Surface Tension Measurements

Surface Tension Measurements BY

MALCOLM DOLE Department of Chemistry, Northwestern University, Evanston,

Illinois

CONTENTS

1. Introduction 1.1. Definitions 1.2. Review of Methods 1.3. Review of Applications 2. Capillary Rise Method 2.1. Absolute Measurements 2.1.1. Introduction 2.1.2. General Theory 2.1.3. Experimental Precautions 2.1.4. Experimental Accuracy and Reproducibility 2.2. Relative Measurements 2.2.1. Double Capillary Tube Methods 2.2.2. Relative Methods of Jones and Ray 2.3. Combined Capillary Tube-Pressure Methods 2.3.1. Single Capillary Tubes 2.3.2. Double Capillary Tubes 3. Maximum Bubble Pressure Methods 3.1. Single Tube Methods 3.1.1. Introduction 3.1.2. Theory 3.1.3. Applications 3.2. Double Tube Methods 3.2.1. Apparatus of Sugden 3.2.2. The Relative Method of Warren 3.2.3. Method of Long and Nutting. 4. Drop-Weight and Pendant Drop Methods 4.1. Drop-Weight Method 4.1.1. Introduction 4.1.2. Theory 4.1.3. Methods 4.2. Pendant Drop Method 5. Ring Methods 5.1. Single Ring Method 5.1.1. Introduction 5.1.2. Theory of the Ring Method 5.1.3. Methods 305

Page S06 306 306 306 308 308 308 308 310 311 312 312 313 314 314 316 317 317 317 317 318 319 319 320 321 321 321 321 321 322 324 325 325 325 325 327

306

MALCOLM

DOLE

Page 328 . 330 . 331

5.2. Double Ring Method.. 5.3. Straight Wire Method. References 1.

INTRODUCTION

1.1.

Definitions

Surface tension is defined as t h e force in t h e interface between a liquid a n d gas phase or between a solid a n d gas phase t h a t opposes a n extension of t h e surface, t h a t is measured along a line, a n d t h a t is expressed with t h e symbol y having t h e units of dynes per centimeter. T h e force lying in t h e interface between two liquid phases, or between solid a n d liquid phase, t h a t opposes an extension of t h e interface is defined as t h e interfacial tension a n d also has the. symbol y with t h e units dynes per centimeter. T h u s surface tension is a force per u n i t of length. Surface energy of a n area A c m . is defined as y · A ergs. 2

1.2.

Methods

T h e r e are m a n y m e t h o d s of surface a n d interfacial tension measurem e n t among which m a y be mentioned t h e capillary rise, t h e ring, t h e m a x i m u m bubble pressure, t h e drop weight, t h e Wilhelmy, t h e p e n d a n t drop, t h e centrifugal, t h e sessile drop, t h e ripple, t h e vibrating jet methods, a n d modifications of these. Double capillary tubes, twinrings, straight wires, plates, discs, parallel plates, horizontal capillary tubes, etc. h a v e been used. I n fact t h e s t u d y of surface tension techniques might be described as a s t u d y of scientific inventiveness a n d ingenuity. We do not h a v e space here t o describe a n d review all m e t h o d s a n d modifications t h a t h a v e been used in t h e p a s t ; instead t h e four most i m p o r t a n t a n d convenient m e t h o d s will be discussed. Of these, t h e m a x i m u m bubble pressure m e t h o d a n d t h e drop weight m e t h o d h a v e most often been used in studying t h e surface tension of liquid metals a n d alloys, a n d t h e m a x i m u m bubble pressure m e t h o d in t h e analysis of solutions. M a n y of t h e principles of one m e t h o d are a t once t r a n s ferable t o a n o t h e r method, so t h a t if, for example, t h e t h e o r y underlying t h e capillary rise m e t h o d is well understood, it is not difficult t o comprehend t h e techniques of m a n y of t h e other m e t h o d s . 1.3.

Applications

As most metals are formed in t h e liquid s t a t e it is clear t h a t surface tension forces m a y influence some of their properties, in particular t h e spreading of one liquid metal over another, possibly solid, m e t a l is

SURFACE T E N S I O N

MEASUREMENTS

307

affected b y t h e surface forces. T h u s , Chalmers (10) has investigated t h e relationship between surface tension a n d t h e t i n p l a t i n g of steel b y t h e hot dipping process. Coffman a n d P a r r (11) found t h a t H C 1 gas not only lowers t h e surface tension of a Zn-Pb solder, b u t also m a r k e d l y improves t h e spreading. T h e connection is obvious since, as t h e surface tension of t h e liquid phase is larger, t h e t e n d e n c y for it t o spread is less (the work of adhesion of t h e liquid t o t h e solid a n d t h e contact angles m u s t also be considered). As t h e surface tension of molten m e t a l s is r e m a r k a b l y high ( 1 0 times or more greater t h a n t h a t of w a t e r in m a n y cases) with sometimes a n u n u s u a l positive t e m p e r a t u r e coefficient, it is not surprising t h a t surface tension forces play a significant role in all processes where t h e spreading of a liquid m e t a l is concerned. T h e accurate d e t e r m i n a t i o n of t h e surface tension of molten metals is difficult because of t w o factors, first t h e ease with which metals combine with gases of different t y p e s t o form surface compounds such as oxides or hydrides t h a t upset t h e m e a s u r e m e n t s , a n d second t h e large contact angle usually exhibited between m e t a l s a n d glass or q u a r t z . I n t h e drop weight m e t h o d , for example, this m e a n s t h a t t h e inner radius determines t h e size of t h e drop whereas when w a t e r is used with a q u a r t z capillary, it is t h e outer radius which m u s t be used in t h e surface tension calculation. Grain size in alloys is u n d o u b t e d l y affected b y surface tension: see, for example, t h e r e m a r k s of Bastien on grain size in Al-Mg alloys (5). M a n y solutions containing surface active solutes can be analyzed b y adding base, let us say, which converts t h e surface active acid t o a surface inactive c o m p o u n d a n d causes a sharp rise in t h e surface tension until t h e end point in t h e t i t r a t i o n is reached, a t which t i m e t h e surface tension becomes c o n s t a n t (see T a u b m a n n , 63, a n d Preston, 48). T h e m a x i m u m bubble pressure m e t h o d is used, t h e pressure rising rapidly t o t h e end point. Reference can also be m a d e t o t h e filter-paper strip m e t h o d of capillary analysis carried out b y Liesegang (38). T h e flotation of solids, as in t h e separation of minerals b y flotation, is entirely d e p e n d e n t on surface forces; in particular t h e p r o p e r t y of t h e solid, or of t h e solid plus " c o l l e c t o r / ' t h a t largely determines t h e flotation is t h e c o n t a c t angle between t h e liquid a n d solid phase. T h e stability of t h e floated ore will increase with increase in t h e value of 7 ( 1 — cos 0) where 7 is t h e surface tension of t h e liquid phase a n d 0 is t h e contact angle. T h e r a t e of p e n e t r a t i o n of liquids into solid powders a n d capillary t u b e s is a function of t h e " p e n e t r a t i n g p r e s s u r e / ' which is given b y t h e term 2γ cos 0 r '

t

again showing t h e i m p o r t a n c e of surface tension a n d contact angle.

308

MALCOLM

DOLE

As this c h a p t e r will include only a description of m e t h o d s of surface tension measurement, t h e reader who is interested in contact angles, frothing agents, surface film pressures, a n d other surface p h e n o m e n a is referred t o t h e excellent treatise of A d a m (2). 2.

CAPILLARY

2.1. Absolute

RISE

METHOD

Measurements

2.1.1. Introduction. Since t h e capillary rise m e t h o d has been in t h e p a s t t h e s t a n d a r d surface tension m e t h o d t o which all other m e t h o d s

FIG. 1.

Diagram for discussion of the capillary rise method.

h a v e been referred, we shall consider it first in some detail. T h e t h e o r y underlying this m e t h o d should be well understood because it is fundam e n t a l a n d applicable in p a r t t o all other t y p e s of surface tension measurem e n t . I t is interesting t o n o t e t h a t since t h e exhaustive studies of Richards a n d Coombs (52), R i c h a r d s a n d C a r v e r (51), a n d H a r k i n s a n d Brown (26) t h e r e h a v e been no i m p o r t a n t a t t e m p t s t o improve, t h e precision of absolute surface tension m e a s u r e m e n t s ; t h e t e n d e n c y has been on t h e other h a n d t o increase t h e accuracy b y relative m e t h o d s which enable slight changes in surface tension t o be measured. These relative m e t h o d s will be described later. T h e absolute capillary rise m e t h o d is nearly as precise as we can a t t h e m o m e n t interpret t h e d a t a . 2.1.2. General Theory. T h e forces t h a t , a t equilibrium, act on a capillary t u b e liquid column (see Fig. 1) above t h e surface of t h e liquid in t h e wide t u b e , are as follows: a surface tension force acting a r o u n d a

SURFACE T E N S I O N M E A S U R E M E N T S

309

p e r i p h e r y 2rr, w i t h y d y n e s p e r c e n t i m e t e r of length a n d a vertical c o m p o n e n t proportional t o cos θ where θ is t h e so-called c o n t a c t angle, or t h e angle b e t w e e n t h e vertical wall a n d a t a n g e n t t o t h e meniscus a t t h e point of c o n t a c t ; t h e b u o y a n c y force d u e t o air a n d v a p o r displaced equal t o nr ghp d y n e s where h is t h e corrected height of capillary rise, p is t h e density of t h e v a p o r phase, a n d g is t h e g r a v i t a t i o n c o n s t a n t ; t h e d o w n w a r d pull of g r a v i t y on t h e liquid s u p p o r t e d in t h e column equal t o irr ghpi where pi is t h e density of t h e liquid phase. E q u a t i n g these forces a t equilibrium we h a v e 2

v

v

2

rghfo - p,) 2 cos θ

β 7

KL)

As m o s t p u r e liquids w e t clean glass, t h e c o n t a c t angle Θ is usually assumed t o b e zero. R i c h a r d s a n d C a r v e r (51) in fact could find n o evidence of a finite c o n t a c t angle between w a t e r a n d glass using a sensitive optical method," b u t t h e y do n o t s t a t e how small a c o n t a c t angle could h a v e been detectable in their e q u i p m e n t . T h e weight of liquid s u p p o r t e d b y surface tension forces includes t h a t of t h e meniscus, which m u s t be t a k e n i n t o consideration; in other words t h e t r u e height of rise is n o t h b u t h + hm or h. If t h e radius of t h e capillary t u b e is 0.02 cm. or below, in other words if t h e meniscus h a s t h e shape of a perfect hemisphere, t h e t r u e height can be calculated from t h e e q u a t i o n 0

0

h = ho + I

(2)

which m a y be obtained for small values of r from Poisson's (46) equation h - ho + I - £ (0.1288) o

(3)

or from t h a t of H a g e n a n d Desains (23) Α

=

Λ

°

+

3^Τ7'

( 4 )

where a is t h e capillary c o n s t a n t , a* = rh

(5)

T h e equation of H a g e n a n d Desains is t o be preferred u p t o a value of r = 0.1 cm. F o r still higher values of r/h u p t o r/h = 0.3 t h e equation of P o r t e r (47) can be used

where

310

MALCOLM DOLE

E q u a t i o n (6) is also based on t h e assumption t h a t t h e t u b e holding t h e bulk of t h e liquid is wide enough so t h a t t h e surface of t h e liquid is essentially flat. A correction t o t h e observed height, A , m u s t also be m a d e because of t h e fact t h a t t h e lower level of liquid t h a t serves as a reference point in measuring t h e height, A , is somewhat higher because of capillary rise on t h e walls of t h e wide t u b e t h a n a free flat surface would be. T h e following equation of Lord Rayleigh (50) m a k e s possible t h e calculation of this correction for wide t u b e s : 0

0

(8)

As tested b y R i c h a r d s a n d C a r v e r (51) this e q u a t i o n is valid for values of r/a greater t h a n 2.75. T h e correction factor in t h e case of smaller t u b e s c a n be obtained from t h e experimental curve given b y these a u t h o r s . F o r t h e most refined work a final correction needs t o be m a d e if t h e capillary t u b e is n o t perfectly circular in cross section. If t h e t u b e is elliptical instead of circular, with a ratio of major t o minor axis given b y Q t h e n t h e capillary rise will be greater in h u n d r e d t h s of one per cent b y t h e factor (from R i c h a r d s a n d C a r v e r ) , y

1900(Q - 1.00) - 4

(9)

This expression is valid only for Q values u p t o 1.10 ( 1 0 % ellipticity). A p p a r e n t l y u n a w a r e of t h e work of R i c h a r d s a n d Carver, S m i t h and F o o t e (58) h a v e also discussed a n d given m a t h e m a t i c a l equations for t h e surface tension in elliptical t u b e s . 2.1.8. Experimental Precautions. Since t h e surface tension as measured b y t h e capillary rise m e t h o d is directly proportional t o t h e height, t h e density, a n d t h e radius of cross section, it is essential t h a t all of these q u a n t i t i e s be k n o w n w i t h as great a precision as desired in t h e final surface tension value. T h e density of t h e p u r e liquid is readily determined with great accuracy, t h e height also is fairly readily measured, b u t t h e radius of cross section offers t h e greatest difficulty in its determination. T h e usual procedure is t o force a small slug of m e r c u r y through t h e capillary measuring its length a t various points along t h e t u b e with an accurate c o m p a r a t o r . H a r k i n s a n d Brown (26) point out t h a t gravitational forces m a y distort t h e meniscus when t h e t u b e is in a horizontal position a n d H a r k i n s (25) recommends t h e adoption of Y o u n g ' s scheme, which eliminates t h e meniscus correction b y using a long a n d short section of mercury. R i c h a r d s a n d Carver (51) could not observe a n y gravitational distortion in t h e case of small bore tubes, b u t applied a correction for t h e m e r c u r y meniscus b y measuring its length

SURFACE T E N S I O N

MEASUREMENTS

311

(a distance corresponding t o hm) a n d c o m p u t i n g t h e volume of mercury in t h e meniscus, assuming it t o be a hemisphere. One wonders w h y capillary t u b e s h a v e not been studied in a vertical position with t h e m e r c u r y column supported on a column of w a t e r or some other liquid. F r o m theoretical considerations which we shall discuss later, it would a p p e a r t h a t t h e diameter of t h e t u b e wet with a film of w a t e r is of greater significance for surface tension m e a s u r e m e n t s t h a n t h a t of a d r y t u b e . T h e greatest care in selecting capillary t u b e s of uniform t r u e right cylindrical shape should be exercised. Capillary height m e a s u r e m e n t s are m a d e with accurate c a t h e t o m e t e r s with a s h a r p edged black screen immersed in t h e t h e r m o s t a t t a n k j u s t u n d e r a n d back of t h e meniscus, as recommended b y R i c h a r d s a n d Coombs (52). T h e a p p a r a t u s should be tested for optical distortion b y measuring t h e distance between t w o ruled lines on a glass p l a t e inserted in t h e b a t h a t t h e location of t h e capillarimeter a n d comparing this dist a n c e w i t h a similar m e a s u r e m e n t m a d e in t h e air. R i c h a r d s a n d co-workers measured t h e height of rise w i t h t h e capillary t u b e in four positions, front, back, inverted front, a n d inverted back, a n d took t h e average t o eliminate t h e distortion of t h e image. T h e capillarimeter, as well as t h e plates t h r o u g h which t h e observation is m a d e , should be, of course, exactly vertical. T h e final experimental precaution h a s t o do with cleanliness of equipm e n t a n d p u r i t y of liquids studied. A slight a m o u n t of grease on glass surfaces will change t h e c o n t a c t angle between liquid a n d glass, t h u s vitiating t h e m e a s u r e m e n t . T h e best technique for t h e removal of grease is t o wash t h e glass a p p a r a t u s w i t h a h o t m i x t u r e of nitric a n d sulfuric acids (cleaning solution should n o t be used since chromic oxide seems t o p e n e t r a t e slightly into t h e glass s t r u c t u r e — a s we h a v e often noticed in m a k i n g a c c u r a t e density m e a s u r e m e n t s in t h e N o r t h w e s t e r n L a b o r a t o r y ) , t o rinse with redistilled water, a n d finally t o s t e a m out t h e a p p a r a t u s for a b o u t a n h o u r using s t e a m generated from redistilled water. T h e chief criticism of t h e work of R i c h a r d s a n d his school lies in their use of chromic acid cleaning solution. Nevertheless, their results agreed v e r y closely w i t h those of H a r k i n s a n d Brown who applied t h e steaming out technique t o t h e cleansing of their glass capillarimeters. Y o u n g et al. (69) describe a useful overflow m e t h o d of renewing t h e surface b y flowing t h e liquid in t h e capillary t u b e out into a t r a p . (The surface could also be renewed in t h e a p p a r a t u s of R i c h a r d s a n d Coombs (52) and, indeed, was, in their h a b i t of inverting their a p p a r a t u s . ) 2.1.4. Experimental Accuracy and Reproducibility. T a b l e I gives some d a t a from which t h e degree of accuracy obtainable can be judged. R i c h a r d s a n d Carver (51) found t h a t removal of air increased t h e

312

MALCOLM DOLE

surface tension b y t h e following a m o u n t s : w a t e r 0.02, benzene 0.14, chloroform 0.10, carbon tetrachloride 0.15, ether 0.05, a n d dimethyl aniline 0.10 d y n e s / c m . These values represent t h e increase in surface tensions on r e a d m i t t i n g air t o t h e evacuated capillarimeter; one wonders TABLE I Surface Tension Data by Capillary Rise Method Observer 34.33 mm. .143 .013 34.49 mm. 72.75 dynes/cm. 72.77 72.80 28.88 28.88

Κ (r = 0.4, R = 20 mm.) Small meniscus correction Large meniscus correction Corrected Height Surface tension of water at 20°

Surface tension of benzene at 20°

Richards and Carver (51)

Richards and Carver Richards and Coombs (52) Harkins and Brown (26) Richards and Carver Harkins and Brown

if sufficient time was allowed for t h e liquids t o become r e s a t u r a t e d with air. 2.2. Relative Measurements 2.2.1. Double Capillary Tube Methods. Sugden (60), Mills a n d Robinson (43), a n d Bowden (8) are a m o n g those who h a v e advocated t h e use of t w o small capillaries a t t a c h e d t o a large t u b e instead of one small t u b e . T h e a p p a r a t u s of Sugden is illustrated in Fig. 2 where r a n d r represent t h e t w o small capillary t u b e s of radii ri a n d r respec­ tively, A is a solid rod on which t u b e s η a n d r are fused a n d which fits into t h e socket Β of t h e wide t u b e C. T h e capillary system is t h u s easily removable from C for cleansing purposes. If b o t h capillary t u b e s η a n d r are so small t h a t each meniscus has t h e shape of a hemisphere, a n d if h is t h e observed difference in t h e height of rise in t h e t w o capillaries, t h e n t h e surface tension is given b y t h e equation (for zero contact angle) (43) x

2

2

2

2

ri · r · g (PI - p ){3h 2

7

=

v

6(n -

r)

+ r - rQ 2

n n

.

( 1 0 )

2

As is obvious from equation (10) this m e t h o d requires a n a c c u r a t e knowledge of t h e capillary radii a n d of t h e heights of rise. A d v a n t a g e s are first, t h a t it is suitable for small quantities of liquid, second, for corrosive liquids, a n d third, t h a t it p e r m i t s a s t u d y of changes of height of rise with time. T h u s Mills a n d Robinson (43) observed irregularly falling or rising menisci, followed b y a slow rise t o a sta­ tionary m a x i m u m value in b o t h t u b e s .

SURFACE T E N S I O N

MEASUREMENTS

313

2.2.2. Relative Method of Jones and Ray. Although it h a d been realized b y previous workers t h a t changes in t h e height of rise could b e measured b y weighing t h e q u a n t i t y of liquid in t h e wide t u b e required t o bring t h e meniscus in t h e n a r r o w t u b e always t o t h e same point, it was

FIG. 2 . Double tube capillarimeter of Sugden ( 1 9 2 1 ) .

FIG. 3 .

Silica capillarimeter

of Jones and Ray ( 1 9 3 7 ) .

Jones a n d R a y (33) w h o first brilliantly carried this m e t h o d t o a high s t a t e of perfection. Using a fused q u a r t z capillarimeter, illustrated in Fig. 3, whose wide t u b e w a s ground internally a n d externally t o a t r u e right circular cylinder, t h e y were able t o measure changes in surface tension a m o u n t i n g t o 0.001 % or 0.0007 d y n e / c m . After w a t e r h a d been dropped, b y pipet, into t h e wide t u b e until t h e u p p e r meniscus came t o M, t h e a p p a r a t u s w a s weighed t o obtain t h e weight of water, Wo, con-

314

MALCOLM

DOLE

tained therein. After drying, solution was a d m i t t e d t o t h e capillarimeter until once again t h e u p p e r meniscus stood a t M . Knowing t h e weight of solution W required t o bring this about, knowing t h e densities of w a t e r a n d solution p a n d pi, a n d knowing t h e radii of t h e larger a n d smaller t u b e s R a n d r respectively (an exact knowledge of t h e radius of t h e large t u b e became i m p o r t a n t in concentrated solutions, b u t a p a r t from this it was unnecessary t o determine t h e radii exactly), t h e relative surface tension, γ, could be calculated from t h e equation c

i t 0

=

7c

To

=

Vpi.c

— Pt.cl

LPi.o — Pv.o J

e

1 + nR*h

_l (

L

(Wo

(Π)

Pi

_ 0 U ,

where h is t h e t r u e height of rise with pure water in t h e capillarimeter. T h e o u t s t a n d i n g observation of Jones a n d R a y was t h a t addition of salts u p t o 0.001 Ν concentration lowered t h e surface tension, apparently, b y 0 . 0 2 % . A t higher concentrations, t h e surface tension t h e n rose in accordance with t h e prediction of t h e Debye-Wagner-Onsager-Samaras surface tension t h e o r y of strong electrolytes (45). Langmuir (36) has explained t h e initial decrease in surface tension, called t h e J o n e s - R a y effect, as t h e result of a methodological error, arising from a vertical film of w a t e r held above t h e meniscus because of f-potential forces which diminishes in thickness in t h e presence of electrolytes, t h u s producing an a p p a r e n t widening of t h e small t u b e a n d an a p p a r e n t decrease of surface tension. L a n g m u i r ' s theory has been further investigated b y Jones a n d Frizzell (32), Jones a n d Wood (34), a n d Wood a n d Robinson (67), with nearly complete verification. H a r k i n s (25) s t a t e s t h a t t h e water film is a b o u t 25 A. thick, b u t L a n g m u i r ' s calculations a n d t h e J o n e s - R a y effect require it t o be a b o u t 500 A. thick a t t h e meniscus in t h e capillary t u b e . Until this methodological u n c e r t a i n t y is resolved, all surface tension m e a s u r e m e n t s b y t h e capillary rise m e t h o d will be uncertain t o t h e extent of a few t h o u s a n d t h s or h u n d r e d t h s of a per cent. 2.8. Combined Capillary

Tube-Pressure

Methods

2.8.1. Single Capillary Tubes. Single capillary t u b e s with t h e meniscus forced t o a predetermined point b y means of air pressure h a v e been used in b o t h t h e vertical a n d horizontal positions. T h e essential p a r t of Ferguson a n d Dowson's (17) a p p a r a t u s is shown in Fig. 4 where A is t h e t i p of t h e capillary t u b e t h a t is immersed in a vertical position u n d e r t h e surface of t h e liquid whose surface tension is desired. Ε is t h e s h a r p end of a pointer which is sealed into t h e capillary t u b e a t a con­ venient height a n d serves as a reference m a r k so t h a t t h e height of t h e liquid in t h e wide dish can always be adjusted t o t h e distance h above 2

SURFACE

TENSION

315

MEASUREMENTS

t h e flat b o t t o m end of t h e capillary t u b e . This a d j u s t m e n t can be m a d e with great accuracy. Pressure is now applied a t Β until t h e lowest point of t h e meniscus of liquid in t h e capillary t u b e falls t o a position flush with t h e flat end. If t h e capillary t u b e is small enough so t h a t t h e meniscus is hemispherical, t h e surface tension is given b y t h e e q u a t i o n

- ν (*-.-£)

«>

If t h e liquid in t h e m a n o m e t e r used t o m e a s u r e t h e pressure is t h e same

ι FIG. 4 .

I

Apparatus of Ferguson and Dowson ( 1 9 2 1 ) .

as t h e liquid u n d e r test a n d if hi is t h e difference between t h e heights in t h e m a n o m e t e r , e q u a t i o n (12) m a y be w r i t t e n (*.-*,-{).

(13)

This m e t h o d can be carried out with great accuracy a n d has t h e a d v a n ­ tages t h a t (1) t h e same point on t h e capillary t u b e , namely its t i p end, is always used, (2) t h e radius is easily m e a s u r e d a t various orientations with a dividing engine, (3) it is unnecessary t o measure t h e height of rise in t h e capillary, only t h e relative m e a s u r e m e n t s of hi in t h e m a n o m e t e r h a v e t o b e carried out w i t h a c a t h e t o m e t e r , (4) t h e capillary t u b e can be m a d e q u i t e short a n d is t h u s m o r e easily cleaned, a n d (5) t h e experiment can be quickly performed. Ferguson a n d H a k e s (18) point out t h a t b y v a r y i n g A a n d m a k i n g simultaneous m e a s u r e m e n t s of hi a n d A , t h e density of t h e u n k n o w n liquid can be determined from t h e slope of a plot of pih\ versus A (in t h i s case t h e m a n o m e t e r liquid m u s t h a v e a k n o w n a n d different density). Ferguson a n d K e n n e d y (19) eliminate density considerations entirely b y measuring t h e pressure necessary t o p r o d u c e a flat meniscus of liquid 2

2

2

316

MALCOLM DOLE

a t t h e open end of a horizontal capillary t u b e (contact angle of 90° a t open e n d ) . N o height of rise m e a s u r e m e n t is necessary a n d no meniscus corrections are involved, t h e surface tension being given b y t h e equation

where r is t h e radius a t t h e curved meniscus end of t h e liquid column. 2.8.2. Double Capillary Tubes. Double capillary t u b e s h a v e also been used in b o t h vertical a n d horizontal positions. S u t t o n (62) seals t w o t u b e s of radii ΤΊ a n d r together end t o end a n d measures t h e pressure required t o bring a column of liquid of length h t o a p r e d e t e r m i n e d point on t h e smallest capillary with t h e system in a vertical position. T h e a p p a r a t u s is inverted a n d t h e pressure again recorded. If P i a n d P are t h e pressures in t h e t w o positions, we h a v e 2

2

7 =

mPi

"

~ w

=

! - J k

+

(i5)

Pi)

( 6

)

L

27ΓΓΙ

( 1 7 )

2πΓ2

where r± is t h e radius of t h e smaller t u b e . T h u s from these t w o pressure m e a s u r e m e n t s b o t h t h e density a n d t h e surface tension can be determined. If t h e a p p a r a t u s is calibrated with a liquid of k n o w n surface tension, y', we can write

I n these equations meniscus corrections h a v e been neglected. S u t t o n obtained results accurate t o a b o u t 1 %, b u t t h e technique could no d o u b t be refined. S p e a k m a n (59) seals t w o parallel capillary t u b e s of radius ri a n d r i n t o a wider t u b e whose vertical a r m has a radius r . H e t h e n measures first t h e pressure required t o bring t h e liquid in r t o a pre­ determined level a n d second t h e pressure required t o bring t h e liquid in r t o t h e same level, t h e surface tension is t h e n given b y t h e equation 2

3

x

2

y =

^

() 19

where AP is t h e difference in t h e t w o pressure m e a s u r e m e n t s . For accurate calculations meniscus corrections m u s t be applied. A c h m a t o v (1) uses a double capillary t u b e system similar t o S u t t o n ' s described above, b u t b y laying t h e t u b e in a horizontal position, t h e surface tension can be c o m p u t e d from t h e following equation w i t h o u t a knowledge of t h e density of t h e liquid (20)

SURFACE TENSION

MEASUREMENTS

317

where Ρ is t h e pressure difference a t t h e ends of t h e t w o capillaries just sufficient t o p r e v e n t t h e liquid from m o v i n g in either horizontal direction. N o capillary correction is necessary for this m e t h o d b u t t h e possibility of g r a v i t y distortion of t h e meniscus would h a v e t o be investigated for precise results. 3.

MAXIMUM

BUBBLE

PRESSURE

3.1. Single Tube

METHOD

Methods

3.1.1. Introduction. One of t h e most a t t r a c t i v e m e t h o d s of surface tension m e a s u r e m e n t involves t h e m e a s u r e m e n t of t h e pressure required t o form a b u b b l e of gas in t h e liquid whose surface tension is desired. I t is particularly applicable t o corrosive liquids like molten phosphorus ( 3 0 ) or molten metals a n d alloys ( 7 ) a n d h a s t h e distinct a d v a n t a g e of

FIG. 5.

Diagram for discussion of maximum bubble pressure method.

giving results independent of t h e contact angle. B y exerting t h e neces­ sary precautions great precision of t e c h n i q u e is obtainable. 3.1.2. Theory. If we assume for t h e m o m e n t t h a t t h e radius of t h e capillary t u b e , Fig. 5 , is so small t h a t t h e shape of t h e bubble a t m a x i m u m pressure is hemispherical, t h e n t h e equation for t h e t o t a l gas pressure in t h e capillary t u b e is Ptotal = Ρ + Pi

= — + Qhl(pi -

Pv).

(21)

r

T h e c o n t a c t angle is zero a t this p o i n t ; a n y lowering of t h e pressure will cause t h e b u b b l e t o grow smaller, a n y a t t e m p t t o increase t h e pressure will produce a n increase in t h e size of t h e b u b b l e with a n increase in t h e c o n t a c t angle t o a value greater t h a n 1 8 0 ° , as illustrated in Fig. 5 . T h e pressure will decrease as t h e b u b b l e rapidly expands.

3 18

MALCOLM DOLE

T h e pressure across t h e interface, P , is given for small values of r/L b y t h e equation of Schroedinger (54)

*-?[-!£-*©"] where h is given b y t h e equation Ρ = gh(j>i -

)

(23)

P9

(In t h e case of a perfect hemisphere, h of equation (23) would be identical with Ζ of Fig. 5.) F o r more accurate calculations t h e tables of Bashford a n d A d a m s (4) can be used. Sugden (61) h a s worked o u t a m e t h o d for t h e use of these tables in connection with t h e m a x i m u m bubble pressure m e t h o d a n d gives additional tables which m a k e it unnecessary t o refer t o t h e work of Bashford a n d A d a m s . T h e height A, m u s t be measured with reference t o a flat surface; i.e., if t h e outer vessel holding t h e liquid under investigation is n o t wide enough t o give a flat surface, a correction for capillary rise m u s t be included. 8.1.3. Applications. H a r k i n s (25) quotes Y o u n g as recommending t h a t t h e m a x i m u m pressure be measured in t h e formation of a single bubble, r a t h e r t h a n measuring t h e pressure necessary t o give a s t r e a m of bubbles. Long a n d N u l t i n g (40) could detect n o difference between a r a t e of 9 a n d 100 seconds per bubble in their accurate relative surface tension studies. T h e capillary t i p should be thin-walled. I n a s m u c h as t h e pressure drops as each bubble breaks a w a y from t h e tip, it is possible t o measure t h e m a x i m u m pressure even t h o u g h t h e bubble cannot be watched. T h u s , H u t c h i n s o n (30) has recently meas­ ured t h e surface tension of white phosphorus against C 0 b y observing t h e m a x i m u m pressure required t o form bubbles of this gas in t h e molten phosphorus. His a p p a r a t u s was calibrated w i t h k n o w n liquids before use, a n d a B o u r d o n gauge was used t o measure t h e pressure (as t h e system h a d t o be completely e v a c u a t e d before use). Using a q u a r t z capillary t u b e placed u n d e r t h e surface of fused metals, Sauerwald (53) a n d D r a t h a n d Sauerwald (13) were able t o measure t h e surface tension of a n u m b e r of fused m e t a l s a n d alloys. I n this case hydrogen was t h e gas forced t h r o u g h t h e capillary t i p . Hogness (29) h a s developed a m a x i m u m pressure m e t h o d for t h e m e a s u r e m e n t of t h e surface tension of m e r c u r y a n d fused metals in which t h e pressure necessary t o force a drop of t h e liquid m e t a l u p w a r d s t h r o u g h a vertical capillary is measured. His a p p a r a t u s is illustrated in Fig. 6 where A is a t u b e i n t o which a cylinder of t h e m e t a l is inserted a n d later melted b y raising t h e t e m p e r a t u r e . Pressure is applied a t Β until liquid m e t a l drops begin t o flow out of t h e q u a r t z capillary t u b e D . At this point t h e difference in height between t h e column of metal in C 2

SURFACE T E N S I O N

MEASUREMENTS

319

a n d capillary t i p is measured a n d t h e surface tension calculated from t h e equation 2 V

7

3 Ρ

6

Ρ

2

/

K

}

where Ρ is t h e m a x i m u m pressure a n d ρ is t h e density of t h e liquid metal. Hogness found it necessary t o use hydrogen gas a n d t o b a k e out his glass a p p a r a t u s thoroughly before a d m i t t i n g t h e m e t a l in order t o eliminate all traces of water. Bering a n d P o k r o w s k y ( 6 ) h a v e more recently carried out a similar investigation in which t h e y studied t h e surface tension of m e r c u r y a n d a m a l g a m s against a v a c u u m as well as hydrogen gas. Hogness's m e t h o d h a s t h e a d v a n t a g e s of continually supplying a fresh surface a n d of being independent of t h e c o n t a c t angle.

FIG. 6. Apparatus of Hogness (1921) for the measurement of the surface tension of fused metals and alloys.

3.2. Double Tube

FIG. 7. D o u b l e capillary tip surface tension apparatus of Sugden (1924).

Methods

3.2.1. Apparatus of Sugden. Figure 7 illustrates a convenient a p p a ­ r a t u s invented b y Sugden (60) for t h e m e a s u r e m e n t of surface tension b y a relative m e t h o d . First t h e pressure necessary t o produce bubbles from t h e small tip, radius r is determined. T h e stop cock is t h e n opened iy

320

MALCOLM DOLE

a n d t h e m a x i m u m pressure measured for bubbles formed a t t h e tip of t h e larger capillary t u b e , radius r . If Ρ is t h e difference in pressures measured, t h e surface tension can be calculated from t h e equation, 2

where χ = (61). tube

a n d m u s t be calculated from t h e tables given b y Sugden

This is particularly t r u e for t h e large capillary t u b e ; for t h e small (26)

with sufficient accuracy. centimeters are

T h e recommended values of η

and r

2

in

0.005 < r i < 0.01 0.1 < r < 0.2 c m . 2

Sugden points out t h a t for a p p r o x i m a t e calculations, good t o 1 p a r t in 1000, t h e following equation is satisfactory (27)

where A is a constant, r is expressed in centimeters a n d Ρ in d y n e s / c m . B o t h capillary tips m u s t be a t t h e same level in t h e liquid. Bircumshaw (7) carried out an extensive s t u d y of t h e surface tension of liquid metals a n d alloys using t h e double t i p m a x i m u m bubble pressure method. Good agreement with t h e d a t a of Hogness was obtained. Using a similar double capillary t i p a p p a r a t u s H u t c h i n s o n (30) deter­ mined t h e interfacial tension of a n u m b e r of liquid pairs b y measuring t h e pressure required t o form a liquid bubble of one liquid in another. This is a particularly good m e t h o d for interfacial tension m e a s u r e m e n t s as here again t h e contact angle does not enter into t h e phenomenon. 3.2.2. The Relative Method of Warren. I n t h e double t u b e a p p a r a t u s of W a r r e n (66) t w o identical tips (made b y carefully breaking a capillary t u b e a t one point) are immersed in separate vessels, b o t h containing t h e same fluid a t first. B y suitable mechanical m e a n s it is possible t o adjust a n d measure accurately t h e d e p t h of immersion of t h e jets. One of t h e jets is m o v e d u p or down until t h e r a t e of escape of bubbles from its tip is exactly equal t o t h e r a t e of bubble formation a t t h e other t i p . T h e liquid in t h e second vessel is t h e n removed a n d replaced b y t h e liquid u n d e r investigation. T h e difference in surface tension between t h e t w o liquids is t h e n given b y t h e equation 2

2

-

r 1 7 2 = g 7y (P2^ — Pihi) + £ gr (pi 2

2

— p) 2

(28)

SURFACE TENSION

321

MEASUREMENTS

where hi a n d h are t h e d e p t h s of immersion of t h e t i p in t h e experiments on t h e t w o liquids plus t h e radius r in each ease. W a r r e n ' s m e a n error in t h e d e t e r m i n a t i o n of t h e surface tension of sodium chloride solutions was 0.022 d y n e s / c m . 3.2.3. Method of Long and Nutting. Long a n d N u t t i n g (40) describe a relative m e t h o d similar t o W a r r e n ' s in which t h e change in t h e d e p t h of immersion was calculated from t h e weight of liquid a d d e d a n d from t h e d e p t h of immersion of a rod of k n o w n volume. (By careful regulation of t h e d e p t h of t h e rod t h e height of t h e liquid level in one of t h e vessels is varied until t h e bubbling r a t e is equal from t h e t w o jets.) W i t h p u r e water initially in b o t h vessels, t h e d e p t h of immersion, ho, m u s t necessarily be equal for t h e t w o jets. After a small a m o u n t of salt solution is a d d e d t o one of t h e halves of t h e a p p a r a t u s , a n d p u r e w a t e r t o balance t h e bubbling r a t e a d d e d t o t h e other half, t h e relative surface tension can be calculated from t h e equation 2

7

= -

= l +

f

[ΛΟ(ΡΟ -

P I ) + Ahopo -

Ah ] lPl

(29)

T h e reproducibility of Long a n d N u t t i n g ' s d a t a is somewhat b e t t e r than 0.01%. A p p a r e n t l y t h e L a n g m u i r film or possibly a finite c o n t a c t angle which resulted in t h e J o n e s - R a y effect does n o t exist in t h e m a x i m u m bubble pressure method—which suggests t h a t this m e t h o d m a y be funda­ mentally sounder for surface tension m e a s u r e m e n t s t h a n others. 4.

DROP-WEIGHT

AND PENDANT

4.1. Drop-Weight

DROP

METHODS

Method

4.1.1. Introduction. A n o t h e r useful m e t h o d of surface a n d interfacial tension m e a s u r e m e n t is t h e drop-weight m e t h o d in which t h e surface tension can be calculated from t h e m a x i m u m weight of a drop. I t is, perhaps, most i m p o r t a n t from t h e s t a n d p o i n t of interfacial tension m e a s u r e m e n t s difficult t o m a k e b y other m e t h o d s . T h e closely analogous p e n d a n t drop m e t h o d is in practice less a c c u r a t e b u t h a s its own a d v a n ­ tage in being particularly suitable for s t u d y i n g t h e variation of surface tension as a function of t i m e . 4.1.2. Theory. T h e t h e o r y of t h e shape of drops has been investi­ g a t e d b y Bashford a n d A d a m s (4), Lohnstein (39), F r e u d a n d H a r k i n s (21) a n d a n u m b e r of early workers. H a r k i n s (25) has stressed t h e principle of similitude, n a m e l y t h a t all drops h a v e t h e same shape if their values of r/V are equal where r is t h e radius of t h e t i p from which t h e drop falls a n d V is t h e volume of t h e d r o p . H a r k i n s a n d Brown (26) l

322

MALCOLM DOLE

give a t a b l e of their so-called F-faetors from which values of F can be obtained applicable t o t h e particular liquid u n d e r s t u d y a n d which when multiplied b y mg/r gives t h e surface tension in dynes per centimeter. I n t h e case of interfacial tension m e a s u r e m e n t s t h e equation for t h e tension is 7 -

V(pi

- P I ) - -F

(30)

Q

where V is t h e volume of a single drop of liquid of density pi formed in a second liquid of density p . T h e F-factors h a v e been determined experimentally b y first finding the surface tension of t h e liquids b y t h e capillary-rise method, a n d t h e n determining t h e drop-weights in a drop-weight a p p a r a t u s . T h e F-factors are finally calculated from t h e equation 2

£ mg <

F=

>

31

T h e y are a p p a r e n t l y valid for liquids having such diverse surface tensions as exhibited b y benzene on t h e one h a n d a n d m e r c u r y on t h e other, as D u n k e n (14) has recently shown. Iredale (31) a n d Michelli (42) h a v e suggested an a l t e r n a t e m e t h o d of surface tension calculation for t h e drop weight m e t h o d based on an equation of W o r t h i n g t o n (68). If r is t h e capillary tip radius a n d a t h e radius of t h e drop assuming it t o be spheri­ cal, t h e n Iredale points out t h a t t h e ratio r/a is roughly a linear function of r. Suppose a is determined for a liquid of u n k n o w n surface tension, t h e value of r/a is t h e n calculated a n d from t h e nearly linear curve of ro/cto as a function of ro for water, t h e value of r for w a t e r is found which would give a value of ro/a equal t o r/a for t h e u n k n o w n liquid. T h e surface tension can t h e n be calculated from t h e equation 0

0

22

= 4

P7o

r

2

(32)

0

where t h e subscript zero identifies t h e values for water. As a m a t t e r of fact this m e t h o d is essentially t h a t of H a r k i n s a n d Brown inasmuch t h a t , if 7

then

7o

ψϊ -

a n d t h e F-factors are equal. 4.1.8. Methods. T h e m e t h o d of H a r k i n s a n d Brown (26) is capable of a precision of 0.02 t o 0 . 0 3 % with certain liquids. T h e following precautions should be observed:

SURFACE T E N S I O N

MEASUREMENTS

323

(a) A flat ground t i p , circular with s h a r p edges a n d n o t polished on t h e b o t t o m should be used. (b) I t s vertical sides should be polished t o p r e v e n t liquid wetting t h e side walls. (c) T h e size of t h e tips should be between 5-7 m m . in diameter for m o s t liquids in t h e case of surface tension m e a s u r e m e n t s a n d between 9-11 m m . in d i a m e t e r for interfacial tension measurem e n t s . H i g h density liquids call for smaller tips t h a n low density liquids. (d) T h e a p p a r a t u s should be held in a vertical position, b u t a 3° inclination from t h e vertical can be tolerated as G a n s a n d H a r k i n s (22) h a v e pointed out (the weight becomes less t h e greater t h e angle of inclination). (e) As t h e weight of t h e drops increases with increasing velocity of flow, it is i m p o r t a n t t o form each drop over a 5-minute interval. Actually t h e liquid is allowed t o flow until t h e drop approaches its m a x i m u m size, t h e n it is allowed t o s t a n d for a few m i n u t e s t o reach equilibrium (some dilute liquids of long linear organic molecules m a y t a k e half an hour t o a t t a i n surface equilibrium). Finally, t h e volume of t h e drop is allowed t o increase slowly a n d preferably automatically until it drops. T h e drops are collected in a suitable weighing bottle a n d weighed. (f) I t is n o t correct t o calibrate t h e i n s t r u m e n t with a liquid of k n o w n surface tension unless t h e proper i'-factor correction is applied b o t h t o t h e k n o w n a n d u n k n o w n surface tension calculation. (g) I n interfacial tension m e a s u r e m e n t s W a r d a n d Tordai (65) collect drops of t h e heavier liquid b y displacement of t h e lighter liquid from a special pycnometer. T h e increase in weight of t h e p y c n o m e t e r gives just t h e required information needed for t h e interfacial tension calculation. T h e a u t h o r s point out t h a t a weight m e a s u r e m e n t of four drops is more accurate t h a n a volume m e a s u r e m e n t of 40 drops. Figure 8 illustrates t h e a p p a r a t u s of H a r k i n s a n d Brown (26), suitable for t h e s t u d y of volatile liquids. T h e capillary t i p is shown a t t h e r i g h t ; t h e rod a t t h e left which is a t t a c h e d t o a rack a n d pinion device serves t o raise gradually t h e reservoir of liquid, t h u s causing t h e d r o p t o grow very slowly; t h e i n t e r m e d i a t e vessel containing a small a m o u n t of liquid prevents excessive evaporation from t h e surface of t h e drop. K u r t z (35) points out t h a t a film of plastic or other solid material forming on t h e surface of t h e drop can v i t i a t e t h e surface tension measurem e n t s b y preventing t h e drop from t a k i n g on its n o r m a l shape. E d w a r d s

324

MALCOLM DOLE

FIG. 8 .

Drop-weight apparatus of Harkins ( 2 5 ) .

(16) uses a n electrical counter in m e a s u r e m e n t s of interfacial tension of sulfuric acid against various oils. 4.2. Pendant Drop

Method

Andreas et at. (3) as well as S m i t h (57) h a v e applied a m e t h o d involving t h e m e a s u r e m e n t of t h e shape of p e n d a n t drops t o t h e s t u d y of surface tension. This m e t h o d has t h e a d v a n t a g e of being a static one, a single drop being investigated over a considerable period of time, or until its shape becomes c o n s t a n t . This m e t h o d is t h e only k n o w n surface tension m e t h o d which permits an accurate s t u d y of surface composition (as indicated b y surface tension) as a function of time.

SURFACE TENSION MEASUREMENTS

325

T h e experimental problem is chiefly a n optical one, once a proper dropping tip has been obtained. B y proper choice of magnifying system a n d camera results having a probable error of ± 0 . 5 % are obtained. As with t h e drop weight m e t h o d , correction factors given in tables m u s t be used t o convert m e a s u r e m e n t s of t h e diameter of t h e drop a t its e q u a t o r a n d a t a selected plane t o surface tension. Good agreement for b o t h surface a n d interfacial tension m e a s u r e m e n t s on s t a n d a r d substances has been obtained. A n d r e a s et al. believe t h a t this m e t h o d will prove t o be particularly valuable for t h e s t u d y of ( 1 ) viscous liquids, ( 2 ) surfaceactive solutions ( 3 ) small samples of rare chemicals a n d ( 4 ) systems in which t h e contact angle is not zero. 5.

RING

METHODS

5.1. Single

Ring

5.1.1. Introduction. Because of t h e ease a n d r a p i d i t y with which t h e force necessary t o pull a ring out of t h e surface of a liquid can be measured, t h e ring m e t h o d of surface tension m e a s u r e m e n t has h a d great p o p u l a r i t y . Like t h e drop weight a n d t h e m a x i m u m b u b b l e pressure m e t h o d s this m e t h o d is a d y n a m i c one a n d requires a knowledge of t h e force necessary t o r u p t u r e t h e liquid-air interface. T h e d a t a obtained b y t h e ring m e t h o d are quite sensitive t o t h e size of wire a n d dimension of ring employed, so t h a t absolute values of surface tension c a n n o t be obtained w i t h o u t applying corrections. I n fact it is r a t h e r surprising t o consider t h e large n u m b e r of ring surface tension determinations in which t h e shape of t h e surface was n o t t a k e n i n t o account. I t was n o t until 1 9 2 4 - 2 6 when L e n a r d ( 3 7 ) who used a straight wire instead of a ring a n d H a r k i n s et al. ( 2 8 ) first correctly calculated surface tension values from t h e surface r u p t u r e forces t h a t t h e t h e o r y of t h e ring m e t h o d was p u t on a sound basis. W e are including t h e work of L e n a r d in this discussion as t h e problems involved in pulling a straight wire out of t h e surface are similar in m a n y ways t o those applicable t o work with circular rings. 5.1.2. Theory of the Ring Method. If a ring pulled a t r u e hollow cylinder of liquid with a vertical plane of contact with t h e ring from t h e surface, t h e n a t t h e m o m e n t t h e liquid surface r u p t u r e d , t h e weight of liquid s u p p o r t e d t o t h e point of r u p t u r e above a flat level surface would be given b y t h e equation W · g = 4 T T# T

(33)

where R is t h e radius of t h e ring measured to t h e center of t h e wire of which t h e ring is composed. However, t h e liquid surface will t a k e on t h e shape illustrated in Fig. 9 as t h e ring is raised (or t h e liquid lowered).

326

MALCOLM DOLE

FIG. 9.

FIG. 10.

Schematic diagram of the ring method.

Cenco Du Noliy tensiometer.

(Courtesy of the Central Scientific Co.)

H a r k i n s a n d J o r d a n (27) m a d e an extensive s t u d y of t h e weight of liquid s u p p o r t e d b y rings of various r a n d R values using liquids of k n o w n surface tension a n d found t h a t in t h e m a j o r i t y of cases t h e weight of liquid supported is greater t h a n t h e simple equation (33) would predict. T h e y have published tables of F-factor corrections for t h e ring m e t h o d which m a y a m o u n t t o as m u c h as 2 5 % u n d e r certain conditions. T h u s , t h e correction factors m a y be extremely large. Knowing F, t h e surface

SURFACE T E N S I O N

MEASUREMENTS

327

tension is t o be calculated from t h e equation W ·g 4 Τ Γ#

•F

(34)

T o determine F from t h e tables b o t h R a n d r m u s t be k n o w n as well as V, t h e volume of liquid s u p p o r t e d a t t h e m o m e n t of break (V = m/p). F r e u d a n d F r e u d (20) h a v e carried out numerical integrations of Laplace's equation relating surface c u r v a t u r e t o surface tension a n d t h u s succeeded in calculating t h e F-factors theoretically. F o r this reason we can now regard t h e ring m e t h o d as being a n absolute m e t h o d . 5.1.3. Methods. F o r t h e most precise d e t e r m i ­ nations using rings t h e technique of H a r k i n s a n d J o r d a n (27) should be followed although Schwenk e r ' s straight wire m e t h o d (55) seems t o be some­ w h a t more sensitive. T h e relative t w i n - r i n g m e t h o d of Dole a n d Swart out (12) described below has t h e greatest precision of all m e t h o d s involving a r u p t u r e of t h e surface. Various commercial t e n siometers are on t h e m a r k e t , t h e best k n o w n being t h e D u Noliy (15) tensiometer sold b y t h e C e n t r a l Scientific Co., Fig. 10. I n t h e last i n s t r u m e n t t h e liquid is lowered from t h e ring a n d t h e force a t FIG. 11. Surface r u p t u r e measured b y a torsion wire balance. T h e tension flask of Harkins torsion force is calibrated b y k n o w n weights in and Jordan (1930). a d v a n c e of t h e surface tension m e a s u r e m e n t . T h e H a r k i n s /^-factor corrections should be applied, of course. R e t u r n i n g t o t h e techniques of H a r k i n s a n d J o r d a n , Fig. 11 illustrates their surface tension flask in which t h e p a n holding t h e liquid is sealed into a n o t h e r flask in order t o allow t h e whole t o be immersed in a c o n s t a n t t e m p e r a t u r e b a t h , a n d which has t h e side t u b e s A a n d Β so t h a t t h e surface can be renewed b y flushing t h r o u g h A a n d b y sucking t h e over­ flow liquid out t h r o u g h B . D u r i n g m e a s u r e m e n t t h e liquid is held s t a t i o n a r y a n d t h e ring slowly raised b y using a mechanical gear arrange­ m e n t t o raise t h e chainomatic balance on whose left b e a m t h e ring is supported. T h e chief difficulty comes from slight impurities, p a r t i c u ­ larly in t h e case of aqueous solutions, which are picked u p b y t h e ring, t h e r e b y changing t h e contact angle. T h e pull on t h e ring a t r u p t u r e is a r a t h e r sensitive function of t h e c o n t a c t angle (44) as it also is of t h e angle of inclination of t h e ring (27). P r e c a u t i o n s a n d experimental recom­ m e n d a t i o n s can be listed as follows.

328

MALCOLM DOLE

(a) H a r k i n s (25) recommends raising t h e ring r a t h e r t h a n lowering t h e solution as t h e l a t t e r might produce disturbing ripples in t h e surface. Dole a n d S w a r t o u t (12), however, show t h a t a precision of 0 . 0 0 2 % is a t t a i n a b l e on lowering t h e liquid (the precision of H a r k i n s a n d J o r d a n was a b o u t 0 . 2 % ) . (b) T h e diameter of t h e p a n should be such t h a t it is 4 - 5 cm. greater t h a n t h e diameter of t h e ring. (c) T h e angle of inclination of t h e plane of t h e ring with t h e free surface should be less t h a n 0.47° for t h e error of m e a s u r e m e n t t o be less t h a n 0.1 %. A positive angle can be detected b y carefully observing t h e ring as it approaches t h e surface of t h e liquid. If it m a k e s c o n t a c t with t h e liquid simultaneously all a b o u t its circumference, t h e n no angle of inclination exists (assuming, of course, t h a t t h e ring is plane). (d) H a r k i n s a n d J o r d a n adjusted t h e volume of liquid in t h e p a n so t h a t t h e surface would be plane a t t h e m o m e n t of r u p t u r e . (e) T h e ring should be circular a n d all in a plane. (f) T h e a p p a r a t u s should be cleaned w i t h a h o t m i x t u r e of nitric a n d sulfuric acids, rinsed with redistilled water, steamed (the steam generated from w a t e r t h a t h a d previously been refluxed with K M n 0 ) , a n d rinsed again. T h e p H of t h e rinse w a t e r should be checked t o insure t h e complete removal of t h e acid. These rigorous cleaning directions are of significance chiefly in t h e m e a s u r e m e n t of t h e surface tension of aqueous solutions. (g) T h e ring is preferably m a d e of p l a t i n u m - 1 0 % iridium a n d should be ignited in a flame shortly before use. (h) T h e d r y weight of t h e ring m u s t be known. T h e W of equation (34) is t h e weight a t t h e m o m e n t of r u p t u r e less t h e d r y weight. T h e fact t h a t drops of liquid adhere t o t h e ring after t h e r u p t u r e is of no significance except t h a t it indicates a desirable wetting of t h e ring b y t h e liquid. 4

5.2. Double Ring

Method

Dole a n d S w a r t o u t (12) h a v e recently invented a twin-ring t e n siometer, illustrated in Fig. 12, which m a k e s possible t h e a t t a i n m e n t of a relative precision t o 0.002%. I n this m e t h o d it is unnecessary t o observe t h e m a x i m u m weight of pull or t h e weight a t t h e m o m e n t of r u p t u r e ; instead notice is t a k e n merely of t h e ring which breaks from t h e surface first as t h e t w o liquid surfaces are lowered. T h e weaker tension on this side is t h e n balanced b y t h e addition of weights t o this side of t h e balance a n d t h e process repeated. I t is possible t o obtain a balance between t h e forces of tension a n d t h e weights such t h a t 0.1 mg. increase in weight

SURFACE

TENSION

MEASUREMENTS

329

on one side will cause t h e ring on t h e other side t o break first from t h e surface. As t h e t o t a l pull on either ring a m o u n t e d t o 5.7 g., t h e relative u n c e r t a i n t y is 1/57,000 or a b o u t 0.002%. W i t h a more accurate balance an even greater sensitivity might be obtainable.

FIG. 1 2 .

Twin-ring tensiometer of Dole and Swartout ( 1 9 4 0 ) .

After t h e surface tension forces h a v e been balanced b y weights, t h e liquid being t h e same in b o t h p a n s , one of t h e liquids is removed a n d replaced b y a n u n k n o w n (in Dole a n d S w a r t o u t ' s work b y a dilute aqueous solution). T h e change in weight required t o bring a b o u t a new balance AW is a measure of t h e difference in surface tensions, or

330

MALCOLM DOLE

where W is t h e t o t a l pull on t h e ring in contact with liquid of surface tension 7 0 . I n t h e range of dilute solutions studied b y Dole a n d S w a r t o u t it was unnecessary t o a p p l y a H a r k i n ' s F-factor correction. T h e J o n e s - R a y effect was observed using t h e twin-ring a p p a r a t u s which indicates t h a t either t h e contact angle is changed slightly b y t h e addition of electrolytes or t h a t something like t h e L a n g m u i r film enters in. This indicates t h a t t h e ring m e t h o d , similar t o t h e capillary rise method, does not give t h e t r u e surface tension of salt solutions, p a r t i c u ­ larly in t h e dilute range. A theoretical explanation of t h e J o n e s - R a y effect as exhibited b y t h e ring m e t h o d is badly needed, because t h e r e will be some d o u b t as t o t h e precise significance of all ring surface tension m e a s u r e m e n t s until we u n d e r s t a n d t h e reason for its existence. 5.3. Straight Wire Method Lenard a n d co-workers (37) a n d Schwenker (55) measure t h e force necessary t o pull a straight wire out of t h e surface. This wire is supported in a hori­ zontal position on a s t o u t frame a n d in Schwenker's work was b u o y e d u p b y a submerged float so t h a t t h e residual r u p t u r e force a m o u n t i n g only t o a few milli­ g r a m s could be measured on a sensitive torsion bal­ ance. Figure 13 illustrates t h e wire, A, in its frame F I G . 1 3 . Β sealed into a glass float C which has a side a r m D Straight wire tensifor t h e admission of m e r c u r y t o adjust it t o a suitable ometer and float of weight. On t h e hook Ε are h u n g weights after t h e Schwenker ( 1 9 3 1 ) . wire has been pulled t h r o u g h t h e surface so as to o b t a i n w h a t we might call t h e d r y weight. Letting W

- Wo 21

(36)

where W is t h e weight of m a x i m u m pull, Wo is t h e weight after t h e wire has r u p t u r e d t h e surface a n d I is t h e length of t h e wire, t h e surface tension can be calculated from t h e equation (37)

I n equation (37) r is t h e diameter of cross section of t h e wire. Schwenker obtained results with a n u n c e r t a i n t y of somewhat less t h a n 0 . 0 1 % . I t is interesting t o note t h a t this straight wire or rod m e t h o d was suggested b y Michelson in 1891 while a t Clark University a n d was

SURFACE T E N S I O N

MEASUREMENTS

331

first carried o u t e x p e r i m e n t a l l y b y H a l l (24). H a l l discovered t h e m a x i m u m in t h e weight as a function of r o d d i s t a n c e a b o v e t h e surface (see also H a r k i n s a n d J o r d a n (27)) a n d eliminated e n d effects b y t h e use of t w o rods of different l e n g t h . T h e r e a r e a n u m b e r of o t h e r m e t h o d s of m e a s u r i n g surface tension a m o n g which c a n be m e n t i o n e d centrifugal m e t h o d s (41, 56), m e t h o d of i m p a c t i n g j e t s (9, 49) ripple m e t h o d (64), etc. all of which r e q u i r e r a t h e r complicated a p p a r a t u s or h a v e n o t y e t been developed t o g r e a t a c c u r a c y ; hence t h e y will n o t be discussed here. REFERENCES

1. Achmatov, Α., Kolloid. Z. 66, 266 (1934). 2. Adam, Ν. K., The Physics and Chemistry of Surfaces. 3rd ed. Oxford University Press, London, 1941. 3. Andreas, J. M., Hauser, Ε. Α., and Tucker, W. B., J. Phys. Chem. 42,1001 (1938). 4. Bashford and Adams, An Attempt to Test the Theory of Capillary Action. Cambridge, 1883. 5. Bastien, P., Chimie & Industrie 46, No. 3 bis, 27 (1941). 6. Bering, B. P., and Pokrowsky, N . L., Acta Physicochim. U.R.S.S. 4, 861 (1936). 7. Bircumshaw, L. L., Phil. Mag. [7] 3, 1286 (1927); 12, 596 (1931); 17, 181 (1934); and others. 8. Bowden, S. T., J. Phys. Chem. 34, 1866 (1930). 9. Buchwald, E., and Konig, H., Ann. Physik. 26, 659 (1936). 10. Chalmers, B., Trans. Faraday Soc. 33, 1167 (1937). 11. Coffman, A. W., and Parr, S. W., Ind. Eng. Chem. 19, 1308 (1927). 12. Dole, M., and Swartout, J. Α., J. Am. Chem. Soc. 62, 3039 (1940). 13. Drath, G., and Sauerwald, F., Z. anorg. allgem. Chem. 162, 301 (1927). 14. Dunken, H., Ann. Physik 41, 567 (1942). 15. Du Nouy, P. Lecomte, Surface Equilibria of Biological and Organic Colloids. Chemical Catalog Co., New York, 1926. 16. Edwards, J. C , / . Set. Instruments 6, 90 (1929). 17. Ferguson, Α., and Dowson, P. E., Trans. Faraday Soc. 17, 384 (1921). 18. Ferguson, Α., and Hakes, J. Α., Proc. Phys. Soc. London 41, 214 (1929). 19. Ferguson, Α., and Kennedy, S. J., Proc. Phys. Soc. London 44, 511 (1932). 20. Freud, Β. B., and Freud, Η. Z., Science 71, 345 (1930); J. Am. Chem. Soc. 62, 1772 (1930). 21. Freud, Β. B., and Harkins, W. D., Phys. Chem. 33, 1217 (1929). 22. Gans, D . M., and Harkins, W. D., J. Am. Chem. Soc. 52, 2287 (1930). 23. Hagen and Desains, Ann. chim. phys. [3] 61, 417 (1857). 24. Hall, T. P., Phil. Mag. 36, 390 (1893). 25. Harkins, W. D., in Physical Methods of Organic Chemistry. Edited by Arnold Weissberger, Interscience, New York, 1945, Chapter VI. 26. Harkins, W. D., and Brown, F. E., / . Am. Chem. Soc. 38, 246 (1916); 41, 499 (1919). 27. Harkins, W. D., and Jordan, H. F., J. Am. Chem. Soc. 62, 1751 (1930). 28. Harkins, W. D., Young, T. F., and Cheng, L. H., Science 64, 333 (1926). 29. Hogness, T. R., J. Am. Chem. Soc. 43, 1621 (1921). 30. Hutchinson, E., Trans. Faraday Soc. 39, 229 (1943).

332 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69.

MALCOLM DOLE

Iredale, T., Phil. Mag. [6] 46, 1088 (1923). Jones, Grinnell, and Frizzell, L. D., / . Chem. Phys. 8, 986 (1940). Jones, Grinnell, and Ray, W. Α., Am. Chem. Soc. 69, 187 (1937). Jones, Grinnell, and Wood, L. Α., J. Chem. Phys. 13, 106 (1945). Kurtz, S. S., Jr., J. Am. Chem. Soc. 49, 1991 (1927). Langmuir, I., Science 88, 430 (1938); J. Chem. Phys. 6, 894 (1938). Lenard, P., v. Dallwitz-Wegener, R., and Zachmann, E., Ann. Physik. 74, 381 (1924). Liesegang, Ε., Z. anal. Chem. 126, 172 (1943); 126, 334 (1944). Lohnstein, T., Ann. Physik. 20, 237 (1906). Long, F. Α., and Nutting, G. C , J. Am. Chem. Soc. 64, 2476 (1942). Meyerstein, W., and Morgan, J. D., Phil Mag. 35, 335 (1944). Michelli, L. I. Α., Phil. Mag. [7] 3, 581 (1927). Mills, H., and Robinson, P. L., / . Chem. Soc. 1927, 1823. Nietz, A. H., and Lambert, R. H., / . Phys. Chem. 33, 1460 (1929). Onsager, L., and Samaras, Ν. Ν. T., / . Chem. Phys. 2, 528 (1934); also Wagner, C., Physik. Z. 26, 474 (1924). Poisson, Nouv. Theor. d. Tact, capill. Paris, 1831. Porter, A. W., Trans. Faraday Soc. 27, 205 (1931); 29, 1307 (1933). Preston, J. M., / . Soc. Dyers Colourists. 61, 161 (1945). Puis, H. O., Phil Mag. 22, 970 (1936). Rayleigh, Lord, Proc. Roy. Soc. A92, 184 (1915). Richards, T. W., and Carver, Ε. K., J. Am. Chem. Soc. 43, 827 (1921). Richards, T. W., and Coombs, L. B., J. Am. Chem. Soc. 37, 1656 (1915). Sauerwald, F., Z. Metallkunde 18, 137, 193 (1926). Schroedinger, E., Ann. Physik. 46, 410 (1915). Schwenker, G., Ann. Physik. 11, 525 (1931). Searle, G. F. C , Proc. Phys. Soc. London 63, 681 (1941). Smith, G. W.,