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1LASSR APPLICAT IONS TO ANALYTI CAL ULTRACENTRIFUGATION'
A THES IS PRES ENTED TO
MASSEY UN I VERSITY, PALMERSTON NORTH, NE� ZEALAN D
IN
P�RTIAL FULFILMENT O F THE RE0UIREMENTS OF
DOCTOR OF PH ILOSOPH Y
BY
JAMES ANTHONY LEWIS MAY , 1 972.
F R 0 N T I S P I E C E A GENEJ:UL VI:S.v OF THE ,\NALYTICA.L ULTRACENTRIFUGE ','JITH THE L/,SER ,\ND ITS 1\.SSOCIJ\TED MODULh.TION EQUIPMENT.
1 . •
ACKNOWLEDGEHEN TS
I should l i k e t o e xpre s s my s i n c e r e t hanks t o
Doc t or J ohn J. Lyt t le t on of t h e App l i e d B i ochemistry Divi s i on , Depart ment of S c i e nt if i c and I ndust rial Res earch , Palmerst on N orth , f or his f r i endship and gui dan c e during t h e s e past f our years . I am p art i c ular ly grat ef u l f or t he many h ours
he has spent w i t h me in adap t i n g the analyt i c a l u l t r a c e n t r if u ge f or use with t he laser sys t e m when he was a lways a vai lab l e
with b o t h prac t i c a l a s s i stance and c on s t r u c ti ve advi c e .
I am gr e a t l y indebt e d t o P r of es s or N or man F . Barb e r , of the Physic s Depart ment , Vic t oria U n i v e r s i t y of 'l e l lingt on , J e l lingt on , N ew Z ealand who was my m a j or t he ore t i c al advi s or . H i s int erest a n d ent husiasm c ould not fa i l t o s t i mu la t e
c onstruc t i ve i de a s and my d i s c u s s i ons w i t h him have b e en most rewarding .
I n ad d i t i on , I w ou l d like t o t hank P r of e s s or G e offrey N . Malc olm , P r of e ss o r of Physi c a l Chem i s t ry , Mas s e y Univer s i t y
who has c o-or d i na t e d t h i s research f or t he Depart ment of Gradua t e St udi e s. His int erest and fri endship duri n g t he c ours e of t h i s r e s ea r c h pr o j e c t has b e en of great a s s i s t an c e , and I am indeb t e d par t i cularly f or h i s a i d and supp ort i n
obt aining funds f or the pr o j e c t .
Final ly, I w ould like t o thank a l l p e r s ons b ot h a t Massey and D . S . I . R . , whom i t has b e en my pri v i l e ge t o know and who have c ont r ibut e d their advi c e and a s s i s t anc e at var i ous t i me s .
The a s s i s t anc e of grant s ( URC 68/337 and URC 7 0/3 1 4 ) from t he Uni v e r s i t y Grant s C ommi t te e of N ew Zealan d i s
ackn ow l e d ge d .
TABLE OF CONTE N TS
f\. CKNO'NLEDGEMENTS
LIS T OF I LLUS TRATION S PRE FA C E
CHf->PTER 1 •
2 .
11 THE RAYLEIGH I N T ER FE R.2;N CE .OPTICAL SYS TEM I N THE ANA LYTI CA L ULTRA CENTRIFUGE"
1 •
2 . 3 .
H i st or ical I n t r oduct i on
The or e t i ca l Analy s i s of Basic Rayle i gh I nt e rferom e t e r
Summary
11 THE COMPA RISON OF !Vl:2:;R CURY ARC AND HELIUH
N EON Gi\.S LA SE R LIGHT SOURCES "
1 •
2 .
3 .
Int r oduc t i on
Basi c C oh e r en c e The ory ( a )
( b ) Summ ary
S pat i a l C oherence T e mp or a l C oherenc e
3 . " ,\ MODULATZD Lii.SE R SYS TEH FOR .1\Ni\ LY TI CA L ULTRA CENTRIFUGE I N TSRFEREN CE STUDIES 11 1 •
2 .
3-·
4 • .
5 . 6 .
I n t r oduc t i on
D e sc ript i on o f Sys t em I . The Las e r
I I . The E l e c t r o-Opt i c L i ght II I . Th e R ot or P i c k-up
I V . The E l e c t r oni c C ont rol V. The E.H.T. M odulat or VI . T he S ou r c e Optics
�1 odulat or
Unit
The Opt i cR l A li gnment and F oc u s s i n g ( a )
( b ) ( c ) ( d )
Lase r A li gnment on Opt i c Axis
Ad j u st ment of El e c t r o-Opt i c M odu lat or F o c u s si n g the L aser Lens O pt i c s
A d j u st m e nt of t h e A pe rt u r e M a sk Exp eriment a l
( a) M at er i al and M et hQ d.
Discus s i on C on c lusi on
1 . 5 8.
1 3 . 1 3 .
1 6 . 27.
28 . 28 . 29.
32.
37.
46.
46 . 4 6 .
49 . 5 0 . 50 . 52 . 55 . 58. 58 . 6 0 . 60( a ) 6 1.
62 . 63 . 66 . 76 .
CHA PTER 3.
4. 11 DEVEL0Pf.1ENT AND PRELH1INARY EXPERIMENTS ON A NE'.J CELL F OR INTERFE"<ENCE STUDIES IN THE ANALYTICAL ULTRACENTRI_FUGE"
1 • I n t r oduc t i on 2. Th e or e t i ca l
3.
4.
5.
6.
( a ) B asic Th e ory with N on-absorbing S olut i ons
( b ) Absorbing S olut ions i n C e ntral S e c t or
I nstrument ation ( a )
(b) (c) ( d )
T ri p l e Se c t or Centr e p ie ce s
·1 indow H ol ders and Aperture Masks Cent r e pi e c e Gaske t s and Gasket Punch
C e l l A s s em b ly
( e ) C ount e r b a lanc e s and Radial Re f er e n c e
8 xperimental ( a )
( b )
J! e t hod
Ph ot ograph i c P lat e M easu r ement s R e su l t s and Di s c u s s i on
Summary 7. Ap pendix
Th e ory of Pr op o s e d B as e li n e C orr e c t i on
78.
78.
79.
84.
90.
90.
92.
93.
95.
95.
96.
96.
97.
101.
107.
M easur ement s 108.
" THE �FFECTS OF RSFRACTIVE INPEX GRADIENTS ON
�XPERIMENTAL DATA 03TAINED USING INTERFERENCE
OPTICS IN TH-ij ANA LYT.LCAL ULTRACENTBIFUGE"" 1 1 1 •
1. I ntr oduc t i on 111.
2. D�f ini t ion o f Problem 1 1 1.
3. The ory 1- 1 5.
4. Exp e r i mental Appli c ati on 11J,
5. Result s and Dis c u s s i on 121.
6. Gradi en t s f r om O f f•Axis ( Re fe re n ce ) Se c t or s 123.
7.
8.
( a ) ( b ) ( c )
I n t r o du c t i on The ory
Discussi on and R esult s Summary
Appendix
123.
124.
130.
1�1.
132·
4.
CHAPTER
6. " MATHE;MATICAL FORHULATIONS OF THE EFFECTS OF CELL DISTORTION AND LIQUI D COLUMN HEIGHT
COMPRESSI ON IN ANALYTICAL ULTRACENTRIFUGATI ON" 135.
1 . Int r oduc t i on 135.
2. M o d e l and The ory 136.
3. App l i c at i on of The ory and Dis c u s s i on 1 42.
4. Summary 1 52.
5. Appendix 1 53.
REFERENCES 157.
A PP EN DICES : I .
I I . I I I . I V . V .
Vi ews o f ( a ) Laser Cup board and
(b) Cont r o l Unit f or U lt r a c e n t r i fuge Ap erture Mask Alignment Pat t erns
Yphant i s P at t erns f or Las e r and Me rcury S our c e s S u c r os e E q u i librium - La ser Line S ourc e
Typ i c a l T o o l P i e c e s
VI . Publi c at i on
VII S upple ment t o Chapt er 5.
161 .
161.
1 G2·.
1�3.
LIS T OF I LLUS TRA TIONS
FIGURE PAGE
Fr ont i spie c e : A gener al view of t he Anal yt i c al U ltra c e ntr i fuge w it h the Las er and it s a s s oc i at e d M odula t i on Eq uipment
1-1.
1-2.
1-3.
1-4.
1-5.
1-6.
1-7.
2- 1 . 2- 2 .
2-3.
2-4.
2 -5 .
3-1.
3-
2.Th e B as i c R a y le i gh Int er fer omet er
14.
The I nt er fe r en c e Opt i c a l S yst em in t h e
A na lyt i c al U l tr a c entri fuge
15.
The Ba sic C ol limat ing S y s t e m D e fi n i ng t h e
C o or dinat e Axes
17.
Ba s i c S yst e m wit h R ayle i gh M ask 20 . M athemat i c a l R epr es e nt at i on o f t h e R ay l e i gh
Apert ur e M as k 23 .
The Int e ns it y Pat t ern Obser ve d i n t h e Foca l Plane o f Lens L2 ow ing t o t h e
Ra y l e i gh M ask 24(a).
S c hema t i c Diagr am of t he C e l l s and A p ert ur e
M ask 2 4(a)
Dia gr am for B as i c C oher en c e T h e or y
31.
Diagr am f or t he Der i vat i on of t he
Spat ial C oh er en c e C ondit i on
31.
The I nt er fer omet er I lluminat i on 34.
S p e c tr a l E n er gy Distr ibuti ons o f t h e
I nt er fer omet er S our c e s
41.
Fr inge Int ensi t y P at t er n s ow ing t o
Li mi t e d T e mp or al C oher en c e
43.
S ch e mat i c B lock Diagr am of the U ltr ac ent -
r i fuge and M odulat ed Laser S y s t e m
47.
Diagr ams s h ow i n g the M od e of A ct i on o f the
Ele c tr o-Opt i c M odulat er
51.
3-3.
Block Dia gr am o f t he E l e ctr oni c C ontr o l Unit3-4.
3-5.
3�6.
3-7.
C ir cuit D i a gr am of E . H. T . Sup p ly and Ther mi oni c Val� e Modulater
C a l i br at i on Gr aph for E le ctr o-O pt i c Devi c e Las er S ourc e O pt i c s and Pr ism
Su cr ose Equ i li br ium R ayl e i gh I nt er fer e n c e Patt er ns w it h Las er S our c e
54.
56.
56.
FIGURE 3 - 8 . 3 -9 .
3-
1
0 .3- 1 1 . 3 - 1 2 . 4 - 1 .
4 ... 2 .
4 - 3 . 4 - 4 . 4 ... 5. 4 - 6 . 4 -7 .
4 - 8 . 4 - 9 .
4-10.
4 - 1 1 . 4 - 1 2 .
5- 1
. .... PAGE C ompari s on o f M e rc ury and Las e r Sou r c e s .
Pr o t e in Equi librium Exp e rimen t. 68. Synt he t i c B oundary P at t erns for Laser and
Merc ury S ourc e s 69 .
Comparat i ve p l ot s of l o g1 0 c versus r 2
for M er c ury and Laser s o ur c e s 70 .
� xamp l e s of t he Modula t i on Fa c i l i t y in
t h e Ultrac entri fug e 7 3 .
Laser Int er ferenc e Pat t erns for H i gh
S pe e d Zqu i l ibrium E xp eriment 7 4. Basic Int e r fer ence Syst em w it h t h e Triple
A perture Ma sk 80.
Graphs of Fringe Int ensit y and Vi s i bi li t y
versus Amp l i t ude Transmi ssi o n 8 8. Trip l e -S e ct or Centrepi e c e s and C e l l H ous ing 9 1, Triple A p e r t ure � indow H ol ders 9 1 . A s sort ed A p e rture Ma sks f or us e w i t h
Triple-Se ctor C e l l 9 4 . V i ew o f Gasket Punch and Ga sket s f or
Triple -S e c t or Ce l l Usage 9 4 .
T h e oret i ca l P l o t of Fringe int en s it y
versus pha s e advanc e i n � r ip le - S e ct or C e l l 9 8. Triple-Se ctor Fringe Patt erns 9 9 . Dens i t omet e r T r a c e o f Ce ntral 7 r i n ge t o
�q ui librium Patt ern show n in F i gure 4 -8 ( b ) 99 ( a ) Va ri ous P a t t erns obt aine d using M odulat i on
Sy st em w i th Triple-S e c t or C e l l 1 04 ( a ) Bas i c Fringe Patt e rns f or Ape r t u r e Masks
in the U l t rac ent r i fuge 10 5.
Views of Vari ous Orient a t i ons b e tw e e n the C e l l Diaphragm in low er W indow H older
and fixe d A p er t ure Mask 10 6 ( a )
Int er ferenc e Opt ic a l S ys t em i n t he
Analyt i c a l U lt rac entr i fuge 1 1 2 ( a ) 5-2 S ch e mat i c Diagram of t h e Effe c t o f Linear
5-3 5- 4 .
Gradie nt
S c he mat i c Diagram of t he Effe c t o f N on Linear Gradient
Diagram of Gradients in C en t ri fuge C e l l
113 114.
1 2 5 .
? IGURE PAGE 5-5 . Di agram of C e l l Grad ient s and
Asymm et r i c a l Mask 1 26 .
6 - 1 . D iagram o f t h e R e c t angular C e l l C e n t r e pi e c e and i t s C o or d i nat e axi s system 1 40 . 6-2 . Di agra� of t h e symme t r i c a l Re c t angular
Cavit y in t h e M od e l C e l l Centrep i e c e 1 40 . 6-3 . Diagra mat i c R epre s entat i on of t he Cavity
shown in f i gure 6-2 a ft er De format i on owing t o the Cent r i fugal B ody F orc e s 1 43. 6-4 Graph show i ng t he P erc ent age C on t ra c t i on
of L i quid C olumn H e i ght with R o t or S p e e d 1 46 . 6-5 Graph showing the P e r c ent age C on t ra c t i on of
Li qui d C olumn H e i ght w i th Li qui d C o lumn H e i ght 1 46. 6-6. D iagram o f the Three Channel Y phant i s- t ype
Ce l l Cent r e p i e c e appl i c able to the mod e l 1 47 . 6 -7. Graph Showing C e l l Bas e Di sp lac ement
versus Rot or Speed 1 47 .
6-8. G raph show i n g the va riati on o f C e l l Bas e
D isplac ement ver sus C e l l Base P o s i t i on 1 49. 6 - 9 . Graph showi n g t he Perc entage C on t rac t i on
o f Li qu i d C olumn H e i ght s in t h e Y phant i s -
6 - 1 0 . 6 - 1 1 . 6 - 1 2 .
typ e C e l l M od e l 1 49 .
£2:. 2
2E w versus .R ot or Speed 2a (2R-a ) - 2R ( 2 zb + h) + zb 2 + versus h
( z b + h) 2
Perc ent age C ompre ssi on ver s u s Li qui d
151 .
1 51 .
C o lumn H e i ght owing t o Liqui d C ompr e s s ibility 1 51 •
PREFACE.
8 .
PRSFACE
Th e wor o k f �ve erg an � db 1 d h" �s eo a ora ors ll b t in the early 1920's heralded the use of centrifugal fields
for the study of macromolecular systems. Following this work the developments in both theoretical and experimental aspects have been dramatic, so much so that the majority of current researchers take the use of the analytical ultra
centrifuge for granted as a basic tool for the determination of molecular weights of macromolecules. Th8 l�tter is just- ified in view of the theoretical and experimental evidence to date, and reviews citing original references and covering the state of the art from its inception to the present day are available.
2-8
Physically, the problem associated with a study
involving the analytical �ltracentrifuge is to obtain measure
ments that will enable a specific solution of the Lamm9 equation to be obtained. For an ideal two-component system in which the partial specific volumes v (solvent) and
0
v1 (solute) are constant the Lamm equation may be written5
1
X
() dX
2 2 I i
- S W X c1:
-·
(P1)
where c1 represents the concentration of solute (component 1) with respect to solvent (component o), at a radial position x in a centrifuge cell. D and s represent the diffusion and sedimentation coefficients respectively for component 1, and (Jl is the angular frequency of the rotor. Lamm 1 s9 original derivation of this second order partial differential equation was non-rigorous, but the work of Goldberg 10 using
the concepts of irreversible thermodynamics has established clearly the conditions under which the equation applies.
Similar equations exist for more complex molecular systems, but exact analytical solutions are difficult since the coefficients D and s are not constant but functions of the variables. Thus workers with the ultracentrifuge are confronted with the all too familiar problem in science of attempting the solution of partial differential equations with non-constant coefficients. Naturally, attempts have been made to derive analytical solutions to the Lamm equations
9.
under specified conditi ons, and the monograph by
Fujita5 cont ains a useful summary of work in this area . O f particular interest b oth theoret ically and in the cont ext of t his present study is the concentrati on dist r ibut i on in a centri fuge cell at sedimentat i on-di f fusi on equilibrium . This is a thermodynamic equilibrium state and is de fined as the state in which the t ot al p otential of any component in a solut i on being cent ri fuged is constant, and where the temperature is uni form thr oughout the centri - fuge cell . Experimentally, this state is achieved under isothermal conditi ons when t he concent rat i on distr i but i on no longer changes with t ime wi t hin the accuracy o f the experiment . Obvi ously, this allows the time dependent terms in t he solut i on o f the relevant equat i ons to be equat ed t o zer o . The lat ter condition greatly simpli fies the analysis and the solut i ons then obtained are the most rigorous theoretically .
It is 2ho�n by Creeth and Pain6 and elsewhere3-5 that the ideal two component system considered in equat i on (P1) is distributed at sedimentati on equilibrium according t o the expressi on
(P2)
where M is the molecular wei ght of the solute (comp onent 1 ) and � and v the chemical p otential and partial speci fic -
volume respect ively of the solute at concent rat i on c1 ( measured on a scale mass / unit volume) . The st andard relat i onshi ps between � and c lead t o the fundamental expressi on that is used in all experiments at sediment ati on equilibrium
1
dc1 t-�(1-vp)w 2 Mapp(1-vp)w 2 i . e . xc1 dx = RT(1�
£nyld£nc1)k -
= RT
Here R is the universal gas c onstant, T is the absolut e temperature, y is the activity coefficient on t he c scale, and
weight o f the solute .
M i s the apparent molecular
a pp
The lat ter may be related to the (P3)
true molecular weight by use o f the thermodynami c non-ideality
10.
.en y = BMc +
in which B is a n empirical c oeffic ient and where higher terms i n the seri es can frequently be neglected.
Using equati ons (P3) and ( P4 ) we note that M a pp = 1 H +Bt-'ic
The imp ortance o f equ�ti ons (P3) and ( P5 ) i�
that the molecular weight ia determinable from measure�
ments o f c ( x) at equilibrium .
(P4)
(P5)
The ultracentri fuge operator has the choice of three separate optical techniques in the �odern instrument
for the evaluation of the c oncentration distribution in the centrifuge c ell. Firstly , there is the Schlieren system that relies on the refractometri c pr operties o f the soluti on and gives a rec ord o f refractive index gradient versus radial positi on for a c ell . Here it is assumed that the inc rement- al solution refracti ve index is pr oportional to the solute c oncentration . Sec ondly, there is the Rayleigh i nter - ference system which a�ain relies on the refractometri c properties of the solution but gi ves a photographic rec or�
of difference in refractive index between the soluti on and solvent ( solute c oncentration ) versus the radial p ositi on in the cell . The interference and S chlieren systems c ommonly share the same opti cal c omp�nents in the ultra- centrifuge . Finally , there is the ultraviolet absorption system that utilises the specific absorption of radiation at 254 nm by mac r omolec ules suc h as nucleic acids and pr oteins as the sensing phenomena f or determining the solute c oncentration .
The comparati ve merits of the three systems 4 11 ;>3
have been evaluated by S c hachman ' ,_ but the inter ference system is the primary c oncern of the present study . It has been demonstrated adequately 12 that the i nterferenc e system is c apable of giving simple and ac curate data that is suited parti c ularly f or sedimentati on diffusion equilibrium work. To a Physicist this is not surprising, sinc e interferometry has pr ovided the means of maki ng some of the most precise measurements available to man.
H owever, with the advent of the first operati onal gas laser
11 •
b y J a van e t a l1 3 i n 19 6 1 , t h e who le f i e ld o f i nt er-
ferometry has undergone a r e v o lut i on . Thi s t he si s i s t h e c ulmina t i on of a s tudy i ni t ia t e d b y t he aut hor in lat e
1967 int o th e possible appli cati ons of a gas laser t o i nt e r fe r e n c e studi e s i n t h e analy t ic a l ultrac e nt r i fuge .
Dr. J . �. Lyt t l e t on o f the Appli e d B i oc hemi stry D i vi sion , D.S.I.R., Pa lmer st on N orth , was k ind e nough t o a l l ow t he us e of his B e c kma n M od e l ' �' analyt i c a l ultra
c en t r i fuge t o b e used f or t hi s work , and a l s o a gr e e d t o a c t as one o f t h e supervis ors f or the a uth or when t h e w o r k w a s deemed appropriat e a s a s t a f f Ph.D • . pr o j e c t b y Mass e y Univers i ty . Obvi ous ly , t he ultra c en t r i fuge was in r outine labora t ory u s e , and any modi f i c a t i ons t o t h e inst rument h a d t o b e c ompatible with this usage.
In chap t er 1 , a t h e or et i c a l st udy o f t h e
R ay l e i gh interferenc e opt i c s in the analyt i c a l ultrac ent- ri fugc i s undertaken . Ext e ns i ve us e is made o f t h e Fouri er theory of opt i c s, and t h e basis u p o n whi c h t he r e fra c t ome tric me asur e ment s are ma d e in t he i ns t rument is firmly e st ab l i sh e d .
A discussi on o f c oh e renc e the ory i s inc lud e d i n c hapt e r 2. The t he or e t i ca l findings are appli e d t o t h e c onvent i onal mercury source and a h e lium-ne on g a s l a s e r employe d in t he w ork , a l l owing a d e f in it i ve c ompari s on b e t w e e n the two ligh t s ourc e s t o be made.
Chap t e r 3 inc ludes a descr ipt ion o f the a c t ua l i n strumentat i on t hat was de signed and c onst ruc t ed b y t he aut hor , for us e in t he ult rac entri fug e . A d i s c us s i on o f t he opt i c a l ali gnment pr oc e dur e i s given and e xp e ri men t a l r e su l t s obt aine d b ot h w i t h t he modula t ed l a se r and me r c ur y s ourc e s a r e c ompare d and d i s c ussed.
T he d e s i gn and c onstruct i on o f a n e w type o f i nt er ferenc e c e ll i s t h e c onc ern of chap t e r 4 , t oge t h e r w i th t h e t h e ory u p o n which t he measurements using t hi s c e l l a r e ba s e d . A n c i l liary equipment n e c e s sary for t he u s e o f t he new c e ll i n t he ultrac e ntr i fuge i s de s c r ib e d , t oget h e r w i t h a c r i t i c a l analysi s o f the r e s u l t s s o far ob taine d· .
Chapt er 5 i s a d et a i l e d t he ore t i c al analysis o f the e f f e c t s o f t he r e fr a c t ive index gra d ie n ts on t h e
12.
experimental data derived fr om t he i nt er fer e n c e syst em in t he analy t i c al ultr acentr i fuge . The study indi c at e s that t h e e f f e c t s ar e small f or t he assump t i ons made , but the analysis d oes pr ovi de c orr e c t i on pr o c e dur es based on the raw exp e r i me n t a l dat a t hat c an be app l i e d i n prac t i c e .
Finally , in chap t er 6 t he e f fe c t s of c e l l dist or t i on i n t he c e ntr i fuga l fi e l d ar e ev aluat e d mat h - emat i c al l y. It s importa nc e in t he c ont ext of th i s t h e s i s is t hat s e diment at i on e qui libr ium s t udi e s fr e quent ly r eq u i r e
a pre c i s e know le d ge of t he r adial p osit i ons o f t he me n i s c us and base of t he s olut i on c olumn . The t h e or et ic a l and exper iment al w or k shows that the la ser gi ves shar p er de fini t i on of the meni s c i t han d o e s t he mer c ury s our c e , and t h i s i n c r e as e d pre c isi on gain e d by t he las e r c ould w e l l b e lost i f t he menisc i posit i ons var y owing t o extr an e ous unknow n fac t or s . The w ork in this c hapt er has b e e n publi she d 1 4 by t he aut h or in c on j unc t i on w i t h Pr o f e s s or N.F. B arber w h o is a c t ing a s a s e c ond sup er v i s or for t h i s pr o j e c t . A reprint o f the publicat i on i s inc l u d e d in a n app endix t o t his w or k .
