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UBC Theses and Dissertations

Viscoelastic effects in boundary lubrication Green, Marjorie Ann Carlson 1974

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VISCOELASTIC  EFFECTS  IN BOUNDARY LUBRICATION  BY  MARJORIE ANN CARLSON GREEN B . A . S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , Vancouver, B r i t i s h Columbia, 1967 M.A.Sc., The U n i v e r s i t y o f B r i t i s h C o l u m b i a , Vancouver, B r i t i s h C o l u m b i a , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department of Mechanical Engineering We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1974  In p r e s e n t i n g f o r an that  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  advanced d e g r e e a t The  the L i b r a r y  study.  the  requirements  U n i v e r s i t y of B r i t i s h C o l u m b i a , I  s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g  t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may  be  Department or by  I t i s understood that  tion, gain  his representatives.  g r a n t e d by  s h a l l not  be  a l l o w e d w i t h o u t my  written  The  University  Vancouver,  Date  of B r i t i s h Columbia  B.C.  C|fwA  I (inC-  of  Ann  Carlson  my  publicafinancial  permission.  Marjorie  Department of M e c h a n i c a l E n g i n e e r i n g  and  the Head o f  i n p a r t o r i n whole, c r the c o p y i n g o f t h i s t h e s i s f o r  agree  Green  ABSTRACT  The s t a t i c f r i c t i o n of steel under boundary lubricated conditions was investigated both experimentally and theoretically. The theoretical model was developed using the assumption that during the application of a tangential load to a f r i c t i o n couple, the real area of contact grows i n a viscoelastic manner u n t i l a c r i t i c a l shear stress i s reached. Using this model, i t was possible to d i s t i n guish the effect of s t a t i c and dynamic contact time on area growth and thus to show why the t r a d i t i o n a l "time dependence of s t a t i c f r i c t i o n " theories have limited v a l i d i t y .  The model predicts that u , the g  s t a t i c f r i c t i o n coefficient, i s a function of the rate parameter 0, and that a relaxation time can be assigned  to a given interface.  Subsequent experimental work using steel surfaces i n vacuum as well as steel surfaces lubricated by various surface films showed that surface conditions play a large role i n determining the exact U  G  - 6 relationship for a given f r i c t i o n couple.  Over the range of 9  investigated the s t a t i c f r i c t i o n coefficient of steel i s constant i f certain surface films are present; for other films the s t a t i c f r i c t i o n coefficient vs 8 curve shows an upper and lower asymptote.  In the  l a t t e r case a relaxation time was assigned to each boundary lubricant. For given asymptotes these relaxation times can be used to predict whether the f i l m w i l l be a useful lubricant at a particular 8. A subsequent investigation showed that the relaxation times are strongly affected by temperature.  Since raising the substratum  temperature results i n smaller relaxation times, i t i s obvious that a particular lubricant may become ineffective as the substratum temperature changes.  iii  Both the e x p e r i m e n t a l  and t h e o r e t i c a l work c l e a r l y  demonstrate  t h a t the s t a t i c f r i c t i o n o f s t e e l can be s i g n i f i c a n t l y m o d i f i e d by t h e application  o f a p p r o p r i a t e boundary  lubricants.  TABLE OF CONTENTS Page CHAPTER  I.  CHAPTER  II.  CHAPTER I I I .  CHAPTER  IV.  INTRODUCTION . .  '.  HISTORICAL BACKGROUND  5  THEORY  .'..  V.  16  3.1  Introduction  16  3.2  Models f o r S t a t i c  3.3  The N o n - d i m e n s i o n a l u  3.4  s Changing t h e R e l a x a t i o n Time of an Interface  24  3.5  The E f f e c t of. Temperature on T V a l u e s  28  Friction  18  v s T* P l o t  23  EXPERIMENTAL APPARATUS AND EXPERIMENTAL PROCEDURE  CHAPTER  1  .  32  4.1  Apparatus  ,.32  4.2  P r e t e s t P r e p a r a t i o n of Samples  41  4.3  General Experimental Procedure  46  RESULTS AND DISCUSSION 5.1  Introduction  5.2  Obtaining S t a t i c  47  the S t e e l / S t e e l 5.3  47  F r i c t i o n Information f o r System  D i s c u s s i o n of u  47  - 6 Results  55  ~ 6 Curves  64  s 5.4  Dimensionless u  5.5  E f f e c t of Temperature on S t a t i c  s Friction . . . . .  65  Page CHAPTER  VI.  SUMMARY AND GENERAL DISCUSSION OF RESULTS  69  6.1  Summary  69  6.2  The C o n t a c t A r e a a t S l i p  70  6.3  Applicability Selection  71  6.4  CHAPTER V I I .  of R e s u l t s t o L u b r i c a n t  A Note on t h e Time-dependence o f S t a t i c Friction  CONCLUSIONS  BIBLIOGRAPHY  APPENDIX  APPENDIX  I.  73  77  80  THE VACUUM SYSTEM  I I . PROPERTIES OF REAGENTS USED  85  88  APPENDIX I I I  90  FIGURES  91  vi LIST OF TABLES Page TABLE  TABLE  I.  II.  C a l c u l a t e d V a l u e s of R e l a x a t i o n Time, V i s c o s i t y , E l a s t i c Modulus and Shear S t r e n g t h f o r t h e 2-Parameter Model E l a s t i c M o d u l i i and V i s c o s i t y V a l u e s as a F u n c t i o n of T /p f o r t h e 3-Parameter Model o m  TABLE I I I . V i s c o s i t i e s o f Some M a t e r i a l s  59  62 63  vii LIST OF FIGURES Page FIGURE 1.  FIGURE 2a.  FIGURE 2b.  V i s c o e l a s t i c Model o f S t a t i c F r i c t i o n Developed Johannes [19] . ....  by 91  The C o n t a c t A r e a Between Two S o l i d S u r f a c e s i s t h e Sum o f t h e S m a l l D i s c r e t e A r e a s o f C o n t a c t Formed Where Opposing A s p e r i t i e s Meet  92  The A r e a o f C o n t a c t . a n d t h e Shear S t r e n g t h a s F u n c t i o n s o f t h e Rate o f A p p l i c a t i o n o f t h e T a n g e n t i a l Shearing Force  93  ,  FIGURE 3.  T a n g e n t i a l Loading During a S t a t i c F r i c t i o n Test  FIGURE 4.  Models f o r S t a t i c F r i c t i o n  FIGURE 5.  G e n e r a l Form o f t h e u  ....  ...  94 95  - 6 Curve  96  s FIGURE 6.  Changing c R e s u l t s i n a F a m i l y o f y  FIGURE 7.  The G e n e r a l S t a t i c F r i c t i o n Curve  FIGURE 8.  G e n e r a l Arrangement o f Vacuum System and E x p e r i m e n t a l  g  -'6 Curves  97 98  Apparatus  99  FIGURE 9.  I s o m e t r i c Diagram o f E x p e r i m e n t a l Apparatus  , 100  FIGURE 10.  Schematic  FIGURE 11.  I s o m e t r i c S k e t c h o f F r i c t i o n Couple  102  FIGURE 12,  S t a t i c F r i c t i o n o f C1020 S t e e l i n Vacuum o f 2 x 1 0 " t o r r a t 20°C S t a t i c F r i c t i o n o f C1020 S t e e l i n Vacuum and A f t e r Exposure t o Atmosphere  103 104  Comparison o f S t a t i c F r i c t i o n o f C1020 S t e e l i n Vacuum  105  S t a t i c F r i c t i o n o f C1020 S t e e l Covered Films  106  o f t h e H y d r a u l i c C o n t r o l System  101  8  FIGURE 13. FIGURE 14.  FIGURE 15.  FIGURE 16.  FIGURE 17.  FIGURE 18.  Comparison o f S t a t i c F r i c t i o n C1020 S t e e l  with  Oxide  of.Oxide-covered ,  107  S t a t i c F r i c t i o n o f C1020 S t e e l A f t e r A b r a d i n g S u r f a c e Under S t e a r i c Acid-Hexane S o l u t i o n  108  S t a t i c F r i c t i o n o f C1020 S t e e l Covered w i t h a Monolayer o f E i t h e r a B a s i c I r o n S t e a r a t e o r a Basic Iron Oleate  109  viii Page FIGURE 19.  The E f f e c t o f a C a ( S t ) Monolayer on S t a t i c F r i c t i o n a s Compared t o t h e E f f e c t o f an Fe(0H)2St Monolayer , ... 110  FIGURE 20.  The E f f e c t o f a C a ( 0 J 0 Monolayer on S t a t i c F r i c t i o n Compared t o t h e E f f e c t o f an Fe(0H)2 OZ M o n o l a y e r ... I l l  FIGURE 21.  E x p e r i m e n t a l Data and T h e o r e t i c a l y - 6 Curve f o r S t a t i c F r i c t i o n : F e ( 0 H ) S t Monolayer  112  E x p e r i m e n t a l Data and T h e o r e t i c a l y Static Friction: C a ( S t ) Monolayer  113  2  2  2  FIGURE 22.  - 0 Curve f o r 8  2  FIGURE 23.  E x p e r i m e n t a l D a t a and T h e o r e t i c a l y -8 Static Friction: F e ( 0 H ) 01 Monolayer  Curve f o r 114  2  FIGURE 24.  E x p e r i m e n t a l Data and T h e o r e t i c a l y Static Friction: Ca(0&) Monolayer  - 0 Curve f o r 115  5  2  FIGURE 25.  FIGURE 26.  FIGURE 27.  E x p e r i m e n t a l Data C o l l a p s e s on G e n e r a l y Curve P r e d i c t e d f r o m M a t h e m a t i c a l Model  - T* 116  E f f e c t o f R a i s i n g S u r f a c e Temperature Ca S t e a r a t e Soap Monolayer  t o 35°C.  Effect  t o 50°C.  o f R a i s i n g S u r f a c e Temperature  117  Ca S t e a r a t e Soap Monolayer  .•  118  FIGURE 28.  Log c v s 1/T f o r C a l c i u m S t e a r a t e Soap M o n o l a y e r s  FIGURE 29.  y  - 8 - T Surfaces f o r Various Conditions  ... 119  ..........  120  s FIGURE 30. FIGURE 31.  y - T C h a r a c t e r i s t i c s o f S t e e l Covered w i t h C a l c i u m s t e a r a t e Monolayer  121  Experimental T e m p e r a t u r e - F r i c t i o n Data f o r C a l c i u m S t e a r a t e Monolayer Covered S u r f a c e  ,  122  FIGURE 32.  Loading H i s t o r y During Delayed S t i c k  123  FIGURE 33.  A r e a Growth Due t o D e l a y Time i f t h e System h a s a R e l a x a t i o n Time o f 40 Sees  124  iz ACKNOWLEDGEMENT  The e x p e r i m e n t a l Tribology Laboratory  p a r t o f t h i s program was c a r r i e d  o f t h e Department o f M e c h a n i c a l  The U n i v e r s i t y o f B r i t i s h Columbia. Dr.  C.A. B r o c k l e y  The author  out i n the  Engineering a t  wishes t o thank .  f o r h i s a d v i c e and encouragement d u r i n g t h e program.  S p e c i a l t h a n k s a r e due D r . E.G. Hauptmann o f t h e Department o f Mechanical  E n g i n e e r i n g and Dr. J . L e j a o f t h e Department o f M i n e r a l  Engineering  for their  Financial  suggestions  and comments.  a s s i s t a n c e was r e c e i v e d through t h e N a t i o n a l  R e s e a r c h C o u n c i l o f Canada and i s g r a t e f u l l y  acknowledged.  LIST OF  SYMBOLS  Units contact area at time t  in  2  i n i t i a l contact area  in  2  activation energy  Kcal-gm-mole  shearing force, tangential force  lbs  rate of application of shearing force  lbs-sec  surface shear modulus  dynes-cm  creep compliance  dimensionless  normal load  lbs .-•  shear stress  lb-in "  c r i t i c a l shear stress of interface  lb-in"  shear strength of l u b r i cating films ^  lbs-in  - 2  shear strength of s o l i d  lbs-in  - 2  temperature  °K  shear strength of i n t e r face  lbs-in"  v i s c o s i t y parameter i n mathematical model  in-sec-lb  e l a s t i c parameter i n mathematical model  lb-in  yield pressure of material  lbs-in"  time, time to f a i l u r e  sec  a constant  dimensionless  proportion of s o l i d - s o l i d contacts i n an interface  dimensionless  -1  -1  _1  . 2  2  2  _1  _1  2  Symbol  Units  e(t)  strain  m  c(t)  stress  lbs-in"  8  r a t i o of r a t e of a p p l i c a t i o n of s h e a r i n g f o r c e , F to t h e normal l o a d , N.  sec  surface v i s c o s i t y  gm/sec  IT  surface pressure  dynes/cm  U ,U , U s s s . max. mm.  static friction coefficients  n  s  ,n ,n. o i  r e l a x a t i o n time  per i n 2  1  dimensionless sec  I.  Given c a s u a l observer understood.  INTRODUCTION  the l o n g h i s t o r y of f r i c t i o n - o r i e n t e d r e s e a r c h , t o i t might appear t h a t f r i c t i o n and  C e r t a i n l y t h e r e i s ample e v i d e n c e  civilizations  were aware of f r i c t i o n and  the  l u b r i c a t i o n are w e l l  to show t h a t even e a r l y  knew enough about i t t o pour  l u b r i c a t i n g l i q u i d s i n f r o n t of s l e d g e s and  to use r o l l e r s  t o move  heavy l o a d s . T h i s same o b s e r v e r might a l s o p o i n t t o the e x t e n s i v e  18th  C e n t u r y work o f a number of European s c i e n t i s t s i n c l u d i n g Coulomb Amontons.  The  t h r e e "fundamental laws of f r i c t i o n " —  p r o p o r t i o n a l t o l o a d but arose  independent o f a r e a and  and  friction i s  sliding  velocity  —  from t h i s work. Unfortunately,  t h e s e laws would suggest valid.  Thus f r i c t i o n  exceptions  friction and  i s not  the simple phenomenon t h a t  i n c e r t a i n s i t u a t i o n s t h e laws a r e  studies s t i l l  c o n t i n u e , not j u s t to d e f i n e  the  t o Amontons' laws, but because modem b a s i c r e s e a r c h seeks a  much b e t t e r u n d e r s t a n d i n g  of the mechanisms of f r i c t i o n and  phenomena, l u b r i c a t i o n , wear and t h e p r e v i o u s r e s e a r c h can One  r e a s o n why  adhesion  than e i t h e r t h e s e  i t s allied "laws" or  provide. f r i c t i o n r e s e a r c h has p r o g r e s s e d  t h a t s u i t a b l e r e s e a r c h t o o l s have been developed ments such as the e l e c t r o n m i c r o s c o p e and have a i d e d  not  so s l o w l y i s  only l a t e l y .  Instru-  s u r f a c e roughness i n d i c a t o r s  f r i c t i o n r e s e a r c h immensely i n the s h o r t time t h e y have been  available. In a d d i t i o n , the r e c e n t demand f o r s o p h i s t i c a t e d m a c h i n e r y capable  of o p e r a t i n g i n space, at h i g h temperatures,  a t h i g h speeds o r  2  i n adverse  environments,  has s t i m u l a t e d f r i c t i o n r e s e a r c h .  some o f t h e r e s e a r c h has been o f an ad hoc type, c a r r i e d  out t o p r o v i d e  immediate d e s i g n d a t a on d i f f e r e n t m a t e r i a l combinations, s c i e n t i f i c work was a l s o funded. the most s e r i o u s shortcoming dict  f r i c t i o n values.  Although  systematic  The l a c k o f d e s i g n d a t a p o i n t e d out  of f r i c t i o n research:  an i n a b i l i t y t o p r e -  T h i s problem i s p a r t i c u l a r l y acute f o r systems  o p e r a t i n g under boundary l u b r i c a t e d of boundary l u b r i c a t i o n ,  conditions.  One p a r t i c u l a r  the s t a t i c f r i c t i o n of m e t a l s  f i l m s , was examined i n the p r e s e n t  aspect  coated w i t h  thin  study.  U n l i k e hydrodynamic l u b r i c a t i o n where t h e s l i d i n g s u r f a c e s a r e fully due  s e p a r a t e d by a f l u i d  f i l m and the f r i c t i o n l o s s e s i n the system a r e  to the v i s c o s i t y o f the f l u i d , boundary l u b r i c a t i o n  s e p a r a t i n g f i l m i s o n l y a few m o l e c u l e s and  h i g h l o a d s may cause l u b r i c a t i o n  type.  I n any case, t h e important  thick.  o c c u r s when the  Slow s l i d i n g speeds  t o be o f the boundary  lubrication  f a c t i s t h a t the f r i c t i o n i s determined  by both t h e p r o p e r t i e s o f the f i l m and by the c h e m i c a l and p h y s i c a l n a t u r e o f the s o l i d s i n c o n t a c t . When d i s c u s s i n g boundary l u b r i c a t i o n , two  i t i s usual to recognize  k i n d s o f boundary f r i c t i o n •— s t a t i c f r i c t i o n and k i n e t i c  Static  friction.  f r i c t i o n i s d e f i n e d as the f o r c e r e q u i r e d t o cause one o f the  c o n t a c t i n g s u r f a c e s t o b e g i n t o s l i d e over the o t h e r .  Kinetic  friction  i s the f o r c e r e q u i r e d to keep.the s u r f a c e s s l i d i n g w i t h a c o n s t a n t velocity. B e s i d e s the u s u a l s l i d i n g t e s t s ,  s t a t i c and k i n e t i c  can be s t u d i e d u s i n g a type of f r i c t i o n - - i n d u c e d tion oscillations.  vibration  friction  called  relaxa-  From d a t a o b t a i n e d i n t h i s way, and from s l i d i n g  tests,  i t was g e n e r a l l y b e l i e v e d t h a t s t a t i c f r i c t i o n was time-dependent and t h a t  3  kinetic  f r i c t i o n was v e l o c i t y dependent.  dependency o f s t a t i c actual contact  f r i c t i o n centered  The e x p l a n a t i o n o f t h e t i m e -  around the assumption t h a t t h e  a r e a between t h e s u r f a c e s i n c r e a s e d d u r i n g  l o a d i n g time t h a t preceeded g r o s s  slip.  be  by t h e normal l o a d .  i n c r e a s e d by the c r e e p  induced  The c o n t a c t  the " s t a t i c "  a r e a was thought t o  On c r i t i c a l l y examining t h e p r e v i o u s work, e s p e c i a l l y Johannes has  [ 1 9 ] , i t becomes o b v i o u s t h a t the "time-dependent"  some s e v e r e  that o f  explanation  l i m i t a t i o n s . By i n t e r r u p t i n g a f r i c t i o n t e s t f o r a g i v e n  p e r i o d o f time, then r e s t a r t i n g t h e t e s t Johannes demonstrated t h a t t h e e f f e c t of creep  time on s t a t i c f r i c t i o n was m i n i m a l .  i n c r e a s e s i n s t a t i c f r i c t i o n were noted.' him  to reject  No  significant  This observation  encouraged  t h e o l d e r e x p l a n a t i o n and t o c o n s i d e r a s i n g l e a s p e r i t y  as a v i s c o e l a s t i c body so t h a t t h e i n c r e a s e i n c o n t a c t a r e a i s due t o the l o a d r a t e s e n s i t i v e d e f o r m a t i o n  o f t h a t body when t h e s h e a r i n g  force  i s applied. Obviously,  time i s i n v o l v e d i n t h i s model t o o , s i n c e t h e s t r a i n  of a v i s c o e l a s t i c body i s c o m p l e t e l y but  determined by i t s l o a d i n g h i s t o r y ,  i t i s a l s o o b v i o u s t h a t e q u a l amounts o f l o a d i n g time and c r e e p  cannot have t h e same e f f e c t on t h e c o n t a c t friction *  e=  i s very promising.  T h i s approach t o s t a t i c  The u s e o f t h e l o a d i n g r a t e p a r a m e t e r , .  r a t e of a p p l i c a t i o n of shearing normal l o a d  reporting f r i c t i o n results.  area.  time  force immensely  simplifies  The use o f e l a s t i c and v i s c o u s  parameters  i n d i c a t e s which p r o p e r t i e s o f a f r i c t i o n c o u p l e might a f f e c t  static  friction. Under boundary l u b r i c a t i o n c o n d i t i o n s , t h e f r i c t i o n  i s deter-  mined by t h e p r o p e r t i e s o f t h e l u b r i c a t i n g f i l m and by t h e p h y s i c a l and chemical  p r o p e r t i e s of the u n d e r l y i n g  solid.  For a given  solid, i t i s  4  w e l l known t h a t  s u r f a c e f i l m s o f both o r g a n i c and i n o r g a n i c compounds c a n  markedly a f f e c t  its friction  characteristics.  The aim o f t h e p r e s e n t  work i s t o expand t h e t h e o r e t i c a l  base and t o i d e n t i f y the o r i g i n s o f  the  in static  observed v i s c o e l a s t i c e f f e c t s  friction.  5  II.  Although it  HISTORICAL BACKGROUND  f r i c t i o n phenomena have been s t u d i e d f o r a l o n g  i s only during the l a s t  our u n d e r s t a n d i n g  time,  60 y e a r s t h a t r e a l advances have been made i n .  o f t h e fundamental p h y s i c a l and c h e m i c a l  i n v o l v e d i n f r i c t i o n and l u b r i c a t i o n .  processes  A comprehensive r e v i e w o f e v e r y  c o n t r i b u t i o n would be i m p o s s i b l e because o f t h e volume of. m a t e r i a l generated exist.  and u n n e c e s s a r y  because s e v e r a l good r e v i e w s  Because o f t h i s and because p u b l i s h e d papers  [22] a l r e a d y  can vary  greatly,  b o t h i n q u a l i t y and a p p l i c a b i l i t y t o a s p e c i f i c problem, t h i s s u r v e y be l i m i t e d  t o a s e l e c t i o n o f p a p e r s c o n s i d e r e d t o be most  will  significant  contributions to s t a t i c f r i c t i o n research. Most s t a t i c f r i c t i o n r e s e a r c h would f a l l general categories.  In the f i r s t  category, a r e s t u d i e s concerned  t h e c h e m i c a l and p h y s i c a l p r o p e r t i e s o f s u r f a c e s . c a t e g o r y i s p r i m a r i l y concerned  i n t o one o f two  Research  with  i n this  with the e f f e c t s of surface f i l m s ,  n a t u r a l l y o c c u r r i n g and d e l i b e r a t e l y a p p l i e d , on f r i c t i o n .  both  The e x p e r i -  m e n t a l r e s u l t s o f t h i s r e s e a r c h a r e used m a i n l y f o r d e s c r i p t i v e  purposes.  They tend t o be more u s e f u l i n p r e d i c t i n g t r e n d s than i n p r e d i c t i n g a c t u a l boundary f r i c t i o n v a l u e s .  Because o f e f f o r t s i n t h i s  direction,  however, t h e b o u n d a r y - l u b r i c a t i n g q u a l i t i e s o f v a r i o u s o r g a n i c and i n o r g a n i c compounds have been w i d e l y r e c o g n i z e d and s u c c e s s f u l l y a p p l i e d . A t t h e same time, c e r t a i n a s p e c t s o f s o l i d - s t a t e and f r i c t i o n w e l d i n g and o t h e r p r o c e s s e s w h i c h r e q u i r e h i g h f r i c t i o n v a l u e s , were c l a r i f i e d by this research. In t h e second towards the m a t h e m a t i c a l  c a t e g o r y , t h e r e s e a r c h tends t o be o r i e n t e d modelling of s t a t i c  friction.  Placed i n t h i s  c a t e g o r y , i s t h e l a r g e volume o f p u b l i s h e d work d e a l i n g w i t h t h e v a r i o u s  aspects and  of f r i c t i o n - i n d u c e d o s c i l l a t i o n s ,  s e v e r a l attempts at modelling  t h i s type  of r e s e a r c h , b e s i d e s  static  time-dependent s t a t i c friction.  One o f t h e g o a l s o f  a b e t t e r understanding  of f r i c t i o n ,  f i n d a way t o p r e d i c t q u a n t i t a t i v e l y boundary f r i c t i o n The during  c h e m i s t , had r e c o g n i z e d were c a p a b l e  by Hardy [23]  By 1920, b o t h Hardy and Langmuir  t h a t s m a l l amounts of c e r t a i n o r g a n i c  of reducing  static  friction.  [56], a compounds  Langmuir was t h e f i r s t t o  d e m o n s t r a t e t h a t even a s i n g l e monolayer c o u l d l u b r i c a t e a s u r f a c e Hardy was the f i r s t  t o p r o v e t h a t the m o l e c u l a r  compound was an important systematic straight organic  i s to  values.  study o f boundary l u b r i c a t i o n was p i o n e e r e d  the p e r i o d 1918-1932.  friction  f a c t o r i n reducing  while  x<reight o f an o r g a n i c  static friction.  His  i n v e s t i g a t i o n of a s e r i e s o f o r g a n i c a c i d s , a l c o h o l s , and  c h a i n p a r a f f i n s , showed t h a t i n c r e a s i n g t h e c h a i n l e n g t h o f a n compound p r o g r e s s i v e l y d e c r e a s e d  the s t a t i c f r i c t i o n  coefficient.  Hardy went on t o d e v e l o p a t h e o r y of boundary l u b r i c a t i o n i n w h i c h adsorbed f i l m s of h y d r o c a r b o n s p l a y e d t h e o p p o s i n g s u r f a c e s as b e i n g  completely  a major r o l e .  separated  He v i s u a l i z e d  by a d s o r b e d m o n o l a y e r  of t h e s u r f a c t a n t . His  theory f u r t h e r s p e c i f i e d  t h a t t h e r e was no s o l i d - s o l i d  t a c t o v e r any p a r t o f t h e i n t e r f a c e between the s l i d i n g  con-  s o l i d s and t h a t  t h e f r i c t i o n a l r e s i s t a n c e was s o l e l y due t o t h e s l i d i n g o f one boundary l a y e r o v e r the o t h e r . The  work of Hardy and Langmuir s t i m u l a t e d f u r t h e r r e s e a r c h i n  boundary l u b r i c a t i o n and i n s u r f a c t a n t a d s o r p t i o n on s o l i d T h e i r work g e n e r a t e d an i n t e r e s t  i n the c h e m i s t r y  of a d s o r p t i o n , the  s t r u c t u r e and m e c h a n i c a l p r o p e r t i e s of s u r f a c e f i l m s , topography of s o l i d  surfaces.  the r e a c t i v i t y and.  s u r f a c e s and the mechanics of s u r f a c e - s u r f a c e  inter-  7  a c t i o n t h a t c o n t i n u e s today. D u r i n g the c o u r s e of l a t e r r e s e a r c h Hardy's o r i g i n a l  t h e o r y was  actual f r i c t i o n conditions  considered and  i t was  t h e o r i e s of boundary f r i c t i o n and surface-active strength solid  substance can  f i l m s but  contact  t o be  on boundary  friction,  an o v e r - s i m p l i f i c a t i o n o f  subsequently m o d i f i e d .  a d s o r b onto s u r f a c e s  expected.  current  l u b r i c a t i o n a c c e p t Hardy's i d e a to form low  they a l s o s p e c i f y t h a t a c e r t a i n amount o f  must be  The  T h i s m o d i f i c a t i o n was  that  shear solid-  l a r g e l y the r e s u l t  of s e v e r a l s t u d i e s of wear p a r t i c l e s , s u r f a c e damage and m a t e r i a l  trans-  f e r generated during  [20] .  s l i d i n g under boundary l u b r i c a t e d c o n d i t i o n s  A l t h o u g h the amount of wear i s d r a s t i c a l l y reduced by t h e surfactants, that  there  the  f a c t that  is solid-solid  it still contact  o c c u r s s t r o n g l y s u p p o r t s the  t h r o u g h the f i l m .  boundary l u b r i c a t i o n t h e o r y a t t r i b u t e s the r e s i s t a n c e of the following  s o l i d - s o l i d and  represents  Q  F = A Ta S  +  [_os  S.  o  t o the  areas i n  combined  the  )S ~], where S n  Zj  •  s  and  solid-solid  contacts  in  an  t h e n the f r i c t i o n f o r c e i s  S„ a r e the shear s t r e n g t h s o f  the  I  Assigning  because the m e c h a n i c a l p r o p e r t i e s  an  exact v a l u e  to  of l u b r i c a t i n g f i l m s  •  Scruton  such as the recent  to measure.  [47]  Akhmatov  [17] , B a i l e y and  Courtney-Pratt  have been a b l e t o d e t e r m i n e a number of  shear modulus and  the y i e l d  s t r e s s , of the  a c o n s t a n t v a l u e but  that  the  shear s t r e n g t h  Scruton's  to boundary  of m e t a l s t e a r a t e s  i t i s s t r o n g l y a f f e c t e d by  [58]  properties,  films.  work on m e t a l l i c soaps i s p a r t i c u l a r l y a p p l i c a b l e  f r i c t i o n because i t shows t h a t not  a r e a A,  of  the l u b r i c a t i n g f i l m r e s p e c t i v e l y .  are d i f f i c u l t and  (1 - a  is difficult  Xr  argument  modified  f r i c t i o n force  f i l m - f i l m contact  the p r o p o r t i o n  i n t e r f a c e having a t o t a l contact  and  The  of  way. If a  solid  addition  the  contact  is  8  pressure.  A t 1 Kg/mm , f o r example, t h e shear s t r e n g t h o f c a l c i u m 2  s t e a r a t e i s .2 Kg/mm , but when the c o n t a c t 2  shear s t r e n g t h i s i n c r e a s e d  by a f a c t o r o f 50,  Another i n t e r e s t i n g a s p e c t chemistry  pressure  m e t a l s a r e more " r e a c t i v e " than o t h e r s .  boundary f i l m s . present  2  compounds a r e much  on the o t h e r  hand, some  Bowden and Leben [ 1 6 ] , G r e e n h i l l  and many o t h e r  i n v e s t i g a t o r s have used a  t o study the f o r m a t i o n  The g e n e r a l  t o 10 Kg/mm .  Some o r g a n i c  more e f f e c t i v e a s l u b r i c a n t s t h a n o t h e r s and,  v a r i e t y o f techniques  2  o f boundary f r i c t i o n i n v o l v e s t h e  of s u r f a c t a n t - s o l i d r e a c t i o n s .  [ 4 6 ] , Schulman e t a l . [24]  i s 200 Kg/mm , t h e  conclusions  and e f f e c t i v e n e s s o f  ( s p e c i f i c a l l y applicable to the  study) t o be drawn from t h e i r work a r e : 1) O r g a n i c compounds can  form o r i e n t e d , h i g h l y s t r u c t u r e d  f i l m s on m e t a l s u r f a c e s . and  wear.  These f i l m s w i l l r e d u c e  Depending on the m e t a l i n v o l v e d , the  friction  surfactant  can be c h e m i c a l l y o r p h y s i c a l l y adsorbed onto the  surface.  With s p e c i f i c r e f e r e n c e  to f a t t y acids, a p a r t i c u l a r f a t t y  a c i d may r e a c t w i t h  s u b s t r a t a t o form a m e t a l l i c soap  the  or i t may o n l y be p h y s i c a l l y adsorbed. the s u r f a c t a n t c o n c e n t r a t i o n  A l s o , depending o n  and the time o f exposure, t h e  s u r f a c e may be c o v e r e d w i t h a p a r t i a l monolayer, a monolayer o r m u l t i l a y e r s o f adsorbed 2) The e f f e c t o f h e a t i n g t u r e o f the the s t a t i c  film  the  [20].  friction  the b u l k m e l t i n g  s u b s t r a t a i s t o change the  Over a c r i t i c a l  coefficient  Upon c o o l i n g , the e f f e c t m e t a l s , the c r i t i c a l  species.  will  struc-  temperature range,  increase  i s r e v e r s i b l e [20].  markedly. F o r some  temperature i s a p p r o x i m a t e l y e q u a l t o  p o i n t o f the f a t t y a c i d ; f o r o t h e r s , t h e  temperature c o r r e s p o n d s to t h e b u l k m e l t i n g appropriate  organometallic  point of the  soap.  3) The m e c h a n i c a l d i s r u p t i o n o f t h e s u r f a c e d u r i n g t e s t c a n have two e f f e c t s . a v a i l a b l e to the surface,  I f the s u r f a c t a n t  a friction  i s no  longer  then t h e l u b r i c a n t l a y e r s a r e  worn away by r e p e a t e d t e s t i n g and h i g h e r  static  friction  v a l u e s x j i l l r e s u l t [16] . I n some s i t u a t i o n s , however, m e c h a n i c a l d i s r u p t i o n o f the  surface a s s i s t s i n the formation  o f m e t a l soaps [ 5 3 ] .  o f chemisorbed f i l m s  B e s i d e s making f r e s h m e t a l a v a i l a b l e  to t h e s u r f a c t a n t , t h e d i s r u p t i o n may cause t h e s u r f a c e s to be " m e c h a n i c a l l y  activated".  T h i s i s known a s t h e Kramer  e f f e c t and i t enhances t h e c h e m i c a l r e a c t i v i t y o f a Smith and A l l a n [52] and Smith and M c G i l l t h i s e f f e c t f o r a s e r i e s of metals using  surface.  [53] i n v e s t i g a t e d n-nonadecanoic  a c i d as the surfactant. They e s t i m a t e d t h a t t h e Kramer e f f e c t e n e r g y can s u p p l y about 23 K c a l / m o l e so t h a t m e t a l - a c i d not  p r o c e e d s p o n t a n e o u s l y under normal c i r c u m s t a n c e s may  occur i f the surface the  r e a c t i o n s t h a t would  surfactant.  i s disrupted  Therefore,  while i n contact  r e p e t i t i v e runs a c r o s s  s u r f a c e might d e c r e a s e t h e s t a t i c f r i c t i o n  with a  coefficient.  A l t e r n a t e l y , m a c h i n i n g a m e t a l s u r f a c e under a s o l u tion containing  a s u r f a c t a n t would be a r e a s o n a b l e way o f  d e p o s i t i n g a monolayer o f m e t a l l i c soap on t h a t A f a v o r i t e method o f s t u d y i n g organic  t h e l u b r i c a t i n g e f f e c t of v a r i o u s  a c i d monolayers and m u l t i l a y e r s i s to d e p o s i t  surface using  the L a n g m u i r - B l o d g e t t  surface.  technique.  them on a s o l i d  Many i n v e s t i g a t o r s have  10  used  t h i s technique t o study the e f f e c t s of molecular weight,  temperature, c o n t a c t friction. nized  pressure,  substrata  e t c . , on f i l m d u r a b i l i t y and on boundary  Because o f e x t e n s i v e  research  on m o n o l a y e r s , i t i s now  t h a t t h e pH and m e t a l i o n c o n t e n t o f t h e water s u b s t r a t a  recog-  determine  t h e c h e m i c a l c o m p o s i t i o n and p h y s i c a l p r o p e r t i e s o f t h e monolayer formed on  i t s surface  [32],  [34],  [41].  I n view o f t h e f a c t  ments i n monolayer s c i e n c e o c c u r r e d interpret  that these develop-  a f t e r 1950, i t i s p r o b a b l y w i s e t o  t h e e a r l i e r work on t h e f r i c t i o n o f L a n g m u i r - B l o d g e t t mono-  layers with care.  P r i o r t o 1950, i n v e s t i g a t o r s c o u l d n o t have b e e n  f u l l y aware o f t h e e f f e c t s t h a t pH o r s m a l l amounts o f s t r a y m e t a l can produce.  F o r example, i t i s p o s s i b l e t h a t a monolayer d e s i g n a t e d  a s t e a r i c a c i d monolayer may i n f a c t be a c a l c i u m ate  friction,  stear  d i s c u s s i o n o f t h e chemical a s p e c t s o f boundary  t h e d i s t i n c t i o n between s t a t i c and k i n e t i c f r i c t i o n h a s n o t  been s t r e s s e d .  A c t u a l l y there  i s a growing f e e l i n g t h a t  t i o n between them i s a r t i f i c i a l a very  [2], [59].  the d i s t i n c -  I t i s g e n e r a l l y , agreed  s e n s i t i v e v e l o c i t y o r displacement transducer,  that  s e t up t o measure  r e l a t i v e movement between two s u r f a c e s , would show t h a t , b e g i n n i n g ,  with the f i r s t  a p p l i c a t i o n o f t a n g e n t i a l f o r c e , t h e r e i s always a s m a l l  amount o f d i s p l a c e m e n t faces. tion.  (of the order  Thus, t h e s u r f a c e s  friction  o f m i c r o - i n c h e s ) between t h e s u r -  a r e never i n a t r u e " s t a t i c " c o n t a c t  Recognizing t h i s f a c t ,  friction coefficient  some r e s e a r c h e r s  situa-  [59] a r g u e t h a t t h e " s t a t i c  i s m e r e l y t h e l o c a l maximum on t h e " k i n e t i c "  curve. On  it  s t e a r a t e o r copper  as  soap monolayer a s t h e s e m e t a l l i c i o n s a r e common i m p u r i t i e s i n w a t e r . In the foregoing  any  ions  the other  hand, t h e term s t a t i c f r i c t i o n  i s u s e f u l because  does d i s t i n g u i s h t h e f o r c e needed t o g e t an o b j e c t moving from r e s t  11  from the  f o r c e needed to keep i t moving a t a c o n s t a n t  one  observes s t i c k - s l i p o s c i l l a t i o n s ,  and  kinetic  rate.  Also, i f  then the d i f f e r e n c e between  f r i c t i o n becomes q u i t e d i s t i n c t :  the s l i d e r  static  a p p e a r s to  r e m a i n s t a t i o n a r y f o r a p e r i o d of time, then i t i s s u d d e n l y r e l e a s e d the e l a s t i c  f o r c e s i n the system overcome the  at  the  1)  that small displacements " m i c r o s l i p s " take place p r i o r  and  2)  ends.  interface.  With r e g a r d  t o the p r e s e n t  "static" frictional study, i t i s  and  kinetic  forces  recognized, to gross  t h a t i t i s d i f f i c u l t t o d e f i n e e x a c t l y when the " s t a t i c " However, t h e terms s t a t i c  as  friction will s t i l l  sliding  period be  used.  I n the a t t e n t i o n w i l l be The the  effect  second p a r t o f t h i s r e v i e w o f s t a t i c f r i c t i o n focussed  simplest  l o a d N and  flow  r e g i o n of o r i g i n a l  criterion  area A , q  tangential force F  where A i s the any  theories of s t a t i c  o f boundary f i l m s i n the f o l l o w i n g  N •A  at  the  model, o u t l i n e d by Bowden and  Using a p l a s t i c a contact  on  +  and p  2  Tabor  [3]  includes  way.  to d e s c r i b e  the area  that i s subjected  F 2 A  a  instantaneous area  i n s t a n t i s p = N/A  friction.  growth o f :  to a normal  gives:  2 ...  research,  N 2 A o  of c o n t a c t .  The  normal p r e s s u r e  t h e shear s t r e s s i s S = F/A + aS  = p  2  2  so  p,  that:  .  o This  i s the e q u a t i o n f o r j u n c t i o n growth [3].  determined f o r v a r i o u s metals value,  [3].  S e l e c t i n g a = 9 as a r e a s o n a b l e  then: p  2  4-  9S  2  V a l u e s of a have been  = p  2  o  .  However, t h i s e q u a t i o n will  end.  does.not p r e d i c t when j u n c t i o n growth  Bowden and Tabor a r r i v e a t a c o n d i t i o n f o r m a c r o s c o p i c  sliding  of l u b r i c a t e d c o n t a c t s by c o n s i d e r i n g t h e i n t e r f a c i a l m a t e r i a l t o have a critical  shear  s t r e s s , S., which i s l e s s than S„, t h e c r i t i c a l  x s t r e s s of the metal.  Therefore,  s  is: p  + 9y S  2  2  = p .  2  2  M  M The P  Q  yield = 3S^  o  p r e s s u r e p^ i s r e l a t e d t o t h e c r i t i c a l [3].  Therefore, gross p  + 9S.  2  shear  M i f S. = Y „,, then t h e f a i l u r e c o n d i t i o n x M  shear  s t r e s s of metal:  s l i d i n g o c c u r s when:  = 9S. x  2  x  2  Y"  2  or  V:  '• i 3(Y  and  the c o e f f i c i e n t of s t a t i c  V  =  F  S  W  p A  i  - 2  " -  '  D ' 1  friction is:  1  A  3(y-  2  -  1)  1 / 2  C o n s i d e r i n g y t o b e a measure o f t h e " c l e a n l i n e s s " o f t h e s u r f a c e s  leads  to the f o l l o w i n g conclusions: 1) i f y = 1 ( f o r " p e r f e c t l y c l e a n " s u r f a c e s where then u =  0 0  and j u n c t i o n growth c o n t i n u e s  indefinitely;  2) i f Y = 0 . 8 , y = 0 . 4 5 so t h a t a s m a l l d e c r e a s e shear Although  s t r e n g t h markedly a f f e c t s t h e s t a t i c  fails  i n interfacial  friction.  Bowden and Tabor's e x p l a n a t i o n c l e a r l y shows t h e c r i t i c a l  i n f l u e n c e of i n t e r f a c i a l it  = S ) ,  s t r e n g t h on t h e s t a t i c f r i c t i o n  coefficient,  t o e x p l a i n how t h e s t a t i c f r i c t i o n c o e f f i c i e n t c o u l d b e  i n f l u e n c e d by t h e l o a d i n g h i s t o r y .  From s t u d i e s o f s t i c k - s l i p  type  13  v i b r a t i o n s , a number of i n v e s t i g a t o r s have c o n c l u d e d t h a t i s time dependent because c r e e p t a k e s p l a c e failure —  that At  i s during  during  "the s t a t i c contact  static  the period  friction  before  time".  l e a s t f i v e d i f f e r e n t groups have i n v e s t i g a t e d  this  static  f r i c t i o n - t i m e phenomenon and t h r e e d i f f e r e n t r e l a t i o n s h i p s have been proposed:  _  1 P  2  -  s  ^s  3. y  , "s d + t  D e r j a g u i n , Push and T o l s t o i (1957) [ 6 1 ] .  C<  y  k  = \  c  -ct -i s 1 - e  +  Howe e t a l (1955) [62] and K o s t e r i n and K r a g e l s k i i (1962) [ 6 3 ] .  = u + at "k s  Rabinowicz (1940 [64] and B r o c k l e y and D a v i s (1965)  b  s  [12]. These s e m i - e m p i r i c a l r e l a t i o n s h i p s s h a r e two a s s u m p t i o n s : (1) t h a t a t z e r o time o f s t i c k ( t = 0 ) , t h e s t a t i c c o e f f i c i e n t o f friction u  i s equivalent  important — the  that  t o t h e k i n e t i c c o e f f i c i e n t , u, > and (2) most  t h e normal f o r c e , n o t t a n g e n t i a l l o a d i n g  controlling factor i n increasing Results  [66]  o f model s t u d i e s  was  that  mal  load.  is  the s t a t i c f r i c t i o n c o e f f i c i e n t .  by S p u r r  [65] and Moore and T a b o r  s u p p o r t e d a " j u n c t i o n - g r o w t h by c r e e p " e x p l a n a t i o n  s t a t i c f r i c t i o n with increasing the contact  s t a t i c contact  area increased  Hardness-time  to creep:  increased  The common c o n s e n s u s  w i t h time under t h e a c t i o n o f t h e nor-:  S i l v e r i o and Tabor  However, Johannes [19] c o n c l u s i v e l y t i o n had l i m i t e d v a l i d i t y .  interaction  i n t e r a c t i o n ) and h a r d n e s s - t e m p e r a t u r e  s u p p o r t e d t h e argument t h a t  Atkins,  time.  of  (the geometry o f t h e i n d e n t e r - s u r f a c e  similar to the asperity-surface  experiments a l s o  force, i s  [67],  the j u n c t i o n  growth was due  Mulhearn and Tabor [68].  demonstrated t h a t  t h e creep  By i n t e r r u p t i n g a s t a t i c f r i c t i o n  explana-  test  14  during  the s t a t i c c o n t a c t  a constant was  normal and  area  the f r i c t i o n c o u p l e under  appreciable  increase  periods  in static  From t h i s , he concluded t h a t the c o n t a c t  creep was static  holding  t a n g e n t i a l load for various  a b l e t o show t h a t no  occurred.  p e r i o d and  minimal.'  Further  of time,  friction  to c o n s i d e r  growth would be more a p p r o p r i a t e  i n any  Voigt  and  t h a t the t a n g e n t i a l l o a d i n g  v i s c o e l a s t i c model, but  v i s c o e l a s t i c model to e x p l a i n area  mental r e s u l t s r e a s o n a b l y w e l l . greater  mation model to s t a t i c f r i c t i o n , the c o n t a c t  slip  Of c o u r s e , time  loading  times are  area  S e i r e g and  U s i n g the K e l v i n -  growth, Johannes was  f r i c t i o n that f i t t e d  able  to  his experi-  T h i s model w i l l be d i s c u s s e d  the f i r s t  to apply  in  a v i s c o e l a s t i c defor-  a number of people had  c o u l d grow i n a v i s c o e l a s t i c f a s h i o n .  Welter  suggested  that  Schredrov  [30]  [57], f o r example, were i n t e r e s t e d i n the m i c r o -  t h a t precedes g r o s s s l i p p i n g .  Schredrov developed a mathematical  model f o r m i c r o s l i p which assumed t h a t the i n t e r f a c e c o u l d be as a v i s c o e l a s t i c body. mental p r o o f  Unfortunately,  of h i s t h e o r y .  placement t r a n s d u c e r s  of time.  model d e s c r i b e d  S e i r e g and  he d i d not  present  Weiter used v e r y  considered  any  experi-  sensitive dis-  to monitor the h o r i z o n t a l creep which  when they a p p l i e d a constant periods  not  d e t a i l i n Chapter I I I . A l t h o u g h Johannes was  and  rate  the e q u a t i o n s of v i s c o e l a s t i c  i n terms of the s t r a i n s they produce.  d e r i v e a mathematical model f o r s t a t i c  in  t h a t a v i s c o e l a s t i c model of  d e f o r m a t i o n c l e a r l y show t h a t c r e e p times and equivalent  to  e x a m i n a t i o n of the. parameters i n v o l v e d  f r i c t i o n t e s t s l e d him  involved  force  area growth due  i s an important parameter i n d e t e r m i n i n g s t a t i c f r i c t i o n . is  he  occurred  t a n g e n t i a l f o r c e to the i n t e r f a c e f o r  given  They found t h a t a 3-parameter (Boltzmann) v i s c o e l a s t i c their results.  It  i s i n t e r e s t i n g to c o n s i d e r  f u r t h e r why  might show a v i s c o e l a s t i c t y p e of b e h a v i o u r . to m i l d  steel,  there  i s some e v i d e n c e t h a t  the deformation p r o p e r t i e s  static  friction  With s p e c i f i c  reference  the s t r a i n r a t e can a f f e c t  ( f r a c t u r e s t r e n g t h and  d u c t i l i t y ) of s t e e l s  [69].  A rough c a l c u l a t i o n would show, however, t h a t t h e n e t  static  f r i c t i o n xrould be  ductility  quite small —  a t low  i s maximum, t h e f r a c t u r e s t r e n g t h  e f f e c t on  s t r a i n r a t e s where  i s a t a minimum and  the  vice  versa. When c o n s i d e r i n g  s t a t i c f r i c t i o n studies, i t i s also  t o n o t e t h a t a l l t e s t s i n w h i c h r a t e - e f f e c t s were r e p o r t e d under boundary l u b r i c a t e d c o n d i t i o n s . it  i s known t h a t o r g a n i c  friction —  From p r e v i o u s  were c o n d u c t e d  investigations  compounds have a p r o f o u n d i n f l u e n c e on  a d d i n g c e r t a i n s u r f a c t a n t s can  oscillations.  I d e n t i f y i n g the  even s u p p r e s s  Thus, p a r t o f t h e p r e s e n t  of d e t e r m i n i n g i f t h e  r a t e dependent) and  o f o x i d e s on m e t a l l i c soap m o n o l a y e r s on c a l b a s e was  a l s o expanded.  welding  i s desired.  study i s a study of s t a t i c  ( t h e b e s t way  f r i c t i o n o f " c l e a n " s t e e l was  static  s o u r c e o f the v i s c o e l a s t i c b e h a v i o u r  a d h e s i o n where maximum s u r f a c e c o n t a c t  under vacuum c o n d i t i o n s  [16]  stick-slip  could prove u s e f u l both i n l u b r i c a n t s e l e c t i o n or i n p r e s s u r e and  interestin  friction  static  a s t u d y of t h e e f f e c t  static friction.  The  theoreti-  16  III.  3.1  THEORY  Introduction As d i s c u s s e d  i n Chapter I I , the  f r i c t i o n has been a s u b j e c t t h e o r e t i c a l work. other static  time dependency of  f o r a c e r t a i n amount o f e x p e r i m e n t a l  B e s i d e s the s t a t i c  f r i c t i o n c o e f f i c i e n t f o r a given  obtained  D i f f e r e n t values  claims  that  f r i c t i o n c o u p l e i s not  f o r i d e n t i c a l samples may  because the breakaway f o r c e  (and  thus the s t a t i c  test period.  For  the  necesbe  friction  c o e f f i c i e n t ) i s determined by parameters which i n v o l v e r a t e , or d u r a t i o n of the p r e - s l i p  and  f r i c t i o n measurements themselves,  independent e x p e r i m e n t a l e v i d e n c e s u b s t a n t i a t e s  s a r i l y a constant.  static  the  example, i t i s w e l l known  t h a t a s m a l l amount of h o r i z o n t a l d i s p l a c e m e n t or " m i c r o s l i p " of  the  order  period  of 40 m i c r o i n c h e s  which precedes s l i p .  takes place during  the " s t a t i c " c o n t a c t  T h i s m i c r o s l i p r e f l e c t s the j u n c t i o n growth  o c c u r r i n g at the i n t e r f a c e . m i c r o s l i p v a r i e s from one  Shchedrov p o i n t e d  t e s t to another and  out  t h a t the amount of  i n h i s 1957  paper [30],  d e r i v e d a f u n c t i o n which p r e d i c t e d  the amount of m i c r o s l i p .  v a t i o n , i n v o l v i n g s p e c i f i c contact  pressure,  of t a n g e n t i a l l o a d i n g was  the assumption t h a t the  based on  zone behaved l i k e a K e l v i n - V o i g t reached.  solid after  His  he  deri-  t a n g e n t i a l l o a d and  time  deforming  i t s elastic limit  was  More r e c e n t l y , measurements o f the e l e c t r i c a l r e s i s t a n c e of  the i n t e r f a c e have shown t h a t the m e t a l l i c c o n t a c t  area  valued  f o r g i v e n normal  f u n c t i o n of the a p p l i e d t a n g e n t i a l l o a d but  tangential loads, at a slower r a t e  i t i s l a r g e r i f the [15].  p a r a l l e l e d t h i s increase Of  As might be  i s not  t a n g e n t i a l l o a d has  a uni-  been a p p l i e d  expected, the s t a t i c f r i c t i o n  i n m e t a l l i c contact  and  values  area  the v a r i o u s m a t h e m a t i c a l models t h a t have been  postulated  17  to e x p l a i n the observed e s t a b l i s h e d concept  u  g  b e h a v i o u r , models which i n c o r p o r a t e the w e l l  of c o n t a c t a r e a growth and  the i d e a t h a t t h i s  area  growth o c c u r s because the i n t e r f a c e deforms i n a manner c o n s i s t e n t w i t h the d e f o r m a t i o n of a l i n e a r v i s c o e l a s t i c body seem to be the most promising.  There i s ample evidence t h a t other, p e o p l e b e s i d e s Shchedrov  [30], Ahkmatov [17] and  S e i r e g and Welter  [57] f o r example, r e c o g n i z e d  t h a t the i n t e r f a c e between c o n t a c t i n g b o d i e s might be c a p a b l e of d i s p l a y i n g v i s c o e l a s t i c behaviour.  A l s o , as noted  i n the p r e c e d i n g  sec-  t i o n s , the e f f e c t of v i s c o e l a s t i c i t y on the f r i c t i o n of e l a s t o m e r i c m a t e r i a l s has been w e l l e s t a b l i s h e d [27] by e x p e r i m e n t a l and work over the l a s t 20 y e a r s .  However, Johannes [19] was  a p p l y t h i s i d e a to the s t a t i c  f r i c t i o n of s t e e l and  a p p r o p r i a t e v a r i a b l e i n v o l v i n g time was  theoretical  the f i r s t  to  to show t h a t the  8, where:  r a t e of a p p l i c a t i o n of s h e a r i n g f o r c e , F normal l o a d , N The g o a l of the p r e s e n t work was  to expand the t h e o r e t i c a l base and  i d e n t i f y the o r i g i n s of the observed  to  viscoelastic effects in static  friction. Johannes d i d not a s s i g n e l a s t i c or v i s c o u s p r o p e r t i e s t o s p e c i f i c components of the i n t e r f a c e but undergoing responds stance  i n s t e a d viewed i t as a u n i t  d e f o r m a t i o n because of the s h e a r i n g f o r c e , F.  This unit  t o the shear s t r e s s as a l i n e a r , 2-parameter v i s c o e l a s t i c  (a K e l v i n - V o i g t  s o l i d ) which has an u l t i m a t e shear  u n i t a r e a r e p r e s e n t e d by a P r a n d t l - t y p e element. shown i n F i g u r e 1.  While  a Kelvin-Voigt  sub-  s t r e n g t h per  The model he used i s  model i s the s i m p l e s t mechani-  c a l model which d e s c r i b e s s o l i d - l i k e b e h a v i o u r rubber)  any  and  substances  (cork and  been found  to p r o v i d e a much b e t t e r approximation  i t r e p r e s e n t s some  r e a s o n a b l y w e l l , a 3-parameter model has to the behaviour  of  18  most m a t e r i a l s . Kelvin-Voigt  I t i s regarded  as t h e " g e n e r a l l i n e a r s o l i d " model.  model i s a s p e c i a l case o f t h i s g e n e r a l l i n e a r  The  solid  model. In t h e absence of any o t h e r i n f o r m a t i o n such as creep r e l a x a t i o n t e s t data  ( m a t e r i a l s o f the g e n e r a l l i n e a r s o l i d  l i m i t e d s t r e s s r e l a x a t i o n behaviour Kelvin-Voigt  type show  d u r i n g l o n g l o a d i n g times whereas  s o l i d s do n o t ) , c h o o s i n g which model b e s t r e p r e s e n t s t h e  v i s c o e l a s t i c p r o p e r t i e s o f t h e i n t e r f a c e s c o n s i d e r e d here When t h e e x p e r i m e n t a l to  test or  i s difficult.  d a t a a r e a n a l y z e d and n u m e r i c a l v a l u e s a r e a s s i g n e d  each of t h e e l a s t i c and v i s c o u s components of t h e i n t e r f a c e , t h e  c h o i c e between models w i l l be e a s i e r .  I n t h e i n t e r i m , b o t h models  were c o n s i d e r e d .  3.2  Models f o r S t a t i c  Friction  When t h e 2 samples a r e f i r s t  placed together, N e s t a b l i s h e s  the i n i t i a l  c o n t a c t area A / b e t w e e n t h e s u r f a c e s so t h a t A = (N/p ) o o m where p , t h e l o c a l p l a s t i c y i e l d p r e s s u r e , has a v a l u e of about 3 m times t h e y i e l d  stress  [3].  T h i s area i s made up o f t h e numerous  s m a l l , d i s c r e t e areas where opposing  a s p e r i t i e s meet, see F i g u r e 2 ( a ) .  F i s a p p l i e d p e r p e n d i c u l a r t o N, and a t t = 0, F = 0. at  a constant r a t e , F, so t h a t F ( t ) = F t .  F i s applied  The c o r r e s p o n d i n g  on the i n t e r f a c e i s a ( t ) = ( F t / A ) as shown i n F i g u r e 3. Q  of  stress  The e f f e c t  F on each d i s c r e t e a r e a i s t o cause t h a t a r e a to grow, i n c r e a s i n g  the o r i g i n a l l e n g t h i n t h e d i r e c t i o n of F. growth i s . determined  The extent o f t h e area  by t h e a p p r o p r i a t e v i s c o e l a s t i c d e f o r m a t i o n law  • defining A ( t ) .  F o r a g i v e n normal l o a d N over a range of r a t e s F,  the area growth a t f a i l u r e would resemble t h a t shown i n F i g u r e 2 ( b ) . F i s a p p l i e d a t a c o n s t a n t r a t e F u n t i l t h e shear s t r e n g t h  19  per u n i t a r e a , T , of t h e i n t e r f a c e i s reached and f a i l u r e movement) r e s u l t s a t time t ^ . that T  q  Note t h a t i n t h i s model i t i s assumed  does not change w i t h F, so t h a t the shear s t r e n g t h per u n i t  a r e a remains c o n s t a n t Therefore,  across  the f u l l  range of F as shown i n F i g u r e 2 ( b ) .  any i n c r e a s e i n t h e s t a t i c  only to increases i n the contact  f r i c t i o n c o e f f i c i e n t would be due  area.  Thus, the problem i s t o determine U type of v i s c o e l a s t i c d e f o r m a t i o n and  (gross  expected.  g  i n terms of 6 g i v e n the  The f o l l o w i n g d e f i n i t i o n s  f u n c t i o n s a r e used f o r both t h e K e l v i n - V o i g t  and g e n e r a l  linear  s o l i d models:  -JL  A °  P  m  •  F  F  y  s  f N  final N  h  a ( t ) = f t = X o  a  =  f  T  q  F _linal A  o  =  f Ft _ f A  o  o  = shear s t r e n g t h per u n i t a r e a o f t h e i n t e r f a c e ....  The  criterion for failure T  o  (gross s l i p p i n g )  (1)  is:  A (1 + e ( t , ) ) = F t o t r  .... (2)  For a l i n e a r v i s c o e l a s t i c body under g e n e r a l l o a d i n g , e ( t ) i s found u s i n g an h e r e d i t a r y i n t e g r a l i n t h e f o l l o w i n g form [ 3 1 ] :  20  f  e ( t ) = a ( t ) J(O) +  a  (  t  >  dJ(t-t') dt' d(t-t')  (3)  •'O where J ( t ) , the creep compliance, i s the s t r a i n per u n i t a r e a due to the a p p l i e d a p p l i e d u n i t s t r e s s .  I t describes  c o m p l e t e l y the s t r e s s - s t r a i n  b e h a v i o u r o f a g i v e n m a t e r i a l up t o the f a i l u r e  3.2.1  Kelvin-Voigt  point.  Body  For a 2-parameter s o l i d , where the v i s c o e l a s t i c i t y i s represented  by a s p r i n g and dashpot, i f k i s t h e e l a s t i c modulus o f  the s p r i n g member and c i s t h e v i s c o s i t y of t h e dashpot, t h e creep compliance i s : k  The  ratio  c/k i s c a l l e d  t h e r e t a r d a t i o n time f o r a K e l v i n - V o i g t  A f t e r s u b s t i t u t i n g equation  (4)  i s found t h a t t h e i n c r e a s e d  area  A  Q  ...  1 - e  J(t) =  (3)  into equation  f  t,  k  k c  fc  (1),  u  g  i s obtained  and i n t e g r a t i n g , i t  f  (5)  I-  z  From t h e f a i l u r e c o n d i t i o n i n e q u a t i o n in  body.  at s l i p i s :  k t ^ - c + ce  e(t ) =  (4)  ( 2 ) and t h e i d e n t i t i e s  as a f u n c t i o n o f 0 and t h e p h y s i c a l  properties  T , p of the i n t e r f a c e : o m k  — p  m  u =  (6) f u r t h e r , i t i s found  that:  +  -  s  (6)  0  k  In examining e q u a t i o n 1)  s 1  1 - e  + e£  y  the u  s  - 0 c u r v e e x h i b i t s upper and lower  asymptotes  21  c o r r e s p o n d i n g t o v e r y s m a l l and v e r y l a r g e v a l u e s of 6 respectively. T P  o  m  The upper asymptote i s :  r y  k - T  s  o  w h i l e t h e lower asymptote  max. is y  . s mm.  = (T /p ) . o m  These  v a l u e s a r e i n d e p e n d e n t o f t h e v i s c o s i t y parameter c.  2) i f c changes, t h e r e t a r d a t i o n time, c/k, changes and t h e y  v s 0 c u r v e may  s  but  be s h i f t e d  to the r i g h t  or to the  i t remains between t h e b o u n d a r i e s d e s c r i b e d b y  left, the  upper and lower a s y m p t o t e s : T lower asymptote:  — p  o  = y  s  . mm.  and  upper asymptote:  k T — — r r — ^ r y = V p (.k — i ; s m " c  T n o v  max  3) i f t h e r e i s no v i s c o s i t y c/k -> 0 and t h e y becomes a s t r a i g h t From (T  o  (5),  l i n e l y i n g on t h e upper  the growth i n a r e a i s A  /k) i n t h i s c a s e .  q  e(t) =  g  vs 9 curve asymptote.  (a^/k) =  The g e n e r a l form o f t h e y  s  vs 0  c u r v e w h i c h t h i s model p r e d i c t s f o r a v a l u e o f c/k > 0 is  3.2.2  shown i n F i g u r e  3-parameter For  5.  General Linear  a 3-parameter  Solid  s o l i d where k^,  m e t e r s , and c i s t h e v i s c o s i t y parameter compliance i s [31]:  k^ a r e t h e e l a s t i c  para-  (see. F i g u r e 4 ( b ) ) , t h e c r e e p  22  r J(t) =  _  k  1  k  +  k  l  i  k i k2 +  k  r  _t c  2.  1 k-,  +  2  _ 1 - e  k  \  i  i2 k  +  .  k  _t c  2  (7)  k  The  ratio  l  +  k  identities  c i s known as t h e r e l a x a t i o n time.  l 2 e q u a t i o n (7) i n t o k  stituting  2  After  sub-  k  ( 2 ) , t h e f a i l u r e c o n d i t i o n , and u s i n g the  given i n (1), the U  v s 0 c u r v e has t h e form:  g  s k  m  1  k  +  k  where:  T  =  l k  This U  •  g  +  k  l  k  - 1  +  1 - e 2  (8)  2  2  v s 0 c u r v e a l s o has an upper and lower asymptote f o r  •  •  0 << 1 and 0 »  1.  A l s o , i t has the same g e n e r a l shape as t h e y  curve f o r t h e 2-parameter  Kelvin-Voigt  t h i s model, t h e upper asymptote  s o l i d shown i n F i g u r e 5.  i s determined by k^, T  q  and p^ as  follows: from  (8) f o r 0 «  s max.  The lower asymptote, J  r  u . "s min.  i s a l s o found from k  s Note t h a t i f k„ » 2  mm.  1:  k, - T 1 o  m  m  k  1  1  T , then y o s min.  +  g  1  +  k  k  9  ~  2  2  T  „  o  (8) f o r  »  1:  vs 0 In  23  The Non-dimensional y  3.3  .  s  vs T * P l o t  C o n s i d e r a t i o n of the r o l e of c and k^, U  g  -  k^ i n d e t e r m i n i n g  the  8 curve l e a d s to the f o r m a t i o n of a more g e n e r a l p r e d i c t i o n of  static friction  results.  I f the upper and varied models.  lower asymptotes were f i x e d and  i n d e p e n d e n t l y , a f a m i l y of u This i s i l l u s t r a t e d  c  was  vs 0 curves would r e s u l t f o r b o t h  g  i n F i g u r e 6.  I t i s now  obvious  t h a t by  making the a b s c i s s a , 0, d i m e n s i o n l e s s the f a m i l y of curves w i l l c o l l a p s e onto a s i n g l e g e n e r a l c u r v e , u  vs x *. S  I f t h i s reasoning i s applied  j  to the p r e s e n t study, i t i s obvious  t h a t i f the t e s t  interfaces  do •  f o l l o w one of the v i s c o e l a s t i c  laws of d e f o r m a t i o n , and  the u  -  0  s curves a l l have the same upper and  lower asymptotes but d i f f e r e n t  t i o n times, then the e x p e r i m e n t a l l y determined  u  g  -  relaxa-  0 v a l u e s must  fall  on t h i s g e n e r a l c u r v e . I f the upper and  lower asymptotes a r e s e t a t the g e n e r a l  v a l u e s x and y r e s p e c t i v e l y , then e q u a t i o n  (6) becomes:  f o r the K e l v i n - V o i g t - P r a n d t l s o l i d :  k ^s and  equation  (8)  e  c  1 - e  a +  + b u  s  = 0  (9)  becomes f o r the g e n e r a l l i n e a r s o l i d - P r a n d t l model: y„  s  a +  k  where:  8x  1 - e  0T  T  =  J  l k  From (9) and  +  l  k  k  I + b u  s  =0  .  2  2  (10), i t i s o b v i o u s t h a t a f a m i l y of y  g  vs  (10)  24  curves r e s u l t s g i v e n d i f f e r e n t c/k r a t i o s ) .  c values  (and t h e r e f o r e d i f f e r e n t x  Furthermore, t h i s f a m i l y of curves c o l l a p s e s to a  g e n e r a l y^ - x^*  curve  and  single  by:  1) m u l t i p l y i n g 9 by c/k  f o r the K e l v i n - V o i g t - P r a n d t l  solid; 2) m u l t i p l y i n g 0 i n the g e n e r a l l i n e a r s o l i d - P r a n d t l model case by  x.  Then, f o r example, i n the g e n e r a l l i n e a r s o l i d data f o r i n t e r f a c e s having X v a l u e s should y ,6 s  •  r  3.4  the same asymptotes x and  case, a l l  y but  different  c o l l a p s e i f the d a t a a r e p l o t t e d , not on the u s u a l  axes but on y , x„* ^s 3  axes where x~* 3  * = X0 as shown i n F i g u r e  7.  Changing the R e l a x a t i o n Time of an I n t e r f a c e The  q u e s t i o n now  a r i s e s as to whether or not  the p r o p e r t i e s  of an i n t e r f a c e can be changed so as to change i t s r e l a x a t i o n or d a t i o n time. the r h e o l o g y  Very l i t t l e  i s known about how  of the a i r / s o l i d  interface.  retar-  o r g a n i c compounds a f f e c t  In c o n t r a s t , the e f f e c t  of  t h e s e compounds on the s u r f a c e v i s c o s i t y o f the a i r / w a t e r i n t e r f a c e i s w e l l known.  A g r e a t d e a l of e x p e r i m e n t a l  data has been p u b l i s h e d  along w i t h a l i m i t e d amount of t h e o r e t i c a l work [47].  Although  the  a v a i l a b l e data must be i n t e r p r e t e d w i t h c a r e because of c e r t a i n e x p e r i mental v a r i a t i o n s i n the s u r f a c e v i s c o s i t y measurements and e x t r a p o l a t i n g i n f o r m a t i o n gained solid  systems has  by  limited validity,  g e n e r a l c o n c l u s i o n s from t h i s work. and  their metallic a) The  because'  s t u d y i n g a i r / w a t e r systems to a i r / i t i s p o s s i b l e to draw s e v e r a l Considering only c a r b o x y l i c acids  soaps:  s u r f a c e v i s c o s i t i e s of c a r b o x y l i c a c i d monolayers  25  such as s t e a r i c a c i d and o l e i c a c i d a r e o n l y Newtonian.  They have been shown t o e x h i b i t a s m a l l amount  of v i s c o e l a s t i c i t y a t s u r f a c e p r e s s u r e s dynes p e r cm [ 4 5 ] . spread  approximately  Kimizuka  [32]  greater  t h a n 20  found t h a t s t e a r i c a c i d  on an a c i d i c subphase (T = 20°C, a r e a p e r m o l e c u l e  o  20.5  A ) behaved a s a V o i g h t 2  s o l i d having  an a p p a r e n t  sur-  f a c e v i s c o s i t y , n , o f 0.13 gm p e r second, and a s u r f a c e -3 g  s h e a r modulus, G, o f 8.4 x 10 The pressure,  surface rheology  dynes p e r cm.  i s sensitive to surface  t e m p e r a t u r e , pH and t h e c a t i o n c o n t e n t  s u b s t r a t e a s w e l l a s shear .rate. kept constant  of the  I f these v a r i a b l e s a r e  and t h e c h a i n l e n g t h o f t h e o r g a n i c  i s i n c r e a s e d , then t h e s u r f a c e v i s c o s i t y ,  species  (as one measure  o f f i l m p r o p e r t i e s ) would b e e x p e c t e d t o i n c r e a s e b e c a u s e of increased i n t e r c h a i n cohesion. Gaines  [45]  supports  Experimental  t h i s statement.  data  from  Palmitic acid _3  (C^^ H^^ COOH) h a s a s u r f a c e v i s c o s i t y o f 1.8 x 10 per  second,  while  has  gm  (25°C, ir = 15 dynes p e r cm, 0.01 N a c i d )  i t s C^Q homologue, C^g H^^ COOH ( a r a c h i d i c a c i d ) , -2  a s u r f a c e v i s c o s i t y 15 times a s l a r g e (3 x 10  p e r second) a t t h e same t e m p e r a t u r e and s u r f a c e The  e f f e c t of t h e double  pH = 2.0) has n  pressure.  [ - c = c - ] bond o r o f  s i d e c h a i n s would be t o d e c r e a s e t h e s u r f a c e O l e i c a c i d , f o r example  gm  viscosity.  (TT = 15 dynes p e r cm, 1 7 ° C , -4  = 1.43 x 10  gm p e r second  compared  -3 t o 1.5 x 10  gm p e r second f o r s t e a r i c a c i d under  similar conditions.  The p r e s e n c e o f t h e e i s - d o u b l e bond  26  i s r e s p o n s i b l e f o r the s i g n i f i c a n t l y decreased b) More i n t e r e s t i n g t o t h i s study i o n s on s u r f a c e r h e o l o g y  viscosity.  i s the e f f e c t of metal  at the water/air i n t e r f a c e .  Depending on pH of t h e s u b s t r a t e and t h e m e t a l i o n con3+ t e n t , t h e e f f e c t can be marked.  Adding A l  t o an a c i d i c  s u b s t r a t e a t pH = 5.5 (T = 35°C) causes s t e a r i c a c i d f i l m s to assume n e a r - s o l i d p r o p e r t i e s . s t r e s s e s has been a n a l y z e d  T h e i r response t o shear  i n terms of a 4-parameter v i s -  c o e l a s t i c model [40] by Motomura and Matuura.  I f the o  a r e a p e r m o l e c u l e i s kept a t a p p r o x i m a t e l y  33 A, t h e  measured v a l u e s of t h e B u r g e r ' s body a r e of t h e order of n^,  n^ = 5 x 10^ gm per second,  G^ = 100 gm p e r second, of t h e V o i g t  = 500 gm per second,  where n^, G^ a r e the parameters  element o f t h i s 4-parameter model.  a p p r o p r i a t e pH v a l u e s , o t h e r  i o n s such as Ca  At  , Ba  give  m e t a l s t e a r a t e f i l m s which a r e known to behave as K e l v i n I |  3"f  V o i g h t b o d i e s w h i l e Fe  , Cu  j|  , Ca  give stearate films  which have t h e c h a r a c t e r i s t i c s of Maxwell b o d i e s . i o n s , N a , K , NH^ +  +  +  do not form s o l i d i f i e d  Some  f i l m s with  f a t t y a c i d s under these c o n d i t i o n s [ 4 7 ] . A f u r t h e r c o m p l i c a t i o n o f soap f o r m a t i o n  i n monolayers i s  t h a t the a b i l i t y of m e t a l i o n to form a v i s c o u s s o l i d i f i e d an o r g a n i c a c i d i s dependent on s t e r i c f a c t o r s [ 3 5 ] . example, has n e a r l y t h e same m o l e c u l a r  Ca  molecules.  i o n s from forming  with  Oleic acid, f o r  weight and c h a i n l e n g t h as  s t e a r i c a c i d but the p r e s e n c e o f t h e double bond a t the C prevents  film  a complex network w i t h  Q  position  the o l e i c acid  Thus, i t would be expected t h a t , u n l i k e s t e a r i c a c i d ,  27  which w i l l form a h i g h l y s t r u c t u r e d s o l i d - l i k e soap f i l m w i t h Ca  ions,  the v i s c o s i t y o f o l e i c a c i d monolayers would be r e l a t i v e l y u n a f f e c t e d -Hby Ca  i o n s even though soap f o r m a t i o n s t i l l  takes p l a c e .  [ 3 6 ] confirms t h i s expectation.  Deamer and C o r n w e l l  The work o f  E a r l i e r work by  [ 3 5 ] shows t h a t e t h y l groups i n t h e a - p o s i t i o n s o f b r a n c h e d  Durham  c h a i n f a t t y a c i d s may a l s o p r o v i d e enough s t e r i c h i n d r a n c e f i l m s o l i d i f i c a t i o n by Ca It i s d i f f i c u l t present  ions. t o a p p l y these o b s e r v a t i o n s d i r e c t l y  s i t u a t i o n where m o n o l a y e r s o f m e t a l l i c  the s o l i d  to impair  to the  soaps a r e d e p o s i t e d o n  s u r f a c e and then t e s t e d f o r f r i c t i o n p r o p e r t i e s .  However, i t  i s p o s s i b l e t o draw some g e n e r a l c o n c l u s i o n s s i n c e i t i s e x p e c t e d  that -  the deposited  monolayers w i l l r e t a i n t h e same i n t e r n a l s t r u c t u r e a s  they possessed  at the air/water i n t e r f a c e .  expected  T h e r e f o r e , i t i s t o be  that the y ^ - 6 curve f o r the l e s s v i s c o u s Ca-oleate  w i l l l i e to the r i g h t of the corresponding  film  curves f o r C a - s t e a r a t e  because t h e r e l a x a t i o n time f o r a C a - o l e a t e monolayer s h o u l d be s m a l l e r than t h a t o f C a - s t e a r a t e . P r e d i c t i n g the r e l a t i v e p o s i t i o n s of the f i l m s o f t h e s t e a r i c and  oleic acid  soaps d e p o s i t e d a t pH 4 i s more d i f f i c u l t  r h e o l o g i c a l information i s scarce. t h a t a t low pH v a l u e s  S p i n k and Sanders [41] have shown  (pH = 2.7) b a s i c i r o n h y d r o x i d e  aqueous s u b s t r a t a w i l l form s o l i d i f i e d  a s no Fe i o n s were d e l i b e r a t e l y added.  detailed  i n f o r m a t i o n on s u r f a c e r h e o l o g y  soaps was a v a i l a b l e friction  results.  i o n s i n the  f i l m s with f a t t y a c i d s .  the p r e s e n t work, t h e source o f i r o n c o n t a m i n a t i o n itself  as r e l e v a n t  In  i s t h e specimen  U n f o r t u n a t e l y , no  f o r e i t h e r of the b a s i c  so t h a t i t was not p o s s i b l e t o p r e d i c t  iron  the s t a t i c  28  3.5  The  E f f e c t of Temperature on T From p r e s s u r e - a r e a  (IT - A)  Values c u r v e s and  from the s u r f a c e v i s -  c o s i t y s t u d i e s o f numerous m o n o l a y e r s , i t i s w e l l known t h a t temperat u r e changes d r a m a t i c a l l y a f f e c t  the s t r u c t u r e and  the  p r o p e r t i e s of monolayers a t t h e a i r / w a t e r i n t e r f a c e .  rheological Furthermore,  e a r l y work i n the f r i c t i o n and wear a r e a c l e a r l y i n d i c a t e d  that increases  i n t e m p e r a t u r e s e r i o u s l y i m p a i r t h e e f f e c t i v e n e s s of m o n o l a y e r s as lubricants. breaks  At c e r t a i n c h a r a c t e r i s t i c  down c o m p l e t e l y Direct  b e e n o b t a i n e d by [49].  temperatures,  lubrication  [3].  i n f o r m a t i o n on t h e s t r u c t u r e of d e p o s i t e d f i l m s e l e c t r o n microscopy  F i l m s of f a t t y a c i d  and  has  electron d i f f r a c t i o n studies  soaps have a d e f i n i t e s t r u c t u r e and  the  e f f e c t of r a i s i n g t h e temperature i s t o d e s t r o y t h e o r d e r i n the For  example, e l e c t r o n d i f f r a c t i o n p a t t e r n s w i l l f a d e a s t h e  t u r e o f t h e sample i s r a i s e d b e c a u s e t h e m o l e c u l e s ( t h e monolayer "melts")  film.  tempera-  become d i s o r i e n t e d  and b e c a u s e some v a p o r i z a t i o n o c c u r s .  More e x t e n s i v e s t u d i e s of s u r f a c e d i f f u s i o n have shown t h a t molecules  of a d e p o s i t e d f i l m a r e c a p a b l e  s t r a t a i f the temperature i s h i g h enough.  o f moving o v e r a s o l i d Molecules  from s t e a r i c a c i d f i l m s d e p o s i t e d on m i c a s h e e t s over  of s t e a r i c  [48] can  t h e s u r f a c e even a t room t e m p e r a t u r e and a t h i g h e r  subacid  diffuse  tempera-  t u r e s they w i l l move w i t h r e l a t i v e freedom a c r o s s t h e s u r f a c e .  The  a c t i v a t i o n energy f o r the s u r f a c e d i f f u s i o n has been measured a t 8.6 cal/gm atom compared to a v a l u e of 21 K cal/gm atom f o r d e s o r p t i o n o f s t e a r i c a c i d from One  platinum.  r e s u l t of s u r f a c e d i f f u s i o n a t h i g h e r temperatures  i l l u s t r a t e d by an experiment i n which a m i c a s u r f a c e , c o v e r e d  is  with  a  K  29  s t e a r i c a c i d monolayer, f o r 30 minutes  [48].  was h e a t e d to 35°C and h e l d a t t h a t  The i n c r e a s e d  temperature  t h e r m a l a g i t a t i o n c o u p l e d w i t h the  e l a p s e d time, e n a b l e d a s i g n i f i c a n t number o f m o l e c u l e s t o l e a v e t h e i r o r i g i n a l p o s i t i o n s i n t h e f i l m and to m i g r a t e a c r o s s t h e s u r f a c e and accumulate  i n shallow s c r a t c h e s i n the s u r f a c e . How would  U  g  small i n c r e a s e s i n s u r f a c e temperature a f f e c t t h e  - 9 c u r v e s f o r monolayer  covered s t e e l  surfaces?  C o n s i d e r i n g e q u a t i o n s (9) and ( 1 0 ) , p^, t h e mean y i e l d p r e s s u r e o f t h e i n t e r f a c e i s e s t a b l i s h e d by t h e s u b s t r a t u m and i s a p p r o x i m a t e l y e q u a l t o 3Y, where Y i s t h e y i e l d p o i n t o f t h e s u b s t r a t u m . o f m i l d s t e e l i s a f f e c t e d by h i g h temperature b u t remains  The h a r d n e s s c o n s t a n t up  t o a t l e a s t 200°C, so t h a t p ^ would be u n a f f e c t e d by s m a l l  temperature  changes.  T , the shear s t r e n g t h o f the i n t e r f a c e , which  p  a l s o remain a t a p p r o x i m a t e l y i t s room t e m p e r a t u r e v a l u e f o r  m >  would  s m a l l temperature  i s r e l a t e d to  increases.  The r e l a x a t i o n o r r e t a r d a t i o n t i m e , T, o f a v i s c o e l a s t i c m a t e r i a l i s , however, s t r o n g l y i n f l u e n c e d by t e m p e r a t u r e so t h a t T = x(T).  G e n e r a l l y , x decreases with i n c r e a s i n g temperature.  m e n t a l work [27] has shown t h a t materials  Experi-  the r e l a x a t i o n time o f v i s c o e l a s t i c  obeys: l o g x ( T ) = - 3T + a  (11)  so t h a t ,  JL x(T) = a e  (12)  B T  F u r t h e r t h e o r e t i c a l work [47] has i n d i c a t e d E  that: •  a  RT X(T) = Ae  (13)  30  where E  a  i s a c h a r a c t e r i s t i c a c t i v a t i o n energy and R i s t h e g a s c o n s t a n t  approximately,  2 cal/mole.  Therefore,  modified using  (13) t o g i v e a g e n e r a l u  equations  (9) and (10) c a n be  - 6 - T relationship.  r e l a t i o n s h i p w i l l be v a l i d o n l y f o r a l i m i t e d  This  temperature r a n g e b e c a u s e  o f phase changes i n t h e monolayer and d e s o r p t i o n . U n f o r t u n a t e l y , most o b s e r v a t i o n s o f t h e f r i c t i o n - t e m p e r a t u r e r e l a t i o n s h i p y i e l d very l i t t l e extended t o c o v e r  specific  q u a n t i t a t i v e i n f o r m a t i o n t h a t c a n be  f r i c t i o n c o u p l e s b u t some g e n e r a l  effects  a r e known: (1) I f t h e m e t a l l i c s u b s t r a t u m  i s s u f f i c i e n t l y r e a c t i v e , then  a m e t a l l i c soap w i l l be formed when t h e monolayer i s deposited.  As t h e temperature i s r a i s e d , t h e f r i c t i o n  c o e f f i c i e n t remains r e a s o n a b l y tum  reaches  constant u n t i l  the s u b s t r a -  a temperature which i s a p p r o x i m a t e l y  the b u l k m e l t i n g p o i n t o f t h e m e t a l l i c soap. p o i n t , the f r i c t i o n  At this  c o e f f i c i e n t w i l l i n c r e a s e by a f a c t o r  of about 10 and t h e r e i s a c o r r e s p o n d i n g s u r f a c e damage.  equal t o  increase i n  T h i s i n d i c a t e s a phase change i n t h e  monolayer and thus would i n d i c a t e t h a t t h e v i s c o e l a s t i c model may no l o n g e r be v a l i d . (2) I f t h e substratum  i s u n r e a c t i v e o r a monolayer o f a  m e t a l l i c soap i s d e p o s i t e d w i t h o u t the f r i c t i o n  coefficient  strong adhesion,  shows a v e r y l a r g e i n c r e a s e when  the temperature o f the substratum  reaches  the b u l k  point of the a c i d or the deposited m e t a l l i c  soap.  a l s o r e p o r t s t h a t temperature e f f e c t s i n t h i s range a r e r e v e r s i b l e .  then  melting Bowden  temperature  T h i s i n d i c a t e s a phase change i n  31  the  monolayer and not d e c o m p o s i t i o n .  At h i g h e r  tempera-  t u r e s , though, d e s o r p t i o n o f t h e monolayer o c c u r s and the  friction coefficient w i l l  remain h i g h even i f t h e  temperature i s l o w e r e d .  O b v i o u s l y t h e n the  - 6 - T r e l a t i o n s h i p developed i s  a p p l i c a b l e o n l y t o temperature ranges below the m e l t i n g p o i n t o f t h e monolayer.  32  IV.  4.1  EXPERIMENTAL APPARATUS AND EXPERIMENTAL PROCEDURE  Apparatus Three main p i e c e s o f equipment were r e q u i r e d f o r t h e i n v e s t i -  gation.  The f i r s t  item  i s a d e v i c e which measures t h e s t a t i c  o v e r a range o f B v a l u e s ,  friction  t h e second p i e c e o f equipment i s t h e vacuum  system and t h e t h i r d i s t h e equipment needed f o r a p p l y i n g m o n o l a y e r s o f o r g a n i c a c i d s to t h e t e s t by  specimens by t h e a b r a s i o n  the Langmuir-Blodgett technique.  technique  The vacuum system and f r i c t i o n  m e a s u r i n g a p p a r a t u s i s shown i n t h e photograph i n F i g u r e  4.1.1  and  8.  Measuring the S t a t i c F r i c t i o n as a Function of 0 The  apparatus f o r measuring y  and 9 i s r e l a t i v e l y  s  simple.  A u n i t was r e q u i r e d w h i c h c o u l d a p p l y , measure and r e c o r d 3 p a r a m e t e r s : N,  t h e normal f o r c e ; F, t h e s h e a r i n g  ( l a t e r a l o r t a n g e n t i a l ) f o r c e and  F the r a t e of a p p l i c a t i o n of the shearing  force.  N and F were a p p l i e d  s e p a r a t e l y by Bimba h y d r a u l i c c y l i n d e r s , and x^ere measured b y r e c o r d i n g the displacement chart  o f c a l i b r a t e d s t r a i n r i n g s on a d u a l c h a n n e l B r u s h  recorder. The  d e s i g n o f t h e complete u n i t was c o m p l i c a t e d  by the r e s t r i c -  t i o n t h a t some o f t h e f r i c t i o n t e s t s had t o be conducted i n vacuum. The  f i n a l design  i s shown i n F i g u r e 9.  because i t r e q u i r e s o n l y one b e l l o w s vacuum system.  This bellows  T h i s d e s i g n was c h o s e n p a r t l y  f e e d t h r o u g h u n i t , B, i n t o t h e  feedthrough,  ment l i n e a r u n i t was s p e c i a l l y c o n s t r u c t e d s h a f t moves f r e e l y  so t h a t the f e e d t h r o u g h  through a 1-1/4" opening i n the mounting  Unlike conventional tance  a 4" d i a m e t e r , 6" d i s p l a c e -  due t o r u b b i n g  flange.  f e e d t h r o u g h u n i t s , t h e r e was no f r i c t i o n a l of the s h a f t a g a i n s t  flange, or a g a i n s t a p o s i t i o n i n g s l e e v e .  resis-  the i n n e r w a l l o f t h e mounting  33  The stationary  samples a r e  and A^ ( s e e F i g u r e  9 ) . A^ i s k e p t  throughout a t e s t as i t i s f i x e d t o a s t a t i o n a r y  bar x-rtvich i s i t s e l f welded t o the b e l l j a r .  support  A^ has a r e s t r i c t e d  amount o f movement i n t h e x, y d i r e c t i o n f o r adjustment p u r p o s e s . A^, t h e upper sample, i s mounted on t h e e x t e n s i o n s h a f t , S, and i s t h e moving specimen.  to the feedthrough  The r e s t o f t h e assembly i s  mounted on a machine t a b l e w h i c h a l l o w s up t o 10" o f x and y movement f o r c o r r e c t l y p o s i t i o n i n g A^ on A^. rigid  The machine t a b l e i s f i x e d t o a  s u p p o r t t a b l e which i s anchored t o a c o n c r e t e  floor.  A^ and A^ a r e l o a d e d t o g e t h e r i n t h e normal d i r e c t i o n by applying  an upward f o r c e W^ a t Y w i t h t h e h y d r a u l i c  Since the bar i s pivoted of  c y l i n d e r H^.  a t X^, A^ i s f o r c e d o n t o A^.  T h e magnitude,  t h i s normal f o r c e , N, i s known as W, i s measured by t h e c a l i b r a t e d  strain ring  and t h e d i m e n s i o n s o f t h e b a r a r e known.  arrangement, i t was p o s s i b l e  With t h i s  t o measure N t o l e s s t h a n 1/2 l b .  Since  N = 50 l b s . , t h e n N c o u l d be measured t o ± 1%. The by  h o r i z o n t a l f o r c e F was a p p l i e d  the hydraulic  c y l i n d e r H^.  m o n i t o r e d by r e c o r d i n g base u s i n g  The magnitude o f F was  the output o f the s t r a i n r i n g  t h e Brush chart r e c o r d e r .  i s c o n t r o l l e d by r e s t r i c t i n g  s e c . w h i c h was s u f f i c i e n t  by  constantly against  a time  The r a t e o f a p p l i c a t i o n o f F, F,  the flow of f l u i d  c y l i n d e r w i t h a Nupro m i c r o v a l v e .  The  t o t h e A^, A^ i n t e r f a c e ,  from t h e h y d r a u l i c  F v a r i e d from  t o c o v e r 6 v a l u e s from  .005 t o 25 l b s . p e r .0001 t o 0.5 s e c .  s t a t i c f r i c t i o n f o r c e , F , was found from t h e F - t c h a r t  f i n d i n g t h e f o r c e a t which F v s t was no l o n g e r  a straight  line.  When t h e F - t c u r v e i s no l o n g e r  a s t r a i g h t l i n e , t h e n A^ i s s l i d i n g  over A .  even a t v e r y s m a l l v a l u e s o f F -  ?  I t i s w e l l known t h a t  34  " m i c r o s l i p " - t h a t i s s l i d i n g movements o f t h e o r d e r o f 10 micro or so - a r e t a k i n g p l a c e b u t F  inches  was d e f i n e d as t h e f o r c e where sudden  a p p r e c i a b l e movement (of a p p r o x i m a t e l y  150 micro inches)  of  over A^  occurs. S i n c e t h e minimum v a l u e of F measured was 10 l b s . and F c o u l d be measured to l e s s than 1/4 l b . , t h e maximum e r r o r i n measuring F was ± 2.5%. The  two s t r a i n r i n g s used to measure N and F were used i n  conjunction with The  output  two E l l i s A s s o c i a t e s Model BAM-1 b r i d g e a m p l i f i e r s .  from t h e a m p l i f i e r s was f e d t o a d u a l channel Brush  recorder  so t h a t N, F, F c o u l d be c o n s t a n t l y monitored d u r i n g each t e s t . c a l i b r a t i o n of t h e r i n g - a m p l i f i e r - r e c o r d e r system was checked a f t e r , and a t 1 hour i n t e r v a l s d u r i n g each s e t o f runs. necessary drift  before,  T h i s was  because t h e BAM u n i t s a r e s u b j e c t t o a c e r t a i n amount o f D.C.  over l o n g p e r i o d s o f time. The  ders  The  hydraulic c i r c u i t  used t o c o n t r o l t h e two Bimba  i s shown s c h e m a t i c a l l y i n F i g u r e 10.  cylin-  The pump, accumulator, and  r e s e r v o i r s e c t i o n of t h e h y d r a u l i c system was i d e n t i c a l to t h a t used by Johannes [19]. type constant pressure  The p r e s s u r e was s u p p l i e d by a t i l t e d  displacement  axis piston-  pump d r i v e n by an e l e c t r i c motor.  r e l i e f v a l v e r e g u l a t e d t h e output  pressure  A  of the pump.  The  pump was used i n t e r m i t t e n t l y to p r e s s u r i z e t h e accumulator which was used on t h e blow-down p r i n c i p l e thus p r o v i d i n g a p u l s a t i o n f r e e of constant tor pressure  pressure  sufficient  f o rseveral tests.  c o u l d be v a r i e d from a p p r o x i m a t e l y  source  S i n c e t h e accumula-  600 to 1500 p s i , the  range of f l o w r a t e s through t h e micro v a l v e s was f a i r l y  extensive.  35  4.1.2  Vacuum System One  e s s e n t i a l part of t h i s i n v e s t i g a t i o n i n v o l v e d s e p a r a t i n g  the f r i c t i o n c h a r a c t e r i s t i c s of the s t e e l i t s e l f f i l m s on t h e s t e e l . would p r e v e n t  Basically, a unit  o x i d a t i o n and  s e v e r a l runs.  The  from those of a d s o r b e d  suitable for this  general contamination  system s e l e c t e d p r o v i d e d  investigation  f o r the d u r a t i o n of  such an e n v i r o n m e n t .  It  a l s o p r o v i d e d an a n a l y s i s o f t h e environment i n the t e s t chamber i n terms o f t h e c o n c e n t r a t i o n of gases r e m a i n i n g  a f t e r t h e d e s i r e d vacuum  has been .achieved. Another primary test  specimens-  The  c o n s i d e r a t i o n was  i n v e s t i g a t i o n thus r a i s e d t h e i n e v i t a b l e  about "what i s a c l e a n s u r f a c e ? " and achieved?".  the p r e p a r a t i o n of s u i t a b l e  "how  questions  can a c l e a n s u r f a c e  be  These q u e s t i o n s w i l l be d i s c u s s e d f u r t h e r i n t h e  Proce-  d u r e s s e c t i o n d u r i n g t h e d e s c r i p t i o n of sample p r e p a r a t i o n s . The  u l t r a - h i g h vacuum system used i n t h i s work was  a l l m e t a l u n i t c a p a b l e o f r e a c h i n g 5 x 10 2 hour bake-out a t 250°C.  ^  vacuum i s produced by T i t a n i u m  T h i s i s an important  due  (atmosphere to  the h i g h and u l t r a  g e t t e r i n g and  p o s s i b i l i t y of organic contamination oils.  t o r r i n 15 h o u r s w i t h  S i n c e the rough pumping  t o r r ) i s produced by c r y o g e n i c pumping and  a bakeable a 10  high  i o n pumping, t h e r e i s no  to. back s t r e a m i n g  o f pumping  consideration i n lubrication-oriented  research. To d e t e r m i n e which gases a r e p r e s e n t when t h e d e s i r e d vacuum l e v e l i s reached spectrometer)  a r e s i d u a l gas  was  p r e s e n c e o f any  purchased.  (RGA)  (a q u a d r u p o l e - t y p e mass  ( T y p i c a l l y i n t e r e s t c e n t r e s on  organic matter.)  mounted on a 2 1/2"  analyzer  The  p r o b e s e c t i o n of t h e RGA  f l a n g e between the sample and  the xras  the i o n pump s e c t i o n .  36  The  RGA  has  a mass range of 1-250  torr p a r t i a l pressure gauge and  as a v e r y  for  Deposition  10  a l s o used as an a c c u r a t e  the RGA  The  pressure  detailed specifica-  form Appendix I .  of Monolayers  o r t h e i r soaps be d e p o s i t e d  on  The  [53].  t h e equipment r e q u i r e d  a c i d soap was  an a d a p t a t i o n  The  d i l u t e s o l u t i o n of o r g a n i c the f r e s h m e t a l was  two  first  acids  different  f o r each  are  technique  formed on  t h e n t r a n s f e r r e d t o the s o l i d s u b s t r a t e .  second t e c h n i q u e employed was Smith and M c G i l l  The  f i r s t method used t h e L a n g m u i r - B l o d g e t t  whereby a monolayer o f an o r g a n i c aqueous s u r f a c e and  t h a t monolayers of o r g a n i c  the s t e e l specimens.  methods o f a p p l y i n g monolayers and  by  a s e n s i t i v i t y of 1 x  sensitive leak detector.  P a r t of the study r e q u i r e d  d e s c r i b e d below.  and  I t was  t i o n s o f t h e vacuum system and  4.1.3  amu  an  The  of a m a c h i n i n g method used  m e t a l s u r f a c e was  machined under a  a c i d i n an i n a c t i v e ( n o n - p o l a r ) s o l v e n t .  exposed by  the c u t t i n g t o o l , the o r g a n i c  As  acid  chemisorbed onto t h e newly machined s u r f a c e to g i v e a m o n o l a y e r coverage.  (a) L a n g m u i r - B l o d g e t t Type F i l m s The  b e s t known method of a p p l y i n g o r g a n i c  s u r f a c e i s the Langmuir-Blodgett technique. e x t e n s i v e l y i n e a r l y f r i c t i o n and it  these f i l m s ,  surfaces  solid  T h i s t e c h n i q u e was  used  wear r e s e a r c h .  i s p o s s i b l e to d e p o s i t monolayers and  c u l e s onto s o l i d  f i l m s to a  Using  m u l t i l a y e r s of o r g a n i c  in a controlled fashion.  t h e i r p r o p e r t i e s , and  s u b s t r a t a have been s t u d i e d  t h i s method,  The  mole-  s t r u c t u r e . of:  t h e i r reactions with m e t a l l i c  i n t e n s i v e l y i n the l a s t  t h a t t h e i r c h a r a c t e r i s t i c s a r e w e l l known.  The  40 y e a r s  [45]  so  technique f o r monolayer  37  d e p o s i t i o n was d e s c r i b e d t h o r o u g h l y by B l o d g e t t i n h e r 1935 paper [ 4 2 ] , D e p o s i t i n g monolayers by t h e L a n g m u i r - B l o d g e t t requires: tum  (a) a s h a l l o w h y d r o p h o b i c  (a " t r o u g h " ) ; (b) h y d r o p h o b i c  liquid  i n the trough;  container f o r the l i q u i d substra-  b a r r i e r s t o sweep t h e s u r f a c e o f t h e  (c) a hand-windlass  withdraw t h e sample smoothly p l a n i m e t e r t o determine  technique  o r l e a d screw arrangement t o  a t c o n s t a n t speed;  (d) a camera and a  t h e t r a n s f e r r a t i o a f t e r d e p o s i t i o n i s complete  (e) waxed t h r e a d t o c o n t a i n t h e monolayer;  (f) a piston o i l to maintain  a c o n s t a n t p r e s s u r e on t h e monolayer d u r i n g d e p o s i t i o n ; (g) r e a g e n t s : a c i d s and bases  t o c o n t r o l t h e pH o f t h e water b a t h , s o l v e n t s , o r g a n i c  a c i d s , s o l u b l e m e t a l s a l t s t o p r o v i d e m e t a l l i c i o n s i n s o l u t i o n ; and (h) thermometer, pH i n d i c a t o r p a p e r s .  The p u r i t y s p e c i f i c a t i o n s o f  t h e r e a g e n t s a r e g i v e n i n Appendix 2.  A l l r e a g e n t s were used a s  r e c e i v e d from t h e s u p p l i e r .  Attempts  at further p u r i f i c a t i o n of small  amounts o f r e a g e n t s o f t e n l e a d t o g r e a t e r c o n t a m i n a t i o n t h a n  originally  existed. The t r o u g h was a 6" x 10" x 2" deep p y r e x c o n t a i n e r , c o a t e d , a f t e r a thorough  c l e a n i n g w i t h chromic  p a r a f f i n wax t o make i t h y d r o p h o b i c .  a c i d and d i s t i l l e d w a t e r , w i t h The sweep b a r r i e r s were  R Plexiglass  .  The l i q u i d  substratum  was d i s t i l l e d  x^ater.  The pH o f  t h e water was c o n t r o l l e d by a d d i n g s u i t a b l e amounts o f HC1 o r NH^OH. M e t a l l i c i o n s ( e . g . , Ca  ) were p r o v i d e d when n e c e s s a r y by a d d i n g t h e  -4 r e q u i r e d amount o f an a p p r o p r i a t e m e t a l l i c  salt  ( e . g . , 10  M CaCO^)-  C o n t r o l l i n g t h e pH was n e c e s s a r y because t h e f i l m c o m p o s i t i o n i s a f f e c t e d by pH.  A c c o r d i n g t o Gaines  formed on an aqueous s u b s t r a t u m  [45], a s t e a r i c a c i d  c o n t a i n i n g Ca  s t e a r a t e o n l y when t h e pH exceeds 7.5.  After  monolayer  i o n s i s 100% Ca t h e water s u r f a c e was  38  cleaned  t h o r o u g h l y by  sweeping i t w i t h t h e b a r r i e r s , t h e sample  p l a c e d i n the t r o u g h below the water s u r f a c e and t h r e a d was  c a r e f u l l y p l a c e d on t h e s u r f a c e .  t h e waxed c o t t o n  A few d r o p s o f t h e 10 ^ M  o r g a n i c acid-n-hexane s o l u t i o n were then p l a c e d i n the area.  The n-hexane-organic a c i d  water s u r f a c e and  thread-enclosed  s o l u t i o n spread r a p i d l y on t h e c l e a n  exerted a p r e s s u r e a g a i n s t the c o n f i n i n g t h r e a d .  S i n c e t h e hexane was  volatile,  i t evaporated  i n a few m i n u t e s t o l e a v e  a p a r t i a l monolayer f l o a t i n g on the s u r f a c e . oil  The a d d i t i o n of a p i s t o n  (such as o l e i c a c i d ) p l a c e d o u t s i d e t h e t h r e a d caused  the f i l m  c o n t r a c t as t h e o i l compressed t h e t h r e a d e n c l o s e d a r e a x^ith a p r e s s u r e c h a r a c t e r i s t i c of each p i s t o n o i l (measured as 29.7 cm  a t pH = 4.0  for oleic acid).  Each m o l e c u l e  the p i s t o n o i l separated  w i t h i n the t h r e a d b a r r i e r . and  then the sample was  l e a d screw d e v i c e was  The  s l o w l y drawn upwards through  then  thread  confined  a r e a of the monolayer was  recorded  the f i l m .  A  used t o withdraw the sample so t h a t the f i l m  e v e n l y d e p o s i t e d as a monolayer f i l m w i t h o u t  "steps".  the s u r f a c e of  I t has been shown [45] t h a t t h e monolayer d e p o s i t s  on the specimen so t h a t the g e o m e t r i c a l a r e a of t h e specimen i s The  f i l m thus b r i d g e s the l o c a l  topography of t h e s u r f a c e .  s t r e n g t h of most f i l m s i s so g r e a t t h a t Bilcerman d e p o s i t monolayers onto a f i n e w i r e g r i d . ) t h e specimen, t h e a r e a of the monolayer l e f t decreased. of  to c o v e r  the new  itself covered.  (The  cohesive  a b l e to  the withdrawal  of  on the s u r f a c e p r o p o r t i o n a l l y  However, as more water s u r f a c e was  the p i s t o n o i l spread  [51] was  During  was  Accidental  s t o p s o r j e r k s g i v e a d i s c o n t i n u o u s f i l m t h i c k n e s s over the sample.  dynes p e r  The waxed  from the monolayer w h i c h was  to  constant  i n the monolayer  o c c u p i e d a known a r e a a t a g i v e n temperature [ 4 5 ] . kept  was  exposed, p a r t of t h e  a r e a so t h a t a  constant  lens  39  p r e s s u r e was was  m a i n t a i n e d on the f i l m .  some a s s u r a n c e t h a t  a c r o s s the sample.  Because of t h e p i s t o n o i l t h e r e  the monolayer was  By measuring  uniform i n p r o p e r t i e s  the a r e a o f the f i l m r e m a i n i n g on  water s u r f a c e a f t e r d e p o s i t i o n was  complete  and by comparing  the  the  d i f f e r e n c e between the o r i g i n a l a r e a and f i n a l a r e a to the g e o m e t r i c a l a r e a of the sample, i t was coverage.  p o s s i b l e to determine  T h i s f i g u r e i s a rough g u i d e t o t h e s u c c e s s o r f a i l u r e o f  the deposition.  O n l y t h o s e samples h a v i n g t r a n s f e r r a t i o s o f 1 ±  were a c c e p t e d f o r f r i c t i o n sample was  a i r dried  p h e r i c p r e s s u r e and  tests.  f o r 15-20  A f t e r t r a n s f e r was  minutes  and i t was  D e p o s i t i o n by t h e A b r a s i o n  A monolayer t r a n s f e r r e d from a an a r t i f a c t  will  and may  be q u i t e d i f f e r e n t  dimensions.  t h e n t e s t e d a t atmos-  Technique  water s u r f a c e t o a s o l i d i s  from a monomolecular  film  on a s c a l e l a r g e r t h a n m o l e c u l a r  I t i s much more l i k e l y t h a t t h e m a c h i n i n g  by Smith and A l l e n  [52] and  Smith and M c G i l l  t i o n mechanism o f a l o n g c h a i n f a t t y a c i d from a n o n - p o l a r h y d r o c a r b o n  Langmuir-Blodgett  technique  developed  [53] t o s t u d y t h e a d s o r p -  ( e . g . , n-nonadecanoic  ( e . g . , c y c l o h e x a n e ) more c l o s e l y  l a t e s actual f i l m formation conditions during f r i c t i o n  acid) simu-  t e s t s than  the  t r a n s f e r method.  A machining/abrasion generate a f r e s h metal  tion.  the  from s o l u t i o n o r from t h e gas phase s i n c e t h e s o l i d s u r f a c e  always have a s u r f a c e roughness  exposed  complete,  .05  temperature.  (b) Monolayer  adsorbed  the extent of monolayer  t e c h n i q u e r e q u i r e s equipment t h a t  s u r f a c e under the s o l u t i o n so t h a t  newly-  m e t a l atoms a r e a c c e s s i b l e t o t h e p o l a r component of t h e W h i l e Smith and M c G i l l used n-nonadecanoic  acid  will  solu-  i n cyclohexane  as the s o l u t i o n and a p l a n i n g - t y p e c u t t i n g machine f o r g e n e r a t i n g a  AO  f r e s h s u r f a c e , i n t h e p r e s e n t work s t e a r i c a c i d was  used as t h e a d s o r b a t e , n-hexanes as the s o l v e n t and  c u p - b r u s h was  used  Prior the samples  to generate the f r e s h  to immersion  were w i r e - b r u s h e d  in air.  samples  acid-n-hexanes  f o r 2 minutes  were i m m e d i a t e l y  t o an a d s o r p t i o n r u n .  placed i n the s t e a r i c  i n the s o l u t i o n , r i n s e d  then t e s t e d a t atmospheric p r e s s u r e .  [ 5 3 ] spend  l a y e r was  formed.  i n p u r e n-hexane, The  c o n s i d e r a b l e t i m e and e f f o r t  air-dried,  q u e s t i o n a r i s e s as t o Smith, and  d e t e r m i n i n g i f a mono-  They a l s o showed t h a t t h e o r g a n i c a c i d was  s o r b e d on " r e a c t i v e " s u r f a c e s and  that the net r e a c t i o n  Fe + 3 H ( S t ) -> F e ( S t ) where ( S t )  acid-n—  the s o l u t i o n f o r 5 minutes,  t h e e x i s t e n c e o f a monolayer f o l l o w i n g t h i s t r e a t m e n t . McGill  solution,  used p r i m a r i l y t o remove a l a y e r o f  hexane s o l u t i o n and were w i r e - b r u s h e d under left  wire  O b v i o u s l y , t h e s e s u r f a c e s were  l o o s e l y adhering metal oxide s c a l e , p r i o r The  a rotating  surface.  i n the s t e a r i c  o x i d i z e d b u t t h i s t e c h n i q u e was  and  (n-octadecanoic acid)  3  +  |-H  chemi-  was:  2  r e p r e s e n t s t h e s t e a r a t e i o n ( C ^ y H^,. COO)  .  They demon-  s t r a t e d t h a t t h e m e c h a n i c a l a c t i v a t i o n energy which was  supplied  s u r f a c e by c u t t i n g o r b r u s h i n g , a s s i s t e d  Thus, a l t h o u g h  an e v a l u a t i o n o f the f r e e energy might  show t h a t  than s i l v e r ,  involved,  they found t h a t  F u r t h e r m o r e , based  energy).  Even though  the r e a c t i o n  may acti-  F o r m e t a l s more e l e c t r o p o s i -  the c o r r e s p o n d i n g m e t a l l i c  soap  was  on t h e a p p a r e n t a r e a of m e t a l s u b s t r a t e  the amount of soap formed was  of c o v e r a g e .  reaction  can be s u p p l i e d by t h e m e c h a n i c a l  v a t i o n energy -(the Kramer e f f e c t  formed.  change d u r i n g t h e p r o p o s e d  the r e a c t i o n i s not spontaneous,  p r o c e e d i f t h e energy r e q u i r e d  tive  the r e a c t i o n .  to the  sufficient  t o g i v e a monolayer  t h i s method more c l o s e l y r e p r e s e n t s a c t u a l  41  f r i c t i o n c o n d i t i o n s , i t had some shortcomings p r e s e n t work s i n c e m e t a l l i c soaps such as  f o r t h e purposes  calcium or  barium  of the stearate  c o u l d n o t be p l a c e d on the s t e e l s u r f a c e .  4.2  P r e t e s t P r e p a r a t i o n of Samples The  samples were a l l C 1020 s t e e l , annealed  a t 1600°F,  then,  s a n d - b l a s t e d t o remove t h e o x i d e s c a l e formed d u r i n g t h e a n n e a l .  The  s u r f a c e s were then ground g i v i n g a s u r f a c e roughness o f 17 y i n s . CLA. A f t e r g r i n d i n g , t h e samples were v a p o r - d e g r e a s e d t o remove r e s i d u a l m a c h i n i n g treatment,  o i l and l o o s e d i r t .  t h e s u r f a c e s were w i r e - b r u s h e d .  have g e n e r a t e d  with T r i c l o r o e t h y l e n e A f t e r the degreasing  T h i s procedure  should  a new o r g a n i c - f r e e s u r f a c e and t h e w i r e - b r u s h i n g  roughened  t h e s u r f a c e so t h a t , a c c o r d i n g to t h e work o f Greenwood and W i l l i a m s o n [ 7 ] , t h e c o n t a c t w i l l be p l a s t i c .  The roughness o f t h e s u r f a c e s a f t e r  w i r e - b r u s h i n g was 50 y i n s . CLA.  4.2.1  Vacuum F r i c t i o n  Tests  F o l l o w i n g the w i r e - b r u s h i n g , specimens t o be t e s t e d i n t h e vacuum were q u i c k l y t r a n s f e r r e d commenced. minutes;  A p r e s s u r e of. 10  -3  to t h e chamber and t h e pumpdown was t o r r was a c h i e v e d i n a p p r o x i m a t e l y  10 ^ t o r r a f t e r 1 h o u r .  30  F o r t h e r e s u l t s g i v e n i n F i g u r e 12,  —8 t h e t e s t p r e s s u r e of 2 x 10 12 h o u r s . the t e s t  t o r r was reached  after  approximately  V e r y l i t t l e bakeout was needed so t h a t t h e temperature s u r f a c e s never  exceeded 100°F.  of  An a n a l y s i s o f t h e r e s i d u a l  gas a t t h i s p r e s s u r e showed t h a t the p r i n c i p a l r e s i d u a l gases were hydrogen, h e l i u m , water vapour, and n i t r o g e n . v e r y low (a p a r t i a l p r e s s u r e o f 5 x 10 content.  The oxygen c o n t e n t  t o r r ) , as was t h e  The t e l l - t a l e s i g n o f h y d r o c a r b o n  contamination,  was  hydrocarbon  t h e 43  amu  42  peak, was v i s i b l e o n l y a t v e r y carbon content  high a m p l i f i e r gains  was l e s s than 10  of s i g n i f i c a n t  t e s t s were expected t o y i e l d  - 0 p r o p e r t i e s of a  amounts o f c o n t a m i n a t i o n ,  t i o n must y i e l d  the hydro-  torr.  S i n c e t h e vacuum f r i c t i o n m a t i o n about t h e  so t h a t  infor-  steel-steel interface, free the pretest surface  a surface that i s s u f f i c i e n t l y "clean".  The  preparadefinition  o f s u r f a c e c l e a n l i n e s s i s an o p e r a t i o n a l one and i s t i e d t o t h e measuring technique.  Field  i o n i z a t i o n , f o r example, c a n r e v e a l c o n t a m i -  n a t e s on t h e atomic l e v e l but a d h e s i o n and f r i c t i o n s t u d i e s a r e o n l y affected  i f t h e s u r f a c e i s 10% o r more c o v e r e d w i t h  contaminants [ 2 8 ] .  T h e r e a r e two g e n e r a l methods f o r p r o d u c i n g In the f i r s t  category  clean  a r e methods which s y n t h e s i z e a c l e a n s u r f a c e by  d e p o s i t i n g atoms o f t h e d e s i r e d s u r f a c e m a t e r i a l on a s o l i d Obviously,  surfaces.  t h i s deposited  l a y e r can d i f f e r  surface.  from t h e s u b s t r a t u m , i n  h a r d n e s s and s t r e n g t h , so t h a t i n a f r i c t i o n t e s t , i t might a c t a s a low  shear-strength  solid  lubricant.  I n the'second c a t e g o r y  n i q u e s w h i c h remove c o n t a m i n a n t s from t h e s u r f a c e — heating  I n a d d i t i o n , Hordon e t a l [28]  s u c c e s s f u l l y used a method o f s u r f a c e a b r a s i o n copper samples f o r a d h e s i o n s t u d i e s .  coefficient  of copper i n c r e a s e d  constant The  extent,  value  to prepare aluminium  A f t e r two m i n u t e s o f a b r a s i v e  c l e a n i n g w i t h a r o t a t i n g s t a i n l e s s s t e e l wire  mum  temperature  t o d e s o r b gases from t h e s u r f a c e as w e l l as c r u s h i n g and  c l e a v i n g t o g e n e r a t e new s u r f a c e s .  and  high  are tech-  brush, the adhesion  from 0 ( n e g l i g i b l e b o n d i n g ) t o a m a x i -  o f 0.32 a t ZO^C.  method used i n the p r e s e n t  study was b a s e d , t o a c e r t a i n  on the work o f Hordon, but a l s o on t h e work of Bowden and L e b e n  [ 1 6 ] , who  showed t h a t r e p e t i t i v e s l i d i n g  over a r e a s d e l i b e r a t e l y c o v e r e d  43  w i t h monolayers and m u l t i l a y e r s o f l u b r i c a n t s r a p i d l y wore the l a y e r s from t h e s u r f a c e and t h e c o e f f i c i e n t o f f r i c t i o n i n c r e a s e d as d i d t h e amount o f s u r f a c e damage. A f t e r the d e s i r e d vacuum l e v e l was o b t a i n e d , t h e s l i d e r r e p e a t e d l y rubbed a c r o s s t h e t e s t s u r f a c e , immediately testing.  I t was expected  was  p r i o r to  t h a t the d i s r u p t i o n o f t h e s u r f a c e s would  v i r t u a l l y destroy a l l of the o r i g i n a l s u r f a c e . t h a t t h e s u r f a c e s were c o n t a m i n a n t - f r e e  I t was not i m p l i e d  during the t e s t .  At the  p r e s s u r e s used, t h e f r e s h s u r f a c e would be covered w i t h a monolayer o f adsorbed  gas i n about two minutes.  h i g h e r than n o r m a l l y  The f r i c t i o n v a l u e s ,  although  seen i n boundary f r i c t i o n t e s t s , a l s o i n d i c a t e  t h a t the s u r f a c e s were not " c l e a n " .  However, the c o n s i s t e n c y i n the  f r i c t i o n values i n d i c a t e that a c e r t a i n constant l e v e l of surface p r e p a r a t i o n had been a c h i e v e d .  The V~  6 p r o p e r t i e s of s u r f a c e s t r e a t e d  i n t h i s way were v e r y d i f f e r e n t from t h e y^ - 9 v a l u e s o b t a i n e d by o t h e r i n v e s t i g a t i o n s [ 1 5 ] , [ 1 9 ] , [21] and b o t h v a l u e s and t h e shape o f t h e y had  used boundary l u b r i c a t e d  suggested  g  - 9 curve.  i n terms o f maximum y  Since these i n v e s t i g a t o r s  surfaces, the d i f f e r e n c e i n r e s u l t s  t h a t t h e p r e - t e s t c l e a n i n g t e c h n i q u e was adequate. The y  g  - 0 v a l u e s were o b t a i n e d by r u n n i n g  several tests at  d i f f e r e n t 9 v a l u e s a c r o s s t h e same s u r f a c e and measuring y value.  g  The y  noticeable.  s  - 0 v a l u e s were t e s t e d f o r " r u n - i n " .  g  a t each 9  No e f f e c t s were  The normal l o a d s used i n t h e s e t o f r e s u l t s shown i n F i g u r e  12 were i n t h e 50 l b . range, and t h e h i g h 0 v a l u e s were o b t a i n e d by u s i n g h i g h e r t a n g e n t i a l l o a d i n g r a t e s and not by d e c r e a s i n g N.  4.2.2  Air Those samples to be a i r - t e s t e d were l e f t  exposed to t h e atmos-  44  phere f o r t h e a l l o t t e d  time, then t e s t e d  b o t h i n a i r and under vacuum.  I n F i g u r e 13, v a l u e s of 6 > 1.0 were o b t a i n e d by r e d u c i n g N from approximately  25 l b s .  That  was t e s t e d by e x t e n d i n g range of 8 v a l u e s .  t h i s would n o t change t h e y  50 t o  vs 8 values,  t h e N = 25 l b . 8 v a l u e s i n t o t h e N = 50 l b .  The s i x p o i n t s o b t a i n e d i n t h e range .0001 < 6 <  1.0 by u s i n g N = 25 l b s . agreed  very w e l l with the v a l u e s of u ,  o b t a i n e d when N = 50 l b s .  4.2.3  Oxide F i l m s i ) f u r n a c e formed A f t e r d e g r e a s i n g and w i r e - b r u s h i n g t h e samples were h e a t e d  a t 250°C i n t h e a i r f o r 2 h o u r s and were  allowed to furnace c o o l . black oxide f i l m . a i r and i n vacuum  then  The r e s u l t was a t h i c k , b l u e -  F i l m s o f t h i s t y p e were t e s t e d b o t h i n (2 x 10  —8  torr).  i i ) water formed T h i n n e r o x i d e f i l m s were o b t a i n e d by immersing t h e sample i n H 0 2  a t 20°C and pH = 5.0  m i n u t e s f o l l o w e d by a i r d r y i n g . a t room temperature  (HCl) f o r 15  These f i l m s were t e s t e d  and p r e s s u r e i m m e d i a t e l y  after drying  in a i r .  4.2.4  Monolayer D e p o s i t i o n i)  abrasion After procedure,  t h e vapor, d e g r e a s i n g and f i n a l  samples u n d e r g o i n g  a b r a s i o n were immediately  wire-brushing  monolayer d e p o s i t i o n by  placed i n the s t e a r i c acid-n-  hexane s o l u t i o n and abraded,  then r i n s e d  i n n-hexane and  45  tested  immediately a f t e r d r y i n g .  A l l the m o n o l a y e r - c o v e r e d  samples were t e s t e d a t a t m o s p h e r i c p r e s s u r e b e c a u s e can be up t o a 50% l o s s i n monolayer  there  c o v e r a g e under vacuum  c o n d i t i o n s [45].  ii)  Langmuir-Blodgett  films  The d e p o s i t i o n t e c h n i q u e has been d e s c r i b e d earlier  i n t h i s chapter.  After controlling  t h e pH  and  m e t a l i o n c o n c e n t r a t i o n , t h e samples were immersed i n the b a t h , the f i l m was from t h e t r o u g h .  s p r e a d and t h e samples  emerged  "wet"  They were a l l o w e d t o d r y , t h e n t e s t e d  i m m e d i a t e l y a t a t m o s p h e r i c p r e s s u r e and temperature i n the temperature s t u d i e s o f t h e c a l c i u m s t e a r a t e  except films.  Four d i f f e r e n t L a n g m u i r - B l o d g e t t monolayers were formed w i t h o l e i c a c i d as. p i s t o n o i l (TT 1) S t e a r i c a c i d , pH =  = 29.7  dynes/cm):  4.0;  2) O l e i c a c i d , pH =  4.0;  3) S t e a r i c , pH = 9.0  - 10.0;  -4 4) O l e i c a c i d , pH = 9.0  4.2.5  Temperature  10  - 10.0;  ++ M Ca  10~ M 4  ; Ca"*"*".  S t u d i e s of Calcium S t e a r a t e Monolayers  F o r t h e temperature s t u d i e s , c a l c i u m s t e a r a t e  monolayers  were d e p o s i t e d on t h e s t e e l samples u s i n g t h e L a n g m u i r - B l o d g e t t technique.  A f t e r d r y i n g , the f i l m c o v e r e d p l a t e s were t e s t e d a t  a t m o s p h e r i c p r e s s u r e and a t t e m p e r a t u r e s r a n g i n g from 22°C  t o 70°C.  A  p a i r o f q u a r t z - i o d i d e lamps (2,000 w a t t s ) were used a s t h e heat s o u r c e and a YSI was  Telethermometer  employed  equipped w i t h a s u r f a c e t e m p e r a t u r e  probe  to m o n i t o r the temperature o f t h e p l a t e , see F i g u r e  11.  46  The  temperature was  regulated  the c o n t r o l s f o r t h e h e a t i n g Besides  to w i t h i n T ± 2°C by manual o p e r a t i o n lamps.  the u s u a l p r e c a u t i o n of measuring d e p o s i t i o n  to d e t e r m i n e i f f i l m d e p o s i t i o n was heated were t e s t e d f o r  satisfactory,  General  Experimental  from one  at  higher  I n a few  9 values  at a constant  i n s t a n c e s , N had  c o u l d be  obtained;  r a t e u n t i l gross  the s l i d e r was  new  applied.  curve.  t o be d e c r e a s e d  these  cases  A f t e r N was  earlier).  area The  N varied  approxi-  so t h a t U  a r e n o t e d on  a p p l i e d , F was F and  the  applied  N were r e l e a s e d  (with the e x c e p t i o n s l i d e r was  slightly  of  the  a l w a y s moved to a  t e s t area because s u r f a c e f i l m s a r e . d i s r u p t e d d u r i n g a t e s t  t h e r e t e s t i n g o f t h a t a r e a would have y i e l d e d h i g h e r A t y p i c a l d a t a r u n would c o n s i s t o f a t l e a s t c o v e r i n g t h e r a n g e of 9.  Many s e p a r a t e  s u r f a c e s were c a r r i e d out  and  accumulation  The  i n contact  g e n e r a l l y kept at  s l i p occurred.  moved to a new  vacuum t e s t s d e s c r i b e d  - 9  wire-brushed then p l a c e d  N,. the normal l o a d was  a p p r o p r i a t e graphs i n C h a p t e r V.  and  3 h o u r s f o r each  group o f t e s t s t o a n o t h e r but was  m a t e l y 50 l b s .  to h e a t i n g .  r e c e i v e d the appropriate p r e - t e s t  t h e upper s l i d e r was  w i t h t h e sample and  be  Procedure  A f t e r each sample had preparation,  ratios  t h e samples t o  - 0 characteristics prior  temperature t e s t s l a s t e d a p p r o x i m a t e l y  4.3  of  and  values. 25 d a t a  points  data runs of monolayer-covered  the r e s u l t s g i v e n i n t h e g r a p h s a r e  of s e v e r a l s e p a r a t e  runs.  an  47  V.  5.1  RESULTS AND DISCUSSION  .  Introduction The  first  p a r t o f t h e e x p e r i m e n t a l work was concerned  i d e n t i f y i n g the source of the observed tion.  rate-dependence  The p o s s i b i l i t y t h a t t h e s t a t i c f r i c t i o n  of s t a t i c  f o r c e was  dependent because t h e d e f o r m a t i o n of s t e e l i s s t r a i n - r a t e checked  e x p e r i m e n t a l l y by d e t e r m i n i n g u  friction  g  with fric-  ratesensitive  was  vs 6 values f o r s t e e l / s t e e l  c o u p l e s under h i g h vacuum c o n d i t i o n s .  Testing a  friction  c o u p l e under t h e s e c o n d i t i o n s was t h e most s a t i s f a c t o r y method o f m i n i m i z i n g the e f f e c t s of o x i d a t i o n o r o f hydrocarbon friction  a d s o r p t i o n on  characteristics. F o l l o w i n g t h e h i g h vacuum work, s t a t i c f r i c t i o n t e s t s were  also  c a r r i e d o u t on s t e e l samples w h i c h had been d e l i b e r a t e l y  oxidized  and on samples w h i c h had been c o a t e d w i t h a monolayer o f m e t a l - o r g a n i c soap. In  t h e second h a l f  s e v e r a l monolayer-covered v a l i d i t y o f t h e proposed Finally,  5.2  y  g  - 0 data f o r  s t e e l s u r f a c e s were o b t a i n e d a s a c h e c k o f t h e t h e o r e t i c a l model f o r s t a t i c f r i c t i o n .  t h e e x p e r i m e n t a l work was extended  e f f e c t o f s m a l l temperature monolayer-covered  of the study, a d d i t i o n a l  to cover the  i n c r e a s e s on t h e y ^ - 9 c h a r a c t e r i s t i c s o f  surfaces.  O b t a i n i n g S t a t i c F r i c t i o n Information f o r the S t e e l / S t e e l  5.2.1  y  s  System  • -8 v s 0 c u r v e s a t 2 x 10 torr  F i g u r e 12 summarizes two s e p a r a t e d a t a runs o f s t e e l v s s t e e l —8 a t 2 x 10  torr.  The d a t a p o i n t s f o r t h i s graph were o b t a i n e d from  more  48  e x t e n s i v e d a t a by a v e r a g i n g f o u r u t y p i c a l of u  g  v a l u e s a t a g i v e n 6.  - 9 curves o b t a i n e d a t 2 x 10  -8  T h i s graph i s  t o r r and a t lower p r e s s u r e s . -9  The e f f e c t on y noticeable.  g  of l o w e r i n g the vacuum p r e s s u r e to 5 x 10  The most important f e a t u r e of t h i s curve i s t h a t i t i s i n d e -  pendent of 9 through the range ponent  t o r r was not  .001 < 9 < 5.  T h i s means t h a t some o t h e r com-  of the i n t e r f a c e i s r e s p o n s i b l e f o r the v i s c o e l a s t i c behaviour of  the i n t e r f a c e .  The f r i c t i o n v a l u e of 0.75, a l t h o u g h h i g h e r than v a l u e s  o b t a i n e d d u r i n g o t h e r boundary l u b r i c a t i o n s t u d i e s , e.g., Johannes [ 1 9 ] , Marion  [ 2 1 ] , i s r e l a t i v e l y low compared to v a l u e s observed by some  workers.  R i t t e n h o u s e [28] f o r example, has observed v a l u e s of 1.08 w i t h  "clean" s t e e l .  The low f r i c t i o n v a l u e can be e x p l a i n e d by c o n s i d e r i n g  the p r e - t e s t p r e p a r a t i o n . B e f o r e they were p l a c e d i n the t e s t chamber, the t e s t f a c e s were prepared by d e g r e a s i n g them over b o i l i n g to  remove r e s i d u a l machining  them.  o i l s and l o o s e d i r t ,  trichloroethylene  then w i r e - b r u s h i n g  The b r u s h i n g d i s t u r b e d the s u r f a c e and exposed  immediately o x i d i z e d  in air.  sur-  In a matter of seconds,  new s t e e l which the s u r f a c e was  o  covered w i t h a t h i n l a y e r of o x i d e about  20 A t h i c k  [ 5 5 ] . However,  t h i s procedure removed the m a j o r i t y of the s c a l e and accumulated carbons from t h e s u r f a c e .  The specimens were p l a c e d i n the vacuum  chamber immediately a f t e r c l e a n i n g and the pumpdown procedure commenced.  hydro-  was  A p r e s s u r e of 10 ^ t o r r was reached i n a p p r o x i m a t e l y  1-1/2  —8 hours and 10  t o r r i n about  12 hours.  What i s the s t a t e of the s u r f a c e s a t t e s t  time?  From the work of Kruger and Y o l k e n t i o n k i n e t i c s and the i n i t i a t i o n obvious t h a t the i n i t i a l  [55] who  s t u d i e d the o x i d a -  o f o x i d a t i o n on i r o n surfaces*, i t i s  o x i d a t i o n r a t e of the f r e s h l y brushed s u r f a c e s  49  i s v e r y h i g h , but d e c r e a s e s e x p o n e n t i a l l y w i t h t i m e . hours i n p u r e , d r y oxygen a t 760  A t the end o f  17  t o r r , the f i l m t h i c k n e s s would o n l y  o  have r e a c h e d about  30 A.  S i n c e the p a r t i a l p r e s s u r e o f 0^  chamber, as measured by t h e RGA,  was  v e r y low  i n the vacuum  ( a p p r o x i m a t e l y 10 ^  d u r i n g t h e major p a r t of t h e 12 hour pumpdown time, i t was  torr)  doubtful i f  o  t h e f i l m t h i c k n e s s exceeded  30 A.  A l s o , even when t h e bakeout  a p p l i e d , t h e temperature o f the specimen n e v e r exceeded  heat  50°C.  Because  of the low temperature, low 0^ p a r t i a l p r e s s u r e s and t h e h i g h t e n t o f the r e s i d u a l gas d u r i n g bakeout  was  con-  ( t h e hot i o n pumps emit  hydrogen  d u r i n g b a k e o u t ) , i t i s u n l i k e l y t h a t any f u r t h e r o x i d a t i o n would have o c c u r r e d i n t h e chamber. specimens were abraded films.  Prior  t o the a c t u a l f r i c t i o n  tests,  together s e v e r a l times thus d i s r u p t i n g the o x i d e  However, even i f t h i s p r o c e d u r e c o m p l e t e l y removed t h e o x i d e  l a y e r , t h e newly-exposed  gases i n d e f i n i t e l y .  s u r f a c e s would not remain f r e e o f —8  A t 10  t o r r and room temperature,  gas m o l e c u l e s r e m a i n i n g i n t h e chamber was  still  Thus, i t was  3 minutes.  the t e s t  s u r f a c e s were c o v e r e d w i t h a t l e a s t a monolayer  l i k e l y that during the f r i c t i o n  and N 2  gas monolayer  5.2.2  i n explaining  The m i n i m a l e f f e c t o f t h i s  found i n subsequent  tests,  r e l a t i v e l y low compared t o  i s i n t e r e s t i n g when compared t o the e f f e c t o f  o r g a n i c monolayers  gas  of adsorbed  These f i n d i n g s a s s i s t  the o b s e r v e d f r i c t i o n c o e f f i c i e n t was  v a l u e s o b s e r v e d by o t h e r w o r k e r s .  t h e number o f  of adsorbed  i n about  gas, probably a m i x t u r e of  adsorbed  so l a r g e t h a n t h e  c l e a n e d a r e a would have been c o v e r e d w i t h a monolayer  why  the  adsorbed  adsorbed  tests.  A i r Exposed A more i n t e r e s t i n g o b s e r v a t i o n i s t h a t i f t h e  s u r f a c e used i n vacuum was  exposed  test  to the atmosphere f o r 24 h o u r s  then  50  r e t e s t e d , t h e maximum f r i c t i o n v a l u e f e l l  t o 0.55, and the y  vs 0 s [19] and Marion [ 2 1 ] .  b e h a v i o u r i s c l o s e r t o t h a t r e p o r t e d by Johannes  The 24-hour exposure r e s u l t s a r e compared w i t h t h e vacuum r e s u l t s i n F i g u r e 13. in  What caused t h e s h i f t  t h e shape o f the y v s 0 curve?  i n t h e f r i c t i o n v a l u e and t h e change The f i r s t  thought was t h a t t h e s u r -  f a c e o x i d i z e d w i t h f u r t h e r exposure t o a i r . The second was t h a t borne hydrocarbons were adsorbed onto t h e s u r f a c e . pendent present.  air-  There i s some i n d e -  e v i d e n c e t o suggest t h a t h y d r o c a r b o n c o n t a m i n a t i o n c o u l d be When Coelho  [60] was examining  the i n f r a r e d s p e c t r a o f o r g a n i c  a c i d s adsorbed on m e t a l m i r r o r s , he found t h a t extraneous hydrocarbon bands appeared i n the s p e c t r a b e f o r e the a c i d s had been d e p o s i t e d . These bands appeared when t h e m i r r o r s had been exposed phere f o r a p p r o x i m a t e l y 18 hours. of  t o t h e open atmos-  He concluded t h a t t h i s was the r e s u l t  t h e a d s o r p t i o n o f hydrocarbons from the atmosphere. The p o s s i b i l i t y  t h a t o x i d e f i l m s c o u l d be c o n t r i b u t i n g to the  v i s c o e l a s t i c b e h a v i o u r was checked by growing o x i d e f i l m s on t h e s u r f a c e s and t e s t i n g t h e i r y ^ v s 0 c h a r a c t e r i s t i c s . of  Subsequently, a study  d e l i b e r a t e l y d e p o s i t e d hydrocarbon monolayers was a l s o  5.2.3  performed.  Oxide F i l m s The f i r s t  by h e a t i n g t h e specimens  f i l m s t e s t e d were t h i c k o x i d e f i l m s  t o 250°C.  formed  The f r i c t i o n c o e f f i c i e n t s were  h i g h , 0.79, and appear to be independent of 0.  They decreased v e r y  s l i g h t l y a t h i g h e r 0 (see F i g u r e 15). When f a i l u r e or s l i p o c c u r r e d , the  o x i d e ^ f i l m was t o r n from t h e base m e t a l , exposing s e c t i o n s of  steel.  These f r i c t i o n v a l u e s p r o b a b l y r e f l e c t  t h e bond  strength  between o x i d e and parent m e t a l r a t h e r than metal v s o x i d e f r i c t i o n . The f r i c t i o n v a l u e s a r e s l i g h t l y h i g h e r than those o b t a i n e d f o r t h e  51  vacuum t e s t s and  they a r e a l s o h i g h e r than v a l u e s of subsequent t e s t s  the water formed o x i d e f i l m s shown i n F i g u r e 15. observed  t h i s behaviour  also  [29].  f r i c t i o n v a l u e s a r e u s u a l l y lower  Other workers have  When the o x i d e f i l m s a r e t h i n , than v a l u e s of the c o r r e s p o n d i n g  f r e e s u r f a c e , but i n c r e a s i n g the f i l m t h i c k n e s s can i n c r e a s e the tion coefficient. air  In F i g u r e 16,  on  the r e s u l t s of the f r i c t i o n  the oxide-  fric-  tests  on  formed and water formed f i l m s a r e p l o t t e d a l o n g w i t h the r e s u l t s of  Johannes  [19] and Marion  f i l m s by themselves over the ranges  5.2.4  [21] f o r comparison.  do not render  I t i s obvious  the s t e e l / s t e e l i n t e r f a c e  t h a t oxide viscoelastic  of 0 c o n s i d e r e d .  Monolayers of P o l a r O r g a n i c  Compounds  a) Abraded A f t e r the experiments  showed t h a t o x i d e - f i l m s were  not r e s p o n s i b l e f o r the v i s c o e l a s t i c i t y  observed  by other workers, a monolayer of an o r g a n i c m e t a l l i c soap was  d e p o s i t e d on the s t e e l s u r f a c e by a b r a d i n g i t  under a hexane s o l u t i o n c o n t a i n i n g s t e a r i c a c i d .  Unlike  the o x i d e f i l m s j u s t d i s c u s s e d , t h i s f i l m d i d g i v e a y  s  - 6 curve s i m i l a r to the one Johannes had  (see F i g u r e 17). f o r y^.  I t shows an upper and  reported  a lower  asymptote  The v a l u e s of these asymptotes compare f a v o r a b l y  w i t h those o b t a i n e d by Johannes:  y y  max. . mm.  Another encouraging  Johannes  P r e s e n t Work  0.38  0.39  0.18  0.22  f e a t u r e i s t h a t the g e n e r a l shape of  52  the c u r v e s i s q u i t e s i m i l a r .  These r e s u l t s were t h e •»  first  c l e a r i n d i c a t i o n that the u  - 0 curves f o r s t e e l s  were s t r o n g l y i n f l u e n c e d by h y d r o c a r b o n s . technique c l o s e l y simulates under o r d i n a r y  The  the f i l m - f o r m a t i o n  f r i c t i o n c o n d i t i o n s w i t h one  t h e f i l m formed by t h e a b r a s i o n a monolayer i n t h i c k n e s s .  abrasion process  exception:  t e c h n i q u e was l i m i t e d t o  Depending on s u r f a c t a n t  con-  c e n t r a t i o n , t h e f i l m formed d u r i n g t h e " r u n - i n " p e r i o d o f o r d i n a r y f r i c t i o n t e s t s may be t h i c k e r . case,  p r o t e c t i o n was o b t a i n e d  In either  because t h e f a t t y a c i d  r e a c t e d w i t h newly exposed F e atoms on t h e s u r f a c e t o form a m e t a l l i c soap.  T h i s soap was r e l a t i v e l y  immobile  b e c a u s e i t i s s t r o n g l y bound t o t h e s u r f a c e and b e c a u s e it  p o s s e s s e s a n i n t e r n a l c o h e s i v e n e s s due t o t h e l a t e r a l  i n t e r a c t i o n s of the chains Unfortunately,  of the o r i e n t e d a c i d molecules  the abrasion  f l e x i b l e and i t was i m p o s s i b l e m e t a l s onto a s t e e l s u r f a c e .  t e c h n i q u e was n o t v e r y  to deposit  soaps o f o t h e r  C o n s e q u e n t l y , i t was  felt  t h a t t h e L a n g m u i r - B l o d g e t t method o f f e r e d more p o t e n t i a l so i n o t h e r  t e s t s , monolayers were d e p o s i t e d  using  that  technique.  b) L a n g m u i r - B l o d g e t t M o n o l a y e r s After  t h e r e s u l t s of t h e a b r a s i o n - f o r m e d monolayer  were a n a l y z e d ,  f u r t h e r i n v e s t i g a t i o n of the r e s u l t s of  the s t u d i e s on the r h e o l o g y  of surface f i l m s a t the a i r /  water i n t e r f a c e i n d i c a t e d t h a t i t might be p o s s i b l e t o  53  provoke the s t e e l / s t e e l i n t e r f a c e i n t o g i v i n g d i f f e r e n t U  - 6 c u r v e s by  g  changing e i t h e r the m e t a l i o n o r  f a t t y a c i d i n the monolayer.  5.2.5  S t e a r i c A c i d and The  depositing  first  O l e i c A c i d a t pH =  organic  c i a t e d but  S p i n k and  to 4.2.  Saunders  formed i f a f e r r i c  At  t h i s pH,  but  the Fe  s a l t has  Ill .  t h a t when the pH v a l u e  were formed  HCl  had  by  been  carboxylic acids are  undisso-  [ 4 1 ] , have shown t h a t b a s i c i r o n s o a p s  can  b e e n added t o the aqueous s o l u t i o n .  (n-C^^H^^COOH) a s t h e l o n g  They found t h a t  follows.  4.2  f i l m s to be d e p o s i t e d  E a r l i e r work by Wolstenholme and acid  r e s u l t s a r e as  s t e a r i c o r o l e i c a c i d on a water s u r f a c e .  added to r e d u c e the pH  be  The  the  Schulman [70]  using  c h a i n p o l a r compound i s more  myristic  explicit.  i o n s themselves do not p r o d u c e s o l i d i s greater  t h a n 2,  films  t h e f i l m i s condensed  I |  because b a s i c i r o n i o n s ciated organic  [FeCOH)^  a c i d molecules.  o r Fe(OH)  ] i n t e r a c t w i t h the  Wolstenholme and  undisso-  Schulman a l s o p r o p o s e d  a mechanism o f f i l m c o n d e n s a t i o n i n w h i c h hydrogen b o n d i n g between hydroxyl  groups o f t h e b a s i c m e t a l i o n s was  the f i l m .  The  responsible  the  f o r condensing  b a s i c m e t a l i o n s form a complex network s i t u a t e d j u s t  b e n e a t h t h e monolayer.  At pH  Above pH  5,  t i o n and  network f o r m a t i o n  > 5.5,  no  s o l i d f i l m s c o u l d -be  detected.  t h e b a s i c m e t a l i o n s form c o l l o i d a l a g g r e g a t e s i n the under the monolayer w i l l no  longer  solu^  take  place. In the p r e s e n t b a s i c metal ions. sample was for  s t u d y , the  s t e e l sample was  P r i o r to d e p o s i t i n g  the monolayer on  submerged i n the w a t e r f i l l e d  a p p r o x i m a t e l y 20-30 m i n u t e s .  f i l m s a r e not  s t e a r i c or o l e i c  the  (pH 4)  s o u r c e of  the  i t s surface,  t r o u g h and  held  Thus, i t i s expected t h a t t h e  a c i d monolayers but m o n o l a y e r s o f  the  there deposited the  54  appropriate basic iron  soap.  The m e c h a n i c a l  p r o p e r t i e s o f t h e s e f i l m s have n o t been s t u d i e d  i n d e t a i l , b u t from t h e i r performance d u r i n g f r i c t i o n t e s t s , t h e y a r e likely  t o be l e s s v i s c o u s than c a l c i u m s t e a r a t e f i l m s .  c u r v e s f o r b o t h f i l m s a r e shown i n . F i g u r e 18. with 9 .  nounced v a r i a t i o n o f  0.70 and 0.47 r e s p e c t i v e l y .  The ^  vs 0  Both c u r v e s show a p r o -  The upper and lower asymptotes a r e  The u  v a l u e o f 0.70 i s c l o s e t o max.  v a l u e s o b t a i n e d f o r t h e water formed o x i d e . shape t o t h e u and  The c u r v e s a r e s i m i l a r i n  - 0 c u r v e s o b t a i n e d by Johannes b u t a r e d i s p l a c e d upward  to t h e r i g h t . 5.2.6  C a - s t e a r a t e and C a - o l e a t e a t pH = 9.5 As noted  earlier  [ 3 6 ] , [ 3 8 ] , Ca  ions cause  stearic  and m o n o l a y e r s t o become h i g h l y v i s c o u s w i t h an a c t i v a t i o n e n e r g y f o r flow of approximately  11 K c a l / m o l e over c e r t a i n r a n g e s o f pH.  On t h e  -Ho t h e r hand, Ca because Ca  i o n s have v e r y l i t t l e e f f e c t on o l e i c a c i d m o n o l a y e r s  i s s t e r i c a l l y h i n d e r e d from f o r m i n g  t h e same h i g h l y s t r u c -  t u r e d p o l y m e r - l i k e f i l m w i t h o l e i c a c i d a s i t does w i t h s t e a r i c Deamer and C o r n w e l l a c i d monolayer on water t h e a d d i t i o n o f Ca was formed.  its viscosity  i n the u shifts  g  t h a t t h e v i s c o s i t y o f an o l e i c  ( a t pH 2.0) was n o t s i g n i f i c a n t l y  However, s t e a r i c a c i d monolayer became so s o l i d - l i k e -4 i n c r e a s e d from 4 x 10  effect  of their  viscometer.  o f t h i s s o l i d i f i c a t i o n on s t a t i c f r i c t i o n  - 8 curve to the l e f t  while Ca-oleate  l e a v e s the c u r v e  that  t o g r e a t e r t h a n 0.2 d y n e - s e c . p e r  - 0 c u r v e s g i v e n i n F i g u r e s 19 and 20.  the u  increased by  i o n s a t pH 10 even though a c a l c i u m o l e a t e d i - s o a p  cm which was t h e upper l i m i t The  [36] found  acid.  so t h a t u  The C a - s t e a r a t e  i s lower  i n approximately  i s shown film  f o r a given 0j  t h e same p o s i t i o n a s  55  it and  had  a t pH = 4.0.  0.47  i n each  The  upper and  lower asymptotes remain c l o s e t o  case.  I t i s o b v i o u s t h a t t h e p r o p e r t i e s of the d e p o s i t e d the U  can a f f e c t interpreted  5.3  -  g  0 curve  dramatically.  monolayer  These r e s u l t s w i l l now  be  i n terms o f t h e model proposed i n Chapter I I I .  Discussion of H  5.3.1  0.70  s  Applying  - 0 Results  t h e V i s c o e l a s t i c Model to U  Consider  - 0  Results  t h e c o m p o s i t i o n ' of a t y p i c a l i n t e r f a c e and i t s  r e s p o n s e to the a p p l i e d f o r c e s . substratum covered  g  Both s u r f a c e s c o n s i s t of a s o f t  by a l a y e r of deformed m e t a l about 0.1  steel  m i c r o n s deep o-  which i s , i n t u r n , covered  w i t h an o x i d e  l a y e r at l e a s t  a d d i t i o n , t h e s t a t i o n a r y h a l f of t h e f r i c t i o n c o u p l e  i s covered  d e l i b e r a t e l y d e p o s i t e d monolayer of o r g a n i c m a t e r i a l . of N c a u s e s p l a s t i c y i e l d i n g h i g h e s t p o i n t s of a r e formed. G r e e n [15]  exposed. experience p^,  each s u r f a c e so t h a t s m a l l d i s c r e t e a r e a s  Any  and  b e c a u s e the o x i d e  Eisner  f i l m c r a c k s and new  o x i d e or o r g a n i c m a t e r i a l t r a p p e d  reasonably  of [14]  the  contact and  partially  metal i s zone w i l l  h i g h c o m p r e s s i v e s t r e s s e s as t h e y i e l d  pressure,  Kg/mm.  the shear s t r e s s :  1) w i l l be  total  to grow; 2) may  When the t a n g e n t i a l s t r e s s i s a p p l i e d ,  transmitted  During  to the s u b s t r a t u m c a u s i n g  squeeze a p o r t i o n of  monolayer m a t e r i a l out of the c o n t a c t a r e a of contact.'  a  i n a contact  f o r s t e e l i s about 200  contact area  In  The a p p l i c a t i o n  shown t h a t t h e s e c o n t a c t a r e a s a r e a t l e a s t  m e t a l l i c , probably  by  i n t h e s u b s t r a t a immediately b e n e a t h  Independent work by C o u r t n e y - P r a t t has  30 A t h i c k .  the  the  oxide-  zone thus i n c r e a s i n g t h e m e t a l l i c  t h i s t i m e , the s u r f a c e s w i l l show s m a l l amounts  of v e r t i c a l as w e l l as h o r i z o n t a l movement as the i n t e r f a c e a d j u s t s  to  the s t r e s s e s .  A t some p o i n t , however, the a p p l i e d t a n g e n t i a l f o r c e w i l l  c a u s e g r o s s s l i p o f one  s u r f a c e over  the  a) What i s T , t o t h e shear q  i n t e r f a c e , when s l i p  other.  strength/unit area of  the  occurs?  I n t h e most extreme c a s e , the m a j o r i t y of t h e c o n t a c t a r e a would be m e t a l l i c and  the average shear  p e r u n i t a r e a would approach t h e s h e a r metal  s u b s t r a t a , S^.  (Note t h a t substratum  may  s t r e n g t h of  i s approximately  0.2  the  p^ [3].  v a r y from j u n c t i o n t o j u n c t i o n as  i s a n i s o t r o p i c but o n l y average v a l u e s  considered.)  strength  A more u s u a l c i r c u m s t a n c e  the  are  i s that only a  a f r a c t i o n , a, of the t o t a l contact a r e a i s m e t a l l i c , the r e s t ,  (1 - a ) , c o n s i s t s o f an o x i d e - m o n o l a y e r m i x -  t u r e w i t h shear  s t r e n g t h per u n i t area, S  , which i s  nm l e s s than S,,. M  (If S  nm  > S„, s h e a r i n g would t a k e p l a c e M . . . . .  i n t h e u n d e r l y i n g weaker m e t a l . ) Fj. = A_ r (1 - a ) S f f [_ ran  Therefore, at fracture  + a S„ I = T A-. M J o f v  . Thus, t h e  t  shear  s t r e n g t h p e r u n i t a r e a o f t h e i n t e r f a c e , ' T , has a m a x i mum  v a l u e of S^.  b) When w i l l  Therefore,  £ ^ ^P 0  m  J < 0.2  approximately  t h e a r e a growth end?  Measurements o f t h e e l e c t r i c a l  r e s i s t a n c e of  the  i n t e r f a c e show t h a t the f i n a l amount o f c o n t a c t a r e a a t a g i v e n normal l o a d i s a f u n c t i o n of t h e r a t e a t which t h e t a n g e n t i a l f o r c e was  applied.  Because of the complex n a t u r e  of t h e  p r e d i c t i n g t h e amount of a r e a growth by  interface,  c o n s i d e r i n g the  57  d e f o r m a t i o n of each component i s d i f f i c u l t . I I I , a more g e n e r a l approach was  In  taken and  Chapter  i t was  assumed  t h a t the c o n t a c t a r e a growth shows a v i s c o e l a s t i c .  of b e h a v i o u r F  f  =  f  A  =A  so t h a t at T  ±  type  fracture:  o [ l + e ( t  ) ]  f  T  D  = ^ T  [ l + e ( t  o  f  )  ]  and  -T  - r [ -<v ] 1+e  r  m  1  A l s o , i n Chapter  I I I , two  models were used  t o p r e d i c t u^.  J  p o s s i b l e types of v i s c o e l a s t i c From the  d a t a o b t a i n e d from s t a t i c f r i c t i o n covered w i t h Langmuir-Blodgett w i l l be 5.3.2  experimental  t e s t s of s u r f a c e s  monolayers, the two  evaluated.  K e l v i n - V o i g t - P r a n d t l Model In the s i m p l e s t case, the i n t e r f a c e i s a s s i g n e d  e l a s t i c parameter, k, and one v i s c o u s parameter, c, and i t s d e f o r m a t i o n behaviour was  t h a t of a K e l v i n - V o i g t  when a f r a c t u r e s t r e s s , T , i s reached. q  (6) was  models  one  t r e a t e d as i f  body.  Slip  U s i n g t h i s approach,  occurs  equation  derived e a r l i e r .  I t i s i n t e r e s t i n g t o e v a l u a t e c, k and T /p ° p m f o r each of the f o u r c a s e s . Considering equation asymptote i s  (6) i n Chapter  III:  the upper  58  t h e lower asymptote i s u  . . = T /p . mm o m  From t h e d a t a f o r t h e monolayers y 0.47  = 0.70  and  y  max.  i n a l l f o u r c a s e s so t h a t :  0.47  mm.  = 'm  and  0.70  = -2m  From (6) w i t h y  0.70,  y  max.  r + f 0  1.46  1 - e  s  1  = 0.47,  the y  mm-  -  i •  y c  +  s  2.08  y  s  s  =  - 0 curve i s :  0  ....  (11)  ..  (12)  and  — P  = 1.46, m  — = 0.47, P *m  f = a k  The v a l u e f o r a the " r e t a r d a t i o n t i m e " i s d i f f e r e n t  f o r each •  monolayer. from  I t i s o b t a i n e d by s o l v i n g  the experimental curves.  y i e l d value f o r s t e e l t h e n c, k, T film  q  (11) g i v e n a d a t a p o i n t (y  G i v e n t h a t p ^ = 200 Kg/mm  2  ( p u b l i s h e d v a l u e s r a n g e from 100  a r e c a l c u l a t e d from  the set o f equations  is a  t o 300  0.)  reasonabl Kg/mm ), 2  (12) f o r each  (see Table. I ) . The v a l u e o f c g i v e s a b u l k e f f e c t i v e v i s c o s i t y f o r each  interface.  As e x p e c t e d  from  the r e l a t i v e p o s i t i o n s o f t h e y ^ - 0  curves  t h e i n t e r f a c e w i t h c a l c i u m s t e a r a t e as t h e monolayer shows t h e h i g h e s t bulk v i s c o s i t y value. At t h i s p o i n t , i t i s obvious t h e s i m p l e model t o d e s c r i b e s t a t i c  t h a t one  friction  d i f f i c u l t y with using  i s that i t predicts  an  TOT' "-. i1. CTft1i"i tl'.r n.lUil lllillHIll ,  ,  l  l  'I'JITInVJhWil il^lLMTiUCT  MONOLAYER . DEPOSITED ,  c/k  c  k*  T 0  (kg/nnn )  (poise)  (sec.)  (kg/mm )  .69  94  292  1.97 x 1 0  1 0  40  94  292  111.4 x 1 0  1 0  Fe (OH) Oleate  .92  94  292  2.63 x 1 0  1 0  2  Fe (OH) Stearate  •34  94  292  .96 x 1 0  1 0  Ca-oleate Ca-stearate  2  2  in  *k = 2.86 x 10  u  2  9  dyne/cm .  TABLE I. Calculated Values of Relaxation Time, V i s c o s i t y , E l a s t i c Modules and Shear Strength f o r the 2-Parameter Model.  60  large value f o r the f r a c t u r e s t r e s s , T .  unreasonably  q  £ ^ o ^ m J ''" P  S  t o have a maximum v a l u e i n t h e 0 . 2 0 range and t h i s model p r e -  expected  \ T /p  dicts a value  • L °  m  1 = 0 . 4 7 which i s almost  2 - 1 / 2 times  t h e maximum  J  value.  5.3.3  3-Parameter  (Standard L i n e a r S o l i d ) - P r a n d t l Model  In d e v e l o p i n g t h e 3-parameter model, two e l a s t i c m o d u l i i k^ and  were used  described  i t s viscous properties.  o c c u r s when T  t o d e s c r i b e t h e e l a s t i c i t y of t h e i n t e r f a c e w h i l e c  6T  1 - e k  m  l  +  slip  From ( 8 ) : r  i s reached.  °  The f a i l u r e c o n d i t i o n I s t h a t  - 1  2  K  (13) k  Ttfhere:  T  =  l k  The  +  K  l  2 2  K  asymptotes a r e :  k m i l  max.  k  y. mxn. For a l l four i n t e r f a c e s , y  Using  k  •m s  max.  these v a l u e s ,  l  l  +  (14)  - T o +  K  2  K  2  (15)  " o T  = 0.70, y s min.  0.47.  ( 1 3 ) becomes: y.  s  - 1.46 +  TQ  1  0T  + 2.08 y  s  = 0  (16)  k, + k„ The  c = T i s the r e l a x a t i o n time f o r a p a r t i c u l a r  ratio k  l  K  2  6.1  interface. mined from  V a l u e s of T f o r each i n t e r f a c e a r e d i f f e r e n t and the e x p e r i m e n t a l d a t a by s u b s t i t u t i n g  As can be seen from U  g  the data reasonably  i s interesting  f o r each i n t e r f a c e .  to d e t e r m i n e  To do t h i s ,  it  s i n c e k^ and  t h e magnitudes of c, and k^,  assumed t h a t T^  T 1  +  k  2  1 -  y .  mm.  In  k^  the  i s known f o r each By r e a r r a n g i n g ( 1 5 ) , < U  . ; mm.  o  (17) P  m  Thus, T /p has an upper l i m i t o m  o f 0.47-  each i n t e r f a c e were c a l c u l a t e d  f o r a range o f  The  c, k, k„ p a r a m e t e r s f o r 1 2 . . | T /p 1 [_ o m J  T a b l e I I , t h e s e parameters a r e g i v e n f o r s e v e r a l ^ / ] ? Q  0.47  theoretical  t h a t (15) has s o l u t i o n s o n l y when [~T /p "1 • |_ o mj are p o s i t i v e quantities. .  k  (16).  well.  U n f o r t u n a t e l y , t h i s i s not t h e c a s e .  i s obvious  the  into  the v a l u e T /p i s needed. o m  development of t h i s model, i t was interface.  6^)  s  t h e graphs i n F i g u r e s 21 t o 24,  - 0 relationship f i t s It  (U ^>  are d e t e r -  w h i c h r e p r e s e n t s the l a r g e s t p o s s i b l e T / p Q  m  < u  . . min.  v a l u e s up  m  ratio.  In  to  However, as  d i s c u s s e d e a r l i e r , a more r e a s o n a b l e v a l u e of T /p would be about o m 0.20 o r l e s s . I f T /p = 0.15, then the b u l k v i s c o s i t y of t h e i n t e r o m f a c e i s 2 x 10"^  p o i s e f o r c a l c i u m s t e a r a t e , f o r example.  The b u l k v i s c o s i t i e s f o r the i n t e r f a c e s may  be compared  to  p u b l i s h e d v a l u e s of t h e v i s c o s i t i e s of some common m a t e r i a l s g i v e n i n Table I I I . If  the i n t e r f a c e v i s c o s i t y v a l u e s a r e compared t o p u b l i s h e d  v a l u e s f o r t h e v i s c o s i t i e s of monolayers a t the a i r - w a t e r then they seem u n u s u a l l y l a r g e . f o r example, was  The  interface,  s u r f a c e v i s c o s i t y of c a l c i u m o l e a t e -4 measured by Deamer and C o r n w e l l as 3 x 10 surface  T o P  m  h a]  ^  +k  1  2  [mm  -  u  1  [mm  k  M  2 2  2  k  l k  +  l  k  k  2  2  c Ca S t  c Ca 0&  2  (poise) 0.05  10.8  11.20  0.1  23.3  0.15  Fe  2  (poise)  c (0H) St 2  (poise)  Fe  c (0H)  Oil  2  (poise)  .4  2.59  21.5 x 1 0  1 0  4.7 x 10  8  2.3 x 10  8  6.26 x 10  8  25.4  2.1  0.52  4.3 x 1 0  1 0  .9 x 10  8  .45 x 10  8  1.2 x l l O  8  38  44  6  0.19  2 x 10  1 0  .3 x 10  8  .15 x 10  8  .4 x 10  8  0.20  56  69.6  13.6  0.09  .747 x 1 0  1 0  .16 x 10  8  .08 x 10  8  .2 x 10  s  0.30  105  165  60  0.026  .216 x 1 0  1 0  .04 x 10  8  .02 x 10  8  .05 x 10  8  0.40  187  537.  350  0.008  0.66 x 1 0  1 0  .015 x 10  8  .007 x 10  8  .02 x 10  8  0.46  268  405.6  0.004  .03 x 1 0  1 0  .007 x 10  8  .003 x 10  3  .009 x 10  8  4324  0.47  OO  TABLE I I ,  Elastic  00  M o d u l i i and V i s c o s i t y V a l u e s as a F u n c t i o n o f T / p f o r t h e 3-Parameter o m  Model.  MATERIAL  BULK VISCOSITY  ** ""*""'" *' " i H i i i i i M J i H i j<i)i'?nr..Uiii.'inin'T ..n wi.iirrTi ,J  11111 N  i  i  l  g l y c e r i n e (0°C) butter  (20°C)  2  5 x 10 poise 2 5 x 10 poise  p i t c h (0°C)  5 x 10  pitch  1.3 x 1 0  (15°C)  greases  (20°C)  ranges  poise 1 0  poise  from 10 to 1 0  glacier ice  1.2 x 10"^ p o i s e  glass  in 10  (20°C)  1 1  poise  2 2  poise  TABLE I I I . V i s c o s i t i e s  o f Some M a t e r i a l s .  64  poise.  The corresponding bulk v i s c o s i t y  thickness) i s 1.2 x 10  3  (using 20 A as the monolayer  poise, which i s much smaller than the v i s c o s i t y  value j u s t obtained f o r the calcium-oleate covered i n t e r f a c e .  This  apparent discrepancy i n v i s c o s i t y values indicates that the substratum strongly influences the rheology of the i n t e r f a c e .  This i s not sur-  p r i s i n g when.one considers that the apparent v i s c o s i t i e s of monolayers at  the air/water i n t e r f a c e are known to be strongly influenced by the  l i q u i d substratum.  When the surface v i s c o s i t y values f o r the monolayers  are converted to 3-dimensional  bulk v i s c o s i t i e s , the apparent bulk v i s -  c o s i t i e s are much higher than those obtained f o r the actual materials. However, i f the measured v i s c o s i t y i s considered to be the sum of two components, the v i s c o s i t y of the monolayer i t s e l f plus a v i s c o s i t y c o n t r i bution due to the substratum,  then when the substratum's  contribution  i s estimated and subtracted from the apparent v i s c o s i t y , the monolayer v i s c o s i t y values are much closer to the bulk values.  In view of these  observations, i t i s reasonable to expect that the measured i n t e r f a c e v i s c o s i t y may be much higher than the v i s c o s i t y of the monolayer i t s e l f or 5.4  the bulk soap. Dimensionless y - 8 Curves [_s A f t e r examining  y  s  the y^ - 8 data, i t i s apparent that the  • - 0 r e l a t i o n s h i p f i t s each set of data reasonably w e l l .  • The y - 0 s  curves f o r each i n t e r f a c e have the same asymptotes and are separated on the 6 axis because t h e i r r e l a x a t i o n times are d i f f e r e n t . apparent  I t i s also  that a more general form of f r i c t i o n curve could be obtained  by making 6 dimensionless and that a l l the experimental y^, 0 data should c o l l a p s e onto t h i s curve.  M u l t i p l y i n g 8 by the r e l a x a t i o n time  65  w i l l give a dimensionless  p a r a m e t e r , x*, as the a b s c i s s a  f r i c t i o n c u r v e w i l l be i n t h e form of u  vs x  and t h e  . s The r e l a x a t i o n t i m e x . f o r each of t h e f o u r i n t e r f a c e s A  1  determined e a r l i e r . U  g  v s x ^ 9.  general  was  The d a t a f o r a l l f o u r i n t e r f a c e s were p l o t t e d a s  The r e s u l t s a r e g i v e n i n F i g u r e 25.  the experimental data w i l l  It  i s apparent  that  c o l l a p s e onto a s i n g l e c u r v e w h i c h h a s  the  form: s - 1.46 What u s e i s t h i s ? obvious — for  +  X *  1 - e  x*  + 2.08 u  = 0  (18)  F o r t h e f o u r i n t e r f a c e s a l r e a d y t e s t e d , t h e use  knowing x ^ a l l o w s one to p r e d i c t  o t h e r m e t a l soaps x ^ , and k^,  a t any 9.  is  Unfortunately,  k^ must be d e t e r m i n e d by  experimenta-  tion.  5.5  E f f e c t o f Temperature on S t a t i c F r i c t i o n The t e m p e r a t u r e s t u d i e s were n o t meant t o be an  exhaustive  e x a m i n a t i o n o f t h e e f f e c t s o f h e a t on t h e f r i c t i o n c h a r a c t e r i s t i c s monolayer-covered  surfaces.  They were c a r r i e d o u t a s a  supplementary  check o f t h e p o s t u l a t e d v i s c o e l a s t i c i t y of t h e i n t e r f a c e s i n c e i t w e l l known t h a t t h e r e l a x a t i o n t i m e s of v i s c o e l a s t i c m a t e r i a l s a f f e c t e d by  s t u d y because  are  i t s room-temperature  — 0 curve i s  temperature  s i t u a t e d so t h a t  t e m p e r a t u r e e f f e c t s do a l t e r t h e r e l a x a t i o n t i m e , t h e p o s i t i o n o f  values.  is  temperature.  The c a l c i u m s t e a r a t e f i l m was s e l e c t e d f o r t h e  new  of  if  the  - 6 c u r v e s h o u l d s t i l l be w i t h i n t h e e x p e r i m e n t a l r a n g e o f 9 Also,  the m e l t i n g p o i n t of b u l k c a l c i u m s t e a r a t e i s  h i g h (180°C as compared t o 84°C f o r c a l c i u m o l e a t e )  reasonably  so t h a t h i g h e r  test  bb  temperatures  a r e p o s s i b l e b e f o r e f i l m m e l t i n g e f f e c t s might  Heating 26,  shifted  interfere.  the m o n o l a y e r - c o v e r e d s t e e l s u r f a c e to 35°C, F i g u r e  the y  0 c u r v e s l i g h t l y to t h e r i g h t so t h a t X o r - o  -  r  i-  s  * reduced  to 10 s e c .  S i m i l a r l y , h e a t i n g to 50°C s h i f t e d  f u r t h e r to the r i g h t , F i g u r e 25,  T  and  „  i s f u r t h e r reduced  s e c . compared to a v a l u e of 40 s e c . f o r 2 2 ° c ' T  ture curves  and  27,  i t i s obvious  t e m p e r a t u r e i n c r e a s e i s to d e c r e a s e face.  to  .5  higher  tempera-  that the e f f e c t  of  the r e l a x a t i o n time o f t h e  inter-  T h e r e i s a l s o some i n d i c a t i o n t h a t t h e i n c r e a s e i n t e m p e r a t u r e  has caused  t h e upper asymptote to s h i f t upwards s l i g h t l y .  v a l u e of y^ p r e v i o u s l y o b t a i n e d i s 0.705 compared t o y  = 0.73  on the g e n e r a l c u r v e of F i g u r e 25, w i t h i n the experimental fore, y  , y  scatter  f o r the higher temperature  5.5.1  tests.  • i s compared to t h e d a t a  then i t appears t h a t 0.73  plotted i s well  shown by a l l t h e f r i c t i o n d a t a .  a r e c o n s i d e r e d to be u n a f f e c t e d by  max. min. i n c r e a s e s f o r the l i m i t e d  The maximum  f o r C a - s t e a r a t e f i l m s a t room t e m p e r a t u r e  max. However, i f the d a t a f o r t h e s e c u r v e s  of equations s  temperature range i n v e s t i g a t e d .  D i s c u s s i o n of Temperature R e s u l t s  (6) and  a r e determined  ( 8 ) , w h i c h show t h a t t h e upper and by p  m  , T  o  and  k  JL,  a p p e a r s t h a t temperature has v e r y l i t t l e of the i n t e r f a c e . cosity  There-  temperature  I n l i g h t of t h i s i n f o r m a t i o n and by f u r t h e r  for y  0  Comparing room tempera-  f o r C a - s t e a r a t e , F i g u r e 21, w i t h t h e s e two  t u r e c u r v e s , F i g u r e s 26,  t h e y^ -  lower  examination asymptotes  k„, the e l a s t i c m o d u l i i , i t z.  effect  I t has however a s i g n i f i c a n t  on  the. e l a s t i c  modulii  e f f e c t on c, t h e  vis-  parameter. Q u a n t i t a t i v e l y then, over a l i m i t e d  range o f  tempera-  t u r e , the y^ - 0 e q u a t i o n s would be m o d i f i e d by s u b s t i t u t i n g c ( T ) f o r  67  c as f o l l o w s :  c-c(T) =pe  (  A  E  /  B  T  [47]  )  .... (19)  using the viscosity-temperature r e l a t i o n s h i p derived  f o r monolayers.  AE i s t h e a c t i v a t i o n energy f o r f l o w , B i s Boltzman's  c o n s t a n t and  p i s a suitable constant. It  i s i n t e r e s t i n g t o e s t i m a t e AE as M a t i j e v i c  [47] h a s g i v e n  a v a l u e o f 11 K c a l / m o l e f o r t h e a c t i v a t i o n energy f o r f l o w i n c a l c i u m s t e a r a t e monolayers.  From ( 1 9 ) :  m Given t h e . r e l a x a t i o n times, x  c =  p  +  . AE —  , f o r 22°C, 35°C and 50°C, AE i s d e t e r -  mined from a s e m i l o g p l o t , F i g u r e 28 t o be 28.5  (Kcal/gm-mole).  Over a l i m i t e d range o f t e m p e r a t u r e s , t h e u  - 8 equations  would be m o d i f i e d a s f o l l o w s :  - i.46 +  ^p- e  1 - e  k  C(T)  e  J  + 2.08 y  = 0 s .. , •  (21)  or  T(T)  - 1.46 +  k  2  k-r*-  6x(T)  + 2.08 y  g  = 0  (22)  I f t h e s u r f a c e temperatures a r e k e p t w i t h i n a l i m i t e d  range  . ( c e r t a i n l y below t h e d e c o m p o s i t i o n o r d e s o r p t i o n t e m p e r a t u r e s o f t h e film), V  t h e n 6 and temperature e f f e c t s on s t a t i c  -~ 8 - T c u r v e shown i n F i g u r e 2 9 ( a ) .  f r i c t i o n would  The upper and lower  give the  asymptotes  a r e not f u n c t i o n s o f T. If  temperature i n c r e a s e s a f f e c t  w e l l as c v a l u e s a r e temperature dependent  t h e asymptotes  (k v a l u e s a s  but as d i s c u s s e d  earlier  68  T  o  and  p  a r e u n a f f e c t e d ) then the y  m  would be  s  - 0 - T surface of F i g u r e  29(b)  expected. One  s i n g l e c r o s s - s e c t i o n a l c u r v e of the " f r i c t i o n  by y  described  , 8 and  T was  o b t a i n e d and  surface"  i t i s shown i n F i g u r e  30.  -1 0 was  kept  c o n s t a n t a t 0.345 s e c .  s t e a r a t e covered  s u r f a c e was  w h i l e the temperature  raised  t o 60°C i n 5°C  f r i c t i o n c o e f f i c i e n t g r a d u a l l y climbed  from  0.50  o f the c a l c i u m  increments.  The  a t 22°C t o 0.68  as  the  temperature was r a i s e d t o 60°C. S i n c e c h a n g i n g t h e temperature changes t h e r e l a x a t i o n time, T , and not the asymptotes, t h e y - § - T s -  d a t a s h o u l d a l s o c o l l a p s e on t h e g e n e r a l The  r e l a x a t i o n times a t each temperature,  appropriate y ^ replotted  8 data.  i n F i g u r e 31.  Using T * = T  T  T * curve obtained  ^^>  0,  were d e t e r m i n e d  The agreement i s good.  o t h e r temperature,  The  then t h e  relaxation  -  8 c u r v e a t T.  can  (15).  be  J  Of c o u r s e f o r t h i s a p p r o a c h t o be v a l i d , T. must not  exceed  earlier.  More e x t e n s i v e t h e o r e t i c a l and y^ -  was  s i g n i f i c a n c e of  s  the l i m i t s set  the  1\ , can be c a l c u l a t e d u s i n g e q u a t i o n  Knowing t h e r e l a x a t i o n t i m e means t h a t t h e y  predicted.  from  the experimental data  t h i s f i n d i n g i s t h a t , once AE has been d e t e r m i n e d , time a t any  earlier.  0 - T r e l a t i o n s h i p may  f r i c t i o n curves f o r both  yield  experimental  studies of  the  a g e n e r a l method f o r n o r m a l i z i n g  s t a t i c and  kinetic  friction.  Excellent  results  have a l r e a d y been o b t a i n e d i n d e v e l o p i n g a "master c u r v e " w h i c h g i v e s temperature glass  [27].  and  sliding velocity  e f f e c t s on  the f r i c t i o n  of rubber  on  69  VI.  6.1  SUMMARY AND  GENERAL DISCUSSION OF RESULTS  Summary The  experimental  part of t h i s  monolayer of an o r g a n i c compound w i l l cient, u  , of a s t e e l / s t e e l f r i c t i o n  i n v e s t i g a t i o n showed t h a t a  cause the s t a t i c c o u p l e to e x h i b i t  friction  coeffi-  a r a t e depen-  dency. Four o r g a n o - m e t a l l i c soap m o n o l a y e r s , d e p o s i t e d on m i l d samples by the Langmuir B l o d g e t t Over c e r t a i n ranges of 6, 0.47.  t e c h n i q u e were i n t e n s i v e l y s t u d i e d .  the s t a t i c  f r i c t i o n v a l u e s were r e l a t i v e l y  When 6 dropped below a c r i t i c a l v a l u e , however, t h e u  r o s e u n t i l a maximum of u  steel  = 0.70  was  reached.  The  s  u  g  low,  values  - 9 data f o r a l l s  f o u r monolayer-covered s u r f a c e s were a d e q u a t e l y v e r s i o n o f the, t h e o r e t i c a l model f o r y  g  d e s c r i b e d by a m o d i f i e d  - 0 i n t r o d u c e d by Johannes  [19].  The model i s based on t h e p r e m i s e t h a t t h e r e a l a r e a o f c o n t a c t between the s u r f a c e s determines determined  by 9 and  u  and  t h a t t h e amount o f t h i s c o n t a c t a r e a i s  the p h y s i c a l p r o p e r t i e s of t h e i n t e r f a c i a l r e g i o n .  In the t h e o r e t i c a l p r e d i c t i o n o f u - 8 v a l u e s , the • s a r e a a t any  r a t e 0 was  contact  d e r i v e d by assuming t h a t the d e f o r m a t i o n  " i n t e r f a c e " c o u l d be r e p r e s e n t e d by a m e c h a n i c a l  of  model made up o f  the elas-  t i c and v i s c o u s e l e m e n t s . The f a i l u r e c o n d i t i o n was t h a t s l i p o c c u r r e d when T was exceeded. U n f o r t u n a t e l y , the e x a c t v a l u e f o r T i s not o o a v a i l a b l e but i t s h o u l d be l e s s than 0.2 p w h i c h r e p r e s e n t s the s h e a r m J  s t r e n g t h / u n i t a r e a o f the m e t a l  substratum.  r e p r e s e n t a t i o n s of the d e f o r m a t i o n model, the a c t u a l v a l u e of  Two  were examined.  (T /p ) was o m  too h i g h .  mechanical For t h e  model simplest  T h i s model was r e j e c t e d  i n f a v o r of the more g e n e r a l 3-parameter l i n e a r s o l i d - P r a n d t l model f o r area  growth.  70  6.2  The Contact Area a t S l i p Initially,  t h e a r e a of c o n t a c t i s A  posed o f r e g i o n s o f m e t a l contact.  *When s l i p  - nonmetal  T  A o  o  s  f  t a c t a r e a a t s l i p has a v a l u e o f A o  r  i f T , the shear  (1 + e ( O ) = 3.5 A a t u f o s  (1 + e ( t . ) ) = 2.35 A  when u  J  o  9 »  = u max. •  ( f o r (T /p ) - 0.2) f o r a l l 9. o -m  i s t h e c o n t a c t a r e a a t v e r y low l o a d i n g r a t e s , 9 << 1. &  strength/per  I f (T /p ) - 0.2, then t h e cono m  T h i s i s t h e maximum c o n t a c t a r e a  ponding minimum v a l u e i s A ^ for  - metal  (1 + e ( t ) ) .  N  u n i t a r e a o f t h e i n t e r f a c e i s known.  It  I t i s com-  c o n t a c t as w e l l as m e t a l  c o n t a c t area a t s l i p can be c a l c u l a t e d  0.70.  = (N/p ) . m  occurs:  H  The  o  f  o  The c o r r e s = u .  s  =0.47  mm.  1. From t h e t h e o r e t i c a l p r e d i c t i o n f o r t h e upper and lower asymp-  totes, u  , u .  max. obvious  and t h e p r e c e e d i n g d i s c u s s i o n o f c o n t a c t a r e a , i t i s  "mxn.  t h a t both t h e maximum and t h e minimum e x t e n t o f a r e a growth  responds t o the i n t e r f a c e T /p , k., , k„ v a l u e s and not t o t h e i n t e r f a c e o m 1 2 v  viscosity  term:  s max.  m  r  1 -  and T s mxn.  P  o  m  r 1 - T  k  1  +  k  2  At t h i s p o i n t , i t i s u s e f u l t o c o n s i d e r the c o n d i t i o n s under which a rate-dependency w i l l  be  observed.  71  a) S i n c e  f y - u . 1 represents the "spread" [_ s max. s mm. J  t i o n values, i t i s obvious then  f o r a given  I n t h e s e c a s e s , y (6) - y f o r a l l 0. s s max.  t i o n experiments, s  «  fric-  interface,  I y - y . I ->• 0 and no rate-dependency w i l l be d i s r |_ s max. s mxn. J  cernible.  y  that i f  in static  the s c a t t e r  F o r most  i s a t l e a s t 5% so t h a t s m a l l y  -  g  . v a l u e s w i l l not be n o t i c e d , mm.  b) Even though t h e asymptotes a r e not s e n s i t i v e t o t h e v i s c o s i t y the  c  ratio  k  k  1 +  , t h e r e l a x a t i o n time  w i l l l i e on t h e 0 a x i s . g  - 0 curve  the f u l l large.  is still  an  term,  important  2  p r o p e r t y o f an i n t e r f a c e .  y  fric-  I t determines Since  to the r i g h t  small  k  where t h e y  1 +  k  side of the 0 a x i s ,  g  - 0 curve  r a t i o s s h i f t the 2  i t i s p o s s i b l e that  shape o f t h e c u r v e w i l l o n l y be v i s i b l e  i f0 i s relatively  I f t h i s i s the case f o r a p a r t i c u l a r i n t e r f a c e ,  then  over  t h e r e s t o f t h e range o f 0 v a l u e s , y ^ may appear c o n s t a n t a t y  s  = y  s max.  .  Similarly, i f  = y s  . s  l and y k  curve i s s h i f t e d  y  J  to the l e f t  +  k  g  i s l a r g e , the y ^ 2 may appear c o n s t a n t a t  .  mm.  . Because o f t h e s e two f a c t o r s , a g i v e n i n t e r f a c e may appear to 6.3  show no r a t e - s e n s i t i v i t y over a p a r t i c u l a r 0 r a n g e . A p p l i c a b i l i t y of Results to Lubricant S e l e c t i o n Although  low s t a t i c  f r i c t i o n values are not the sole c r i t e r i o n  of  boundary l u b r i c a n t performance, t h e y  in  lubricant  selection.  s w i t c h i n g gear,  g  - 8 curve  s h o u l d be o f v a l u e  C e r t a i n l y i n some a p p l i c a t i o n s ,  s t a t i c f r i c t i o n values are important.  r e l e v a n t d e s i g n d a t a a r e s c a r c e and p o o r l y t a b u l a t e d . y  s  any  - 0 c u r v e s a r e u s e f u l because f i n d i n g y  s  such a s  Unfortunately, Individual  i s a simple matter:  given  normal l o a d a t any t a n g e n t i a l l o a d i n g speed, 0 i s r e a d i l y c a l c u l a t e d .  72  More g e n e r a l l y , f o r a s e r i e s of l u b r i c a n t s w h i c h have known upper and lower asymptotes,  o n l y t h e i r i n d i v i d u a l r e l a x a t i o n times a r e r e q u i r e d  before a p a r t i c u l a r u  - 0 c u r v e o r a (u s  ,0.) s.  value  i s fully  1  x  defined. Although the m a j o r i t y of the preceeding d i s c u s s i o n t h e f r i c t i o n b e h a v i o u r of L a n g m u i r - B l o d g e t t of  the f r i c t i o n behaviour of the f e r r i c  monolayers,  concerns  an e x a m i n a t i o n  s t e a r a t e monolayer d e p o s i t e d  by t h e a b r a s i o n t e c h n i q u e shows t h a t t h i s f i l m  has b e t t e r  lubricating  q u a l i t i e s than any o f t h e o t h e r soap monolayers.  This observation i s  not s u r p r i s i n g when one c o n s i d e r s t h a t monolayers  formed  are  i n t h i s way  s t r o n g l y bound t o t h e s u b s t r a t u m t h r o u g h c h e m i s o r p t i o n w h i l e t h e  Langmuir-Blodgett  soap monolayers  a r e o n l y p h y s i c a l l y adsorbed  p r e s e n t c a s e and thus more e a s i l y d i s r u p t e d by t h e a p p l i e d  i n the  forces.  F u r t h e r c o n s i d e r a t i o n of the e f f e c t s of abrading a m e t a l l i c s u r f a c e i n c o n t a c t w i t h a s u r f a c t a n t may e x p l a i n t h e f r e q u e n t l y phenomenon o f r u n - i n d u r i n g f r i c t i o n  studies.  G e n e r a l l y , one o b s e r v e s  t h a t w i t h r e p e a t e d t r a v e r s a l s o f t h e same t r a c k , t h e f r i c t i o n w i l l decrease u n t i l process i t s e l f  observed  i t reaches a constant v a l u e .  coefficient  Since the s l i d i n g  g e n e r a t e s " c l e a n " a r e a s w h i c h a r e i d e a l s i t e s f o r chemi-  s o r p t i o n , r e p e a t e d t r a v e r s a l s cause t h e f o r m a t i o n o f an a b s o r b e d m e t a l l i c soap and a subsequent  decrease i n f r i c t i o n .  I n a d d i t i o n , one  must c o n s i d e r t h a t c e r t a i n m e t a l s a r e c a p a b l e o f c a t a l y z i n g t h e o x i d a t i o n o f o r g a n i c compounds [3].  The f o r m a t i o n o f t h e s e new  which a r e a l s o c a p a b l e o f f o r m i n g f r i c t i o n  surfactants,  reducing surface films,  may  be another f a c t o r i n r u n - i n . The temperature  work has shown t h a t r e l a x a t i o n  s t r o n g l y i n f l u e n c e d by temperature  increases.  times a r e  I f the r e l a x a t i o n  time  73  for  each of two  temperatures  i s e x p e r i m e n t a l l y determined,  t i o n e n e r g y c a n be c a l c u l a t e d . appropriate  the  activa-  Then, i t i s p o s s i b l e t o c o n s t r u c t  - 6 c u r v e f o r any  the  o t h e r temperature w i t h i n t h e g i v e n  range. U n f o r t u n a t e l y , i t i s not y e t p o s s i b l e to p r e d i c t  quantitatively  * the p  — 0 behaviour  o f an i n t e r f a c e from a simple  substrata properties. 6.4  and  A d d i t i o n a l work a l o n g t h e s e l i n e s i s n e c e s s a r y .  A Note on t h e Time-dependence o f S t a t i c E a r l y i n v e s t i g a t o r s of s t a t i c  f r i c t i o n c o e f f i c i e n t was  Friction  f r i c t i o n observed  s t a t i c f r i c t i o n v a l u e s were not c o n s t a n t  and  that  the time a t w h i c h m a c r o s c o p i c  the  proposed t h a t t h e  a f u n c t i o n of " s t a t i o n a r y contact  meaning t h e time e l a p s e d between t h e f i r s t f o r c e and  study of monolayer  static  time",  a p p l i c a t i o n of the  sliding  shearing  occurred.  Johannes t e s t e d t h e i r h y p o t h e s i s by a p p l y i n g a t a n g e n t i a l load at a given r a t e , h o l d i n g the load constant 100  seconds, then a p p l y i n g f u r t h e r t a n g e n t i a l f o r c e (at the  r a t e ) u n t i l macroscopic "delayed for  f o r time p e r i o d s up  s t i c k " t e s t was  corresponding  static  f r i c t i o n was  10), i t i s o b v i o u s  However, i t i s p r o b a b l e  observed  g  f o r the value  s  static  t h a t time jus i n v o l v e d i n t h a t no  increase i n s t a t i c  d u r i n g Johannes c r e e p t e s t s because t h e amount of  small increase i n p Given  that p  not s i g n i f i c a n t l y l a r g e r t h a n t h e y  a r e a growth d u r i n g the " d e l a y e d resulting  found  In examining the v i s c o e l a s t i c models f o r  ( E q u a t i o n s 6,  friction.  He  initial  t e s t s i n w h i c h t h e t a n g e n t i a l l o a d i n g by u n i n t e r r u p t e d  by a d e l a y p e r i o d . friction  s l i d i n g occurred.  to  g  stick" was  time was  v e r y s m a l l , and  not c o n s i d e r e d  the  significant.  t h e v i s c o e l a s t i c p a r a m e t e r s o f the i n t e r f a c e ,  i t s stress  74  h i s t o r y and a p p r o p r i a t e creep compliance J ( t ) , i t i s p o s s i b l e to c a l c u l a t e t h e i n c r e a s e d a r e a growth due t o the d e l a y time.  C o n s i d e r an  i n t e r f a c e w i t h c a l c i u m s t e a r a t e as t h e monolayer and s t e e l as t h e substratum:  ^ a t 22°C, i f t h e i n t e r f a c e behaves as a K e l v i n - V o i g t  sub-  s t a n c e up t o t h e f r a c t u r e p o i n t , then c/k = 40 s e c , P / k = 1/1.46. •m m  Given 6 = .005,  = 50 s e e s . , and the l o a d i n g h i s t o r y shown i n  F i g u r e 32, t h e amount of a r e a growth f o r d e l a y e d  s t i c k times  of 1  second t o <», was c a l c u l a t e d as f o l l o w s : A , the i n i t i a l o grown t o A  o  (1 + e ( t „ ) ) . 2  c o n t a c t a r e a i s N/p  m  .  At time t„, A has I o  The v a l u e o f e(t„) i s found I  tary i n t e g r a l given i n equation  from t h e h e r e d i -  ( 3 ) , f o r a l o a d i n g time o f t ^ .  Therefore:  A^ (1 + e ( t ) ) = A o / o  °2  1 +  (k t  t k 2  2  °2 c - c) + — — t k  " c 2 e C  2  At t = t ^ , e v a l u a t i n g t h e same i n t e g r a l f o r the l o a d i n g h i s t o r y g i v e n by l i n e 2 o f F i g u r e 32 which i n c l u d e s t h e d e l a y p e r i o d (t  3  - t ) , t h e a r e a w i l l be [ 3 1 ] : 2  k  ko  (1 + E ( t ) = A 3 o  Therefore,  the present  °2 fc  °2 k  c c  1 - ec  i t .  H  c  3  3  a r e a . i n c r e a s e due t o a r e a growth d u r i n g t h e  delay i s :  1-  A (1 + e ( t , ) ) - A (1 + e ( t ) ) D = -2^ — ^ x 100% A (1 + e ( t j ) o I where:  1 + e(t ) 3  1 +e(t ) 2  x 100%  75  c — = 40 s e c . k Using  = 1.46  t„ = 50 s e c . 2  t h e s e v a l u e s , t h e a r e a a t t , immediately  begins, The  k — p m  i s 1.07 A . o  The a r e a a t t„ i s A 3 o  when t h e d e l a y  1.171 - .34e  time  -  L  1  % i n c r e a s e i n a r e a due t o d e l a y time i s p l o t t e d  i n F i g u r e 33. F o r  a d e l a y time o f 1 second, t h e a r e a i s i n c r e a s e d by 0.5%, an i n s i g n i f i c a n t amount. infinite;  The maximum a r e a growth o c c u r s when t h e d e l a y time i s  even then t h e a r e a i n c r e a s e i n o n l y 9.5%.  f o r no d e l a y t a n g e n t i a l l o a d i n g i s 0.60. F,. . final _ = ^ = T  V  s  N  o  I f , due t o t h e d e l a y time, amount, 10%, then U and  g  . A. .  r  Therefore:  n  = . 60 .  final  t h e f i n a l a r e a i n c r e a s e s by t h e maximum  would i n c r e a s e t o a p p r o x i m a t e l y  i n c r e a s e w h i c h might be c o n s i d e r e d s i g n i f i c a n t ,  amount o f s c a t t e r obtained  F o r 0 = .005,  i n the data.  0.66 from 0.60, d e p e n d i n g on t h e  Certainly considering the results  f o r c a l c i u m s t e a r a t e , F i g u r e 21, t h e s c a t t e r band i s such  that  a r e a i n c r e a s e s l e s s t h a n 5% would n o t be c o n s i d e r e d s i g n i f i c a n t .  There-  f o r e , i n t h i s c a s e , f o r d e l a y times  effects  would be n o t i c e a b l e . not o b s e r v e  l e s s than 50 s e c o n d s , no time  T h i s c a l c u l a t i o n i n d i c a t e s why Johannes  significantly  increased  [19] d i d  v a l u e s and why t h e e l e c t r i c a l  r e s i s t a n c e measurements o f Green [16] d i d n o t i n d i c a t e a p p r e c i a b l e a r e a growth d u r i n g t h e d e l a y e d  static  c o n t a c t p e r i o d even though s t a t i c  fric-  t i o n i s t i m e dependent. The additional  experimental  r e s u l t s of S e i r e g and W e i t e r  i n f o r m a t i o n on a v i s c o e l a s t i c model of s t a t i c  They conducted  creep  [57] p r o v i d e friction.  t e s t s i n much t h e same manner a s Johannes w i t h t h e  e x c e p t i o n t h a t t h e y were a b l e t o measure t h e v e r y s m a l l amounts o f m i c r o -  76  slip test.  (of t h e o r d e r of  .00005 i n c h e s ) which took p l a c e d u r i n g the  creep  They a l s o c o n s i d e r e d u s i n g a v i s c o e l a s t i c model t o e x p l a i n t h e i r  r e s u l t s and the observed  found  t h a t the 3-parameter model a d e q u a t e l y  creep.  It i s interesting  approximated  t o examine t h e i r r e s u l t s  Based on t h e i r v a l u e s f o r c r e e p d i s p l a c e m e n t ,  the r e l a x a t i o n time f o r  t h e t h r e e parameter model has been c a l c u l a t e d as 0.13  sec.  T h i s com-  pares very favourably with the r e s u l t s of the present study. n a t e l y , S e i r e g and W e l t e r  further.  Unfortu-  d i d not i n c l u d e s u f f i c i e n t d a t a on l o a d i n g  r a t e s so t h a t c a l c u l a t i n g a U  g  - 6 c u r v e f o r t h e i r system was  impossible.  77  VII.  Previous  CONCLUSIONS  i n v e s t i g a t i o n s o f s t a t i c f r i c t i o n have shown t h a t  the s t a t i c f r i c t i o n c o e f f i c i e n t o f a s t e e l / s t e e l f r i c t i o n c o u p l e l a r g e l y depends on t h e magnitude o f the r a t e parameter, 0, f o r t h e range  0 < 10.  .0001 <  The  first  p a r t o f the p r e s e n t  e x p e r i m e n t a l work was concerned  w i t h f i n d i n g the cause o f t h i s observed r a t e dependence.  Static f r i c -  t i o n vs 8 s t u d i e s under h i g h vacuum c o n d i t i o n s showed no r a t e e f f e c t over t h e range .0001 < 0 < 2 f o r s t e e l s u r f a c e s . v a l u e y , was somewhat lower than i n i t i a l l y g  of r e s i d u a l s u r f a c e a reasonable  The s t a t i c  friction  expected but when the e f f e c t  c o n t a m i n a t i o n was c o n s i d e r e d ,  0.70 was thought t o be  value.  No r a t e e f f e c t s were o b s e r v e d i n t h i s range o f 0  values  when o x i d e f i l m s were d e l i b e r a t e l y grown on the s t e e l s u r f a c e s . f r i c t i o n c o e f f i c i e n t s were h i g h by  two methods:  in H 0 2  heating  The  (0.80 and 0.70) f o r o x i d e f i l m s formed  a t 250°C i n a i r and by immersing the samples  o f pH 4.0.  •  When monolayers o f o r g a n o m e t a l l i c  soaps were d e p o s i t e d  on  i the s u r f a c e , however, t h e s t a t i c f r i c t i o n c o e f f i c i e n t d i d show the expected r a t e dependency.  One c o n c l u s i o n  a r i s i n g from t h i s work was  t h a t , s i n c e the s t a t i c f r i c t i o n o f r e a s o n a b l y c l e a n s t e e l samples was independent o f 8, the r h e p l o g y o f s u r f a c e  f i l m s was a l a r g e f a c t o r i n  d e t e r m i n i n g the s t a t i c f r i c t i o n c h a r a c t e r i s t i c s . the u  s  - 0 c u r v e depended on t h e m e t a l l i c soap d e p o s i t e d  as w e l l as on the method of d e p o s i t i o n . gated.  The exact  Four monolayers, c a l c i u m  shape o f  on the s u r f a c e  F i v e soap monolayers were i n v e s t i -  oleate, calcium  b a s i c i r o n soaps o f s t e a r i c a c i d were d e p o s i t e d  s t e a r a t e , and the using  the Langmuir-  78  Blodgett technique.  The f i f t h monolayer, f e r r i c  s t e a r a t e was grown i n  s i t u by a b r a d i n g t h e s t e e l s u r f a c e under a s o l u t i o n o f s t e a r i c a c i d i n n-hexanes.  For the s t e a r i c a c i d  sion technique, u soap monolayers 0.70 and u  soap monolayer d e p o s i t e d by t h e a b r a -  was 0.39 and u  was 0.22.  max. min. d e p o s i t e d by t h e L a n g m u i r - B l o d g e t t was 0.47.  A l t h o u g h t h e upper  For the four  method, u  was  max. and lower asymptotes  were  min. t h e same f o r each c u r v e , t h e c u r v e s were d i s p l a c e d the 9 a x i s . the s t a t i c  from one a n o t h e r on  An e x a m i n a t i o n o f p o s s i b l e t h e o r e t i c a l models showed  that  f r i c t i o n b e h a v i o u r f o r s t e e l s u r f a c e s covered w i t h any o f  these four Langmuir-Blodgett  monolayers  i s adequately d e s c r i b e d by:  •s x8  - 1.46 + T0  +  2.08  y  (23)  = 0  where x i s t h e r e l a x a t i o n time f o r t h e i n t e r f a c e . The  t h e o r e t i c a l model f o r s t a t i c  friction  that the o r i g i n of f r i c t i o n a l resistance l i e s s h o r t - r a n g e m e t a l - m e t a l bonds formed assumption  i s that the f i n a l  f u n c t i o n o f 9 because of a v i s c o e l a s t i c  implicitly  i n t h e b r e a k i n g of t h e  at areas of contact.  A further  c o n t a c t a r e a between the s u r f a c e s i s a  t h e i n t e r f a c e has t h e d e f o r m a t i o n  solid.  assumes  characteristics  I t i s a l s o assumed t h a t s l i p w i l l  when t h e t a n g e n t i a l s h e a r i n g s t r e s s exceeds  occur only  a certain value, T .  Using  (23), i t was p o s s i b l e t o c a l c u l a t e r e l a x a t i o n t i m e s f o r each o f t h e TTionolayer-covered s u r f a c e s from t h e e x p e r i m e n t a l U  g  -  8 data.  r e l a x a t i o n times p r o v i d e some i n d i c a t i o n o f a p a r t i c u l a r e f f e c t i v e n e s s as a boundary l u b r i c a n t . r e l a x a t i o n times gave low s t a t i c p a r t o f t h e 6 range.  Monolayers  friction  These  monolayer's  which had h i g h  c o e f f i c i e n t s over the l a r g e s t  C o n v e r s e l y low r e l a x a t i o n times mean u  = u max.  f o r most 0 v a l u e s .  79  The  r e l a x a t i o n time of t h e c a l c i u m s t e a r a t e - c o v e r e d  decreased  as t h e substratum  temperature was i n c r e a s e d .  important  because i t shows how u  g  interface  This effect i s  i s a f f e c t e d by temperature —  a particu-  l a r monolayer may be adequate a t room temperature but a t 50°C, the s t a t i c f r i c t i o n c o e f f i c i e n t may be as h i g h as y max. In t h e d i s c u s s i o n s e c t i o n , t h e p r e r e q u i s i t e s f o r o b s e r v i n g r a t e dependence were b r i e f l y d i s c u s s e d .  They a r e : and k^ f o r an i n t e r f a c e must be  1. the n u m e r i c a l v a l u e s o f  such t h a t t h e d i f f e r e n c e between y  s max.  and y  s min.  is  detectable; 2. the r e l a x a t i o n  time,  +  k±  k  , must be l a r g e enough, 2  or t h e range of 6 must be wide enough t o show the expected y  - 8 curve. s  One o f t h e i n a d e q u a c i e s  of f r i c t i o n r e s e a r c h from the d e s i g n e r ' s  p o i n t o f view i s t h a t i t i s s t i l l v e r y d i f f i c u l t f r i c t i o n data i n a concise, useable the g e n e r a l y  g  form.  - x* curve l o o k p r o m i s i n g .  1) t h e asymptotes, 2) the r e l a x a t i o n c o e f f i c i e n t were p u b l i s h e d , then t h e y  to f i n d  the a p p r o p r i a t e  Thus, t h e p o s s i b i l i t i e s of I f 3 v a l u e s f o r an i n t e r f a c e ,  time, and 3) t h e temperature g  value at a given 8 f o r a given  temperature c o u l d be c a l c u l a t e d from t h e g e n e r a l y  g  - T * curve.  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F a r a d a y S o c , 46, p. 475 (1950).  85  APPENDIX I  THE VACUUM SYSTEM  The u l t r a - h i g h vacuum system used i n t h i s work was from Ion Equipment  C o r p o r a t i o n o f Santa C l a r a , C a l i f o r n i a .  purchased The  basic  TTSB-200 system i s a b a k e a b l e , a l l m e t a l u n i t , c a p a b l e o f r e a c h i n g a t o t a l p r e s s u r e o f 5 x 10 bake-out  a t 250°C.  torr  i n 15 h o u r s , i n c l u d i n g a two-hour  The vacuum chamber c o n s i s t s o f 2 major  1) a b a s e w e l l assembly which houses p l u s t e n 1-1/2" I.D. was  custom  built  items  two o f the t h r e e gas pumping  — units  f e e d t h r o u g h p o r t s , and 2) a m e t a l b e l l j a r w h i c h  t o our  specifications.  A q u a d r u p o l e t y p e mass s p e c t r o m e t e r , a l s o p u r c h a s e d from was  added  t o the vacuum system.  I t was  used as a t o t a l p r e s s u r e gauge  and a l e a k d e t e c t o r a s w e l l as a r e s i d u a l gas  a) The Pumping  analyzer.  System  A rough vacuum i s produced by c r y o g e n i c pumping. sorption-pump  u n i t u s e s LN^ as a c o o l a n t and h i g h l y p o r o u s  ( c a l c i u m o r sodium aluminophosphate) sorbant.  IEC  The d u a l synthetic  z e o l i t e m o l e c u l a r s i e v e as t h e  These pumps a r e r a t e d a t 110 l i t r e s per second ^  and  will  -3 produce a vacuum i n t h e 10 f o r t h e i o n pumps.  t o r r range which i s t h e s t a r t i n g p r e s s u r e  A l t h o u g h c r y o g e n i c pumping u n i t s h a n d l e  relatively  s m a l l volumes o f gas when compared w i t h m e c h a n i c a l o r d i f f u s i o n pumps, they a r e v i b r a t i o n f r e e .  One  o t h e r i m p o r t a n t advantage  of u s i n g  c r y o g e n i c pumping i n t r i b o l o g i c a l r e s e a r c h Is t h a t the p o s s i b i l i t y o f c o n t a m i n a t i o n due t o the b a c k s t r e a m i n g o f pumping o i l s  i s eliminated.  86  I f d i f f u s i o n pumps a r e p o o r l y b a f f l e d , contaminated  then t h e vacuum atmosphere w i l l be  by s m a l l amounts o f t h e heavy o i l s used as t h e pumping  Molecules of these o i l s a lubricating  can condense on t h e t e s t s u r f a c e s and t h u s p r o v i d  film.  The u l t r a h i g h vacuum i s produced and  i o n pumping.  using titanium getter  The t i t a n i u m g e t t e r pump i s a f o u r f i l a m e n t  s u b l i m a t o r , c a p a b l e o f pumping 4300 l i t r e s p e r second N^. is  fluid  pumping  titanium  The t i t a n i u m  s u b l i m e d o v e r 370 s q . i n . o f t h e LN^ - c o o l e d s t a i n l e s s s t e e l c r y o -  shroud.  The work a r e a i s s h i e l d e d from t h e t i t a n i u m s u b l i m a t i o n pump.  T h i s t y p e o f pumping e f f e c t i v e l y pumps l a r g e volumes o f gas a t h i g h pressures. magnetic chamber.  The i o n pump c o n s i s t s o f an a r r a y o f e i g h t  diode u n i t s .  25 £/sec.  These u n i t s a r e an i n t e g r a l p a r t o f t h e vacuum  The i o n pump assembly  i s c a p a b l e o f pumping 200 £/sec. a i r ;  60 £/sec. h e l i u m o r 40 £/sec. a r g o n . The pumping s e c t i o n o f t h e b a s e w e l l assembly from t h e upper  p a r t o f t h e chamber by a poppet  valve.  c a n be i s o l a t e d This allows the  —8 pumps t o m a i n t a i n a vacuum l e v e l o f 10  t o r r o r lower i n t h e b a s e w e l l  assembly  w h i l e t h e work a r e a i s a t a t m o s p h e r i c p r e s s u r e .  The b a s e w e l l  assembly  a l s o c o n t a i n s 10 f e e d t h r o u g h p o r t s o f 1-1/2 i n c h I.D.  b) Custom B e l l J a r The custom b e l l j a r u n i t 8" h i g h and 12" i n d i a m e t e r .  i s shown i n s i t u  i n F i g u r e 8.  I t contains 6 feedthrough p o r t s :  w i t h .1-1/2" I.D. o f w h i c h 2 p o r t s a r e o p t i c a l p o r t s , 1 p o r t mounting a s t a n d a r d 3" l i n e a r motion m e c h a n i c a l  f o r a custom-made 6" l i n e a r motion  1) 4 p o r t  i s used f o r  f e e d t h r o u g h and t h e f o u r t  p o r t i s used f o r an e l e c t r i c a l f e e d t h r o u g h ; 2) 1 l a r g e used  I t Is  mechanical  (2-1/2"  I.D.) p o r t  f e e d t h r o u g h , and  87  3) 1 l a r g e (2-1/2" I.D.) o p t i c a l p o r t on t h e b e l l j a r c o v e r . jar unit  a l s o c o n t a i n s a 4" wide by 1" t h i c k work support  The b e l l  platform.  It  i s p o s i t i o n e d a t t h e base o f t h e chamber and i s welded to t h e i n n e r f l a n g e a t t h e chamber base.  c) M e a s u r i n g t h e System P r e s s u r e In f r i c t i o n and a d h e s i o n work, b o t h d u a l gas c o m p o s i t i o n  are important.  system p r e s s u r e s and  From a c a l i b r a t i o n c u r v e o f i o n  pump c u r r e n t v s N i t r o g e n - e q u i v a l e n t p r e s s u r e s u p p l i e d by t h e i t was p o s s i b l e to m o n i t o r  pumped.  manufacturer,  t h e p r e s s u r e i n t h e system down t o 10  by m e a s u r i n g t h e i o n pump c u r r e n t . gauges  resi-  However, i o n pumps and  torr  ionization  (a t y p e o f i o n pump) a r e s e n s i t i v e t o t h e t y p e o f gas b e i n g Therefore, i n order to f i n d  tem, i t i s n e c e s s a r y To a c c o m p l i s h  the true t o t a l pressure of the s y s -  to know t h e c o m p o s i t i o n  t h i s , a quadrupole-type  o f t h e gases b e i n g  pumped.  r e s i d u a l gas a n a l y z e r was  purchased  -14 from IEC.  T h i s instrument  h a s a s e n s i t i v i t y of 1 x 10  torr  p r e s s u r e f o r N i t r o g e n , a mass r a n g e o f 1 - 250 amu and i s  partial  capable of  r e s o l v i n g a d j a c e n t mass peaks t o mass 250 (10% v a l l e y d e f i n i t i o n o f resolution). vacuum system.  The r e s i d u a l ' g a s a n a l y z e r formed an i n t e g r a l p a r t o f t h e I t c o u l d be used i n t h e t o t a l p r e s s u r e mode t o g i v e t h e  N i t r o g e n - e q u i v a l e n t p r e s s u r e i n t h e chamber and i t was used a s a s e n s i t i v e l e a k d e t e c t o r as w e l l as a mass s p e c t r o m e t e r .  T h i s instrument  was  i n v a l u a b l e i n d e t e c t i n g s m a l l amounts of c o n t a m i n a t i o n i n a d v e r t e n t l y -9  left  i n t h e chamber.  A t the t e s t  p r e s s u r e s , 10  torr, a typical analysis  would show t h a t t h e r e s i d u a l gases were p r i m a r i l y l ^ , bake-out).  He, and A r  (after  88  APPENDIX I I  PROPERTIES OF REAGENTS USED  a) S t e a r i c A c i d  (Octadecanoic A c i d ) CH  (OH )  Moi.  2  l f i  COOH  Wt. = 284.49  m.p. •= 67-69°C T h i s a c i d was o b t a i n e d as l a b o r a t o r y  grade from F i s h e r  Scientific.  b)  Hexanes  C  6  H  14  F.W. = 86.18 A m i x t u r e of isomers.  I n t h e as r e c e i v e d  a pH o f 0.00.  Actual Lot Analysis B o i l i n g Range: Density:  66.1° - 68.1°C  g./ml. - 0.668  R e s i d u e A f t e r Evap.: A c i d i t y as C H  3  0.0004%  COOH P.T.  Sulphur Cmpds. (as S ) : Thiophene:  c) HC1, Ca C 0  3  Reagent grade.  P.T.  0.004%  c o n d i t i o n , i t has  89  d)  H 0 2  Double  e) O l e i c A c i d  distilled.  Films  Oleic acid:  (9-octadecenoic  acid)  Moi. Wt. = 282.46 C_ H o 1/  CH:  CH(OH_)_ COOH 2.  I  I n s o l u b l e i n H^O. Approximate s u r f a c e p r e s s u r e on ^ 0  a t 25°C, 30 dynes/cm.  90  APPENDIX I I I  1. E s t i m a t i n g the a c t i v a t i o n T, due  to  energy AE from the s h i f t  temperature: AE l — 2 T  _1_ _ _1_ T T 1 2  k  = e  T  £ n ^ T  =  2  £n  40 .5  1.98  1_  ^ k AE cal/mole  •: AE = 28.7  295  Kcals/mole.  323  relaxation  time,  FIGURES  VVXAAA  Ft  -  •x-  FIGURE 1.  Ft  -AX-  V i s c o e l a s t i c Model o f S t a t i c F r i c t i o n D e v e l o p e d by Johannes [ 1 9 ] .  92  N  Metoiiic Substrata  F= F t  LLLLL/ /  Deformed Metal Layer Oxide  — ^ Metallic Soap |_JL Oxide f Deformed Metal Layer  Metallic Substrata  FIGURE 2a. The C o n t a c t A r e a Between Two S o l i d S u r f a c e s i s t h e Sum o f A^J^JL^ ! A s p e r i t i e s Meet. 8 0  6 1 1 6  A  r  e  a  S  °  f C  o  n  t  a  c  t  Formed Where Opposing  93  A Contact Area  FIGURE 2b.  Shear Strength of the Interface  The A r e a of C o n t a c t and the Shear S t r e n g t h as F u n c t i o n s of the Rate of A p p l i c a t i o n o f t h e T a n g e n t i a l S h e a r i n g Force.  FIGURE 3.  T a n g e n t i a l Loading During  a Static Friction  Test.  VsAAA cr(t)  a) The S i m p l e s t M a t h e m a t i c a l Model f o r S t a t i c F r i c t i o n I n v o l v e s a K e l v i n - V o i g t Element Coupled w i t h a P r a n d t l - T y p e Element.  AAAAA To  o-(t)  A/W\A  b) More Complicated Model. The I n t e r f a c e Deforms as a G e n e r a l L i n e a r S o l i d Having a F a i l u r e S t r e n g t h per U n i t Area o f T . Q  FIGURE 4.  Models f o r S t a t i c  Friction.  96  log  FIGURE 7.  i o  "C(dimensionIes^ 3  The General S t a t i c F r i c t i o n Curve.  FIGURE 8.  G e n e r a l Arrangement o f Vacuum System and E x p e r i m e n t a l  Apparatus.  FIGURE 10.  Schematic o f the H y d r a u l i c  Control  System.  S u b - c i r c u i t A c o n t r o l s t h e a p p l i c a t i o n and t h e r e l e a s e of t h e normal c o n t r o l s t h e t a n g e n t i a l f o r c e F and the t a n g e n t i a l l o a d i n g r a t e F.  load,  Sub-circuit  B o  t—*  FIGURE 11.  Isometric Sketch of F r i c t i o n Couple.  T  .8  .6.  .4  O 2-IO" torr 8  .2 h  _j  4.0  3.0  2.0  log FIGURE 12.  I O  1.0  0.0  1.0  e(secr')  S t a t i c F r i c t i o n of C1020 S t e e l i n Vacuum o f 2 x 1 0 " ° t o r r a t 20°C.  O  "7  .8  1 —  1  -  o  O  o  o  o  °Q  °  °  oo  0 c P o  o  o°  cP  °o  oo  .6  A  A  Ms  A • ± A  A  A AA  A ^ A  A AA A A A  A A  .  A  A  A  ^A  .4  AA^A AA  A£A  A  £T  AA*A  A  -  A  A  A  A A  .2 0 2-10" torr 8  A air exposed-, 20or 48hrs.  I  4.0  3.0  log FIGURE 13.  Static  To  2.0  o.o  1.0  9(sec: ) 1  !0  F r i c t i o n o f C1020 S t e e l  i n Vacuum and A f t e r  Exposure to Atmosphere.  §  T  o OO  o,  000%  o  A  0cP o°  "^"A\.. A i l  cP.  4  o  o  o  °o  _  O 2-!0 torr A air exposed; 20or 48hrs. Marion Johannes 8  J 4.0  1  3.0  2.0  log FIGURE 14.  IO  0.0  e(secr')  Comparison of S t a t i c F r i c t i o n of C1020 Steel i n Vacuum and After Exposure to Atmosphere to S t a t i c F r i c t i o n Values Obtained by Johannes [19] and Marion [21].  1—'  o  © Oxide B  (water)  A Oxide A(250°C-air)  4.0  3.0  ._ FIGURE 15.  2.0  Iog  1.0  0.0  8 (sec: ) 1  lo  S t a t i c F r i c t i o n of C 1020 Steel Covered with Oxide Films.  Ms  4  -0  3.0  TO  2.0  .log-  0  FIGURE 16.  0.0  1.0  9 (sec: ) 1  Comparison o f S t a t i c F r i c t i o n o f O x i d e - c o v e r e d C1020 S t e e l to S t a t i c F r i c t i o n V a l u e s O b t a i n e d by Johannes and M a r i o n .  O  .8  .4  log FIGURE 17.  Static Friction  ! 0  +•  . A f t e r Abrading  —.  Johannes [19]  e(secr')  of C1020 S t e e l A f t e r A b r a d i mg  o  oo  S u r f a c e Under S t e a r i c A c i d - H e x a n e  Solut i o n .  .8  m  A  A  A  £1  ,^0 •  4V ^  A D  D  A A  "^A ^  A A  AA.  .4  iog FIGURE 18.  lllt?X«£  10  A  Basic Iron  Stearate  .P  Basic Iron  Oleate  0(sec:')  o  ^ o V ^ ^ T S TVJ ^ 1  "  E  i  t  h  £  r  \^  vO  S  t  e  a  r  a  t  e o  r  a  .8  a ©  A  A  A  ^A -  A  A  A  A  *  A  A  A  A ^  A  A  A  AAA  A  ^ A  A  A^  est  ©  FIGURE 19.  The Effect of a C a ( S t ) Monolayer.  P  2  AA'  ©  9  log,  AA.  ® Gg© ® © ®  A  Fe(OH) St  *  Ca(St)  2  0  9 (sec: ) 1  0  Monolayer on S t a t i c F r i c t i o n as Compared to the Effect of an Fe(OH) <t  H of Substrata i s 4 f o r Iron-stearate Soap, 9 f o r Calcium-stearate  Soap.  T = 20°C  i i O  T  T  s  a  a^  1  3  a  T  a  •  .4  • 2  Fe(OH)  0£  2  Ca(0£)  o  _j  4.0  3.0  2.0  1.0  log|  0  FIGURE 20.  The E f f e c t Monolayer.  of a C a ( 0 £ )  2  0.0  1.0  e(sec: ) !  Monolayer on S t a t i c F r i c t i o n Compared t o the E f f e c t  pH o f S u b s t r a t e i s 4 f o r I r o n - o l e a t e Soap,  o f an Fe(OH)  9 f o r C a l c i u m - o l e a t e Soap.  0£  T = 20°C.  -  A  - A — A _ &  A  ^ A — A ^  A  .6  A  A  A  7 > A A  AA ^ A A ^ ,  3.0  3.0  2.0 log©  FIGURE 21.  Experimental Data and Theoretical y Covered with Fe(0H)  2  1.0  0.0  A A A  A  1.0  6 (sec: ) 1  - 0 Curve f o r S t a t i c F r i c t i o n When Steel Surface i s s St Monolayer. pH 4, T = 20°C.  I  T  .8 © ©  ®  .2  4.0  3.0  2.0  1.0  l o gno.  Experimental  Data and T h e o r e t i c a l  Covered w i t h C a ( S t >  2  Monolayer.  ]i  1.0  0(sec: ) !  1 0  FIGURE 22.  0.0  -  pH 9,  6 Curve f o r T =  20°C.  i—  Static  F r i c t i o n When S t e e l  Surface  is  1  LO  .8  4.0  3.0  2.0 .  FIGURE 23.  log,  E x p e r i m e n t a l Data and T h e o r e t i c a l Covered  w i t h Fe(0H>  2  01 Monolayer.  ^  0.0 9(sec: ) !  0  - 0 Curve f o r S t a t i c F r i c t i o n When S t e e l S u r f a c e i s pH 4, T = 20°C.  •2 h  4.0  3.0  fog FIGURE  24.  E x p e r i m e n t a l Data and T h e o r e t i c a l Covered  with Ca(0£)  To  2.0  2  Monolayer.  o.o  1.0  e(sec: ) !  i0  y  g  - 6 Curve f o r S t a t i c F r i c t i o n When S t e e l S u r f a c e i s  pH 9, T = 20°C.  hh-  1  1  I  I  I  I  J I I  I  I  I II  I  I I  I I I II1  "I  I  1  1  A •  s  A Stearic Acid Fe(OH) St pH=4 2  j  .0001  .001  .01  i  •  Ca Stearate pH=9  •  Oleic Acid Fe(OH) OI pH=4  B  Ca Oleate pH=9  2  IIIIII  0.1  1.0  10  1000  100  T * - dimensionless  FIGURE 25.  E x p e r i m e n t a l Data C o l l a p s e s on G e n e r a l y T = 20°C.  g  - T * Curve P r e d i c t e d from M a t h e m a t i c a l  Model.  T  .8  E  a  .6  a  I B  H  B  s |a B a _ a S3 n Q a  T = 35°C _ l _  4.0  3.0  2.0  1.0  Iog,  0  FIGURE 26.  0.0  1.0  e(secr')  E f f e c t of Raising'Surface Temperature to 35°C.  Ca Stearate Soap Monolayer,  T  T  1  T  A  A A A A AA  T= 50°C  4.0  3.0  2.0 log,  FIGURE 27.  1.0  0  0.0  LO  e(sec:')  E f f e c t of Raising Surface Temperature to 50°C.  00  Ca Stearate Soap Monolayer,  119  log c  .1  .00300  .00325  .00375  .00350  .00400  t FIGURE 28.  , i / T f o r C a l c i u m S t e a r a t e Soap M o n o l a y e r s . Since Log c v s s Determined t o be 28 K c a l s . (AE/PT) AE wa c(T) = e  120  121  .8  o o  •6 1  o  o  o  O  O  e=.345  20  30  40  50  60  70  r c  FIGURE 30.  y  - T C h a r a c t e r i s t i c s of S t e e l Covered w i t h C a l c i u m S  S t e a r a t e Monolayer  at 0 =0.345  sec.  -3  t  FIGURE 31.  Experimental  Temperature-Friction  Data A l s o C o l l a p s e s on G e n e r a l  S t e a r a t e Monolayer Covered S u r f a c e .  '.  U .  g  - 0 Curve f o r  Calcium  123  FIGURE 32.  Loading H i s t o r y During Delayed  Stick.  10  -1  r—T  1—l—l  i  -i  |•  1—I—i  1  l  |  n  1  i  1—i—i—r-r  0  o  o o o 5 2  a) 6  D  r-  £ < C  CD Q  O  tn  o  >> o-  o  4  o a> o c  o  0 i  i  i  >  i  •—L.  I  1  10  I  I  '  I  100  1  1000  Delay Time (sees) FIGURE 33.  A r e a Growth Due to Delay Time i f t h e System has a R e l a x a t i o n Time of 40  

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