t. c. broyer -- the movement of materials into plants part i. osmosis and the movement of water into...

7/27/2019 T. C. Broyer -- The Movement of Materials Into Plants Part I. Osmosis and the Movement of Water Into Plants

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T H E B O T N I C L R E V I E W

VOL XIII J A N U A R Y , 1947 No 1

THE MOVEMENT OF MATERIALS INTO PLANTS

PART I OSMOSIS AND TH E MOVEME NT OF

WATER INTO PLANTS

T C

B R O Y E R

University of Caliyornia

~ONT NTS

P a g e

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

T h e o r e t i c a l A s p e c t s o f O s m o s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

T h e i de a l g a s l a w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

T h e f r ee e n e r g y c o n c e p t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

D i f f u s i o n d e f i n ed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

O s m o s i s d e f in e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

A s e m i p e r m e a b l e m e m b r a n e d e f i n e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

O s m o t i c s p ec i f ic f r e e e n e r g i e s d e f in e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

O s m o t i c p r e s s u r e d e f in e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

O s m o t i c m e t a b o l i c s p ec i f ic f r e e e n e r g y d e f i n e d . . . . . . . . . . . . . . . . . . . . . 5

O s m o t i c n o n - m e t a b o l i c s p ec i f ic f r e e e n e r g y d e f in e d . . . . . . . . . . . . . . . . 6

O s m o t i c s o l u t e s p e ci f i c f r e e e n e r g y d e f i n ed . . . . . . . . . . . . . . . . . . . . . . 6

H y d r o s t a t i c p r e s s u r e d e f i n ed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

H y d r o s t a t i c s p e ci fi c f r e e e n e r g y d e f i n ed . . . . . . . . . . . . . . . . . . . . . . . . . 8

N e t i n f l u x s p ec i f ic f r e e e n e r g y d e f in e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

O n t h e o r i g i n o f o s m o t i c s o l u t e s p e c i fi c f r e e e n e r g y . . . . . . . . . . . . . . 9

D e v i a t i o n s i n t h e p l a n t , f r o m t h e i de a l o s m o t i c s y s t e m . . . . . . . . . . . . . 1 0

C o m p a r i s o n b e t w e e n t w o a l t e r n a t iv e a s p e c t s o f t h e f u n d a m e n t a l e q u a -

t io n f o r w a t e r m o v e m e n t i n a n o s m o m e t e r . . . . . . . . . . . . . . . . . . . I 1

M o v e m e n t o f W a t e r i n t h e P l a n t : T h e A l t e r n a t i v e G r a p h i c S c h e m e . . . . 1 5

T h e f u n d a m e n t a l e q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7

E f f e c t o f e x t e r n a l s o l u t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1

E f f e c t o f i n t e r n a l s o l u t e ; s o l u t e a c c u m u l a t i o n . . . . . . . . . . . . . . . . . . . . . 2 1

E f f e c t o f i n t e r n a l s o l u t e d e p l e t io n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2

E x u d a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3

E f f e c t o f a m e t a b o l i c s p ec i f ic f r e e e n e r g y . . . . . . . . . . . . . . . . . . . . . . . . 2 4

E f f e c t o f a n o n - m e t a b o l i c s p ec if ic f r e e e n e r g y . . . . . . . . . . . . . . . . . . . . . 2 6

E f f e c t o f s u c t io n , a p p l ie d i n t e r n a l l y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

E f f e c t o f e v a p o r a t i o n ; i n t e rn a l t e n s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8

T h e i n d i v i d u a l c e l l ; p l a s m o l y s i s , e t c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0

T h e i n d i v i d u a l c e l l ; r e l a t io n s h i p s i n a t i s s u e . . . . . . . . . . . . . . . . . . . . . 31

E f f e c t o f e x t e r n a l s a l i n i ty o n t h e o p e n r e f e r e n c e s y s t e m . . . . . . . . . . . . . 3 3

S o i l e f fe c ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3

W i l t i n g a n d d e a t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5

S i g n i f i c a n c e o f t r a n s p i r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6

C o m p r e h e n s i v e o s m o t i c s y s t e m o f t h e p l a n t . . . . . . . . . . . . . . . . . . . . . . . 3 7

C o n d e n s a t i o n o f w a t e r a t s u r f a c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1

E f f e c t o f t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1

M i s c e l l a n e o u s e f fe c ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2

C o n c l u d i n g s t a t e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2

1


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TH E BOTANICAL REVIEW

Page

Experimenta l Evaluation o f Osmotic Quan titie s . . . . . . . . . . . . . . . . . . . . . . . 43

S um m ary of osm otic relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Procedures for the est imat ion of osmotic quanti ties . . . . . . . . . . . . . . . . 45

Osm otic quantities of a cell ; two type cases :

Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Osm otic quantifies of an integrated system ; two type cases :

Case A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Case B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $4

Sum mary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

A cknow ledgm ents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Literature C ited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

INTRODUCTION

N u m e r o u s a r t i c l e s h a v e b e e n p u b l i s h e d o n v a r i o u s p h a s e s o f t h e

m o v e m e n t o f w a t e r i n t o p l a n ts . T h e t h e o r e t ic a l a s p e c t s o f m o s t

s u ch p u b l i ca t i o n s h av e b een l im i t ed t o ex p lan a t io n s o f s p ec i f i c ex -

p e r i m e n t a l d a t a . O n l y i n t e x t - b o o k s a r e c o m p r e h e n s i v e d i s c o u r s e s

p r e s e n t e d , a n d f r e q u e n t l y u n i t y o f t h o u g h t i s lo s t i n t h e c i r c u i t o u s,

i n t e r r e l a t e d d i s c u s s i o n s o n s e v e r a l m a j o r p h y s i o l o g i c a l s u b j e c t s .

T h e r e i s a n eed f o r a u n i f i ed d i s cu s s io n o f o s m o s i s an d i t s r e l a t i o n

t o w a t e r m o v e m e n t ( w a t e r m i g r a t i o n ) i n t o p l an t s. T h e p r e s e n t

t h e o r e t i c a l t r e a t m e n t o f t h e s u b j e c t i s p r e s e n t e d i n t h e h o p e o f

c l a r i f y i n g a n d e x t e n d i n g p r e s e n t c o n c e p t s in t h i s i m p o r t a n t f ie ld o f

s t u d y . A n e w a p p r o a c h is a t t e m p t e d , c i t in g e x a m p l e s , in a c c o r d

q u a l i t a ti v e l y a n d q u a n t i t a t i v e l y w i t h e x p e r i m e n t a l r e s u l ts , a n d b a s e d

u p o n c u r r e n t d e f i n i t i o n s a n d p r i n c i p l e s o f p h y s i c s a n d p h y s i c a l

chemis t ry (4 , 7 , 9 , 11 ,

17-20

3 5 , 4 0 , 4 3 , 4 4 , 6 1 ) . A co m p le m en ta r y

t r e a t i s e o n t h e te n d e n c y f o r s o lu t e t o m o v e ( s o l u t e m i g r a t i o n ) i n t o

p l a n t s w i l l b e g i v e n i n P a r t I I o f t h i s s t u d y .

THEORETICAL ASPECTS OF OSMOSIS

T h e a s s o c i a t i o n o f t h e v a r i o u s f a c t o r s t e n d i n g t o c a u s e w a t e r t o

m o v e t h r o u g h t h e p l a n t m a y b e c o n c is e ly d e v e lo p e d f r o m b a s ic l a w s

o f p h y s i c a l c h e m i s t r y , a s f o l l o w s :

The Ideal Gas Law:

A p e r f ec t g a s s y s t em i s co m p le t e ly d e f in ed

b y th e r e l a t i o n s h ip ( 3 5 , p. 6 3 ) :

P V = n R T , w h e r e ( 1 )

P i s th e p r e s s u r e , d u e t o t h e k i n e t i c e n e r g y o f t h e m o l e c u le s , h e r e

e x p r e s s e d i n a t m o s p h e r e s ; V i s t h e v o l u m e , in l i te r s ; n i s t h e n u m -

b e r o f m o l s o f g a s ; R i s a co n s t an t f a c to r , 0 .0 8 2 0 5 l i t e r - a tm o s -

p h e r e p e r d e g r e e ; T i s t h e a b s o l u t e t e m p e r a t u r e .


3/58

M O V E M E N T O F M T E R I L S I N T O P L N T S

The Free Energy Concept

T h e f u n d a m e n t a l p r i n c i p l e u n d e r -

l y i n g t h e m o v e m e n t o f m a t e r i a l s i s t h a t e a c h m o l e c u l e p o s s e s s e s a

t o t a l i n t e r n a l e n e r g y e q u a l t o t h e s u m o f i t s i n t e r n a l k i n e t i c a n d

p o t e n t i a l e n e r g i e s ( 1 8 , p . 5 7 ) , a n d t h e m o l a l ( o r p a r t i a l m o l a l ) f r e e

e n e r g y i s e q u a l t o t h e p r o d u c t o f t h e m e a n f r e e e n e r g y o f t h e p a r -

t ic le s a n d th e n u m b e r o f p a r t ic l e s i n o n e m o l e . A s y s t e m i s s u b j e c t

t o s p o n t a n e o u s c h a n g e i f t h e r e i s a n y c o n c e iv a b l e p r o c e s s w h e r e b y

t h e i n t e r n a l e n e r g y o f t h e c o n s t i t u e n t m o l e c u l e s c a n b e e f f e c t iv e l y

r e d u c e d . T h e a c t io n , h e r e e sp e c ia ll y t h a t c o n c e r n e d w i t h t ra n s l a -

t io n o f t h e p a rt ic l e i n s p ac e i ts es c a p in g t e n d e n c y - - w h i c h c o u l d b e

p r o d u c e d b y s u c h a c o n c e iv a b l e p r o c e s s , is d e t e r m i n e d b y t h e i n -

t e r n a l f r e e e n e r g y o f t h e i n d iv i d u a l m o l e c ul es . T h e f r e e e n e r g y

o f t h e p a r ti c le s m a y b e m o d i f ie d b y a n y c h a n g e i n c o n d i t io n o f t h e

e x t e r n a l e n v i r o n m e n t .

Diffusion D efined

D i f f u s i o n is t h e p ro c e s s w h e r e b y o n e s u b s t a n c e

m o v e s i n t o o r t h r o u g h a n o t h e r i n r e s p o n s e t o a d i f f e r e n c e o f p a r ti a l

m o l a l f r e e e n e r g y 1, t e n d i n g t o w a r d e q u i l ib r i u m o f e s c a p i n g t e n d e n -

c i e s ( 35 , pp . 179 , 180 ) .

Osm osis Defined

O s m o s i s i s a p r o c e s s o f d i f f u s i o n o f t h e c o m -

p o n e n t c a p a b l e o f f r e e p a s s a g e t h r o u g h a s e m i p e r m e a b l e m e m b r a n e

s e p a r a t i n g t w o c o m p o n e n t s 2, o n l y o n e o f w h i c h i s c a p a b l e o f f r e e

p a s sa g e t h r o u g h th e b o u n d a r y ( 5 4 a ) . A n o s m o t ic s y s te m is a sy s -

t e m i n w h i c h t h e p ro c e s s o f o s m o s is ta k e s p la c e. T h e o s m o t ic re -

l a t i o n s o f t h e s y s t e m a r e d e t e r m i n e d b y t h e c o n s t i t u e n t f a c t o r s o r

i n f l u e n c e s i n v o l v e d i n t h e c o n s u m m a t i o n o f t h e p r o c e s s o f o s m o s i s .

A Semipermeable M embrane D efined

A s e m i p e rm e a b l e m e m -

b r a ne , i n a n i de a l o s m o t i c s y s t e m , i s a l i m i t i ng l a ye r , o f i n f i n i t e s i m a l

t h ic k n e s s , s e p a r a t i n g t w o c o m p o n e n t s , o n l y o n e o f w h i c h i s c a p a b le

o f f r e e pa s sa g e t h r o u g h t h e b o u n d a r y .

a As defined by Lewis and Randall (35), to include also the possible in-

fluences of variables other than pressure, tem perature and com position. T he

phrase free energy w ill be us ed hereinafter with the understanding that

it refers to the partial m ola l free energy o f the m olecules of a com ponen t of the

system . O sm osis may be attended b y m odif ication of the p x V product in

either p ha se. Th e resultant action capacity between phases after any interval

of time w ill in part depend on this pro du ct. Therefore, a free energy dif-

ference (f ' - f~ is here expressed as that, corrected f or any significant p X V

change in either phase, equivalent to a difference in A of Helm holtz (35 ,

pp. 156--159).

2 Since aq ueo us solutions are invariably invo lved in the two mem brane-

separated ph ase s of biolo gical sys tem s, the terms w ater (solvent) and

solute w il l be used, imp lying that the components are ca pa ble an d in-

capable, respectively, of relatively free p as sag e through the semiperm eable

membrane.


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T H E B O T A N I C A L R E V I E W

Osmotic Speci f ic Free Energies Def ined: Osmotic specific free

energies F) are any action capacities of water associated with an

osmotic system, expressed in positive dimensions of m L -t t -~,

e.g.

energy per unit volume, or pressure. An osmotic influx or

emux specific free energy is numerically equal to the difference in

pressure, the osmotic pressure P = p - pO), on a medium necessary

to render the escaping tendency of water in a given state equal to

that of water in a reference state. This pressure difference is re-

lated to the free energy of the water molecules in a dilute solution of

solute and solvent contained in either phase of an osmometer,

through the approximate relation:

___+ ~_fo)

~ P = w - P - P ~ --vo 1.013x109) =F 2) 8

where f is the free energy of water in a given state other than the

standard or reference state, here expressed in erg units; fo is the

molal free energy of water in its standard state, in ergs; v ~ is the

molal volume of water in its standard state, in liters; 1.013 x 109 is

the necessary conversion factor; pO is the pressure on the water in

its standard or reference state, in atmospheres ; and p is the pressure

on the medium in the given state, necessary to make f- equal to f~

in atmospheres.

Since the molal volume of the component water in the standard

state is a constant here equal to 0.018 liter), i ti s evident from equa-

tion 2 that an osmotic influx or efflux specific free energy_F, as well

as an osmotic pressure P, is a measure of the quantity f - f~ see

35, p. 214; 18, pp. 100-104). In this treatise specific free energies

are used as measures of the differences in free energy of the water

molecules due to any constituent osmotic influence, in order to deal

with dimensions commensurate with those generally employed by

the biologist compare 44). However, the action capacities may be

a M a n y p h y s i c a l c h e m i s t s a n d b i o l o g is t s h a v e r e l a t e d t h e e s c a p i n g t e n d e n c y

o f w a t e r t h r o u g h a n i n te r p o se d s e m i p e rm e a b l e m e m b r a n e o f a n o s m o m e t e r t o

t h e p r e ss u r e di ff e re n c e p - p O . H o w e v e r , s i n ce o n l y o n e a c t u a l o r e x e r t e d

p r e s s u r e i s g e n e r a l l y i n v o l v e d i . e . , hy dro s t a t i c ) i t i s be t t e r , i n o rd e r t o avo id

m i s c o n c e p t io n , t o e x p r e s s t h e o s m o t i c v a l u e s o r a c t i o n c a p a c it ie s , i n t e r m s

of t he d if f e rences i n t he f r ee en erg y o f t he wa te r m o lecu l es . T h i s specif ic f r ee

en erg y F i s exp resse d by the qu ot ien t +_(f'-fo__~), re la te d to , bu t n ot cau sed b y ,

,vo

t h e p r e s su r e d if f er e n ce p - p O a s s e t f o r th i n e q u a t io n 2 ( c o m p a r e ( 5 4 a ) ) .

N O T E : A b a r a b o v e t h e s y m b o l s f a n d ~ i n d i c a t e p a r t i a l m o l a l q u a n t i t i e s .

T h e c i r c u l a r z e r o a s s u p e r - s c r i p t t o t h e s y m b o l s fo a n d v ~ i n d i ca t e t h e s t a n d a r d

s t a t e


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MOVEMENT OF MATERIALS INTO PLANTS 5

ex p res se d in fu n d am en ta l d imen s ion s o f en e rg y m L * t2,

(e.g.,

e r g o r

ca lo r ie u n i t s ) . F o r t h e u n i ts u sed in t h i s d i s se r t a ti o n , th e co n v e r -

s io n i s a c co m p l is h ed t h r o u g h th e r el at io n ( ~ _ f o ) = F ( 1 .8 2 3 x

1 0 ' ) , w h e r e F is e x p r e s se d in a t m o s p h e re s , a n d ( T - f o ) i n e r g s.

Osm otic P ressu re Def ined:

Osmo t i c p re s su re i s t h e p re s su re d i f -

f e ren ce wh ich mu s t b e ap p l i ed t o t h e two p h ases o f an o smo mete r ,

under idea l cond i t ions , to es tab l i sh and /o r main ta in equ i l ib r ium of

escap in g t en d en cy fo r wa te r ac ro s s t h e i n t e rp o sed s emip e rmeab le

m em b ran e ( s ee 3 5, p p . 2 1 3 -2 1 5 ) . In eq u a t io n 2 t h e o smo t i c p re s -

su re i s r ep resen t ed b y P , eq u a l t o th e d i f fe ren ce p - pO ( see F ig u re

1) . (S ee the sec t ion en t i tl ed

O n

t h e Or ig in o f Osmo t i c ' So lu t e '

| x x x ~ , x , , | m x . ~ , ~ . x m

Semipermeoble

embrone

Phose e t P ho se i

Com ponen f A Com ponen f B

FIG. 1. Initial condition of an osm otic system in the ideal state.

A = C omponent capable of fre e passage through the membrane.

B = Com ponent incapable of fre e pa ssage through the membrane.

M = Semipermeable membrane.

+ (~ fo)

- vo = -T-p - pO; for analysis, see text, page 4.

Sp ec if ic F r ee E n e rg y , p ag e 9 , an d co m p are w i th t h e so lu te sp ec if ic

f ree en e rg y re l a ted t o t h e p re s su re d i f f e ren ce n eces sa ry t o eq u i l ib ra te

th e e scap in g t en d en c ie s fo r so lu t e b e twee n two so lu tio n p h ases o f an

o s m o m e t e r ( P a r t I I ) . )

Osmot ic Metabol ic Speci f i c Free Energy Def ined: In t h e p l an t ,

m etabo l ic spec if ic f ree energy , F m , i s an y po ss ib le ac t ion ca pac i ty

ma in t a in ed d i r ec t l y t h ro u g h me tab o l i sm o f t h e l i v in g o rg an i sm

wh ich can b e ap p l i ed t o t en d to cau se wa te r t o mo v e , u n i l a t e ra l l y ,

t h ro u g h th e s emip e rmeab le memb ran e wi th o r ag a in s t t h e d i r ec t i o n

in wh ich i t s co n cen t ra t i o n d ec rease# , b y mo d i f i ca t i o n o f t h e f r ee

en e rg y o f t h e wa te r mo lecu le s .

9 It has been suggested that osmosis should be te rmed "anomalous" where

the flow of water through the semipermeable membrane is governed by


6/58

6 TH E BOTANICAL REVIEW

Osmotic Non-metabolic Specific Free Energy Defined:

I n t h e

p l a n t o s m o m e t e r n o n - m e t a b o l i c s p ec if ic f r e e en e r g y , F n m , i s a n y

p o s s i b l e a c t i o n c a p a c i t y ( e x c l u s i v e o f h y d r o s t a t i c s p e c i f i c f r e e

e n e r g y , w h i c h s e e ) n o t d i r e c t l y m a i n t a i n e d t h r o u g h m e t a b o l i s m o f

t h e l iv i n g o r g a n i s m , w h i c h c a n b e a p p l i e d t o t e n d t o c a u s e w a t e r t o

m o v e t h r o u g h t he s e m i p e r m e a b l e m e m b r a n e w i th o r a g a i n s t th e

d i r e c t i o n i n w h i c h i t s c o n c e n t r a t i o n d e c r e a s e s , b y m o d i f i c a t i o n o f t h e

f r e e e n e r g y o f t h e w a t e r . A d s o r p t i o n a n d i m b i b i t io n a r e t w o ty p i c a l

p r o c e s s e s o r i n f l u e n c e s a f f o r d i n g a n a c t i o n c a p a c i t y o f t h i s t y p e

t h r o u g h l o w e r i n g o f th e f r e e e n er gy , o f t h e w a t e r m o l e c u l e s a t

c o ll o id a l s u r f a c e s a n d w i t h in i m b i b a n t s . S u c h p r o c e s s e s i m p l y t h e

p r e s e n c e o f m a t t e r o t h e r t h a n m o l e c u l e s o f s o l v e n t a n d s o l u te i n

s o l u t i o n .

O s m o t i c s o l u t e s p ec if ic f r e e e n e r g y is o n e m a n i f e s t a t i o n o f a

p o s s i b l e n o n - m e t a b o l i c o s m o t i c s p e c i f i c f r e e e n e r g y , b u t b e c a u s e o f

i ts p r i m a r y i m p o r t a n c e i n t he o s m o t i c s y s t e m i t is d i sc u s se d a s a

s e p a r a t e f a c t o r f o r w a t e r f l o w .

Osmotic Solute Spe cific Free Energy D efine d:

O s m o t i c

s o l u t e s p ec if ic f r e e e n e r g y , F s , is t h e a c ti o n c a p a c i t y t e n d i n g t o

c a u se w a t e r t o m o v e t h r o u g h t he s e m i p e rm e a b l e m e m b r a n e e i t h er

i n to a c o m p o n e n t i n c a p ab l e o f f r ee p a s s a g e th r o u g h t h e s e m i p e r m e -

a b le m e m b r a n e o r i n to a s o lu t io n o f t h e t w o c o m p o n e n t s ( s o l v e n t

w a t e r a n d s o l u t e ) . T h e w a t e r f l ow s a c r o s s t h e b o u n d a r y i n t o a

s o l u ti o n w i t h i n w h i c h t h e f r e e e n e r g y o f th e m o l e c u l es o f t h e w a t e r

h a s b e e n l o w e r e d i n r e l a t i o n t o t h e c o n c e n t r a t i o n o f t h e s o l u t e i n

t h e so l u ti o n . I n a n i d ea l o s m o t i c s y s t e m th e r e l a ti o n s h i p b e t w e e n

energies supplem enting the osm otic solute spe cific free ene rgy difference,

as determined by the inequality of the solute concentration between the two

phases of the osm om eter. An om alous osm osis is then designated positive

where the flow is with the direction in which the concentration of water de-

crea ses; negative wh ere the tran spo rt is against the direction in which the

concentration of w ater decreases (9 ). In view of our l imited knowledge of

the factors involved, the term anomalous m ay justly be applied to this un-

known osmotic mechanism. However, in order to maintain a consistent and

m ore expressive terminology, the follow ing definitions are proposed. M et a-

bolic spe cifie free en erg y tends to cause or maintain osm otic, m etabolic

diffusion of w ater , the tendency toward flow being governed by energ y sup-

plementing the osmotic solute specific ~ree energy difference, as determ ined

by the inequality of the solute concentration between the two phases of the

osmom eter. Th e flo w m ay be characterized as an osmotic metabolic simple

diffusion whe re, and w hile , the flo w is with the d irection in which the con-

centration of w ate r decreases; similarly, osm otic m etabolic accum ulation '

where the transport is against the direction in which the concentration of water

decreases.


7/58

M O V E M E N T O F M A T E R I A LS I N T O P L A N T S 7

a measure of this specific free energy and the volume within either

of the two phases involved, shows a formal resemblance to the ideal

gas law (equation 1),

viz

n

Fs = V RT (3) 5

where Fs is the specific free energy of the water, dimensionally

and mathematically equal to the osmotic pressure, related to a dif-

ference in solute concentration in the two phases of the osmometer ;

V is the volume of solution; and n is the number of mols of solute

in the solution (26).

Since V = C, where C is the volume molar (molarity) or, better,

the weight molar (molality) concentration of solute in the solution,

Fs = CRT (3b)

Assuming temperature changes are nil, the osmotic solute

specific free energy may be measured as equal to the pressure which

must be applied to produce a condition such that there is no tendency

for the water to flow in either direction across the semipermeable

boundary (see equation 2 and Figure 1). Employing the van' t

Hoff equation, 3 or 3a or 3b, as applicable in solution8, the osmotic

solute specific free energy is a function of the concentration of

solute in a solution. Thus RT is a coefficient for converting solute

concentration into the related (antiphasically effective) osmotic

solute specific free energy (see equation 3b).

Hydrostatic Pressure Defined

Hydrostatic pressure, Ph, is a

pressure exerted uniformly in all directions from any point in a

5 S o m e i n v e s t i g a t o r s ( s e e 3 5, p . 2 3 6 ) , o n t h e o r e t i c a l a n d e x p e r i m e n t a l

g r o u n d s , p r e f e r t h e e q u a t i o n

Fs

: -~o RT (3a)

w h e re N i s t h e n u m b er o f t o o l s o f s o l u t e i n 1 to o l o f s o l v en t , an d v ~ i s t h e

m o l a l v o l u m e o f t h e p u r e s o l v e n t .

a I f t h e e q u a t i o n o f v a n ' t H o f f i s u s e d t o d e f i n e th e s p e c if ic f r e e e n e r g y

a n d c o n c e n t r a t i o n r e l a t io n s o f a n i d e a l s o lu t io n , th e n d e p a r t u r e f r o m t h e

i d e a l b e h a v i o r m u s t b e i n t e r p r e t e d w i t h r e s p e c t t o s u c h f a c t o r s a s a r e l i k e l y

t o i n fl u e nc e t h e o s m o t i c s o l u t e s p e c if ic f r e e e n e r g y . H e i n t r o d u c e d a c o e f ~ -

c i en t , k , i n t o t h e eq u a t i o n , t o co r rec t fo r a l l t y p es o f d ev i a t i o n f ro m i d ea l

b e h a v i o r w i t h o u t r e c o u r s e t o t h e i r o r i g i n . T h e o s m o t i c s o l u t e s p e ci fi c f r e e

e n e r g y m a y b e m o d i f ie d b y t h e d e g r e e o f d is s o c ia t io n o f t h e m o l e c u l e s o f t h e

so lu te in to cons t i tue n t ions (57 , p . 55) and by hy dr a t io n (45 , pp . 102 , 103) , in

a q u e o u s s y s te m s . F u r t h e r , c o r r e c t i o n s m a y b e a p p l i ed f o r n o n - s o l v e n t v o l u m e

a n d f o r f o r c e s o f a t t r a c t i o n b e t w e e n m o l e c u le s i n s o l u ti o n ( 1 0 ) . F o r e x -

a m p l e s o f p o s s ib l e d e v i a t i o n f r o m t h e i d e al , s e e d a t a o f M o l z ( 4 7 ) , M o r s e

(4 8 ) an d o t h e r s (5 7 , p p . 5 1 -5 6 ) .


8/58

THE BOTANICAL REVIEW

f lu id . O ther fac to rs be ing cons tan t , any change in the hy dro s ta t ic

p re s su re wi th in a p h ase wi l l d i r ec t l y mo d i fy t h e f r ee en e rg y o f t h e

co m p o n en t mo lecu le s , p ro p o r t i o n a t e ly . I f t h e p re s su re o n , an d f r ee

en e rg y o f , t h e mo lecu le s a t an y p o in t a re i n c reased , t h ey a re i n -

c r e a s e d e v e r y w h e r e t h r o u g h o u t t h e f l u i d b y t h e s a m e a m o u n t .

More spec i f ica l ly , wi th in the osmometer the hydros ta t ic p ressure ,

P h t , i s t h e o u t w a r d l y d i r e c t e d p r e s s u r e o f t h e i n n e r c o m p o n e n t o r

so lu t io n o n th e memb ran e , wh ich can b e ex h ib i t ed e i t h e r b y tu rg o r

in an inc losed phase o r by a s imi la r p ressu re in an open inne r ph ase .

Su ch p re s su re , wh en p o s i t i v e , t en d s t o cau se wa te r t o mo v e o u t -

ward ac ro s s t h e s emip e rmeab le b o u n d a ry d u e to t h e i n c reased f r ee

en e rg y o f it s mo lecu le s i n t h e i n n e r p h ase o f th e o sm o m ete r (3 5 ,

pp . 199, 243 , 24 4) . Th is p ressure , pos i t ive o r nega t ive (18 , p . 13 6) ,

i s eq u a l t o t h e a lg eb ra i c r e su l t b e twe en th a t p re s su re (P h t ' ) i n -

t r i n s i ca l l y a s so c i a t ed wi th t h e med iu m in t h e i n n e r p h ase o f t h e

re fe ren ce sy s tem, cau sed b y th e r e s t r i c t io n to ex p an s io n th e re in , an d

an y ex t r in s i c p re s su re (P h i ) wh ich m ay a r i s e d u e to t h e ap p l ica -

t ion o f ene rgy o f ex t ra -phas ic o r ig in , i .e. f ro m o u t s id e t h e r e fe ren ce

sys tem . In an open inner phase , w i th in the p lan t , the in tr ins ic

h y d ro s t a t i c p re s su re (wi th r e fe ren ce t o t h a t a t t h e u p p e r su r face o f

th e i n n e r p h ase t ak en a s ze ro , cap i l l a r i t y ex c lu d ed ) i s cau sed b y

the w eigh t o f the co lum n of f lu id a lone , the res t r ic tion to ex pan s ion

being assoc ia ted wi th the increas ing to ta l fo rce (g rav i ta t ion in -

v o lv e d ) i n t h e l iq u id co lumn . T h e ex t r i n s i c fo rce m ay b e an y

par t ia l so lu t ion p ressure (pos i t ive o r nega t ive , and usua l ly the

l a t t e r i n t h e p l an t ) wh ich may a r i s e wi th in t h e o smo mete r d u e to

the app l ica t ion o f an ac t ion capac i ty to e i ther the ex te rna l o r in -

te rna l phase . In an inc losed inner phase , the in t r ins ic p ressur e ,

n u mer i ca l ly eq u a l t o t h e memb ran e (wa l l ) p re s su re , i s cau sed b y

the res t r ic t ion to expans ion app l ied th rough ex tens ion o f the e las t ic

en c irc li n g m em b ran e o f t h e r e fe ren ce cell. T h i s p re s su re m ay b e

p o s it iv e , ze ro o r n eg a tiv e . H ere , a s i n t h e o p en in n e r p h ase , t h e

ex t r in s i c fo rce m ay b e an y p a r t i a l so lu tio n p re s su re , p o s i t iv e o r

n eg a t iv e , wh ich m ay a r is e w i th in t h e o sm o m ete r d u e to t h e ap p l ica -

t ion o f an ac t ion capac i ty to e i ther the ex te rn a l o r in te rna l phase .

Wi th a re fe rence ce l l , a spec ia l ex t raphas ic energy may be invo lved .

W he re i t i s su r ro und ed by o ther ce lls , as in a ti s sue , an in te rce llu la r

(wal l ) p ressure , pos i t ive o r nega t ive , i s e f fec t ive .

Hydros ta t i c Spec i f i c Free Energy De f ined : Hy d ro s t a t i c sp ec i f i c


9/58

MOVEMENT OF MATERIALS INTO PLANTS

free energy, Fhi, is that action capacity, caused by a hydrostatic

pressure within an osmometer, which tends to cause water to move

across the semipermeable boundary. Hydrostatic specific free en-

ergy is the resultant between the intrinsic hydrostatic specific free

energy, Fh(, and any extrinsic hydrostatic specific free energy,

Fh l . These constituent specific free energies are related to the

comparable constituent hydrostatic pressures.

N e t In f l u x Spec ific Free Ene rgy De fined: The net influx specific

free energy, NIF, is the difference in action capacity between the

algebraic sum of the specific free energies tending to cause water to

move into the system and those tending to cause water to move out

of the system. The net influx specific free energy is equal to the

sum of the influx specific free energies diminished by the sum of the

emux specific free energies, i.e., net influx specific free energy =

(Y'. influx specific free energies) - (]E efflux specific free energies)

or NIF = F J F- ZEF. (4)

O n the Or ig in o f Osm otic So lu te Specif ic F ree En erg y: There

are several views concerning the origin of osmotic phenomena ex-

pressed as pressures (20). Osmosis has been conceived generally

as involving pressures of solute and/or solvent. This approach is

illogical and unnecessary and leads to confusion over the mechanics

of this process. Although the action capacities, tending to cause

water to move through a semipermeable membrane of an ideal

osmometer, may be expressed in dimensions of m L -1 t -~, these spe-

cific free energy quantities are merely measures of the escaping

tendency of solvent water molecules. Based on the free energy

concept, rather than actual exerted pressures of the component

molecules, the process is presented with more clarity. In the study

of osmotic solute specific free energy, the essential feature is that

the free energy of the solvent molecules is less in a solution than in

the pure liquid at constant temperature and pressure; in other

words, the transfer of water through an interposed semipermeable

membrane from its pure (standard) state to that in a solution will

result in a decrease of free energy. Such a flow will, therefore,

always tend to occur whenever solvent and solution are brought

together. Where they are separated by a semipermeable membrane,

the water must flow into the solution until equilibrium is attained

by the building up of a hydrostatic specific free energy, or its equiva-

lent pressure, within the solution phase, ideally equal to the osmotic


10/58

1

TH E BOT NIC L REVIEW

so lu te specif ic f ree energy , and re la ted to the concen t ra t ion o f

so lu te in the so lu t ion , in accordance wi th the van ' t Hoff equa t ion

(see equat ions 3 , 4 ) . Th e ex is tence o f an osm ot ic so lu te spec if ic

f ree energy i s the inev i tab le resu l t o f the in t roduct ion o f a semi-

p e rm eab le mem b ran e b e tween a p u re so lv en t an d a so lu tio n , o r

be tw een two so lu t ions o f d i ss im i la r so lu te concen t ra t ion , on acco un t

of the d i f fe rence o f the f ree energy o f the so lven t molecu les in the

tw o p h ases ( co m p are t h e s ec tio n s h e re in en t it led T h e F r ee E n -

e r g y C o n c e p t , O s m o t i c ' S o l u te ' S p e c if ic F r e e E n e r g y D e f i n e d ,

a n d O n t h e O r i g i n o f O s m o t ic ' S o lu t e ' S p e ci fi c F r e e E n e r g y w i t h

th e s ec tio n en t it led T h e F r ee E n e rg y o f a Co n s t i tu en t S o lu t e i n a

So lu t io n , i n Pa r t I I ) . See fo o tn o te 3 .

Deviations in the Plant from the Ideal Osmotic Sy ste m :

I . S em ip e rmeab le mem b ran e .

a. T h e thick nes s is finite.

1. T im e is finite.

2 . Sem ip e rmeab i l i ty m ay b e d u e to t h e re s t r i c ted p as -

sag e o f t h e co m p o n en t ( so lu t e ) n o t f ree t o mo v e

through the l imi t ing su r face , th rough a cap i l l a ry

of , o r th rough so lu t ion ~n , the bounding layer .

b . Th e m em bran e i s never s tr ic t ly semiperm eab le .

1 . A metabo l ic specif ic f ree ene rgy m ay be ada p ted to

m o v e u n i la t e ra l ly t h e co m p o n en t ( so lu t e ) h e re to -

fo re r eg a rd ed a s i n cap ab le o f f r ee p as sag e th ro u g h

th e s emip e rmeab le memb ran e th ro u g h th i s d i f -

f e ren t i a l l y p e rmeab le b o u n d a ry wi th o r ag a in s t

(metabo l ic accumula t ion o f so lu te ) the d i rec t ion

in which i t s concen t ra t ion decreases .

I I . F o r each phase the chan ge in vo lum e is fin ite .

a. T im e is finite.

b . A f te r a fin ite t ime the sys tem no longer invo lves pu re

c o m p o n e n t s A ( s ol v e nt , w a t e r ) a n d B ( s o l u t e ) , b u t

r a t h e r c o m p o n e n t A ( w a t e r ) in p h a s e e ; a n d i n p h a s e

i, a so lu tio n o f A (w a te r ) an d B ( so lu t e ) . (S ee

F ig u re 1 . ) Fu r th e r , s in ce t h e me m b ran e is n o t s t r ic t l y

semip e rmeab le , t h e sy s t em may su b seq u en t ly i n v o lv e

tw o so lu t ions o [ the com ponen ts , in ph ases e and i.

c . In the idea l aqu eou s osm ot ic sys tem there shou ld be no

ch an g e in v o lu m e d u e to ev ap o ra t io n .


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MOVEMENT OF M TERI LS INTO PL NTS

I I I . T e m p er a tu re ch an g es a re fin ite . H o w ev e r , i n t h is t r ea t is e

th i s fac to r i s assumed to be non-var ian t .

IV . T h e rmo d y n amic eq u i l i b r iu m, wi th in t h e o smo t i c sy s t em

as a wh o le , may b e ap p ro ach ed , b u t i s p ro b ab ly n ev e r

at ta ined.

V. T h e s t a t e o f t h e sy s t em i s n o t d e t e rmin ed so l e ly b y th e

t emp era tu re , p re s su re an d co mp o s i t io n . O th e r in d ep en -

den t var iab les , fo r example , g rav i ta t iona l and e lec t r ica l

f ie lds , and surface effects , may be involved.

In the osmot ic sys tem of the p lan t , as ind ica ted here inbefore , the

co mp o n en t cap ab le o f r e l a t i v e ly f r ee p as sag e th ro u g h th e s emi -

p e rmea b le m em b ran e is t h e so lv en t wa te r . T h e co mp o n en t r e l a-

t ive ly incapab le o f f ree passage i s the so lu te a r i s ing w i th in the p lan t

th ro u g h m e tab o li sm o r su p p li ed t o t h e o rg an i sm f ro m wi th o u t . In

th e im p er fec t o smo t i c sy s t em o f t h e p lan t , w e h av e to d ea l n o t. w i th

two p u re co mp o n en t s , b u t wi th aq u eo u s so lu t io n s , o r co l lo id a l

sy s t ems , i n t h e two memb ran e - sep a ra t ed p h ases .

Comparison Be twe en Tw o A l t e rna t i ve Aspe c t s o~ t he Fund a-

men ta l Equa t ion ~or W a ter M ov em en t i n an Osm om eter :

T h e r e a r e

tw o a l t e rn a t iv e m e th o d s o f v i ewin g th e o smo t i c r el a ti o n s o f p lan ts ,

b o th b ased u p o n th e fu n d amen ta l p h y s i co -ch emica l p r in c ip l e s o f

osmo s is . T he f i r s t m ethod i s usefu l on ly in a pure ly mathemat ica l

an a ly s i s o f t h e sy s tem. T h i s s ch eme h as b een d ev e lo p ed th ro u g h

th e cu mu la t iv e e f fo r t s o f a n u mb er o f i n v es t i g a to r s , mo s t r ecen t ly

ad v an c ed b y M ey er an d o th e r s 4 3 - -4 5 ) . T h e s econ d , a l t e rn a t iv e

method , i s usefu l in a pure ly mathemat ica l ana lys i s o f the sys tem

and a l so serves to p resen t , in a s imple manner , the osmot ic re la t ions

in g rap h ic fo rm , ex t en d in g th e d i ag rams o f T h o d ay an d H6 f l e r

5 9 , 2 7 ) .

C o n s i d e r t h e p r o c e s s i n w h i c h w a t e r m o v e s i n a n o s m o m e t e r

f ro m a p o in t ex t e rn a l t o t h e i n t e rp o sed memb ran e , t o a p o in t i n -

ternal ly , i.e. H 2 0 e x t e r n a l ) i n fl u x H 2 0 i n t e r n a l) s e e 18 , p p .

1 0 0 - 1 0 4 ) . T h e m e a s u r e o f t h e t e n d e n c y f o r w a t e r t o m o v e i s

g iv en b y th e d i f f e ren ce b e tween th e f r ee en e rg y o f wa te r i n t h e

in t e rn a l p h ase an d th a t i n t h e ex t e rn a l p h ase o f t h e o smo mete r ,

f i - f e ) . I f th i s d i f f e ren ce i s n eg a t iv e i n sig n, wa te r wi ll t en d to

m o v e in ward , a s wr i t t en . T h u s , i f i t i s d es i r ed t o k n o w w h e th e r o r

n o t wa te r wi l l t en d to mo v e ac ro s s t h e memb ran e , t h e q u an t i t y

( f l - f . ) m u s t b e d e t er m i n e d .


12/58

2

T HE B OT NIC L R E VIE W

In p rac t i ce t h e f r ee en e rg i e s t h emse lv es a re n o t d e t e rmin ed , b u t

th e d i f f e ren ce b e tween th e f r ee en e rg y in a g iv en s t a t e an d th e f r ee

en e rg y in a r e fe ren ce o r s tan d a rd s t at e . F o r w a te r t h e s t an d a rd

s t a t e i s cu s to mar i ly ch o sen a s t h a t o f p u re wa te r u n d e r s t an d a rd

c o n d it io n s. I f b y t h e r m o d y n a m i c m e t h o d s t h e q u a n ti ti e s ( f i - f o )

a n d ( 7 , - f ~ a r e d e t er m i n e d , t h e n t h e d i ff e re n c e b e t w e e n t h e s e

quan t i ti es i s ( f l - f , ) .

A s wi ll b eco me c l ea r th e re i s an en t i re ly eq u iv a l en t me th o d o f

m e a s u r i n g t h e te n d e n c y fo r t h e a b o v e p r o c e s s t o o cc u r . T h i s

m e th o d in v o lv es t h e m easu rem en t o f t h e o smo t ic sp ec if ic f r ee en e r -

g i e s (F ) i n each p h ase , d i s t i n g u i sh in g b e tween th o se co n s t i t u en t

in f lu en ces wh ich t en d to d ec rease t h e f r ee en e rg y o f t h e co mp o n en t

wa te r i n t h e g iv en s t a t e wi th r e sp ec t t o t h a t i n t h e r e fe ren ce s t a t e

( - A f ) , a n d t h o s e w h i c h c o r r e s p o n d i n g l y t e n d t o i n c r e a s e t h e f r e e

e n e r g y ( A f ) . T h e p r e s e n c e o f s o lu t e o r a h y d r o p h il ic im b i b a n t i n

an aq u e o u s med iu m w i ll t en d to l o w er t h e f r ee en e rg y o f t h e so lv en t

w a te r . A h y d ro s t a t i c p re s su re , o r t u r g o t i n an enc lo sed p h ase , w i l l

r a i s e t h e f r ee en e rg y ab o v e th a t i n t h e r e fe ren ce s ta t e. T h i s p h y s i co -

chemica l ana lys i s o f the osmot ic spec i f ic f ree energ ies invo lved in

th e sy s t em wi ll b e p re sen t ed b y mean s o f eq u a tio n s w h ich ap p ly o n ly

fo r d i l u t e so lu t io n s an d lo w p res su res .

T he osm ot ic so lu te spec if ic f ree ene rgy i s def ined as equa l , bo th

d imen s io n a l ly an d ma th emat i ca l l y , t o t h e i n c rease i n p re s su re o n a

so lu t io n n eces sa ry t o mak e th e f r ee en e rg y o f t h e so lv en t i n t h e

g iv en s ta t e , t h e s ame a s th a t o f t h e p u r e so lv en t. F o r d i lu t e aq u eo u s

so lu t io n s , t h e o smo t i c so lu t e sp ec if ic f r ee en e rg y (F s ) i s g iv en

b y t h e e q u a t i o n :

_ ( i - - f * )

F s = p - p ~ = v o 5 )

wh ere f i s t h e f r ee en e rg y o f wa te r i n t h e so lu t io n ; fo i s t h e f r ee

e n e r g y o f w a t e r i n t h e p u r e s t a t e ; ~ ~ i s t h e m o l a l v o l u m e o f p u r e

w a t e r ; p ~ is th e p r e s s u r e o n t h e w a t e r i n th e p u r e s t a t e ; a n d p i s

t h e p re s su re n eces sa ry t o mak e i eq u a l t o fo .

S in ce t h e mo la l v o lu m e o f p u r e w a te r i s a co n s t an t, i t is ev id en t

f ro m eq u a t io n 5 t h a t t h e o smo t i c so lu t e sp ec if ic f r ee en e rg y (F s )

i s a m e a s u r e o f t h e q u a n t i t y ( f - f ~ I n t h e a b s en c e o f o t h e r

osm ot ic in fluences on th e sy s tem , i t fo l lows tha t

F s , - F s , = - ( f ' - f ' ) ( 6 )

V ~


13/58


w h ere F s i an d Fso a re t h e an t ip h as i c o smo t i c spec if ic f r ee en e rg i e s

re la ted to the p resence o f in te rna l so lu te and ex terna l so lu te , re -

s p ec ti ve ly . A s p r e v i o u s ly s ta te d , ( f , - f e ) i s a m e a s u r e o f t h e

t e n d e n c y f o r w a t e r to m o v e a c r o ss t h e m e m b r a n e. F r o m e q u a t io n

6 i t i s a p p a r e n t t h a t t h e q u a n t i t y ( F s , - F s e ) i s a l s o a m e a s u r e o f

t h e t e n d e n c y f o r w a t e r t o m o v e . A p o s i ti v e v a l u e f o r ( F s , - F s ~

in d i ca t e s a t en d en cy fo r wa te r t o mo v e i n ward , i . e . a n i n f l u x o f

w a t e r .

T h e a b o v e m e t h o d m a y b e a p pl ie d t o c a s es w h e r e e i th e r o r b o t h

o f t h e p h a s e s o f t h e o s m o m e t e r m a y b e s u b j e c t e d t o o t h e r o s m o t i c

in fluences , i so thermal ly . T he re la t ionsh ips app ly on ly fo r d i lu te

so lu t io n s an d l o w p res su res . A n in c rease i n p re s su re o n a p h ase

o f t h e sy s t em o rd in a r i l y i s acco mp an ied b y an i n c rease i n t h e f r ee

e n e r g y o f w a t e r . F o r w a t e r t h e c h a n g e i n f r e e e n e r g y . d u e t o a n

imp o sed p re s su re i s p ro p o r t i o n a l t o t h e ch an g e i n p re s su re ,

i . e .

G - f ~

F cA ,) = - ( p - p ~ v ~ . O n t h e o t h e r h a n d , t h e c h a n g e i n f r e e

en e rg y o f wa te r d u e t o t h e p re sen ce o f d i s so lv ed ma te r i a l i s p ro -

p o r t i o n a l to t h e n eg a t iv e o f t h e o smo t i c so lu t e sp ec if ic f r ee en e rg y ,

- G - f ~

i . e .

F r = ( p _ p O ) = v ~ T h e t w o e q u a ti on s , t h e re f o re ,

hav e the sam e fo rm , bu t opp os i te s igns . I f the spec if ic f ree energ ies ,

e q u al to t h e i m p o s e d p r e s s u re s n e c e s s a r y to m a k e ] - e q u a l t o f ~ a r e

d es ig n a t ed b y t h e sy mb o l Fr fo r co n s t i t u en t i n fl u ences l o wer in g

th e f r ee en e rg y o f t h e so lv en t wa te r , an d b y t h e sy mb o l F Ae) f o r

con s t i tuen t in f luences ra i s ing the f ree en ergy , i t fo l lows tha t

(ZF


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14 TH E BOTANICAL REVIEW

e x a m p l e, t he t e n d en c y f o r w a t e r to m o v e i n w a r d = ( ( F s t ) - ( F h t ) )

- F s ~ ) . 9a)

A g a i n , th e te n d e n c y f o r w a t e r t o m o v e i nw a rd -~ ( ( F s ~ ) - ( F h i ) )

- ( ( F s e + F n m ) - ( F r o ) ) . 9 b ) T

I n t h e t e r m i n o l o g y o f M e y e r t h e s e t e n d e n c i e s f o r w a t e r t o m o v e

i n w a r d a r e e x p r e s s e d i n e a c h c a s e b y t h e d i f f e r e n c e b e t w e e n t h e

a l g e b r a i c s u m o f t h e d i f f u si o n p r e s s u r e d e fi ci ts f o r w a t e r a s s o c i a t e d

w i t h i n t e r n a l f a c t o r s , a n d t h e a lg e b r a i c s u m o f t h e d i f fu s i o n p r e s s u r e

d e f i c i t s f o r w a t e r a s s o c i a t e d w i t h e x t e r n a l f a c t o r s , w h e r e t h e d i f -

f e r e n c e is r e p r e s e n t e d b y th e e q u a t i o n s :

D P D D = ( Y ~ D P D ) , - ( ~ D P D ) e a n d

D P D D = ( O P + ( - T P ) ) , - ( O P ) e ; o r

= O P + . . . + - T P ) ) t - O P + . . . + . . . ) , .

lO)

( 1 0 a - - s e e

e q u a t i o n s

9 a a n d 1 2 )

( 1 0 b - - s e e

e q u a t i o n s

9 b a n d 3 6 )

I n o r d e r t o e x p r e s s t h e s e s p ec if ic f r e e e n e r g i e s i n e q u a t i o n s a n d

i n g r a p h i c f o r m , w h e r e t h e t e n d e n c i e s f o r w a t e r f l o w m a y b e f o l -

l o w e d i n r e l a t i o n t o t h e c h a n g e s i n t h e e x t e r n a l a n d i n t e r n a l s p e c i f i c

f r e e e n e r g i e s a n d t h e c h a n g e s i n t h e i n t e r n a l v o l u m e ( t h e l a t t e r

h e r e t o f o r e c o n s i d e r e d c o n s t a n t ) , a n a l t e r n a t i v e s c h e m e w a s d e -

v e l o p e d . H e r e , t h e d i f f e re n c e b e t w e e n t h e a l g e b r a i c s u m o f t h e

a c t i o n c a p a c i t i e s t e n d i n g t o c a u s e w a t e r t o m o v e i n w a r d a n d t h e

a l g e b r a ic s u m o f t h o se t e n d i n g t o ca u s e w a t e r t o m o v e o u t w a r d i s a

m e a s u r e o f t h e n e t t e n d e n c y f o r w a t e r t o m o v e i n w a r d a c r o s s t h e

m e m b r a n e . T h e o s m o t i c s pe ci fic f r e e e n e r g ie s , r e g r o u p e d i n th e

e q u a t i o n o f n e t t e n d e n c y f o r w a t e r f l o w , a r e e x p r e s s e d i n t e r m s o f

t h e c h a n g e s i n t h e a c t u a l o s m o t i c sp e c if ic f r e e e n e r g y o f t h e w a t e r

m o l e c u l e s , d u e t o e x i s t i n g a c t i o n c a p a c i t i e s r e l a t e d t o t h e c o n s t i t u e n t

i n fl u en c e s i n a n o s m o m e t e r p h a s e . I n o t h e r w o r d s , th e c o n s t i t u e n t

' I t m ay be observed tha t the metabolic specific free en ergy f actor tending

to cause the component (water here) to move inward in the system is desig-

nated as an influence tending to increase the free energy of the component in

favor of the external p hase . Th eov er-aU movement of the component against

the direction in which its concentration decreases, is in the direction opposite

to that in which a flow norm ally would occur and is therefore associated

with an apparent increase in free energy between the two ph ase s. Th e law of

tendency toward flow with the direction in which the specific free energ y of

the component decreases is maintained by asserting a complementary decrease

of free en ergy w ithin the cytoplasm, more than sufficient to compensate for the

increase in q ue stion (3 5, pp. 12 0, 1 2 1 ). Oxidative catabolism would be

required in this w ay for m etabolic accumulation of water.


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M O V E M E N T O F M A T E R I A LS I N T O P L A N T S 1 5

s p e c i f i c f r e e e n e r g i e s o f t h e s y s t e m , r e l a t e d a s e x p r e s s e d i n e q u a t i o n

8 , a r e r e g r o u p e d t o a c c o r d w i t h t h e n e t i n f l u x s p e c i f i c f r e e e n e r g y

e q u a t i o n 4 s e e p . 9 ) . T h u s , t h e e q u a t io n

N I F

=

I F

-

E E F 4 )

i s e q u i v a l e n t t o

N I F = TF _A t,) ,+ ~IF,A , ,)o)- Y F _at ,)~+ 5~F a, )) ,) . 4a)

M O V E M E N T O F W A T E R I N T H E P L A N T : T H E A L T E R N AT IV E

G R A P H I C S C H E M E

I n t h e w a t e r r e la t io n s o f t h e p l a n t s 3 4 , 3 7 ) , t w o r e fe r e n c e

O F T W O P O S S I B U E P L A N T O S M OT IC

S Y S T E M S

9 e r r ~ M e d i u m

I C s - 0 o t m ,

" F ~ - 4 o l ~

V . - O C

W o O

C o s p o r k m

C # o # o s m

i

Voc~ote

r ~ . 2 0 o l i n

~ F g . 4 O l i n .

F ~ - 0 Io X 3

o l m .

t n t ~ n i o l M e d i ~

F :~ -2 0 o t t o .

~ , : ~ ' ~ . . . .

V

11= t h e ~ s l o t e I ~ ~ o t l ~ t f A t ~ m e d iu m ~s

o s ~ m e d t o b e ~ , ff ln i tt .

I~ ot M ~ ~ t e r ~ ~ K , ~ i l e ~

Imall. HXdrDt.tofl tf*t'(~[~t: I t l R r O ~ l r d to ~ z e r o . i ~ i ti o f l X

FIG . 2 . D iagram of two poss ib le p lan t osmot ic sys tems. Th e tw o sys

tems r e p r e s e n t e d a r e , f i r s t , t h e s i m p l i f i e d , i n t e g r a t e d o s m o t i c s y s t e m , e x t e r n a l

m e d i u m w a t e r , n u t r ie n t s o lu t io n , o r s o il m e d i u m ) - - m e m b r a n e e n d o d e r m a l

c y t o p l a s m o r p r o t o p l a s m o f a c o m p a r a b l y s t r u c t u r e d c e l l s e r i e s ) - - i n t e r n a t

m e d i u m x y l e m s o lu t io n , e t c . ; a n d s e c o n d , a r e f e r e n c e c e ll , e x t e r n a l m e d i u m

n u t r i en t s o lu t io n o r in t e rc e ll u la r s o l u t i o n ) - - m e m b r a n e c y t o p l a s m ) - - i u t e r n a l

m e d i u m { v a c u o l a r s o l u t i o n ) .

8 W a t e r m o v e m e n t b y m a s s f l o w a lo n g c o n t i n u o u s w a t e r c o l u m n s u n -

i n t er r u p t e d b y d i f f e r e n t i a l l y p e r m e a b l e se p t a ) f r o m r o o t t o s h o o t , s im i l a r l y

g o v e r n e d b y t h e f r e e e n e r g y d i f f e r e n c e o f t h e s o l v e n t m o l e c u l e s , i n v o l v i n g

e v a p o r a t i o n a n d c o h e s i o n , w i l l n o t b e d i s c u s s e d i n d e t a i l s e e 1 5 , 2 8 , 3 4 , 4 5 , 6 0 ;

c o m p a r e 5 1 , 5 3 ) .


16/58

6

T H E B O T A N I C A L R E V I E W

T A B L E I

S P E C IF IC F R E E E N E R G I ES IN V O L V ED I N T H E M O V E M E N T O F W A T E R I N T O

P L A N T S U N D E R N A T U R A L E N V I R ON M E N T A L C O N D IT IO N S

N e t I n f l u x Sp e cif ic F r e e E n e r g y = ~ . I n f l u x S pe cif ic F r e e E n e r g i e s -

:Z E f flu x S p e cif ic F r e e E n e r g i e s N I F = ~ . I F - ~ . E F

W ater In flux Specific Free Eneroies

( I F )

A . O sm ot i c so lu t e specif ic f r ee

e n e r g y ( a n t i p h a s i c a l l y e f f e c ti v e ) ,

r e l a t e d t o t h e p r e s e n c e o f i n t e r n a l

s o l u t e t , a r i s i n g t h r o u g h s o l u t e

( e l e c t r o l y t e a n d / o r n o n - e l e c t r o -

l y t e ) i n f l u x ( b y s i m p l e d i f fu s i o n ,

D o n n a n d i f f u s i o n , e x c h a n g e a d -

s o r p t i o n o r m e t a b o l i c a c c u m u l a -

t i o n ) i n t o t h e m e d i u m b a t h i n g

t h e i n n e r su H a c e o f th e c e l l ( e n d o -

p l a s m ) , o r o f th e e n d o d e r m i s o r

c o m p a r a b l y s t r u c t u r e d c e l l s e r i e s .

F s l = I F .

B . N e g a t i v e h y d r o s t a t i c s p ec if ic

f r ee e n e r g y r e s u l t i n g f r o m h y d r o -

s t a ti c t e n s i o n ( n e g a t i v e p r e s s u r e ) .

i n t e r n a l , - F h~ = A I F . I n t r i n s i c

h y d r o s t a t i c s p e c i f i c f r e e e n e r g y

p lus ex t r i n s i c h .yd ros t a t i c spec i f i c

f r e e e n e r g y , s . e . , F h j = F h ~ ' +

1. O p e n in n e r p h a s e : h e r e F h ~ '

i s p o s it iv e a n d F h ~ i s n e g a -

t i v e ; t h a t i s , a p a r t i a l s o l u -

t i o n t e n s i o n e x i s t s e x c e e d i n g

F h j ' n u m e r i c a l l y .

2 . I n c lo s e d i n n e r p h a s e : h e r e

F h l ' is z e r o o r n e g a t iv e ( r e -

s u l t i n g f r o m i n t r a c e I l u l a r

t e n s i o n , m e m b r a n e ( , ' w a l l )

t e n s i o n ) . F h t i s z e r o o r

n e g a t iv e , u s u a l l y v a r y i n g d i -

r e c t l y a s F h ~ ' ( r e s u l t i n g

f r o m i n t e rc e l l u la r t e n s i o n ) .

C . H yd ro s t a t i c specif ic f r ee en erg y

r e s u l t i n g f r o m h y d r o s t a t i c p r e s -

s ur e, e x te r n a l. F h . = A I F ( F h . =

F h . ' + F h . ) .

D . M e t a b o l i c sp e c if ic fr e e e n e r g y , i n -

w a r d l y d i re c t ed ; a r i s i n g w i t h i n th e

l i v i n g c y t o p la s m , F m = A I F .

E . N on -m etab o l i c specif ic f r ee e n -

e r g y , i n w a r d l y d i r e c t e d .

F n m = A I F .

1 . I n t e r n a l i m b i b a n t ( F n m ~ ) ,

an t i phas i ca l l y e f fec t i ve .

Water E~ux Specif ic Free Eneroie

( E F )

A . H y d r o s t a t i c s p ec if ic fr e e e n e r g y

r e s u l t i n g f r o m h y d r o s t a t i c p r e s -

s u r e, i n t e rn a l . F h , = E F . I n -

t r i n s i c hydros t a t i c spec i f i c f r ee

e n e r g y p l u s e x t r i n s i c h y d r o s t a t i c

spec i f i c f r ee energy ;

i . e . ,

F h l =

F h l ' + F h / ' .

1. O p e n i n n e r p h a s e : H e r e

F h / i s p o si ti ve a n d F h , i s

e i t h e r z e r o o r n e g a t i v e ; t h a t

i s, a pa r t i a l so lu t i on t ens io n

le ss n u m e r ic a l ly t h a n F h i '

m a y o r m a y n o t e x i s t .

2 . I n c l o s e d in n e r p h a s e ( r e -

s u l t i n g f r o m h y d r o s t a t i c

p r e s s u r e ) : H e r e F h , ' i s

p o s it iv e o r z e r o ( r e s u l t i n g

f r o m i n t r a c e l l u l a r p re s s u r e ,

m e m b r a n e ( w a l l ) p r e s-

s u r e ) . F h t i s p o s it iv e o r

z e ro , u s u a l ly v a r y i n g d i r e c t ly

a s F h~ ( r e s u l t i n g f r o m i n -

t e r c e ll u l a r p r e s s u r e ) .

B . O sm ot i c so lu t e spec if ic f r ee e n -

e r g y ( a n t i p h a s i c a l l y e f f e c ti v e ) r e -

l a t e d t o t h e p r e s e n c e o f e x t e r n a l

s o lu te . F s . = A E F .

C . M etabo l i c specif ic f r ee energ y ,

o u t w a r d l y d i re c te d . F m : A E F .

D. N on- m etab o l i c specif ic f r ee en -

e r g y, o u t w a r d l y d ir ec te d . F n m =

A E F .

1 . E x t e r n a l i m b i b a n t ( F n m . ) ,

an t i ph as i ca l l y e f fect ive .

* U n l e s s o t h e r w i s e s p ec if ie d ( s e e s e c ti o n s o n e f f e c t o f s u c t i o n a n d m i s c e l -

l a n e o u s e ff e c t s ) , a l l p r e s s u r e s a r e a b o v e th e r e f e r e n c e a tm o s p h e r i c p r e s s u re ,


17/58

M O V E M E N T O F M A T E R IA L S I N T O P L A N T S 7

s y s t e m s w i ll b e e x a m i n e d ( s e e F i g u r e 2 ) : f ir st , t h e s i m p l if ie d ,

i n t e g r a te d o s m o t i c s y s t e m ( 6 , 12, 5 2 ) , e x t e r n a l s o l u t i o n - - m e m b r a n e

( e n d o d e r m a l c y t o p la s m o r p r o t o p l a s m o f a c o m p a r a b l y s t ru c t u r e d

c e ll s e r i e s ) m i n t e r n a l s o l u ti o n ; a n d s e c o n d , a r e f e r e n c e c ell, e x t e r n a l

s o l u t i o n - - m e m b r a n e ( c y t o p l a s m ) - - i n t e r n a l s o lu t io n ( v a c u o l e ) .

A l t h o u g h p r o b a b l y n o t s t r i c t l y c o m p a r a b l e , t h e s e w i l l b e d i s c u s s e d

a s s im i l a r s y s t e m s . M o d i f ic a t i o n s o f s i m i l a r i ty w il l b e p r e s e n t e d .

T h e d y n a m i c s o f o s m o t ic w a t e r m o v e m e n t g o v e r n e d i n a n y c a s e b y

t h e o v e r - a l l f r e e e n e r g y d i f f e r e n c e o f t h e w a t e r m o l e c u l e s i n t h e

s y s t e m a r e e x p r e s s e d , i n a s u m m a r i z e d f o r m , b y t h e r e l a ti o n s i n

T a b l e I . T h e n e t f re e e n e r g y o f t h e w a t e r m o l e c u le s t e n d i n g t o

c a u s e it s m o v e m e n t in t o th e p l a n t o s m o m e t e r , e q ua ls t h e f r e e e n e r g y

o f t h e w a t e r m o l e c u l e s i n t h e e x t e r n a l p h a s e d i m i n i s h e d b y t h e f r e e

e n e r g y o f t h e w a t e r m o l e c u l e s i n t h e i n t e r n a l p h a s e s . T h i s t r e a t i s e

p r e s e n t s t h e c o n s t i t u e n t o s m o t i c sp e c if ic f r e e e n e r g i e s w h i c h a r e

m e a s u r e s o f th e f r e e e n e r g ie s o f t h e w a t e r m o l e c u le s in t h e t w o

p h a s e s , r e g r o u p e d i n t o t h e i r c a t e g o r i e s a s i n f l u x o r e f l t u x s p e c i f i c

f r e e e n e r g i e s .

The Fundamental quation

( s e e 6 4 , p . 4 3 7 ) : F r o m e q u a t i o n 3 b

i t m a y b e s e e n th a t t h e g r e a t e r t h e c o n c e n t r a t i o n o f s o l u te i n a s o l u -

t io n , t h e g r e a t e r is t h e a n t i p h a s i c o s m o t i c s o l u t e s p ec if ic f r e e

e n e r g y . S i n c e t h e f r e e e n e r g y o f t h e w a t e r m o l e c u l e s i s l o w e r e d b y

t h i s m e a n s i n t h e i n t e r n a l p h a s e o f a n o s m o m e t e r , th e e t lt u x s p e ci fi c

f r e e e n e r g y f o r w a t e r i s r e d u c e d a n d t h e i n f l u x s p e ci fi c f r e e e n e r g y

f o r w a t e r is p r o p o r t i o n a t e l y i n cr e a se d . W a t e r w i ll e n t e r t h e

o s m o m e t e r d u e t o t h e h i g h e r s o lu t e c o n c e n tr a t io n o f th e i n t e r n a l

which is real and equal throughout ~e systems described. Here, the use of a

reference pressure and the term net influx specific free ene rgy are not open to

the crit icism posed by C rafts (11 , p. 38 7) in connection with o ther m odes of

presentation of osm otic relations.

t Th e externally effective osmotic solute specific free energy is related

to the antiphasic solute concentration, in the internal phase (see equations 3

and 3a). T he internally effective osmotic solute spe cific free energy is

similarly related to the solute concentration in the external phase of the

osmom eter, bathing the ectoplasm of the reference cell or outer surface of the

endodermis or cell series.

9 Th e external or internal phases of either of the reference osmom eters m ay

be considered as individual units (see footnote 10) with respect to the free

energ y of the water. A t equilibrium, the free ene rgy of the wa ter is constant

throughout a phase, with relation to a reference level in spa ce, regardless o f

its shape or size. At a lower posit ion in space within the phase, the free

energ y is diminished on account of the influence of g r av i t y but it is increased

by the intrinsic hydrostatic pressure (due to the mass of the colum n alone) ;

these tw o influences ju st offset one another (35 , pp.

242, 243 .


18/58

18


p h a s e 1~ I f in a n o p e n s y s t e m a p r e s s u r e h e a d o f f lu i d d e v e lo p s , d u e

t o t h e e n t r y o f w a t e r , t h e i n f l u x s p ec if ic f r e e e n e r g y , r e l a t e d t o t h e

s o l u t e c o n c e n t r a t i o n d i f f e r e n c e a l o n e , w i l l b e d i m i n i s h e d b y a

c o u n t e r sp e ci fi c f r e e e n e r g y w i t h i n t h e o s m o m e t e r . T h i s l a t t e r

s p e c i f i c f r e e e n e r g y r e s u l t s f r o m t h e h y d r o s t a t i c p r e s s u r e d u e t o

t h e w e i g h t o f t h e h e i g h t e n e d c o l u m n o f t h e i n n e r s o l u ti o n . T h i s

c o m p l e m e n t a r y sp e cif ic f r ee e n e r g y w i t h i n t h e o s m o m e t e r is t e r m e d

t h e i n t r i n s ic h y d r o s t a t i c s p ec if ic f r e e e n e r g y ( F h ~ ' ) . W a t e r w i l l

e n t e r u n t i l t h i s s p ec if ic f r e e e n e r g y i n t h e i n t e r n a l s o l u t io n c o u n t e r -

b a l a n c e s t h e o s m o t i c s pe c if ic f r e e e n e r g y i n t h e e x t e r n a l p h a s e

( F s i ) , r e l a t e d t o t h e p r e s e n c e o f i n t e r n a l so l u te . I n a n e n c l o s e d

o s m o t i c s y s t e m , e x e m p l i fi e d b y a n i s o l a te d r e f e r e n c e c e ll , a c o u n t e r

p r e s s u r e o n t h e m e m b r a n e is a l so p r o d u c e d . I n s t e a d o f a h y d r o -

s ta t ic p r e s s u r e d u e t o t h e w e i g h t o f a c o l u m n o f l iq u id , a n o u t w a r d l y

d i r e c t e d h y d r o s t a t i c p r e s s u r e i s i n v o l v ed , c o u n t e r a c t e d b y t h e r e -

s t r i c t e d e x p a n s i o n i m p o s e d b y t h e e l a s t i c m e m b r a n e e n c i r c l i n g t h e

i n n e r p h a se . A s i n t h e o p e n in n e r p h a s e s y s te m , w a t e r w i l l e n t e r

t h e i n c l o se d p h a s e u n t i l t h e i n t e r n a l h y d r o s t a t i c s pe c if ic f re e e n e r g y ,

r e s u l t i n g f r o m t h e i n t e r n a l h y d r o s t a t i c p r e s s u r e o n t h e m e m b r a n e ,

c o u n t e r b a l a n c e s t h e o s m o t i c s p e c i f i c f r e e e n e r g y r e l a t e d t o t h e

p r e s e n c e o f i n t e r n a l s o l u te .

O n o s m o t i c e n t r y o f w a t e r , t o s a t i s fy a n e x i s t i n g fr e e e n e r g y d i f -

f e r e n c e , t h e n e t i n f l u x sp e ci fi c f r e e e n e r g y i s d i m i n i s h e d . T h e

o s m o t i c s p e c i f i c f r e e e n e r g y r e l a t e d t o i n t e r n a l s o l u t e i s d e c r e a s e d

b y d i l u t i o n o f t h e i n t e r n a l m e d i u m , a n d t h e h y d r o s t a t i c s p e ci fi c f r e e

e n e r g y is c o n c u r r e n t l y i n c r e as e d . T h e r e l a t iv e c h a n g e s in th e la t t e r

q u a n t i t ie s w i l l d e p e n d u p o n t h e e x t e n s i b i l it y o f t h e i n n e r p h a s e .

T h e l o w e r t h e e x t e n s i b i l i t y o f t h e i n n e r p h a s e , t h e s m a l l e r w i l l b e

t h e w a t e r i n f l u x a c c o m p a n i e d b y a r e l a t iv e l y s m a l l e r d e c r e a s e in

t h e o s m o t i c s o l u t e s p ec if ic f r e e e n e r g y a n d a r e l a ti v e l y l a r g e r

inc re a s e i n the i n t r i n s i c hy d ro s t a t i c s pe c if ic f r e e e n e rgy .

I d e a l l y , t h e r e l a t i o n s b e t w e e n c h a n g e s i n t h e r e l a t i v e v o l u m e o f

t h e i n n e r p h a s e o f a n o s m o m e t e r a n d t h e h y d r o s t a t i c s p e c i f i c f r e e

lo W hen the solute concentration of the medium is not uniform (as in the

xylem, ev en at thermodynam ic equilibrium (35, pp. 243,

244 ,

for example),

an osm otic solute specific free energy (within the opposite ph ase ) related

to the w eigh ted average concentration of the solution within the phase, is

employed. Lo calize d chan ges of solute concentration within a ph ase m ay

m odify the osm otic solute specific free energy relations so as to alter the

rate of water flow , or ev en its direction, through the mem brane. Such

thermodynam ic non-equilibria w ou ld probably be rapidly adjusted, approach-

ing those un der discussion, unless the differential is continuou sly m aintained.


19/58


e n e r g y a r e li n e ar . H o w e v e r , s in g le o r m u l ti p le d e v i a ti o n s fr o m

l ine a r i t y oc c u r i n r e a l i ty . T hu s , a c c e n tua t e d s uc c e ss ive c ha n ge s in

t h e t h i c k n e s s o f t h e m e m b r a n e ( c a u s i n g m o d i f ic a t io n s o f i t s m o d u -

l u s o f e l a s t i c i t y ) , d u e t o i n t e r n a l c h a n g e s o f v o l u m e , m a y l e a d t o a

c u r v i l i n e a r r e l a ti o n i n w h i c h th e s e c o n d d e r i v a ti v e o f t h e h y d r o -

s t a t i c s pe ci fi c f r e e e n e r g y w i th r e s pe c t t o vo lum e i s ne ga t ive . Co n-

t r a r i w i s e , p r o n o u n c e d s u cc e ss iv e c h a n g e s i n r e s t ri c t io n t o m o d i f ic a -

t i o n o f t h e i n t e r n a l v o l u m e m a y l e a d t o a c u r v i l i n e a r r e l a t io n i n

w h i c h t h e s e c o n d d e r i v a t i v e o f t h e h y d r o s t a t i c s p e c i f i c f r e e e n e r g y

w i th r e s pe c t t o vo lum e i s pos i t i ve .

I n t h e i n i ti a l s ta t e o f a s im p l i fi e d o s m o t i c s y s t e m , a s r e p r e s e n t e d

b y t h e i n t e g r a t e d e n d o d e r m a l s y s te m i n F i g u r e 2 , i n w h i c h t h e n u m -

b e r s e m p l o y e d i n a t m o s p h e r e s a r e o f m a g n i t u d e s s i m i la r t o t h o s e

f o u n d e x p e r i m e n t a l l y , t h e f u n d a m e n t a l e q u a t i o n f o r w a t e r m o v e -

m e n t m i g h t r e q u i re , f o r e x a m p l e , t h e f o l l o w i n g v a l u e s :

N I F -- F s t - F h t ' ( 1 1 ) 11

20.0 --- 20.0 - 0 ( se e F ig u re 3) ( 1 la )

I f a d i f f e r e n c e i n f re e e n e r g y o f w a t e r m o l e c u l e s i s p a r t i a l l y

s a ti sf ie d t h r o u g h i n f lu x o f w a t e r ( e n d o s m o s i s ) w i t h c h a n g e s i n

s p ec if ic f r e e e n e r g i e s a n d i n t e r n a l v o l u m e o f th e s y s t e m T M e q u a t i o n

l l a m a y b e c o m e , f o r e x a m p l e , a f t e r a f i n i te i n t e r v a l o f ti m e ,

13.0 = 18.3 - 5.3 (1 1 b )

( i n F i g u r e 3 , N I F = 1 8.3 - 5 .3 = 1 3 .0 ) a n d a t w a t e r e q u i l i b r i u m

0 = 1 6 . 0 - 1 6.0 ( l l c )

I t i s a c o m m o n p r a c t i c e b y i n v e s t i g a t o r s t o i n s e r t m a n o m e t e r s

i n t o t h e h y d r o s t a t i c s y s t e m o f in t a c t p l a n t s, e s p ec i al ly s p e ci es w h i c h

g r o w t o re l a ti v e ly g r e a t h e ig h t s. I t m a y be n o t e d f r o m th e s e

p r e m i s e s a n d t h o s e t o f o l l o w t h a t t h e s e i n s t r u m e n t s r e c o r d t h e

h y d r o s t a t i c p r e s s u r e ( P h i ) , t h e r e s u l t a n t b e t w e e n t h e i n tr in s i c h y -

d r o s t a t i c p r e s s u r e a n d a n y p o ss ib l e e x t r i n s i c h y d r o s t a t i c p r e s s u r e o r

t e n s i o n , e x i s t i n g a t t h a t t i m e a n d l e v e l w i t h i n t h e i n t e r n a l p h a s e o f

t h e re f e r e n c e o s m o m e t e r . T h e r e l a te d h y d r o s t a t i c s p ec if ic

f r e e

e n e r g y ( F h i ) is t h e r e b y e v a lu a t e d .

ix Similar here to the fundamental equation of

M e y e r w h e r e

the resultant

D P D = O P - T P . A lso , see 6, 27, 40, 52, 57, 59, 61, 64.

12 D im in u t ion o f

the internal volum e of the

o s m o m e t e r b y l o ss o f w a t e r m u s t

have the e ffect of increasing the internal concen tration of su bstances to w hich

t h e m e m b r an e i s relatively impermeable. B y m ass action reactions o f which

these substances are compo nents will be accelerated, and increase in volum e

b y

influx of w ater w ill retard such reactions.


20/58

2 0 T H E B O T A N IC A L R E V IE W

" 2 O

~

~ l O -

* 2 "

0

~ '1~ IF '

[

~ [ 0 R e l o h ~ V o l u m e s o f I ~ te e n o J P h o ~

- s I S ubJeCt to W ater F Io w

InJple~|

9 ~ W i l t S 9

W i l l m 9 I

L 5

I

W o I ~ [ q u , h b r k ~

"

~k4

W A T E R R E L A TI O N S O F 'A P L A N T O S I ~ M ~ T E R

T h t N i t ! ~ k ~ , S r ,ec f f, ~ F r t c E r4re f f ; ~ eq , .~ t o t l ~ m~n o f the W ~ ~ f ; c F re ~ E m ~ o i e s

~ e d b / I he a~m O f ~ t F ' ff lu l S peci f i c Free [nerg les I ~ IT ,~ r lF ' -~ ;E ~F ' ) . N IF ; s e~q~ -e)sed by ~ 4 .

difference betwe en the I~olar l . X l l ond Y ~ I . O t ~ny pO r tiCu lO r vo lume m lhe S p eaf ic Free [ r ~ r ( W : V ~ b m e

dioqmm.

FzG. 3 . W ate r relat ions of a p lant osm om eter: the general scheme. Th e

hydrostat ic speci f ic free energies in re lat ion to changes in volume of the in -

ternal phase of the osmometer m ay be represented , wi th in the e las t ic l imi ts of

the m embrane, by e i ther an appr oxim ately l inear or a s igm oid curvi l inear func-

t ion , each pass ing through the orig in of zero speci f ic free energy and uni t

relativ.e volum e. V alu es for the corresponding osmo tic solute specif ic free

energies (ant iphas ica l ly ef fect ive) re lated to the presence of so lute in the

inter nal medium, represented under isother m al conditions, for m a hyperbol ic

funct ion wi th in the limits of appl icabi l ity of the van't H off equat ion . Th e

slopes of the hydrostatic specif ic free energy, and osmotic specif ic free energy

(the latter related to the presence of solute in the internal medium) curves

(E F an d IF ) wi l l be govern ed b y th e e la s t ic i ty o f th e memb ran e and th e

nature of the constituent factors. Fo r sim plic ity, supplementary specific free

en erg y increments or decrements are considered a s constants ; as such, they

are d iagram m atica l ly represented by curves para l le ling the fundamental osm otic

va lu es o f IF an d E F . L ik ewi se , th e two osmot i c sy s tem s exemp l if i ed are

discussed w ith valu es of specif ic free e nerg y, or volum e, of s im ilar magnitude.

Here, where necessary, i t i s assumed that the isothermal temperature was

25 ~ C. Because the specif ic free ene rgy v alues w ere som ewha t arbi trari ly

selected, altho ugh appro xim ating exper im enta l ly observed quantit ies , and

since data are lack ing to jus ti fy the application of an osm otic solute specif ic

free energy correction other than unity, i t i s assumed here that this coefficient

i s equal to one (see footnote 6) .


21/58

M O V E M E N T O F M A T E R I A L S I N T O P L A N T S

2

Effec t o f External Solu te:

I f t h e f re e e n e r g y o f t h e w a t e r m o l e -

c u l e s i s l o w e r e d b y t h e p r e s e n c e o f s o l u t e i n t h e e x t e r n a l p h a s e o f

t h e o s m o m e t e r t h e e f fl u x s p ec if ic f r e e e n e r g y f o r w a t e r i s i n c r e a se d ,

a n d , t h e r e f o r e , o t h e r o s m o t i c q u a n t i t i e s r e m a i n i n g c o n s t a n t , t h e n e t

i n f l u x s p ec if ic f r e e e n e r g y i s r e d u c e d . E n t r y o f w a t e r , to s a t i s f y

t h e n e t s p e ci fi c f r e e e n e r g y t e n d i n g t o c a u s e w a t e r t o m o v e i n w a r d ',

y i e l d s f i g u re s a t e q u i l ib r i u m d i f f e r i n g f r o m t h o s e i n t h e f u n d a m e n t a l

e q u a t i o n . T h e v o l u m e i n c r ea s e i n t h e in t e r n a l p h a s e is l e s se n e d ,

a n d t h e r e f o r e t h e e q u i l i b r i u m v a l u e f o r t h e o s m o t i c s p e c i f i c f r e e

e n e r g y r e l a t e d t o i n t e r n a l s o l u te i s g r e a t e r . T h e c o r r e s p o n d i n g

e f flux s pe c if ic f r e e e ne r gy i s h igh e r . H e r e , t h i s e i t t ux s pe ci fi c f r e e

e n e r g y c o m p r i s e s t w o q u a n t i t ie s , t h e o s m o t i c s o l u t e s p ec if ic f r e e

e n e r g y ( F s e ) , r e l a t e d t o t h e s o l u t e c o n c e n t r a t i o n o f t h e e x t e r n a l

s o l u ti o n ( a s s u m e d t o b e c o n s t a n t ) , a n d a d i m i n i s h e d h y d r o s t a t i c

s pe c if ic f r e e e n e r g y .

I f t h e s y s t e m i s b a t h e d e x t e r n a l l y b y a s o l u t i o n w i t h a s o l u t e

c o n c e n t r a t i o n r e l a t e d t o a n o s m o t i c s o l u t e s p e c i f i c f r e e e n e r g y o f

f o u r a t m o s p h e r e s , f o r e x a m p l e ( i n p l a c e o f t h e i n i t i a l c o m p o n e n t

w a t e r ) , e q u a t i o n l l a t ak e s t h e f o r m

N I F = F s , - ( F h , ' + F s e ) , ( 1 2 )

w h e r e F s , i s a p o s i t i v e A E F ,

16.0 = 20 . 0 - ( 0 + 4 . 0 ) . ( 12 a )

I f f r e e e n e r g y g r a d i e n t s a r e p a r t i a l l y s a t i s f i e d t h r o u g h i n f l u x o f

w a t e r , e q u a t i o n 2a m a y b e c o m e

9.0 = 18 .3 - (5 .3 + 4 .0) (12 b)

( i n F i g u r e 3 , N I F -- 1 8.3 - 9 .3 = 9 . 0 ) a n d a t w a t e r e q u i l ib r i u m

0 = 16 .6 - (12 .6 + 4 .0) (12 c)

E ffec t of Internal Solute: Solu te Accumulation: A d d i t i o n o f

s o l u te to t h e i n t e r n a l p h a s e o f th e o s m o m e t e r , a s r e p r e s e n t e d b y t h e

f u n d a m e n t a l e q u a t i o n , w o u l d i n c r e a s e t h e i n f l u x s p ec if ic f r e e e n e r g y

f o r w a t e r b y l o w e r i n g th e f r e e e n e r g y o f t h e s o l v en t i n t er n a l ly . A t

w a t e r e q u i l i b r i u m a g r e a t e r v o l u m e i s a t t a i n e d t h a n w o u l d b e o b -

t a i n e d w i t h t h e r e l a ti v e l y l o w e r i n t e r n a l s o l u t e c o n c e n t r a ti o n . T h e

c o r r e s p o n d i n g e f fl u x o r h y d r o s t a t i c s p e ci fi c f r e e e n e r g y i s a c c o r d -

ing ly i nc r e a s e d .

I f in t h e s y s t e m a t w a t e r e q u i l i b r iu m , f u r t h e r s o l u t e is a d d e d b y

a n y m e a n s 13, t o t h e s o l u t i o n in t e r n a l l y , re l a t e d t o a n o s m o t i c s o l u t e

13 I n f l u x o f so l u te e l e c t r o l y t e o r n o n - e l e c t r o l y t e ) t h r o u g h r e d i s t r i b u t i o n

w i t h i n t h e p l a n t b y d i ff u s io n , i n v o l v i n g u n d i f f e r e n t i a t e d o r d i f f e r e n t i a t e d c e l l s

or tissues, may e nsu e (52). In effect, this c ou ld occur als o, for exam ple,

throu gh hydrolysis or decondensation of solute already pres ent in the internal

phase.


22/58

2 2


s pe cif ic f r ee e n e r g y o f f o u r a t m o s p h e r e s , f o r e x a m p l e , e q u a t i o n l l c

N I F = F s l - F h t ' ( 1 1 )

0 = 1 6 . 0 - 1 6.0 ( 1 1 c )

m a y b e c om e

N I F = (F s~ + A F s i ) - F h l ' ( 1 3 , s ee 1 i )

4 . 0 = ( 1 6 ; 0 + 4 . 0 ) - 1 6.0 . ( 1 3 a )

I f d i f f e r e n c e s o f f r e e e n e r g y o f w a t e r a r e s a t i s f i e d , t h e n a t e q u i -

l i b r i u m

N I P ' = F s i - F h t ' ( 1 1 )

0 = 1 9 . 4 - 1 9.4 . ( 1 3 b )

S i m i l a r l y , i f t o t h e s y s t e m r e p r e s e n t e d b y e q u a t i o n

12c

i n w h i c h

N I F = F s t - ( F h t ' + F s o ( 1 2 )

0 = 16.6 - ( 12.6 + 4 .0 ) (1 2c )

f u r t h e r s o l u te i n f l u x t a k e s p l a c e, e s p e ci a ll y b y m e t a b o l i c a c c u m u l a -

t i o n f r o m t h e e x t e r n a l m e d i u m , e q u a l t o a n i n t e r n a l i n c r e a s e o f

s o l u t e r e l a t e d t o a n o s m o t i c s o l u t e s p ec if ic f r e e e n e r g y o f f o u r

a t m o s p h e r e s , f o r e x a m p l e , t h e f o l l o w i n g re l a t io n s a r i s e i n w h i c h

N I F = ( F s , + A F s , ) - ( F h / + F s , )

( 1 4 , s e e e q u a -

t i on 12 )

( 1 4 a )

. 0 = (16 . 6 + 4 . 0 ) - ( 12 . 6 + 4 . 0 )

A t w a t e r e q u i l ib r iu m , t h i s b ec o m e s

N I F = F s i - ( F h t ' + F s , ) ( 1 2 )

0 = 2 0 . 0 - ( 1 6 .0 + 4 .0 ) ( 1 4 b )

Effect o f In ternal Solute Deplet ion:

T h e o s m o t i c s y s t e m a t

w a t e r e q u il ib r i u m ex p r e s s e d b y e q u a t i o n 1 c ( c o m p a r e e q u a t i o n 1 6 )

m a y d e c r e a s e w i t h r e s p e c t t o i t s o s m o t i c s pe c if ic f r e e e n e r g y r e l a t e d

t o t h e p r e se n c e o f in t e r n a l s o lu t e, a p a r t f r o m a s o l u te e m u x t o t h e

e x t e r n a l p h a s e o c c a s i o n e d b y p o s s i b l e i n j u r y , a c c o m p a n i e d b y

w a t e r . S u c h a d e c r e a s e i n o s m o t i c s o l u t e s p ec if ic f r e e e n e r g y

m i g h t o c c u r w h e n e i t h e r s o l u t e i s t r a n s l o c a t e d , w i t h o u t r e s u p p l y

f r o m e ( s e e F i g u r e 2 ) , f r o m t h e i n n e r p h a s e o f t h e r e f e r e n c e c e l l

( v a c u o l e ) ; o r o n l o ss o f so l u te f r o m t h e o p e n o s m o m e t e r s y s t e m

d u e t o e x u d a t i o n ; o r d u e t o a p o s s i b l e c o n d e n s a t i o n o f s o l u t e i n -

t e r n a l l y . T h e o s m o t i c s o l u t e s p ec if ic f r e e e n e r g y r e l a t e d t o t h e

p r e s e n c e o f i n t e r n a l s o l u t e w o u l d b e d e c r e a se d w i t h a c o r r e s p o n d i n g

r e d u c t i o n i n t h e n e t i n f l u x s p ec if ic f r e e e n e r g y , f o r w a t e r . I f t h e

s y s t e m w e r e a t e q u i l i b r i u m w i t h r e s p e c t t o w a t e r , a n e t s p e c if ic f r e e

e n e r g y t e n d i n g t o c a u s e w a t e r t o m

t. c. broyer -- the movement of materials into plants part i. osmosis and the movement of water into...

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