第三章表面张力及表面能.ppt

1、第三章表面张力及表面能,3.1表面能及表面张力 3.2弯曲液面下的附加压力 3.3表面过剩及吉布斯吸附公式,表面现象,水滴为什么是圆形而不是方形,表面现象,它们为什么可以漂在水面上,表面张力与表面自由能,表面张力 (surface tension) 表面自由能 (surface free energy),表面张力(Surface Tension),Surface tension,Surface tension of water drop,表面张力(Surface Tension),在两相界面上，处处存在着一种张力，它垂直于表面的单位线段上，指向使表面紧缩的方向并与表面相切。,注意： 表面张力是

2、作用在单位长度线段上的力，量纲为 m-1。 表面张力也常被称为表面张力系数。,作用于单位边界线上的这种力称为表面张力，用 表示，单位是Nm-1。,2.1.3 surface free energy,表面自由能(Surface Free Energy),使液体表面积增大的过程是克服液相分子吸引力, 使体相分子转移到表面相的过程，需要环境对体系做功。以可逆方式做功最少，称之为表面功：,由吉布斯自由能性质可知，在恒温、恒压、组成不变的条件下，此表面功即等于体系吉布斯自由能的增量：,表面自由能(Surface Free Energy),1. 狭义定义：保持体系温度、压力、组成不变时，增加单位表面积，体

3、系吉布斯自由能的增量。,也称为比表面吉布斯自由能,表面自由能(Surface Free Energy),表面化学基本热力学关系式：,表面自由能(Surface Free Energy),2. 广义定义：保持体系相应变量不变时，增加单位表面积，体系热力学函数的增量。,表面自由能与表面张力,对于表面相，我们从“能”和“力”的角度引出了两个不同的概念：表面自由能与表面张力。事实上这两个概念有着密切的联系,一、两者量纲相同,表面自由能的量纲,表面张力量纲,表面自由能与表面张力,二、对于同一体系的同一个表面或界面其数值相等，物理意义不同。,例如：T=20,若以表面自由能的单位：J/m2来表示，其数值应该

4、为多少？,思考题：,已知：,Table 2.1: Surface tensions of some liquids at different temperatures T.,表面张力的微观成因,表面相分子受力不均匀，其分子有被拉入液相的趋势。 这种受力不均匀性是表面现象产生的微观成因。,液体的表面积因而有自发收缩的趋势。,思考题,表面张力与哪些因素有关？即表面张力受哪些因素影响？,With this view can be interpreted as the energy required to bring molecules from inside the liquid to the su

5、rface and to create new surface area. Therefore often the term “surface energy” is used for .,Figure 2.1 Schematic representation of a liquid molecule in the bulk liquid and at the surface. A downward attraction force is operative on the surface molecule due to the lack of liquid molecules above it.

6、,4. 影响纯物质的的因素,(1) 物质本身的性质（极性液体比非极性液体大， 固体比液体大）,(2) 与另一相物质有关,/(N m-1) 水 -正庚烷 0.0502 苯 0.0350 汞 0.415,纯液体的表面张力是指与饱和了其本身蒸汽的 空气之间的界面张力。,(3)与温度有关：一般随温度升高而下降 (4)受压力影响较小,一些液体的表面张力,一些油水界面张力（20）,小结： 表面张力与表面自由能,表面张力（surface tension）是垂直作用于液体表面上任一单位长度、与液面相切的收缩表面的力。表面张力是液体的基本物理化学性质之一。单位：mN/m(毫牛/米) 表面自由能（surface

7、free energy）：是恒温恒压下增加单位表面积时体系自由能的增量，称作比表面自由能，简称表面自由能。单位：mJ/m2（毫焦/米2）,Figure 2.2: Schematic set-up to verify Eq. (2.2) and define the surface tension,W =A.,If a water film is formed on a frame with a slider length of 1 cm, then the film pulls on the slider with a force of,2 0.01 m 0.072 Jm2 = 1.44 10

8、3N That corresponds to a weight of 0.15 g.,How can we interpret the concept of surface tension on the molecular level?,For molecules it is energetically favorable to be surrounded by other molecules. Molecules attract each other by different interactions such as van der Waals forces or hydrogen bond

9、s.,Without this attraction there would not be a condensed phase at all, there would only be a vapor phase. The sheer existence of a condensed phase is evidence for an attractive interaction between the molecules. At the surface, molecules are only partially surrounded by other molecules and the numb

10、er of adjacent molecules is smaller than in the bulk(Fig. 2.3).,2.3 Schematic molecular structure of a liquidvapor interface.,This is energetically unfavorable. In order to bring a molecule from the bulk to the surface, work has to be done. With this view can be interpreted as the energy required to

11、 bring molecules from inside the liquid to the surface and to create new surface area. Therefore often the term “surface energy” is used for .,Example:Estimate the surface tension of cyclohexane from the energy of vaporization vapU = 30.5 kJ/mol at 25C. The density of cyclohexane is = 773 kg/m3, its

12、 molecular weight is M = 84.16 g/mol.,For a rough estimate we picture the liquid as being arranged in a cubic structure. Each molecule is surrounded by 6 nearest neighbors. Thus each bond contributes roughly vapU/6 = 5.08 kJ/mol. At the surface one neighbor and hence one bond is missing. Per mole we

13、 therefore estimate a surface tension of 5.08 kJ/mol.,To estimate the surface tension we need to know the surface area occupied by one molecule. If the molecules form a cubic structure, the volume of one unit cell is a3, where a is the distance between nearest neighbors. This distance can be calcula

14、ted from the density:,For such a rough estimate the result is surprisingly close to the experimental value of 0.0247 J/m2.,例题,例1、将1g水分散成半径为 m的小水滴（视为球形），其表面积增加了多少倍？ 解：对大水滴 对小水滴,弯曲液面下的附加压力Curved liquid surfaces with additional pressure,s,=P0+Ps,s,=P0-Ps,弯曲液面的力平衡条件,1. 水平液面：,此结果与不考虑表面相时的结果完全一致，说明一般情况下，经

15、典的力平衡条件是成立的,弯曲液面的力平衡条件,2. 凸液面（液滴）：,杨-拉普拉斯公式,弯曲液面的力平衡条件,3. 凹液面（气泡）：,From a comparison of similar triangles, it follows that,If the surface is to be in mechanical equilibrium, the two work terms as given must be equal, and on equating them and substituting in the expressions for dx and dy, the final r

16、esult obtained is,R1 and R2 are the two principal radii of curvature. P is also called Laplace pressure.,s,=P0-Ps,s,=P0+Ps,Derection:pointing to the radius circle center,毛细现象,平面下液体的压强大于凹面下的压强,液体从高压向低压流动，毛细管内液体上升,毛细管内液体上升直至，同一水平面的液体压强相等,弯曲液面的力平衡条件,毛细现象：,式中R为弯曲液面的曲率半径,水在毛细管中得上升显然应满足如下关系：,弯曲液面的力平衡条件,毛细

17、现象基本公式亦可表示如下：,曲率半径与毛细管半径R的关系： R=R/cosq 为液面与管壁的接触角,Capillary rise problem,Given that the surface tension of water is 0.0728 J/m2 calculate the capillary rise in a glass tube that is 1 mm in radius. A. 1 mm B. 1.5 mm C. 10 mm D. 15 mm,Capillary rise problem,Given that the surface tension of ethanol is

18、 0.032 J/m2 calculate the capillary rise in a glass tube that is 0.1 mm in radius. Assume that density of ethanol is 0.71 g/cm3. A. 47 mm B. 65 mm C. 91 mm D. 110 mm,在298K和101.325kPa下，将直径为1m的毛细管插入水中，问需要外加多大的压力才能防止毛细管内的水面上升？或不加额外的压力，让水面上升，达平衡后管内液面上升了多高？（己知该温度下水的表面张力为0.072N/m，水的密度为1000kg/m3，设接触角为0，重力加

19、速度为g=9.8m/s2）,Techniques to measure the surface tension,毛细管升高法(Capillary rise method) 环法(Du-Noy tensiometer) 板法(the Wilhelmy plate method) 最大气泡压力法(Maximum-bubble-pressure method) 滴重(体积)法(Drop weight or drop volume) 悬滴法(Pendant liquid drop),Capillary rise method,Capillary radius r and curvature R hav

20、e the following equation:,Maximum-bubble-pressure method,The maximum pressure is reached when the bubble forms a half-sphere with a radius rB = rC. This maximum pressure is related to the surface tension by Young-Laplace equation.,表面张力测定装置,Drop-weight method,The radius of the capillary is rc,The equ

21、ation is :,When correction factors are used, the equation becomes:,ring tensiometer, called also the Du-Noy tensiometer,What the equation?,theWilhelmy plate method,Equation:?,吊片法,吊片法即为Wilhelmy method,亦称为板法,脱环法(环法),滴体积法：,停滴法和悬滴法：,表面过剩和吉布斯等温吸附式(surface excess and Gibbs adsorption isotherm),Effects of

22、simple electrolytes on the surface tension of water: (a) LiCl; (b) NaCl;(c) NaBr.,1. 非表面活性物质 如无机盐、不挥发酸碱以及蔗糖、甘露醇等多羟基有机物的水溶液,2. 表面活性物质 短链脂肪酸、醇、醛,3. 表面活性剂：具有两亲性质能明显降低水的表面张力的有机化合物。,表面过剩和吉布斯等温吸附式,The Gibbs adsorption equation, in its most general form,Where = the change in surface or interfacial tension

23、of the solvent.,= the surface excess concentration of any component of the system.,= the change in chemical potential of any component of the system,is fundamental to all adsorption processes.,在溶液中，1mol溶剂A中所含溶质B的摩尔数,单位面积表面层中的溶剂A在溶液中所应 含溶质B的摩尔数,单位面积表面层实际所含溶质的摩尔数,上标s表示表面(surface)，令A为溶剂，B为溶质。,定义：,Is ca

24、lled (relative) surface excess or amount of surface adsorption (表面超额或表面吸附量),物理意义:单位面积表面层中溶剂所含溶质的物 质的量与同样数量的溶剂在溶液中所含溶质的 物质的量的差值.,稀溶液中,吉布斯吸附等温式,讨论：,表面活性物质,正吸附,非表面活性物质, 负吸附,应用吉布斯公式,先要由实验或经验公式得到 c之间的关系,然后求出 ( /c)T,p,再求值 .,为了证实吉布斯公式，有人做了下列实验，在25时配制一浓度为4.00g/L的苯基丙酸溶液，然后用特制的刮片机在310cm2的溶液表面上刮下2.3g溶液，经分析可知表面

25、层与本体溶液浓度差为 .试根据此计算表面吸附量。另外，已知不同浓度 下该溶液的表面张力 为：,作业：,试用吉布斯吸附公式计算表面吸附量。并比较二者结果。已知苯基丙酸的摩尔质量为 。,Which is commonly used for dilute solutions of nonionic surfactants containing no other materials.,溶液表面吸附量的计算：,For dilute solutions(10-2M or less) containing only one non-dissociating surface-active solute, th

26、e Gibbs equation is:,For solutions of a completely dissociated surfactant of the 1:1 electrolyte type, M+R-, as the only solute,Since to maintain electron neutrality and , then,where is the mean activity coefficient of the surfactant.,For 1:1 type ionic surfactant dilute solutions (10-2M or less),Si

27、nce under these conditions the change in the activity of the non-surfactant common ion with adsorption is zero. This is the same form as for a nonionic surfactant in dilute solution.,For dilute solutions of a completely dissociated surface-active 1:1 electrolyte in the presence of a swamping, consta

28、nt amount of electrolyte containing a common non-surfactant counterion,You add 0.5 mM SDS (sodium dodecylsulfate, NaSO4(CH2)11CH3) to pure water at 25C. This leads to a decrease in the surface tension from 71.99mJ/m2 to 69.09 mJ/m2. What is the surface excess of SDS?,Example,At such low concentratio

29、n and as an approximation we replace the activity a by the concentration c and get /a /c=(0.06909 0.07199)Nm1 (0.0005 0)molm3 = 5.80Nm2/mol,It follows,1.17 106 mol/m2,表面活性剂在溶液表面上的吸附等温线,一定温度下，吸附量与浓度之间的平衡关系曲线，叫做吸附等温线。,吸附等温线是Gibbs等温吸附公式的直接应用。,测定恒温时不同浓度溶液的表面张力，根据Gibbs公式求得吸附量 ，作曲线 ，即得吸附等温线。,十二烷基硫酸钠的吸附等温线,表面活性剂在溶液表面上的吸附等温线,吸附等温线的数学表达式的导出。,K：吸附平衡常数， :代表表面活性剂分子的表面占有分数， ， 分别为吸附量和极限吸附量（即最大吸附量）。 x:代表溶液中表面活性剂单体的摩尔分数。,因为在很稀的溶液中，,所以，,又因为溶液浓度很小时， 为物质的量浓度（mol/L），上式可改写为,Langmuir单分子层吸附等温式,将上式进一步改写，可得,讨论:,1）吸附等温线的应用,求得表面相上单个分子所占有的面积。,得