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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：表面张力是作用在单位长
2、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，体系吉布斯自由能的增
3、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，其数值应该为多少？,思考题：,
4、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 surface and to
5、 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.,4.影响纯物质的的因素,(1)物
6、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 free energy）：是恒温恒压下增加单位表面积时
7、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 103NThat corresponds to a weight of
8、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 bonds.,Without this attraction there wou
9、ld 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 number of adjacent molecules is smaller than
10、 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 bringmolecules from inside the liquid to th
11、e 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 molecular weight is M=84.16 g/mol.,For a rough estimat
12、e 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 therefore estimate a surface tension of 5.08 kJ/mol.,To estima
13、te the surface tension we need to know the surface area occupied by onemolecule.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 calculated from the density:,For such a rough estimate the result is surpri
14、singly 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
15、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 result obtained is,R1 and R2 are the two principal radii of curvature.P is al
16、so 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
17、 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 mmB.1.5 mmC.10 mmD.15 mm,Capillary rise problem,Given that the surface tension of ethanol is 0.032 J/m2 calculate the capillary rise in a glass tube that is 0.1 mm in radius.Assu
18、me that density of ethanol is 0.71 g/cm3.A.47 mmB.65 mmC.91 mmD.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
19、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 have the following equation:,Maximum-bubble-pressure method,The maximum pressure is reached when the bu
20、bble 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 equation is:,When correction factors are used,the equation becomes:,ring tensiometer,called also the Du-No
21、y 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 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
22、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 of the solvent.,=the surface excess concentration of any component of the system.,=the change in chemical potential o
23、f 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 called(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
24、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 soluti
25、ons 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,the Gibbs equation is:,For solutions of a completely dissociated surfactant of the 1:1 electrolyte type,M+R-,as the only solute,Since t
26、o 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),Since under these conditions the change in the activity of the non-surfactant common ion with adsorption is zero.This is the same form as fo
27、r a nonionic surfactant in dilute solution.,For dilute solutions of a completely dissociated surface-active 1:1 electrolyte in the presence of a swamping,constant amount of electrolyte containing a common non-surfactant counterion,You add 0.5 mM SDS(sodium dodecylsulfate,NaSO4(CH2)11CH3)to pure wate
28、r 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 concentration 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
29、,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,
30、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。,得到极限吸附量，进一步得到极限吸附时单个分子所占面积，进而判断表面活性分子在溶液表面上的状态（包括吸附层的厚度）。,两亲分子在气液界面上的定向排列,根据实验，脂肪酸在水中的浓度达到一定数值后，它在表面层中的超额为一定值，与本体浓度无关，并且和它的碳氢链的长度也无关。,这时，表面吸附已达到饱和，脂肪酸分子合理的排列是羧基向水，碳氢链向空气。,两亲分子在气液界面上的定向排列,根据这种紧密排列的形式，可以计算每个分子所占的截面积Am。,式中L为阿伏加德罗常数，G原来是表面超额
31、，当达到饱和吸附时,G 可以作为单位表面上溶质的物质的量。,由这种方法求得醇分子的的S=0.2780.289nm2,脂肪酸S=0.3020.310nm2，结果一般偏大。这是因为表面层中达饱和吸附时仍夹杂着水分子.从还可以求算饱和吸附层的厚度:=M/M：溶质的摩尔质量；：溶质的密度；M 为单位面积上的溶质质量,量纲为m。实验结果表明，同系物碳链增加一个-CH2-时，增加0.130.15nm.与X光分析结果一致。,某表面活性剂的稀溶液，表面张力随浓度的增加而线性下降，当表面活性剂的浓度为10-4 mol/dm3时，表面张力下降了310-3 mN/m,计算表面吸附量2(设温度为25)；求每平方米上该
32、表面活性剂分子的个数以及每个表面活性剂分子所占有的表面积。,作业：,1、试求25时，1g 水形成一个球形水滴时的表面积和表面自由能。若将其分散成直接为2nm的微小水滴时，总表面积和表面自由能又是多少？,2、20时汞的表面张力为485mN/m，求此温度及101.325kPa的压力下，将半径r1=1mm的汞滴分散成半径r2=10-5mm的微小汞滴至少需要消耗多少功？,作业：,3、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，重力加速度为g=9.8m/s2）,作业：,4、将内径为110-4m的毛细管插入水银中，问管内液面将上升还是下降多少？已知该温度下水银的表面张力这0.48N/m，水银的密度为13.510-3kg/m3，重力加速度g=9.8m/s2，设接触角近似等于180。,
