Critical Assessment of the Relationship between Biological

29

C r i t i c a l A s s e s s m e n t of t h e R e l a t i o n s h i p b e t w e e n B i o l o g i c a l T h e r m o d y n a m i c a n d Electrochemical Availability

Downloaded by NORTHWESTERN UNIV on October 17, 2017 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch029

M. WHITFIELD and D. R. TURNER Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth, EnglandPL12PB Much of the current i n t e r e s t i n the B-subgroup t r a c e metals (e.g. Zn, Cu, Cd, Pb, Hg) i n n a t u r a l waters centers around t h e i r i n f l u e n c e on the b i o t a . I t i s c l e a r from the work published so f a r (JL, 2_, _3) that the b i o l o g i c a l l y a v a i l a b l e f r a c t i o n o f a p a r t i c u l a r element ( i . e . the f r a c t i o n o f the t o t a l c o n c e n t r a t i o n of that element that i s a v a i l a b l e f o r b i o l o g i c a l uptake) i s i n t i m a t e l y dependent on the chemical form o f the element i n s o l u t i o n . Where the solution composition i s c l e a r l y defined and a l l the r e l e v a n t c o n d i t i o n a l s t a b i l i t y constants are known i t i s p o s s i b l e t o c a l c u l a t e the e q u i l i b r i u m s p e c i a t i o n o f a metal from thermodynamic p r i n c i p l e s (2). By s u i t a b l e manipulation o f the s o l u t i o n chemistry the response of organisms t o p a r t i c u l a r chemical species can then be studied CL, _3). Such d e t a i l e d knowledge of the medium composition i s r a r e l y a v a i l a b l e f o r n a t u r a l waters which can e x h i b i t c o n s i d e r a b l e v a r i a t i o n s i n the concentrations o f the major ions and o f the s u i t e o f t r a c e metals present. In a d d i t i o n , s i g n i f i c a n t and v a r i a b l e q u a n t i t i e s o f u n i d e n t i f i e d organic compounds, p o s s i b l y w i t h a p p r e c i a b l e complexing c a p a c i t i e s , might be present and exert a c o n s i d e r a b l e i n f l u e n c e on the b i o l o g i c a l a v a i l a b i l i t y o f t r a c e metals (_3, 4_). Not only do these v a r i a t i o n s make the e q u i l i b r i u m c a l c u l a t i o n s d i f f i c u l t but the presence o f organic matter, and a l s o the presence o f s o l i d phases, might make the e q u i l i b r i u m concept i t s e l f untenable (_5). In response to such d i f a c u i t i e s a number o f o p e r a t i o n a l procedures have been developed t o determine the f r a c t i o n o f ' a v a i l a b l e ' metal i n s o l u t i o n . The most d i r e c t a r e the bioassay procedures i n which the response o f a t e s t organism to changes i n the s o l u t i o n chemistry ( u s u a l l y simply t o changes i n the t o t a l c o n c e n t r a t i o n o f the metal) i s monitored. Frequently, problems have a r i s e n because o f v a r i a b i l i t y i n the t e s t organism i t s e l f and because inadequate a t t e n t i o n has been given t o ensuring consistency i n the s o l u t i o n chemistry. Recent studies suggest that these problems can be s u c c e s s f u l l y circumvented (_1,_3_) and that u s e f u l techniques may soon be a v a i l a b l e f o r d e t a i l e d studies o f s u b l e t h a l e f f e c t s (_6, 7). Such procedures are time 0-8412-0479-9/79/47-093-657$06.00/0 © 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

CHEMICAL


658

M O D E L I N G IN

AQUEOUS

SYSTEMS

consuming, however, and t h e i r u s e f u l n e s s r e s t s h e a v i l y on the aptness of c h o i c e of the t e s t organism. D i r e c t chemical measure ments of ' a v a i l a b l e ' metal are more s u i t a b l e f o r a r a p i d a s s e s s ment of metal a v a i l a b i l i t y i n the f i e l d and i n r o u t i n e water samples. Where metal c o n c e n t r a t i o n s are s u f f i c i e n t l y high, i o n s e l e c t i v e e l e c t r o d e s (ISE's) can be used t o g i v e a d i r e c t measure o f c o n v e n t i o n a l metal i o n a c t i v i t i e s . In some i n s t a n c e s such measurements have been shown to p r o v i d e a d i r e c t c o r r e l a t i o n w i t h the response o f organisms t o changes i n s o l u t i o n chemistry (8, _£ and C r i s p , D.J., Marine Science L a b o r a t o r i e s , Menai B r i d g e , North Wales, personal communication, 1978). Since p o t e n t i o m e t r i c techniques r e q u i r e r e l a t i v e l y h i g h c o n c e n t r a t i o n s o f the s e l e c t e d i o n (not l e s s than 10~^M u n l e s s the metal i s w e l l b u f f e r e d i n s o l u t i o n ) they are r a r e l y s u f f i c i e n t l y s e n s i t i v e f o r the d i r e c t a n a l y s i s of n a t u r a l waters. Consequently, c o n s i d e r a b l e i n t e r e s t has r e c e n t l y been shown i n anodic s t r i p p i n g voltammetry (ASV) which i s a b l e to make s e l e c t i v e , d i r e c t and n o n - d e s t r u c t i v e measurements of amalgam forming metals (e.g. Cu, Pb, Cd, Zn) a t c o n c e n t r a t i o n s down to 10" M (_10, 11). ASV i s s e n s i t i v e t o the chemical form of the metal i n s o l u t i o n and i t has been suggested t h a t the f r a c t i o n o f metal determined by t h i s procedure might provide a u s e f u l guide to the b i o l o g i c a l a v a i l a b i l i t y of t h a t metal i n s o l u t i o n (_3). When we use chemical procedures measuring t r a c e metal a v a i l a b i l i t y we are, i n e f f e c t , assuming t h a t these procedures p r o v i d e u s e f u l models of b i o l o g i c a l uptake. The s i g n i f i c a n c e of the r e s u l t s obtained w i l l t h e r e f o r e depend on the s u i t a b i l i t y of the uptake mechanism i m p l i e d by the experiment a l measurement. S i n c e e l e c t r o c h e m i c a l procedures i n v o l v e the t r a n s f e r of metal ions to an e l e c t r o d e s u r f a c e i n d i r e c t c o n t a c t w i t h the s o l u t i o n we w i l l c o n f i n e our t h e o r e t i c a l a n a l y s i s t o the uptake of t r a c e metals by phytoplankton c e l l s which might be expected to u t i l i s e a s i m i l a r mechanism. The uptake of i o n i c l e a d from sea water w i l l be used as the model process. We w i l l f i r s t c l a r i f y the chemical d e f i n i t i o n s of the a v a i l a b l e metal f r a c t i o n and then i n v e s t i g a t e the r e l a t i o n s h i p of these c h e m i c a l l y d e f i n e d f r a c t i o n s to the f r a c t i o n of metal a v a i l a b l e f o r uptake by a model phytoplankton c e l l . 10

Chemical D e f i n i t i o n s of Trace Metal A v a i l a b i l i t y Thermodynamically a v a i l a b l e f r a c t i o n (TAF). E a r l y s t u d i e s of the i n f l u e n c e of n o n - e l e c t r o l y t e s o l u t e s on a q u a t i c organisms i d e n t i f i e d two k i n d s of t o x i c i t y - p h y s i c a l t o x i c i t y (or n a r c o s i s ) and chemical t o x i c i t y (12). N a r c o s i s Xs caused by a wide v a r i e t y of substances ( i n c l u d i n g the atmospheric gases) and seems to a r i s e because e s s e n t i a l pathways are p h y s i c a l l y blocked by an excess o f i n e r t molecules t h a t have entered the organism v i a an e q u i l i b r i u m d i s t r i b u t i o n across an outer membrane. At e q u i l i b r i u m the a c t i v i t i e s o f the t o x i c compound are the same i n the organic phase and i n the aqueous phase. Consequently, the thermodynamic

Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


29.

WHITFIELD

659

Assessment of Availability

AND TURNER

a c t i v i t y of the n a r c o t i c compound i n the aqueous phase i s d i r e c t l y r e l a t e d t o i t s b i o l o g i c a l a v a i l a b i l i t y . This thermodynamic s c a l e of n a r c o t i c potency was f i r s t proposed by Ferguson (12) and has s i n c e been confirmed f o r a wide range of compounds (13)· This s c a l e i m p l i e s t h a t a l l compounds that exert n a r c o t i c e f f e c t s w i l l have the same i n f l u e n c e on a given organism i f they have the same thermodynamic a c t i v i t y . Chemical t o x i c i t y , which i s caused by c h e m i c a l l y r e a c t i v e agents (such as heavy metals and organom e t a l l i c compounds), should not show such a simple o v e r a l l c o r r e l a t i o n w i t h thermodynamic a c t i v i t y since the t o x i c i t y of each component w i l l depend on i t s own unique a b i l i t y t o i n t e r f e r e w i t h v i t a l chemical processes. Nonetheless, the continued development of the theory o f b i o l o g i c a l membranes (14, 15) and p a r t i c u l a r l y the recent i n t e n s e i n t e r e s t i n a r t i f i c i a l i o n s e l e c t i v e membranes (16, 17, 18) has emphasised the s i g n i f i c a n c e of gradients i n thermodynamic a c t i v i t y r a t h e r than c o n c e n t r a t i o n i n c o n t r o l l i n g the t r a n s p o r t of chemical components across membranes. As a r e s u l t , i t has been assumed, on the b a s i s o f very l i t t l e d i r e c t evidence, that the b i o l o g i c a l a v a i l a b i l i t y o f an element i s r e l a t e d t o the a c t i v i t y i n s o l u t i o n of the p a r t i c u l a r chemical form t h a t i s taken up p r e f e r e n t i a l l y by the organism. This d e f i n i t i o n o f the thermodynamically a v a i l a b l e f r a c t i o n of the element (TAF) i s c o n s i s t e n t w i t h the thermodynamic scale' of n a r c o t i c potency but i t does not imply a common a c t i v i t y t h r e s h o l d f o r a l l elements. The parameter r e l e v a n t t o our model uptake process i s the a c t i v i t y of lead i n sea water, which can be w r i t t e n as a

Pb

= ^

f

( 1 )

P b

where f ^ i s the conventional f r e e s i n g l e - i o n a c t i v i t y c o e f f i c i e n t and [Pb] i s the c o n c e n t r a t i o n of f r e e l e a d . The n a t u r a l c o n c e n t r a t i o n of l e a d i n sea water i s so low ( ^ 10-^-^M) t h a t the complexes formed by the metal w i t h i n o r g a n i c anions w i l l have a n e g l i g i b l e e f f e c t on the c o n c e n t r a t i o n of the f r e e l i g a n d s which can be c a l c u l a t e d from a conventional chemical model f o r sea water (19). Against t h i s background of constant l i g a n d c o n c e n t r a t i o n the e q u i l i b r i u m s p e c i a t i o n o f lead can be c a l c u l a t e d u s i n g the s i d e r e a c t i o n concept of Ringbom (20) which can be summarised i n t h e equations p

(Γ

.=

T

[Pb]

T

β*

(D[L]

j

= [PbL.] /[Pb]

= [Pb] (1+ « 2 ) = [Pb] oC p b

p b

(2)

(4)

[PbL.] = [ P b ] c r . / 5 c (5) where £j(L)i the o v e r a l l s t o i c h i o m e t r i c e q u i l i b r i u m constant d e s c r i b i n g the formation of PbLj from the f r e e components, [ P b ] T

L j

p b

s


T

660

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

i s the t o t a l c o n c e n t r a t i o n of l e a d and OL p i s termed the o v e r a l l s i d e r e a c t i o n c o e f f i c i e n t . The c a l c u l a t e d e q u i l i b r i u m s p e c i a t i o n of l e a d i n sea water, u s i n g the above equations, i s shown i n Table I . In d e f i n i n g (R. pb a number of assumptions have been made concerning the conventional values of fχ a s c r i b e d to the i n d i v i d u a l chemical species i n v o l v e d i n the v a r i o u s e q u i l i b r i a (see footnotes to Table I ) . In p a r t i c u l a r i t was assumed t h a t , a t constant i o n i c s t r e n g t h , fX i s a l s o constant and a l l changes i n the a c t i v i t y of X a s s o c i a t e d w i t h changes i n s o l u t i o n composition are a t t r i b u t e d to changes i n [ X ] . Consequently, the a c t i v i t y of l e a d i n sea water of constant s a l i n i t y i s p r o p o r t i o n a l t o [ P b ] , In view of the number o f assumptions i n v o l v e d i n the determination of oi and fpb (21, 23, 25, 25) i t would be f o o l h a r d y to go beyond t h i s and to p l a c e too much s i g n i f i c a n c e on the value of apb t h a t can be c a l c u l a t e d . In e s t a b l i s h i n g our model f o r b i o l o g i c a l uptake we w i l l consider c o n d i t i o n s where a c t i v i t y c o e f f i c i e n t s remain constant throughout. The thermodynamically a v a i l a b l e f r a c t i o n (TAF) w i l l t h e r e f o r e be equal to & P b equation 4). I f l e a d a l s o forms a complex w i t h an organic l i g a n d (J) i t i s r e a d i l y shown t h a t


b

p b

_ 1

-log

[Pb] = l o g ( c*

p b

+

ΤPb

) - log[Pb]

T

(6)

so t h a t a p l o t of - l o g [Pb] versus l o g (Γ Pb j w i l l give a curve common t o a l l organic l i g a n d s (21). At low l i g a n d concentrations •Pb O"*" pb j t h a t the curve i s a h o r i z o n t a l s t r a i g h t l i n e and [Pb] i s u n a f f e c t e d by i n c r e a s e s i n the l i g a n d c o n c e n t r a t i o n although the b u f f e r c a p a c i t y f o r the f r e e metal i s increased s l i g h t l y . At high l i g a n d c o n c e n t r a t i o n s C T p b , j 2 3 £ pb and the curve i s a s t r a i g h t l i n e of u n i t s l o p e . Here the f r e e metal c o n c e n t r a t i o n drops o f f r a p i d l y w i t h i n c r e a s i n g l i g a n d c o n c e n t r a t i o n s . Equation 6 t h e r e f o r e provides a simple b a s i s f o r r a t i o n a l i s i n g many of the o b s e r v a t i o n s , summarised by S i e g e l (_4) and Mancy and A l l e n (3) on the i n f l u e n c e of organic complexing agents on the b i o l o g i c a l a v a i l a b i l i t y of metals and thus strengthens the c o r r e l a t i o n w i t h the TAF. OCpb can be c a l c u l a t e d d i r e c t l y i f the concentrations of a l l l i g a n d s and of a l l competing c a t i o n s are known (21). Where t h i s i n f o r m a t i o n i s not a v a i l a b l e , ISE's can i n p r i n c i p l e enable c o n v e n t i o n a l s i n g l e - i o n a c t i v i t e s t o be measured d i r e c t l y . The l i m i t e d s e n s i t i v i t y of present-day ISE's precludes t h e i r use i n n a t u r a l waters, although they can be used i n experimental systems i n v o l v i n g elevated c o n c e n t r a t i o n s of t r a c e metals. Provided t h a t the s a l i n i t y remains constant, a c e l l without l i q u i d j u n c t i o n , composed o f p e r f e c t l y s e l e c t i v e c h l o r i d e and l e a d ISE's c o u l d be used. The d i f f e r e n c e between the emfs measured i n the sample (Ε ) and i n a standard s o l u t i o n w i t h the same temperature and major i o n composition (E ) would be given by s o

χ

s


WHITFIELD

29.


AND TURNER

Table I . e q u i l i b r i u m s p e c i a t i o n o f lead i n sea water at pH 8 (21)

The

Species

log

(Γ

β

b

%[Pb]

4.50

PbCl °

1.32

6.70

PbCl "

1.20

2.87

5

1.06

1.18

2

6.21

2.62

4

+

2

3

2

Pbci 4

PbOH

+

11

Pb(OH) °

10.35

5.88 χ 1 0 "

2

-

Pb(OH) ~

13.08

5.10 χ 1 0 "

5

-

2

3

PbC0 °

55

34.7

6.12

3

2

Pb(co ) "

9.32

1.44

PbS0 °

1.4

3.69 χ 1 0 "

Pb(Cl,OH)°

6.14

1.25

2

Pb(Cl,CO )~

5.62

6.21

10

2

3

2

4

Pb(OH,C0 )~ Pb a b

5.8 χ 1 0 "

10.14

3

1

1

1

1

-

-

2 +

T

7

0.90

PbCl


661

2

Values c o r r e c t e d t o I = 0.72 using the Davies equation (22) to c a l c u l a t e f. values, The f o l l o w i n g f r e e l i g a n d concentrations were c a l c u l a t e d f o r an i o n - p a i r model based on f. values c a l c u l a t e d from the Maclnnes convention (_23) using the sea water r e c i p e o f M i l l e r o (24). Ion

CI"

OH"

pX

0.247

5.79

s o

2 4

~

1.833

C 0

2

3 ~ 4.58

H C 0

3~

2.80


662

CHEMICAL


E

x

-

E

s

MODELING

= «£/2) log[Pb] /[Pb] x

IN

AQUEOUS

s

SYSTEMS

(7)

where k = 0.1986 TmV (T = temperature i n °K). For measurements i n sea water the standard s o l u t i o n could be prepared i n an o r g a n i c f r e e sea water adjusted t o pH 5 t o 6 where lead s p e c i a t i o n depends only on the c o n c e n t r a t i o n of c h l o r i d e and sulphate (21). There i s a l i t t l e evidence i n the l i t e r a t u r e suggesting t h a t both c a l c u l a t e d values of f r e e metal c o n c e n t r a t i o n (1) and values measured w i t h ISE's (8_, 9) can be c o r r e l a t e d w i t h the b i o l o g i c a l a v a i l a b i l i t y of copper. A d d i t i o n a l l y , Sunda e t a l . (27) have presented evidence t h a t the t o x i c i t y o f cadmium i n seawater c o n t a i n i n g NTA can be c o r r e l a t e d w i t h the observed and c a l c u l a t e d c o n c e n t r a t i o n of f r e e cadmium i o n s . E l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n (EAF). The s i g n i f i c a n c e of the e l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n o f a t r a c e metal, as measured by ASV, can best be appreciated by comparison w i t h measurements o f the thermodynamic a v a i l a b i l i t y made u s i n g an ISE. We w i l l consider i n each case an e l e c t r o d e i n a s t i r r e d s o l u t i o n with a d i f f u s i o n layer of thickness S at i t s surface. A l l changes induced i n the e q u i l i b r i u m s p e c i a t i o n by r e a c t i o n s a t the e l e c t r o d e surface w i l l be assumed t o take p l a c e w i t h i n t h i s d i f f u s i o n l a y e r . P o t e n t i o m e t r i c measurements are c a r r i e d out a t e q u i l i b r i u m so t h a t there i s no c o n c e n t r a t i o n g r a d i e n t and no net metal f l u x across the d i f f u s i o n l a y e r . In c o n t r a s t , d u r i n g the p l a t i n g step o f an ASV a n a l y s i s , metal i s deposited e l e c t r o l y t i c a l l y a t a mercury e l e c t r o d e from a r a p i d l y s t i r r e d s o l u t i o n . This d e p o s i t i o n process generates a gradient o f metal c o n c e n t r a t i o n w i t h i n the d i f f u s i o n l a y e r and the only species t h a t w i l l be sensed by the method w i l l be those that can c o n t r i b u t e t o the metal f l u x a t the e l e c t r o d e s u r f a c e . The time s c a l e of the p l a t i n g process i s defined by the d i f f u s i o n l a y e r t h i c k n e s s (6 ) and by the d i f f u s i o n c o e f f i c i e n t s of the i n d i v i d u a l species ( D j ) . I f the e l e c t r o d e process i s the r e v e r s i b l e r e d u c t i o n of metal ions, only complexes t h a t d i s s o c i a t e s u f f i c i e n t l y r a p i d l y t o r e l e a s e the f r e e metal w i t h i n the d i f f u s i o n l a y e r w i l l c o n t r i b u t e t o t h e metal f l u x (J) a t the e l e c t r o d e surface. In a recent study (28, 29) we have described a general theory which enables J t o be c a l c u l a t e d f o r a m u l t i - l i g a n d system. From t h i s we o b t a i n J = M [Pb] - M^Pb] Q

0

T

(8)

where M and a r e complicated m a t r i x f u n c t i o n s of S and D and a l s o o f the k i n e t i c s and thermodynamics of the m e t a l - l i g a n d i n t e r a c t i o n s . [Pb]° i s the c o n c e n t r a t i o n of the f r e e metal a t the e l e c t r o d e s u r f a c e . Under c u r r e n t l i m i t i n g c o n d i t i o n s ( i . e . on the p l a t e a u of the peak s t r i p p i n g c u r r e n t versus p l a t i n g p o t e n t i a l curve) [Pb]° - 0 and the l i m i t i n g f l u x i n the presence of k i n e t i c c o n t r o l can be w r i t t e n as Q


29.

WHITFIELD


AND TURNER

J

= M [Pb]

k

Q

663

.

T

(9)

I f there were no k i n e t i c c o n t r o l ( i . e . , i f a l l species could d i s s o c i a t e s u f f i c i e n t l y r a p i d l y t o c o n t r i b u t e f u l l y t o the metal f l u x ) then, under the same c o n d i t i o n s , the d i f f u s i o n l i m i t e d f l u x of the metal would be


J

= D[Pb] / £

d

UO)

T

i f we assume t h a t the metal and i t s complexes a l l have the same d i f f u s i o n c o e f f i c i e n t . The e l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n (28, 29) w i l l t h e r e f o r e be J

/J

M

k d =o

&

/ D

(11)

Z

V d

where 1^ and 1^ a r e the s t r i p p i n g peak currents measured under k i n e t i c a l l y and d i f f u s i o n a l l y l i m i t e d c o n d i t i o n s , r e s p e c t i v e l y . ASV and potentiometry t h e r e f o r e impose q u i t e d i f f e r e n t l i m i t i n g c o n d i t i o n s f o r the measurement of t r a c e metal a v a i l a b i l i t y (Figure 1, (a) and (b), and Table I I ) . Table I I Comparison o f p o t e n t i o m e t r i c and voltammetric techniques Potentiometry

Voltammetry

Measured q u a n t i t y

Electrode p o t e n t i a l

Metal f l u x a t the e l e c t r o d e surface

Measure o f t r a c e metal obtained

Thermodynamic A c t i v i t y

Electrochemical availability

Concentration o f f r e e Bulk c o n c e n t r a t i o n metal a t the e l e c t r o d e [Pb] surface [Pb]

Zero

Trace metal f l u x (J) at the e l e c t r o d e surface

Zero

Kinetically limited flux J k

Mathematical summary

[Pb] /[Pb] J/ J, = 0 k

[Pb^°/[Pb] I =

J / J

v

Combining equations 8 and 9 we f i n d that J/J

k

= 1 - M [Pb]°/M [Pb] . 1

0

T


(12)

CHEMICAL

664

Γ Downloaded by NORTHWESTERN UNIV on October 17, 2017 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch029

bulk solution

diffusion layer

MODELING

IN AQUEOUS

SYSTEMS

ion-selective electrode

(a) J=0

J=0

surface: [Pbf=[Pb]

8 bulk solution

1

asv electrode

diffusion layer

(b)

surface: [pb]°=0

bulk solution j diffusion layer (c)

model cell

! =V lf f J

M

Pb

surface: θ =[Pb]°/(b.[Pb]°)

Figure 1. Comparison of conditions imposed for the sensing of trace metal by (a) an ion-selective electrode, (b) a mercuryfilmasv electrode, and (c) the model cell. In each case the system is divided into four zones: bulk solution, diffusion layer of thickness (8), cell/electrode surface, and cell/electrode interior.


29.

WHITFIELD

Since [Pb] M /M - 5(. 1

Q


A N D TURNER

p b

665

> [Pb] as J / J > 0 we a l s o f i n d t h a t (equation 47 so that J/J

+ [Pb]°/[Pb] = 1 .

k

(13)

Under c u r r e n t l i m i t i n g c o n d i t i o n s [Pb]° = 0 so t h a t J / J = 1. To s i m p l i f y matters we w i l l s e t J / J = £ so that [Pb]°/[Pb] = 1-|. By e s t i m a t i n g ξ f o r a model c e l l we should be able t o decide whether the uptake o f metal w i l l r e f l e c t t h e thermodynamic or the e l e c t r o c h e m i c a l a v a i l a b i l i t y o f l e a d i n the s o l u t i o n (Table I I ) .


k

D e f i n i t i o n o f the Model C e l l D e s c r i p t i o n . The model organism i s a f r e e - f l o a t i n g u n i c e l l u l a r sphere w i t h c h a r a c t e r i s t i c s s e l e c t e d , where p o s s i b l e , to match those o f a phytoplankton c e l l . The organism and i t s environment (Figure l c ) are d i v i d e d i n t o four c o n c e n t r i c zones the bulk s o l u t i o n , the d i f f u s i o n l a y e r , the c o n t a i n i n g membrane and the c e l l contents. We w i l l assume t h a t t h e species taken up by the c e l l i s t h e f r e e metal i o n s i n c e most o f the s t u d i e s of the uptake o f B-subgroup metals by organisms support t h i s hypothesis Ui> A* A' Jji —i AA) · steady-state t r a n s p o r t processes are considered, namely ( i ) t r a n s p o r t o f t r a c e metal t o the c e l l surface described by equation 8 and ( i i ) a s s i m i l a t i o n o f the t r a c e metal i n t o the i n t e r i o r o f the c e l l described by T

w

o

= kQ (14) c where k i s a constant and θ i s the f r a c t i o n o f t h e a v a i l a b l e surface adsorption s i t e s occupied by the t r a c e metal i o n s . The form of equation 14 assumes t h a t metal already present i n t h e c e l l has no e f f e c t on the a s s i m i l a t i o n r a t e , and i s thus best considered as a d e s c r i p t i o n o f the e a r l y stages of metal uptake. The f r a c t i o n a l coverage θ i s described by the Langmuir isotherm J

θ

= [Pb]°/(b + [Pb]°)

(15)

which assumes t h a t adsorption and desorption processes a r e r a p i d compared t o t r a n s p o r t processes. From equations 14 and 15 we have J

c

= k[Pb]°/(b + [Pb]°) .

(16)

At steady s t a t e J = J so t h a t , e l i m i n a t i n g [Pb]° from equations 8 and 16 r e s u l t s i n , J

2

- JCMjb + M [Pb]

+ k) + k M [ P b ] 0

T

= 0 .


(17)

CHEMICAL

666

M O D E L I N G IN

AQUEOUS

SYSTEMS


Only one r o o t of t h i s equation l i e s i n the range 0 4 J ^ J^.Combination of t h i s r o o t w i t h equation 9 enables £ t o be calculated. Before we can c o n s i d e r the response of our model organism to lead i n sea water we must d e f i n e k (equation 14) and b (equation 15) and estimate the range of d i f f u s i o n l a y e r thicknesses ( S ) t h a t are c h a r a c t e r i s t i c of phytoplankton c e l l s . Since we have no d i r e c t experimental evidence on which to base an estimate of k we w i l l t r e a t i t as a v a r i a b l e i n the c a l c u l a t i o n s . E s t i m a t i o n of h a l f s a t u r a t i o n constant (b). Values of b determined a t the surfaces of phytoplankton c e l l s , c o r r e c t e d t o r e f e r to [M] i n the sea water i o n i c medium, are shown i n Table I I I . S i m i l a r values are found f o r l e a d and z i n c and a somewhat lower value f o r cadmium. The value estimated f o r mercury i s u n r e a l i s t i c a l l y low and suggests t h a t here the species adsorbed i s not the f r e e metal. I n i t i a l l y we w i l l take b = 50 nM as an order of magnitude f i g u r e t o d e s c r i b e the s u r f a c e or our model cell. E s t i m a t i o n of d i f f u s i o n l a y e r t h i c k n e s s ( cS ). ί f o r a moving p a r t i c l e i s r e l a t e d to the v e l o c i t y o f motion (u) o f the p a r t i c l e through the water. For a sphere of r a d i u s a_ moving through the water a t a constant v e l o c i t y i t can be shown u s i n g the equations given by L e v i c h (34, p. 84-85) t h a t the average d i f f u s i o n l a y e r t h i c k n e s s (?^y i s given by, £

A V

=

TTD

1 / 3

2

(u/a )

_ 1 / 3

/2

.

(18)

A l l q u a n t i t i e s i n equations, i n c l u d i n g numerical constants, are expressed i n c.g.s. u n i t s . With D = 10"" ^ cm sec~^- equation 18 becomes 2

£

2

A V

= 0.034 ( u / a r

1 / 3

.

(19)

The problem of e s t i m a t i n g the d i f f u s i o n l a y e r t h i c k n e s s t h e r e f o r e reduces t o t h a t of e s t i m a t i n g u and a. We have considered three p o s s i b l e mechanisms f o r the movement of phytoplankton through the water: g r a v i t a t i o n a l s i n k i n g , c o n v e c t i v e water movements and the swimming o f f l a g e l l a t e s . G r a v i t a t i o n a l s i n k i n g . Phytoplankton c e l l s are g e n e r a l l y denser than the surrounding sea water and t h e r e f o r e s i n k unless kept i n suspension by c o n v e c t i v e water movements (35). S Λ ° s i n k i n g c e l l s was estimated from a t a b l e of s i n k i n g r a t e s f o r a v a r i e t y of phytoplankton c e l l s given by Smayda (35) - A value of a. was estimated from the c e l l volume assuming a s p h e r i c a l c e l l . Only data f o r l i v i n g c e l l s were used and a histogram of S\γ (Figure 2) i n d i c a t e s values c l o s e l y grouped i n the range 2 t o 5 χ ΙΟ" cm. V

3


F

R

R

29.


WHITFIELD A N D TURNER

667

Convective water movements. Wind-driven Langmuir c e l l s are considered t o be among the most important convective mechanisms which keep phytoplankton i n the euphotic zone (_35 ). Phytoplankton c e l l s which are denser than the water w i l l not be f u l l y entrained by these motions and w i l l have a r e s u l t a n t net v e l o c i t y through the water. L e v i c h ( 3M- , p. 182) gives an approximate expression f o r t h i s motion, u/a

2

~

/ jO ) ( u / y 9

0.39 (

Q

5

L

3

L )*

where A/9 / β i s the r e l a t i v e d e n s i t y excess of t h e c e l l over sea water, L and u_ are the s c a l e and v e l o c i t y o f the convective motion r e s p e c t i v e l y and V i s the kinematic v i s c o s i t y . Taking /0 = 1.024 and *V = 1 0 " cm s (s i s defined below) we obtain, ^ u/a a 119 A ρ (UL / L ) . (20)


Q

L

2

Q

2

- 1

- 1

4

I n v e s t i g a t i o n s i n t o Langmuir c e l l s have r e s u l t e d i n t h e approximate expressions u^ ca 0.008W (36) and L a 4.8W (37) where W i s the wind speed i n cms"- -. Using these expressions equation 20 becomes 1

u/a

2

—

0.00077

Δ ρ

3/2

W .

(21)

A histogram o f Δ ^ values f o r phytoplankton c e l l s (Figure 3) i n d i c a t e s that most values l i e i n the range 0 < A/> ^ 0.08. A p l o t o f C£AV versus W f o r s e v e r a l values o f A ( F i g u r e 4) i n d i c a t e s t h a t even a t high wind speeds the d i f f u s i o n l a y e r t h i c k n e s s w i l l not be l e s s than the value o f 10"" cm normally maintained by chance convective motion (39, p. 2 ) . Gavis (40) has a l s o considered the e f f e c t of open water turbulence, which may be c h a r a c t e r i s e d by a r a t e o f shear S, w i t h a maximum value of 6 s~~^, where S i s given by 2

S = u/a . The extreme e f f e c t of open water turbulence can then be c h a r a c t e r i s e d by u/a

2

= 6/a .

(22)

S u b s t i t u t i o n o f equation 22 i n equation 19 shows t h a t the maximum shear r a t e o f 6 s ~ l w i l l r e s u l t i n values o f S A V ^- "^ ^ 9 2 χ 10~ to 4 χ Ι Ο cm f o r c e l l s o f r a d i u s .10~ to 10"* cm, s i m i l a r t o t h a t r e s u l t i n g from g r a v i t a t i o n a l s i n k i n g (Figure 2 ) . N

3

- 3

3

NE

a n

e

2

Swimming o f m o t i l e c e l l s . When expressed i n body lengths, s~^. the speed a t t a i n e d by animals from paramecia t o tuna i n water v a r i e s l i t t l e with s i z e (41) and most organisms have a maximum speed o f 10 lengths, s~^. Taking u = 20_a as a maximum f o r m o t i l e


C H E M I C A L MODELING I N AQUEOUS SYSTEMS

668

lOf-


5h

ε

ίο

Figure 2. Histogram of estimated values of (S) v for gravitational sinking of phytoplankton cells. Estimates obtained from data given for live cells by Smayda A

(35) using Equation 19.

10r

8 Ϊ

Ε i

0-1

0-2

y/,gmcm Figure 3.

Histogram of excess density (Δρ) for phytoplankton cells; data taken from Ref. 38


29.

WHITFIELD

A N D TURNER


669


Table I I I . Measured values o f h a l f - s a t u r a t i o n constant (b) f o r metal adsorption a t phytoplankton c e l l surfaces

b/nM measured u s i n g t o t a l metal concentrations

b/nM c o r r e c t e d t o f r e e metal concentration

Species

Metal

Phaeodactylum tricornutum

Zn

91

43

(30)

Phaeodactylum tricornutum

Pb

2100

42

(31)

Platymonas subcordi formi s

Pb

3800

76

Isochrysis galbana

Cd

400

Isochrysis galbana

Hg

97 50

Dunaliella tertiolecta

a b

c d e f g

Ί0

Hg

Reference

-13 g

(32)

23 25

determined using Langmuir isotherm. determined u s i n g F r e u n d l i c h isotherm: the f i g u r e given i s the metal c o n c e n t r a t i o n corresponding t o h a l f s a t u r a t i o n o f the surface. assuming 47% f r e e z i n c i n sea water (33) assuming 2% f r e e lead i n sea water (21) assuming 2% f r e e cadmium i n sea water (33) Davies, A.G., Marine B i o l o g i c a l A s s o c i a t i o n , Plymouth, personal communication 1978. estimated using data given i n Mantoura et a l . ( 3 3 ) .


CHEMICAL

670

MODELING IN AQUEOUS

SYSTEMS

cells results i n

S

AV

= 0.013 a

1 / 3

.

(23)

T h i s equation gives SAV l u e s i n much the same range as g r a v i t a t i o n a l s i n k i n g arid open water turbulence (Figure 5 ) . The values of S A V obtained by these three procedures a r e order o f magnitude estimates only since the r e l a t i o n s h i p s used to c a l c u l a t e (u/a ) are approximate and e n a t i o n 19 i s not s t r i c t l y v a l i d when^t p- a (34, p. 84-85). Nonetheless, the values obtained suggest that the movement of phytoplankton c e l l s through the water i s u n l i k e l y to produce a d i f f u s i o n l a y e r t h i c k n e s s l e s s than 1 0 ~ cm. This i s o f the same order as the d i f f u s i o n l a y e r t h i c k n e s s d u r i n g an ASV a n a l y s i s . A t the r o t a t i n g d i s c electrode, r o t a t i o n speeds i n the range 25 to 2500 rpm give d i f f u s i o n l a y e r thicknesses o f 1 0 ~ cm t o 1 0 ~ cm, and d i f f u s i o n l a y e r thicknesses at conventional s t a t i o n a r y e l e c t r o d e s i n s t i r r e d s o l u t i o n s w i l l a l s o be i n t h i s range. Measurements o f the e l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n made by ASV a r e t h e r e f o r e l i k e l y t o be r e l e v a n t t o s i t u a t i o n s where b i o l o g i c a l uptake i s c o n t r o l l e d by t r a n s p o r t o f t r a c e metal t o the c e l l surface. v a

2


A V

3

2

3

Trace Metal A v a i l a b i l i t y f o r the Model C e l l - C a l c u l a t i o n and Discussion. The c a l c u l a t i o n o f £(= J/J^? Table II) under d i f f e r e n t c o n d i t i o n s w i l l enable us t o d e f i n e the parameters that d i c t a t e whether the model c e l l responds t o the thermodynamically o r t o the k i n e t i c a l l y a v a i l a b l e f r a c t i o n o f the t r a c e metal i n s o l u t i o n . Values o f M and M-j_ (Table IV) were c a l c u l a t e d f o r lead i n sea water a t pH 8 u s i n g the s p e c i a t i o n p i c t u r e given i n Table I . 0

Table IV. M a t r i x terms (M and M]_) f o r the c a l c u l a t i o n o f the e l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n o f lead i n sea water (28,29) Q

Log

10

M

(cm s

)

M

(cm s

-2.00

0.98

0.060

-2.25

1.72

0.105

-2.50

2.97

0.182

-2.75

5.05

0.309

-3.00

8.33

0.510

)



29.

WHITFIELD

A N D TURNER

671


Figure 4. Estimated average diffusion layer thickness (S) resulting from Lang muir convection as a function of wind speed W. (a) (Δρ) = 0.02 g cm' , (b) (Δρ) = 0.05 g cm , (c) (Δ ) = 0.08 g cm' . AV

3

3

Ρ

3

Figure 5. Estimated average diffusion layer thickness (B) for motile cells of radius a swimming at maximum rate (Equation 23) AV

log a/cm


672

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

I n f l u e n c e of a s s i m i l a t i o n r a t e constant ( k ) . Values of i were c a l c u l a t e d as a f u n c t i o n of k u s i n g f i x e d values f o r [Pb] ( 1 0 " M ) , b (50 nM) and S ( l o g 1 and the c e l l begins to sense the e l e c t r o c h e m i c a l l y a v a i l a b l e f r a c t i o n of the metal. Under these l i m i t i n g c o n d i t i o n s the t r a n s p o r t of metal across the d i f f u s i o n l a y e r i s the r a t e determining process. Conversely at low values of k, corresponding to a slow a s s i m i l a t i o n of l e a d , £ > 0 ( i . e . , [Fb]°/[Pb] --> 1) so t h a t the c e l l begins to sense the thermodynamically a v a i l a b l e f r a c t i o n of the metal. In t h i s case the t r a n s p o r t of metal from the surface to the i n t e r i o r of the c e l l i s the r a t e determining process. There i s no sharp d i v i s i o n between these l i m i t i n g cases and i n t h i s i n s t a n c e (Figure 6) there i s a range of two to three orders of magnitude i n k over which n e i t h e r d e s c r i b e s the t r a c e metal a v a l a b i l i t y . To see how these l i m i t s depend on other f a c t o r s we w i l l assume a r b i t r a r i l y t h a t when £ > 0.9 the c e l l responds to the EAF and when ξ 0.9) the c e l l responds to the TAF. We can rearrange equations 9 and 17 t o g i v e


10

k =

M [Pb] Q

T

- ( ξ /( $

-

1))Μ1

.

(24)

The value o f k a t the ' e l e c t r o c h e m i c a l l i m i t ' (when & = 0.9) w i l l be r e f e r r e d t o as k and the value at the 'thermodynamic l i m i t ' (when £ = 0.1) as k (Figure 6 ) . The k-values used i n the c a l c u l a t i o n s so f a r can be compared w i t h experimental observations (Davies, A.G., Marine B i o l o g i c a l A s s o c i a t i o n , Plymouth, personal communication, 1978) i f we remove a l l reference to the c e l l s u r f a c e and work simply i n terms of the a s s i m i l a t i o n f l u x (J ). The change-over from thermodynamic to k i n e t i c c o n t r o l w i l l occur i n the r e g i o n 0.1 < J

Critical Assessment of the Relationship between Biological

Recommend Documents