平衡（实验测定）重力平衡（实验测定）If we imagine(设想设想) the surface to be “hanging” from the wall of the capillary and supported by the vertical component (cos) of the surface tension.“表面张力将流体拉入毛细管表面张力将流体拉入毛细管”，表面张力的分力与，表面张力的分力与重力平衡。重力平衡。2 coshgrqghrrq

35、2cos2表面化学表面化学，363页页Pressure difference across a curved interface as （6-20）LVSurface tension between liquid and vapor; r Radius of capillarycos2LVPrq（3 3）固气、固液界面张力差）固气、固液界面张力差SVsurface tension between solid and vapor;SL surface tension between solid and liquid；cosSVSLLVqFrom Young-Equation（6-21） P2（

36、SVSL）/r （6-22）P only depend on the difference of SV and SL，and not related to LV.For（ SVSL ） 0，capillary rise；For （SVSL ） 0，capillary depression “毛细下降毛细下降”。Taking Eq.6-21 into Eq. 6-20 gives（4 4）与表面张力反向力作用）与表面张力反向力作用 界面化学基础界面化学基础，1515页页 毛细管壁对液体的作用力将液体拉毛细管壁对液体的作用力将液体拉进毛细管。进毛细管。It imagine f ，and f opp

37、osite from .2 coshgrqfConclusions for capillary rise： 1 (SVSL) is the driving force; 2For a specified system，（，（SVSL）is fixed，h1/r，rh。6.6 Kelvin EquationKelvin EquationFrom Laplace-Equation, for a plane surface P = 0.The vapor pressure is P0.For a spherical surface the pressure difference is 2PRFor liquid-vapor equilibrium at a spherical surface, both the liquid and the vapor must be brought to the same pressure P0 + P.If we a