Physicochemical and environmental plant physiology 4th ed p nobel (elsevier, 2009)

Physicochemical and
Environmental

Plant Physiology
FOURTH EDITION


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Physicochemical and
Environmental

Plant Physiology
FOURTH EDITION

Park S. Nobel
Department of Ecology and Evolutionary Biology
University of California, Los Angeles
Los Angeles, California

AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Academic Press is an imprint of Elsevier


Academic Press is an imprint of Elsevier
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Fourth Edition 2009
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Contents
Preface

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Symbols and Abbreviations

xv

1. Cells and Diffusion
1.1. Cell Structure
1.1A. Generalized Plant Cell
1.1B. Leaf Anatomy
1.1C. Vascular Tissue
1.1D. Root Anatomy
1.2. Diffusion
1.2A. Fick’s First Law
1.2B. Continuity Equation and Fick’s Second Law
1.2C. Time–Distance Relation for Diffusion
1.2D. Diffusion in Air
1.3. Membrane Structure
1.3A. Membrane Models
1.3B. Organelle Membranes
1.4. Membrane Permeability
1.4A. Concentration Difference Across a Membrane
1.4B. Permeability Coefficient
1.4C. Diffusion and Cellular Concentration
1.5. Cell Walls
1.5A. Chemistry and Morphology
1.5B. Diffusion Across Cell Walls
1.5C. Stress–Strain Relations of Cell Walls
1.5D. Elastic Modulus, Viscoelasticity
1.6. Problems
1.7. References and Further Reading

2. Water
2.1. Physical Properties
2.1A. Hydrogen Bonding—Thermal Relations
2.1B. Surface Tension
2.1C. Capillary Rise
2.1D. Capillary Rise in the Xylem

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Contents

2.2.

2.3.

2.4.

2.5.
2.6.

2.1E. Tensile Strength, Viscosity
2.1F. Electrical Properties
Chemical Potential
2.2A. Free Energy and Chemical Potential

2.2B. Analysis of Chemical Potential
2.2C. Standard State
2.2D. Hydrostatic Pressure
2.2E. Water Activity and Osmotic Pressure
2.2F. Van’t Hoff Relation
2.2G. Matric Pressure
2.2H. Water Potential
Central Vacuole and Chloroplasts
2.3A. Water Relations of the Central Vacuole
2.3B. Boyle–Van’t Hoff Relation
2.3C. Osmotic Responses of Chloroplasts
Water Potential and Plant Cells
2.4A. Incipient Plasmolysis
2.4B. Höfler Diagram and Pressure–Volume Curve
2.4C. Chemical Potential and Water Potential of Water Vapor
2.4D. Plant–Air Interface
2.4E. Pressure in the Cell Wall Water
2.4F. Water Flux
2.4G. Cell Growth
2.4H. Kinetics of Volume Changes
Problems
References and Further Reading

3. Solutes
3.1. Chemical Potential of Ions
3.1A. Electrical Potential
3.1B. Electroneutrality and Membrane Capacitance
3.1C. Activity Coefficients of Ions
3.1D. Nernst Potential
3.1E. Example of ENK

3.2. Fluxes and Diffusion Potentials
3.2A. Flux and Mobility
3.2B. Diffusion Potential in a Solution
3.2C. Membrane Fluxes
3.2D. Membrane Diffusion Potential—Goldman Equation
3.2E. Application of Goldman Equation
3.2F. Donnan Potential
3.3. Characteristics of Crossing Membranes
3.3A. Electrogenicity
3.3B. Boltzmann Energy Distribution and Q10, a Temperature
Coefficient
3.3C. Activation Energy and Arrhenius Plots
3.3D. Ussing–Teorell Equation
3.3E. Example of Active Transport

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Contents

3.4.

3.5.

3.6.

3.7.
3.8.

3.3F. Energy for Active Transport
3.3G. Speculation on Active Transport
Mechanisms for Crossing Membranes
3.4A. Carriers, Porters, Channels, and Pumps
3.4B. Michaelis–Menten Formalism
3.4C. Facilitated Diffusion
Principles of Irreversible Thermodynamics
3.5A. Fluxes, Forces, and Onsager Coefficients
3.5B. Water and Solute Flow
3.5C. Flux Densities, LP , and σ
3.5D. Values for Reflection Coefficients
Solute Movement Across Membranes
3.6A. Influence of Reflection Coefficients on Incipient

Plasmolysis
3.6B. Extension of the Boyle–Van’t Hoff Relation
3.6C. Reflection Coefficients of Chloroplasts
3.6D. Solute Flux Density
Problems
References and Further Reading

4. Light
4.1. Wavelength and Energy
4.1A. Light Waves
4.1B. Energy of Light
4.1C. Illumination, Photon Flux Density, and Irradiance
4.1D. Sunlight
4.1E. Planck’s and Wien’s Formulae
4.2. Absorption of Light by Molecules
4.2A. Role of Electrons in Absorption Event
4.2B. Electron Spin and State Multiplicity
4.2C. Molecular Orbitals
4.2D. Photoisomerization
4.2E. Light Absorption by Chlorophyll
4.3. Deexcitation
4.3A. Fluorescence, Radiationless Transition, and
Phosphorescence
4.3B. Competing Pathways for Deexcitation
4.3C. Lifetimes
4.3D. Quantum Yields
4.4. Absorption Spectra and Action Spectra
4.4A. Vibrational Sublevels
4.4B. The Franck–Condon Principle
4.4C. Absorption Bands, Absorption Coefficients,

and Beer’s Law
4.4D. Application of Beer’s Law
4.4E. Conjugation
4.4F. Action Spectra
4.4G. Absorption and Action Spectra of Phytochrome

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Contents

4.5. Problems
4.6. References and Further Reading

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5. Photochemistry of Photosynthesis

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5.1. Chlorophyll—Chemistry and Spectra
5.1A. Types and Structures
5.1B. Absorption and Fluorescence Emission Spectra
5.1C. Absorption in Vivo—Polarized Light
5.2. Other Photosynthetic Pigments
5.2A. Carotenoids
5.2B. Phycobilins
5.2C. General Comments
5.3. Excitation Transfers Among Photosynthetic Pigments
5.3A. Pigments and the Photochemical Reaction
5.3B. Resonance Transfer of Excitation
5.3C. Specific Transfers of Excitation
5.3D. Excitation Trapping
5.4. Groupings of Photosynthetic Pigments
5.4A. Photon Processing
5.4B. Excitation Processing
5.4C. Photosynthetic Action Spectra and Enhancement Effects
5.4D. Two Photosystems Plus Light-Harvesting Antennae
5.5. Electron Flow
5.5A. Electron Flow Model
5.5B. Components of the Electron Transfer Pathway
5.5C. Types of Electron Flow
5.5D. Assessing Photochemistry using Fluorescence

5.5E. Photophosphorylation
5.5F. Vectorial Aspects of Electron Flow
5.6. Problems
5.7. References and Further Reading

6. Bioenergetics
6.1. Gibbs Free Energy
6.1A. Chemical Reactions and Equilibrium Constants
6.1B. Interconversion of Chemical and Electrical Energy
6.1C. Redox Potentials
6.2. Biological Energy Currencies
6.2A. ATP—Structure and Reactions
6.2B. Gibbs Free Energy Change for ATP Formation
6.2C. NADP+–NADPH Redox Couple
6.3. Chloroplast Bioenergetics
6.3A. Redox Couples
6.3B. H+ Chemical Potential Differences Caused by Electron Flow
6.3C. Evidence for Chemiosmotic Hypothesis
6.3D. Coupling of Flows

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Contents

6.4. Mitochondrial Bioenergetics
6.4A. Electron Flow Components—Redox Potentials
6.4B. Oxidative Phosphorylation
6.5. Energy Flow in the Biosphere
6.5A. Incident Light—Stefan–Boltzmann Law
6.5B. Absorbed Light and Photosynthetic Efficiency
6.5C. Food Chains and Material Cycles
6.6. Problems
6.7. References and Further Reading

7. Temperature and Energy Budgets
7.1. Energy Budget—Radiation
7.1A. Solar Irradiation
7.1B. Absorbed Infrared Irradiation
7.1C. Emitted Infrared Radiation
7.1D. Values for a, aIR, and eIR
7.1E. Net Radiation
7.1F. Examples for Radiation Terms
7.2. Heat Conduction and Convection
7.2A. Wind
7.2B. Air Boundary Layers
7.2C. Boundary Layers for Bluff Bodies

7.2D. Heat Conduction/Convection Equations
7.2E. Dimensionless Numbers
7.2F. Examples of Heat Conduction/Convection
7.3. Latent Heat—Transpiration
7.3A. Heat Flux Density Accompanying Transpiration
7.3B. Heat Flux Density for Dew or Frost Formation
7.3C. Examples of Frost and Dew Formation
7.4. Further Examples of Energy Budgets
7.4A. Leaf Shape and Orientation
7.4B. Shaded Leaves within Plant Communities
7.4C. Heat Storage
7.4D. Time Constants
7.5. Soil
7.5A. Thermal Properties
7.5B. Soil Energy Balance
7.5C. Variations in Soil Temperature
7.6. Problems
7.7. References and Further Reading

8. Leaves and Fluxes
8.1. Resistances and Conductances—Transpiration
8.1A. Boundary Layer Adjacent to Leaf
8.1B. Stomata
8.1C. Stomatal Conductance and Resistance

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Contents

8.2.

8.3.

8.4.

8.5.

8.6.
8.7.

8.1D. Cuticle
8.1E. Intercellular Air Spaces

8.1F. Fick’s First Law and Conductances
Water Vapor Fluxes Accompanying Transpiration
8.2A. Conductance and Resistance Network
8.2B. Values of Conductances
8.2C. Effective Lengths and Resistance
8.2D. Water Vapor Concentrations, Mole Fractions and
Partial Pressures for Leaves
8.2E. Examples of Water Vapor Levels in a Leaf
8.2F. Water Vapor Fluxes
8.2G. Control of Transpiration
CO2 Conductances and Resistances
8.3A. Resistance and Conductance Network
8.3B. Mesophyll Area
8.3C. Resistance Formulation for Cell Components
8.3D. Partition Coefficient for CO2
8.3E. Cell Wall Resistance
8.3F. Plasma Membrane Resistance
8.3G. Cytosol Resistance
8.3H. Mesophyll Resistance
8.3I. Chloroplast Resistance
CO2 Fluxes Accompanying Photosynthesis
8.4A. Photosynthesis
8.4B. Respiration and Photorespiration
8.4C. Comprehensive CO2 Resistance Network
8.4D. Compensation Points
8.4E. Fluxes of CO2
8.4F. CO2 Conductances
8.4G. Photosynthetic Rates
8.4H. Environmental Productivity Index
Water-Use Efficiency

8.5A. Values for WUE
8.5B. Elevational Effects on WUE
8.5C. Stomatal Control of WUE
8.5D. C3 versus C4 Plants
Problems
References and Further Reading

9. Plants and Fluxes
9.1. Gas Fluxes above Plant Canopy
9.1A. Wind Speed Profiles
9.1B. Flux Densities
9.1C. Eddy Diffusion Coefficients
9.1D. Resistance of Air above Canopy
9.1E. Transpiration and Photosynthesis
9.1F. Values for Fluxes and Concentrations
9.1G. Condensation
9.2. Gas Fluxes within Plant Communities
9.2A. Eddy Diffusion Coefficient and Resistance

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Contents

9.3.

9.4.

9.5.

9.6.
9.7.

9.2B. Water Vapor
9.2C. Attenuation of the Photosynthetic Photon Flux
9.2D. Values for Foliar Absorption Coefficient
9.2E. Light Compensation Point
9.2F. CO2 Concentrations and Fluxes
9.2G. CO2 at Night
Water Movement in Soil

9.3A. Soil Water Potential
9.3B. Darcy’s Law
9.3C. Soil Hydraulic Conductivity Coefficient
9.3D. Fluxes for Cylindrical Symmetry
9.3E. Fluxes for Spherical Symmetry
Water Movement in the Xylem and the Phloem
9.4A. Root Tissues
9.4B. Xylem
9.4C. Poiseuille’s Law
9.4D. Applications of Poiseuille’s Law
9.4E. Phloem
9.4F. Phloem Contents and Speed of Movement
9.4G. Mechanism of Phloem Flow
9.4H. Values for Components of the Phloem Water Potential
Soil–Plant–Atmosphere Continuum
9.5A. Values for Water Potential Components
9.5B. Resistances and Areas
9.5C. Values for Resistances and Resistivities
9.5D. Root–Soil Air Gap and Hydraulic Conductances
9.5E. Capacitance and Time Constants
9.5F. Daily Changes
9.5G. Global Climate Change
Problems
References and Further Reading

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Solutions To Problems

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Appendix I. Numerical Values of Constants and Coefficients

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Appendix II. Conversion Factors and Definitions

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Appendix III. Mathematical Relations
III.A. Prefixes (for units of measure)
III.B. Areas and Volumes
III.C. Logarithms
III.D. Quadratic Equation
III.E. Trignometric Functions
III.F. Differential Equations

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Appendix IV. Gibbs Free Energy and Chemical Potential
IV.A. Entropy and Equilibrium
IV.B. Gibbs Free Energy
IV.C. Chemical Potential
IV.D. Pressure Dependence of µj

IV.E. Concentration Dependence of µj

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Index

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Preface
Let us begin with some comments on the title. “Physiology,” which is the
study of the function of cells, organs, and organisms, derives from the Latin
physiologia, which in turn comes from the Greek physi- or physio-, a prefix
meaning natural, and logos, meaning reason or thought. Thus physiology
suggests natural science and is now a branch of biology dealing with processes and activities that are characteristic of living things. “Physicochemical” relates to physical and chemical properties, and “Environmental”
refers to topics such as solar irradiation and wind. “Plant” indicates the main
focus of this book, but the approach, equations developed, and appendices
apply equally well to animals and other organisms.
We will specifically consider water relations, solute transport, photosynthesis, transpiration, respiration, and environmental interactions. A
physiologist endeavors to understand such topics in physical and chemical
terms; accurate models can then be constructed and responses to the internal and the external environment can be predicted. Elementary chemistry, physics, and mathematics are used to develop concepts that are key to
understanding biology—the intent is to provide a rigorous development,

not a compendium of facts. References provide further details, although in
some cases the enunciated principles carry the reader to the forefront of
current research. Calculations are used to indicate the physiological consequences of the various equations, and problems at the end of chapters provide further such exercises. Solutions to all of the problems are provided,
and the appendixes have a large list of values for constants and conversion
factors at various temperatures.
Chapters 1 through 3 describe water relations and ion transport for plant
cells. In Chapter 1, after discussing the concept of diffusion, we consider the
physical barriers to diffusion imposed by cellular and organelle membranes.
Another physical barrier associated with plant cells is the cell wall, which
limits cell size. In the treatment of the movement of water through cells in
response to specific forces presented in Chapter 2, we employ the thermodynamic argument of chemical potential gradients. Chapter 3 considers solute
movement into and out of plant cells, leading to an explanation of electrical
potential differences across membranes and establishing the formal criteria
for distinguishing diffusion from active transport. Based on concepts from
irreversible thermodynamics, an important parameter called the reflection
coefficient is derived, which permits a precise evaluation of the influence of
osmotic pressures on flow.
The next three chapters deal primarily with the interconversion of various forms of energy. In Chapter 4 we consider the properties of light and

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Preface

its absorption. After light is absorbed, its radiant energy usually is rapidly
converted to heat. However, the arrangement of photosynthetic pigments
and their special molecular structures allow some radiant energy from the
sun to be converted by plants into chemical energy. In Chapter 5 we discuss the particular features of chlorophyll and the accessory pigments for

photosynthesis that allow this energy conversion. Light energy absorbed by
chloroplasts leads to the formation of ATP and NADPH. These compounds
represent currencies for carrying chemical and electrical (redox potential)
energy, respectively. How much energy they actually carry is discussed in
Chapter 6.
In the last three chapters we consider the various forms in which energy
and matter enter and leave a plant as it interacts with its environment. The
physical quantities involved in an energy budget analysis are presented in
Chapter 7 so that the relative importance of the various factors affecting the
temperature of leaves or other plant parts can be quantitatively evaluated.
The resistances (or their reciprocals, conductances) affecting the movement
of both water vapor during transpiration and carbon dioxide during photosynthesis are discussed in detail for leaves in Chapter 8, paying particular
attention to the individual parts of the pathway and to flux density equations. The movement of water from the soil through the plant to the atmosphere is discussed in Chapter 9. Because these and other topics depend
on material introduced elsewhere in the book, the text is extensively crossreferenced.
This text is the fourth edition of Physicochemical and Environmental
Plant Physiology (Academic Press, 3rd ed., 2005; 2nd ed., 1999; 1st ed., 1991),
which evolved from Biophysical Plant Physiology and Ecology (Freeman,
1983), Introduction to Biophysical Plant Physiology (Freeman, 1974), and
Plant Cell Physiology: A Physicochemical Approach (Freeman, 1970). The
text has been updated based on the ever-increasing quality of plant research
as well as comments of colleagues and students. The goal is to integrate the
physical sciences, engineering, and mathematics to help understand biology,
especially for plants. Physicochemical and Environmental Plant Physiology,
4th ed., thus continues a tradition to emphasize a quantitative approach that
is suitable for existing situations and habitats as well as new applications.
Park S. Nobel
October 20, 2008


Symbols and

Abbreviations
Where appropriate, typical units are indicated in parentheses.
Quantity

Description

a
ast
aIR
aj
at
A
A
A
Aj
Al
ABA
ADP
ATP

absorptance or absorptivity (dimensionless)
mean area of stomata (m2)
absorptance or absorptivity in infrared region (dimensionless)
activity of species j (same as concentration)a
subscript indicating active transport
Angstrom (10À10 m)
electron acceptor
area (m2)
area of component j (m2)
absorbance (also called “optical density”) at wavelength l

(dimensionless)
abscisic acid
adenosine diphosphate
adenosine triphosphate

b
b
bl

nonosmotic volume (m3)
optical path length (m)
superscript for boundary layer

c
c
cd
cj
cs
cal

centi (as a prefix), 10À2
superscript for cuticle
drag coefficient (dimensionless)
concentration of species j (mol mÀ3)b
a mean concentration of solute s
calorie

a. The activity, aj, is often considered to be dimensionless, in which case the activity coefficient, gj,
has the units of reciprocal concentration (aj = g jcj; Eq. 2.5).
b. We note that mol literÀ1, or molarity (M), is a concentration unit of widespread use, although it is

not an SI unit.

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Symbols and Abbreviations

Quantity

Description

chl
clm
cw
cyt
C
C
Cj
C0
Chl
Cl
CP
Cyt

superscript for chloroplast
superscript for chloroplast limiting membranes
superscript for cell wall
superscript for cytosol

superscript for conduction
capacitance, electrical (F)
capacitance for water storage in component j (m3 MPaÀ1)
capacitance/unit area (F mÀ2)
chlorophyll
subscript for chloride ion
volumetric heat capacity (J mÀ3  CÀ1)
cytochrome

d
d
d
dyn
D
D
Dj

deci (as a prefix), 10À1
depth or distance (m)
diameter (m)
dyne
electron donor
dielectric constant (dimensionless)
diffusion coefficient of species j (m2 sÀ1)

e
e
e
eIR
eV

E
E
E
Ej
E*H
j
EM
ENj

electron
superscript for water evaporation site
base of natural logarithm
emissivity or emittance in infrared region (dimensionless)
electron volt
light energy (J)
kinetic energy (J)
electrical potential (mV)
redox potential of species j (mV)
midpoint redox potential of species j referred to standard
hydrogen electrode (mV)
electrical potential difference across a membrane (mV)
Nernst potential of species j (mV)

f
F
F
F
F
FAD
FADH2

FMN

femto (as a prefix), 10À15
farad
subscript for fluorescence
Faraday’s constant (C molÀ1)
average cumulative leaf area/ground area (dimensionless)
flavin adenine dinucleotide (oxidized form)
reduced form of flavin adenine dinucleotide
flavin mononucleotide

g
gj

gram
conductance of species j (mm sÀ1 with Dcj, and mmol mÀ2 sÀ1
with DNj)


xvii

Symbols and Abbreviations

Quantity

Description

G
G
Gr

G/nj

giga (as a prefix), 109
Gibbs free energy (J)
Grashof number (dimensionless)
Gibbs free energy/mole of some product or reactant j (J molÀ1)

h
hc
hn
H

height (m)
heat convection coefficient (W mÀ2  CÀ1)
a quantum of light energy
subscript for heat

i
i
ias
in
in vitro
in vivo
I
IR

superscript for inside
electrical current (ampere)
superscript for intercellular air spaces
superscript for inward

in a test tube, beaker, flask (literally, in glass)
in a living organism (literally, in the living)
electrical current (ampere)
infrared

j
J
Jj
Jin
Jout
JVj
JV

subscript for species j
joule
flux density of species j (mol mÀ2 sÀ1)
inward flux density (influx) of species j (mol mÀ2 sÀ1)
outward flux density (efflux) of species j (mol mÀ2 sÀ1)
volume flux density of species j (m3 mÀ2 sÀ1, i.e., m sÀ1)
total volume flux density (m sÀ1)

k
k
kj
K
K
K
Kh
Kj
Kj

Kj

kilo (as a prefix), 103
foliar absorption coefficient (dimensionless)
first-order rate constant for the jth process (sÀ1)
temperature on Kelvin scale
subscript for potassium ion
equilibrium constant (concentration raised to some power)
hydraulic conductance per unit length (m4 MPaÀ1 sÀ1)
thermal conductivity coefficient of region j (W mÀ1  CÀ1)
partition coefficient of species j (dimensionless)
concentration for half-maximal uptake rate of species j
(Michaelis constant) (mol mÀ3, or M)
eddy diffusion coefficient of gaseous species j (m2 sÀ1)
equilibrium constant at pH 7

Kj
KpH 7
l
l
l
ln
log

liter
superscript for lower
length (m), e.g., mean distance across leaf in wind direction
natural or Napierian logarithm (to the base e, where e is
2.71828. . .)
common or Briggsian logarithm (to the base 10)

xviii

Symbols and Abbreviations

Quantity

Description

Lsoil
Ljk

soil hydraulic conductivity coefficient (m2 PaÀ1 sÀ1)
Onsager or phenomenological coefficient
(flux density per unit force)
hydraulic conductivity coefficient (in irreversible
thermodynamics) (m PaÀ1 sÀ1)
water conductivity coefficient (m PaÀ1 sÀ1)

LP
Lw

Mj

milli (as a prefix), 10À3
meter
molal (mol/kg solvent)
mass per mole of species j (molar mass) (kg molÀ1)
subscript for maximum

superscript for membrane
superscript for mesophyll
subscript for minimum
mole, a mass equal to the molecular weight of the species
in grams; contains Avogadro’s number of molecules
mega (as a prefix), 106
molar (mol literÀ1)
amount of species j per unit area (mol mÀ2)

n
n
n(E)
nj
N
Na
NAD+
NADH
NADP+
NADPH
Nj
Nu

nano (as a prefix), 10À9
number of stomata per unit area (mÀ2)
number of moles with energy of E or greater
amount of species j (mol)
newton
subscript for sodium ion
nicotinamide adenine dinucleotide (oxidized form)
reduced form of nicotinamide adenine dinucleotide

nicotinamide adenine dinucleotide phosphate (oxidized form)
reduced form of nicotinamide dinucleotide phosphate
mole fraction of species j (dimensionless)
Nusselt number (dimensionless)

o
0
out

superscript for outside
subscript for initial value (at t = 0)
superscript for outside

p
p
pH
pm
ps
P
P
P
Pa

pico (as a prefix), 10À12
period (s)
Àlog(aHþ )
superscript for plasma membrane
superscript for photosynthesis
pigment
subscript for phosphorescence

hydrostatic pressure (MPa)
pascal

m
m
m
mj
max
memb
mes
min
mol
M
M


xix

Symbols and Abbreviations

Quantity

Description

Pj
Pj
PPF
PPFD

permeability coefficient of species j (m sÀ1)

partial pressure of gaseous species j (kPa)
photosynthetic photon flux (400–700 nm)
photosynthetic photon flux density (same as PPF)

q
Q
Q10

number of electrons transferred per molecule (dimensionless)
charge (C)
temperature coefficient (dimensionless)

r
r
r + pr
rj
R
R
Rj

radius (m)
reflectivity (dimensionless)
superscript for respiration plus photorespiration
resistance for gaseous species j (s mÀ1)
electrical resistance (W)
gas constant (J molÀ1 KÀ1)
resistance of component j across which water moves as a liquid
(MPa s mÀ3)
Reynolds number (dimensionless)
relative humidity (%)

Re
RH
s
s
sj
st
surf
surr
S
S(p,p)
Sðp;p* Þ
S
S

subscript for solute
second
amount of species j (mol)
superscript for stoma(ta)
superscript for surface
superscript for surroundings
singlet
singlet ground state
singlet excited state in which a p electron has been promoted to
a p* orbital
magnitude of net spin (dimensionless)
total flux density of solar irradiation, i.e., global
irradiation (W mÀ2)

t

tcw
ta
T
T
Tðp;p* Þ
T

time (s)
cell wall thickness (m)
superscript for turbulent air
superscript for transpiration
triplet
excited triplet state
temperature (K,  C)

u
uj
u+
uÀ
U

superscript for upper
mobility of species j (velocity per unit force)
mobility of monovalent cation
mobility of monovalent anion
kinetic energy (J molÀ1)


xx

Symbols and Abbreviations

Quantity

Description

UB
UV

minimum kinetic energy to cross barrier (J molÀ1)
ultraviolet

y
y
y wind
yj
y CO2
vac
V
V
V
Vj
Vmax

magnitude of velocity (m sÀ1)
wind speed (m sÀ1)
wind speed (m sÀ1)
magnitude of velocity of species j (m sÀ1)
rate of photosynthesis per unit volume (mol mÀ3 sÀ1)
subscript for vacuum

volt
subscript for volume
volume (m3)
partial molal volume of species j (m3 molÀ1)
maximum rate of CO2 fixation (mol mÀ3 sÀ1)

w
wv
W

subscript for water
subscript for water vapor
watt (J sÀ1)

x

distance (m)

z
zj

altitude (m)
charge number of ionic species j (dimensionless)

a
gj
gÆ
d

contact angle ( )

activity coefficient of species j (dimensionless, but see aj)
mean activity coefficient of cation–anion pair (dimensionless)
delta, a small quantity of something, e.g., dÀ refers to a small
fraction of an electronic charge
distance (m)
thickness of air boundary layer (mm)
delta, the difference or change in the quantity that follows it
volumetric elastic modulus (MPa)
absorption coefficient at wavelength l (m2 molÀ1)
permittivity of a vacuum
viscosity (N s mÀ2, Pa s)
wavelength of light (nm)
wavelength position for the maximum absorption coefficient in
an absorption band or for the maximum photon (or energy)
emission in an emission spectrum
micro (as a prefix), 10À6
chemical potential of species j (J molÀ1)
frequency of electromagnetic radiation (sÀ1, hertz)
kinematic viscosity (m2 sÀ1)
ratio of circumference to diameter of a circle (3.14159. . .)
an electron orbital in a molecule or an electron in
such an orbital

d
dbl
D
e
el
e0
h

l
lmax
m
mj
v
v
p
p


xxi

Symbols and Abbreviations

Quantity
p*
P
Pj
Ps
r
r
rj
s
s
sj
sL
sT
t
t
tj

wj
Fi
Y
YP



C

*
*
*

¥

Description
an excited or antibonding electron orbital in a molecule or
an electron in such an orbital
total osmotic pressure (MPa)
osmotic pressure of species j (MPa)
osmotic pressure due to solutes (MPa)
density (kg mÀ3)
resistivity, electrical (W m)
hydraulic resistivity of component j (MPa s mÀ2)
surface tension (N mÀ1)
reflection coefficient (dimensionless)
reflection coefficient of species j (dimensionless)
longitudinal stress (MPa)
tangential stress (MPa)
matric pressure (MPa)

lifetime (s)
lifetime for the jth deexcitation process (s)
osmotic coefficient of species j (dimensionless)
quantum yield or efficiency for ith deexcitation pathway
(dimensionless)
water potential (MPa)
osmotic potential (MPa)
degree Celsius
angular degree
superscript for a standard or reference state
superscript for a molecule in an excited electronic state
superscript for saturation of air with water vapor
infinity


Physicochemical and
Environmental

Plant Physiology
FOURTH EDITION



1
Cells and Diffusion
1.1. Cell Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1A. Generalized Plant Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1B. Leaf Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1C. Vascular Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1D. Root Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2. Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2A. Fick's First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2B. Continuity Equation and Fick's Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2C. Time–Distance Relation for Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2D. Diffusion in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3. Membrane Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3A. Membrane Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3B. Organelle Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4. Membrane Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.4A. Concentration Difference Across a Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4B. Permeability Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.4C. Diffusion and Cellular Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5. Cell Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5A. Chemistry and Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.5B. Diffusion Across Cell Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5C. Stress–Strain Relations of Cell Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.5D. Elastic Modulus, Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.6. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.7. References and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1.1. Cell Structure
Before formally considering diffusion and related topics, we will outline the
structures of certain plant cells and tissues, thus introducing most of the
anatomical terms used throughout this book.
1.1A. Generalized Plant Cell
Figure 1-1 depicts a representative leaf cell from a higher plant and illustrates the larger subcellular structures. The living material of a cell, known as
the protoplast, is surrounded by the cell wall. The cell wall is composed of
cellulose and other polysaccharides, which helps provide rigidity to

3