1

Describing Soil Adsorption ProcessesEquilibrium Based Adsorption Models

Adsorption Isotherms

x = KdC

S

in Soil Solution

SS

SS

S

S

S

Soil SS

S

Adsorbed to Soil

x = amount adsorbed per unit mass (mmol/kg soil)C is the equilibrium concentrationKd is the Distribution Coefficient

Chemical adsorbed to Soil Chemical in Soil SolutionKd =

xin mmol/kg

C (in Molar)

Slope = Kd

Kd = 1no preference for soil or solution

Kd > 1preference for soil over solution

Kd < 1preference for solution over soil

2

Surface Thermodynamics and Surface Loading

Time 1

Time 2

adsorbate molecules go on easyFavorable thermodyamics, ∆ G < 0

Harder to put adsorbate moleculeson soil surface∆ G < 0 but ∆ Gtime 1 < ∆ Gtime 2

Time 3Harder to put adsorbate moleculeson soil surface∆ G < 0 but ∆ Gtime 2 < ∆ Gtime 3

xin mmol/kg

C (in Molar)

Surface Loading and Kd

Increasing Surface Loading

xmax

Adsorption Maxima or “plateau”

Kd is a function of Surface LoadingKd decreases with Surface Loading

3

Types of Adsorption IsothermsC-Type – simple partitioning

“physical” not “chemical”Adsorption of non-polar organic chemicals by SOM (soil)

L-Type – most common Decrease in Kd with surface loading

H-Type – high affinity for soilstrong specific adsorption

S-Type – competing reactions at soil surface and in solution

Cu adsmmol/kg

Equilibrium (Cu)

Dissolved SOM

SoilCuCuCu

Cu2+

Cu2+

SOM

O

CO

O

Competing reactions

low loadingdissolved SOM-Cuhas preference

Dissolved SOM saturated with CuCu only can bind to soilLooks like a L-isotherm

4

Adsorption Models

Empirical adsorption models –description of chemical adsorption data without a “theoretical” basis– without a detailed description of chemical adsorption processes

Langmuir Adsorption Isotherm ModelFreundlich Adsorption Isotherm ModelTemkin Adsorption Isotherm Equation

Chemical adsorption modelsdescription of chemical adsorption data with a theoretical basis--with a detailed description of chemical adsorption processes

Constant Capacitance ModelTriple Layer ModelStern variable surface charge-surface potential (VSC-VSP) modelCation Exchange equations

Adsorption Models

Allow you to predict partitioning of chemical betweensoil and solution

Provide information on the strength of adsorptionbetween soil and chemical

Provide information on the maximum amount of chemical that the soil can adsorbadsorption capacity or adsorption maxima.

5

Langmuir Adsorption Isotherm Model

SSS S

S

S

S

SSoil S

SS

Developed by Langmuir to describe adsorption of gas on metal surfaceAssume adsorption sites are all sameFixed number of adsorption sitesMonolayer coverage of surfaceAdsorption is reversible

x = bKC

1 + KCx

C

x = amount adsorbed/mass soilb = adsorption maximaK = bonding energy coefficientC = equil. conc. in solution

Linear transformation of Langmuir EquationReciprocal Langmuir plot

1Kbx

C=

Cb

+

x C

C

1Kb

slope =1b

b = adsorption maxima

K = bonding energy coefficientlarge K means strong bonding

6

Generating a Langmuir Adsorption IsothermPhosphate adsorption to soil

Shake soil (know weight, 1 g) with solution containing known phosphateMeasure phosphate in solution at equilibrium [Initial solution – final solution phosphate] / kg soil = adsorbed P/soil = x

mmol / L x # L mmol / kg

C = [P]eq in mmol/L

x = [P]ads in mmol/kg

Calculate C/x in kg/L

3.1 5.2 6.7 8.5 10.8

2.0 11.0 20.0 40.0 80.0

0.65 2.1 3.0 4.7 7.4

Linear transformation of P Langmuir Equation

1Kbx

C=

Cb

+

x C

C

1Kb

slope =1b

y = 0.863 + 0.842

b = (0.842)-1 = 11.9 mmol P/kg soil

K = (yintercept x b)-1 = (0.863 x 11.9)-1 = 0.0974 kg soil/mmol P

7

b = P ads max = 11.9 mmol/kg = 3.7 x 10-4 kg P/kg soil

(2.24 x 106 kg/ha soil ) (3.7 x 10-4 kg P/kg soil) = 829 kg P/ha

kg/ha (0.893) = lbs/acre

so P ads max = 740 lbs/acre

What is the P adsorption max of this soil mean?

Freundlich Adsorption Isotherm Model

SSS S

S

S

S

SSoil S

SS

Freundlich vs LangmuirFreundlich assumes heterogeneous adsorption surfaces (not all same)Freundlich does not have an adsorption maxima

x = KC1/n

x

C

K and n are empirical constants

8

Log transformation of Freundlich Equation

log C

slope =1n

K = related to bonding strengthlog x

log K

log x = log K + log C1n

Advantage: experimental data usually fits log-log plotDisadvantage: cannot predict and adsorption maxima

x = KC1/n

Hydrophobic partitioning and the Freundlich equation

n = 1.0 for very dilute solutions of C (ppm or less levels)

x = KC1 = KC

x

C

Slope = K Common for adsorption of non polar organic chemicals to soil matter

K = Kocfoc

where foc= fraction OC in soil

= (%OC/100%)

a single Koc value for each organic chemicalKoc is independent of soil organic matter content

9

Adsorption of atrazine by soil

atrazine adsorbedx in mg/kg soil

atrazine concin solution, mg/L Kd

Soil 1

Soil 2

SOM(%)

SOC(%) Koc

0.25 0.25 1.0 2.0 1.0 100

0.39 0.13 3.0 6.0 3.0 100

Koc is independent of soil organic matter contentKoc is an inherent property of the organic chemical

Large Koc (>1000) – strong preference for SOM – little dissolved in water

Small Koc (< 100) -- little preference for SOM – lots dissolved in water

Only need Koc and Soil OC content (foc) to calculate dissolved chemicalcommonly used in computer transport/fate models for organics/pesticides

Shortcomings of Soil Langmuir Adsorption Model

May be more than one type of adsorption site in soil

Fe-OHO

Fe – O – P – OHO

Fe-OH2+

Fe-OHO

FeO

FeO – P – OH

OH

O

Binuclear inner spheresurface complex

Must use multi-surface Langmuir Adsorption Isotherms

b1K1C

1 + K1C

b2K2C

1 + K2Cx = +

10

x C

C

Binuclear P adsorptionb = (slope)-1

BEC = 1/Kb

Mononuclear P adorptionb = (slope)-1

BEC = 1/Kb

Reciprocol plot for linearized 2 surfaceLangmuir Adsorption Isotherm

Adsorption of GasesDetermination of Surface Area

using BET EquationBrunauer, Emmett, and Teller -- BET Equation

Multilayer adsorption of gases

C - 1

XmC

1

XmC

PPo

X ( 1- PPo

)= + P

Po

Y = yintercept + slope x

P

Po

= partial pressure of gas

C = constant

X = moles gas adsorbedXm = moles gas adsorbed

for monolayer“Surface Area”

11

PPo

X ( 1- PPo

) 1

XmC

C - 1

XmCslope =

1

XmC

C - 1

XmC

BET plot for adsorption of nitrogen gas on MnO2 surface0.314 g MnO2slope = 14760yintercept = 272What is the surface area of the mineral?

yint =

slopeyint

=

1

XmC

= C - 114760272

= 54.26 C - 1=C = 55.26

= yint C1

Xm

= yint C1

Xm

= (272)(55.26) = 15030

12

=1

Xm15030 Xm = 6.65 x 10-5 moles N2

MnO2 surface area =(6.65 x 10-5 moles N2)(9.757 x 104 m2/mole N2) = 6.73 m2

MnO2 specific surface area =6.73 m2

3.14 x 10-4 kg MnO2

2.1 x 104 m2

kg MnO2=

Total Surface Area = External Surface + Internal Surface

Only polar gas can measure internal sites

Measuring Surface Area of Soil Minerals

Only External Sites – use N2 gas (non-polar)

Internal + External Sites – use EGME (polar)

EGME – ethylene glygol monoethyl etherpolar organic liquid –evaporates easily and adsorbs

Internal area = Total (EGME) – External (N2)

13

Chemical Adsorption ModelsChapter 5 - Sparks

SoilSurface

Inner sphereanion site

Inner spherecation site

Outer spherecation site

Soil surface - collection of adsorption sites

Different adsorption mechanismsDifferent models

Adsorption of cations by CECIon-exchange models

Specific adsorption of anions / cationsConstant capacitance model, others

Must know the dominant adsorption mechanism of chemical speciesto select a chemical adsorption model

Chemical Adsorption ModelsIon Exchange Models

Diffuse Electric Double Layer (DDL) Model

Soil orClay Particle

+++

+

+ +

++

++

+

+

+

++

+

+

+ +

Diffuse Layer+ > -

Bulk solution+ = -

14

from Essington 2004

DDL Model

ElectricalPotential

Ψ

+++

+

+ +

++

++

+

+

+

++

+

+

+ +

Diffuse Layer

Bulk solution+ = -

Ψo

Electrical potential – Potential of in an electrical fieldtanh [ZeΨ/4kT] = tanh [ZeΨo/4kT]e-kx]

15

DDL Model Derivations

Soil orClay Particle

+++

+

+ +

++

++

+

+

+

++

+

+

+ +

Bulk solution+ = -

n+

n-

ni = nio

n+ = number of cationsn- = number of anions

[

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−+

−−−

−

])4/tanh(1[])4/tanh(1[

kxo

kxo

ekTZeekTZe

ψψ

Important consequences of DDL Model

Soil orClay Particle n +1 cations

Bulk SolN

Bulk SolN

n +2 cationsDDL

DDL

DDL decreases with DDL cation charge

DDL decreases with soil solution ionic strength (I)

16

CEC Composition & Soil Structure2 State of Clay Colloids

STABLE Dispersed in SolutionDoesn’t Settle Out

Few Aggregates – Poor Soil Structure

UNSTABLE Acts as one big structural unit

FlocculatedSettles Out of Solution

Aggregates – Good Soil Structure

CEC Composition & Soil StructureCEC Composition Determines Colloidal Stability

Repulsive Force - DDL Cations (push clay apart)Attractive Force - Van Der Waals (pull clay together)– Only when Clay are Very Close

Repulsive > Attractive DispersionAttractive > Repulsive Flocculation

Repulsion

----

Clay 1

+++

DDL

----

Clay 2

+++

DDL

Van der Waals

17

CEC Composition & Soil Structure

Hydrated Ion Size directs affects size of DDLNa+ > K+ > Mg2+ > Ca2+ > Al3+

Repulsion

----

Clay 1

----

Clay 2

Van Der Waals

Na+

Repulsion > Attraction = Dispersion

Too much Na on CEC --- Dispersed Soil – No Structure

Poor Drainage, Poor Aeration, High Erosion

Na+

Repulsion----

Clay 1

----

Clay 2Ca2+ Ca2+

Attraction

Smaller ion hydrated radius, smaller DDL than Na+

Less Repulsion, clays have closer approach

Attraction > Repulsion

DDL thickness Al3+ < Ca2+, Mg2+ < K+ < Na+

Attraction > Repulsion = Flocculated Soil

Good Structure, Good Drainage, Aeration, Low Erosion

CEC Composition & Soil Structure

18

Net surface charge of soil

σp = σ0 + σH + σIS + σOS

Permanentcharge

Particlecharge

Variablecharge

Inner spherecharge

Outer spherecharge

Fe-OHO

Fe – PbOHO

Fe-OH2+

Chemisorption of transition metal cations to hydrous oxide sorption sites

Chemisorbed Lead

Step 1 Metal Hydrolysis

Step 2 Inner sphere adsorption of metal hydroxocomplex

Most metal cations exceptalkali and alkaline earth metals

Pb2+ + H2O = PbOH+ + H+

Pb hydroxocomplex

PbOH+ + X = XPbOH+

19

Pb2+ + H2O = PbOH+ + H+

K = (PbOH+)(H+)(Pb2+)

Lead is a “weak acid”

pH - pK = (PbOH+)(Pb2+)

As pH increasesPbOH+ increases

Specific adsorption of Pb increases

log

Adsorption by Hematite Adsorption by Goethite

Strong soil pH dependence of heavy metal cation adsorption by oxides

Adsorption Edge = pH at which adsorption increasesfrom very low to very high

Adsorption Edge Occurs at pH = pKmetal – 1 (or 2)

Metal pKPb 6.2Cu 8.0Zn 9.0Co 9.7Ni 9.9Mn 10.6

20

Specific Adsorption of Oxyanionsto hydrous oxide sorption sites

O P O

O

OO As O

O

O

O S O

O

O

PO43-

AsO43-

SO42-

MoO42-

PhosphateArsenateSulfateMolybdateOrganic acid anionsCOO-

Fe-OHO

Fe – O – P – OHO

Fe-OH2+OH

O

Chemisorbed Phosphate

Soil pH dependence of oxyanion adsorption by oxides

Acids that loose one proton HF, silicic acid

have a maxima at their pK1 value

Polyprotic acids have an inflection point

at their pK values

This behavior is termedthe anion’s

Adsorption Envelope

Adsorption by Goethite

21

Chemical Specific Adsorption ModelsConstant Capacitance Model

Fe-OHO

Fe–OHO

Fe-OH2+

Finite number of specific adsorption sites on oxideOnly inner sphere complexes

σ = σH + σIS

SOH + H+ = SOH2+

SOH = SO- + H+

SOH + Mn+ = SOM(n-1) + H+

2SOH + M2+ = (SO)2M(n-2) + 2H+

SOH + Lq- = SOL(q-1)- + OH-

2SOH + Lq- = S2L (q-2) +2OH-

Charge of all surface species = σ

22

Constant Capacitance Modelaccounts for changes in surface charge

for variable charge oxide surfaces

TotalCharge

Soil pH

+

-

0

SOH2+

SOH2+ = SO- = SOH

SO-

SOH + H+ = SOH2+

SOH = SO- + H+

SOH + Mn+ = SOM(n-1) + H+

2SOH + M2+ = (SO)2M(n-2) + 2H+

SOH + Lq- = SOL(q-1)- + OH-

2SOH + Lq- = S2L (q-2) +2OH-

Each reaction has an equilibrium expression

K+ = ]][[

][ 2+

+

HSOHSOH

exp (FΨi /RT)

K values for each reaction calculated (computer model)Used to predict adsorption species to oxide surface

23

Application of the Constant Capacitance Model

in Soil Solution

SoilCEC

Ca2+

Mg2+

K+

Quantity-Intensity (Q-I) Curves

Ca2+

Mg2+

K+

K+

K+

K+

Quantity Potentially available K

Intensity Available K

Predict the effect of solution chemistry on adsorption or desorption of K

24

(Ca,Mg)½X + K+ = KX + ½ (Ca,Mg)2+

Kads

(Ca + Mg)½X= Kex

(K)(Ca + Mg)√ 2

Quantity Intensity

K = Kex ARK

K = Kex ARK

∆Kcmol/kg

0

+

- Kx

∆Ko

ARKeq

ARK

Intensity

∆(∆K)

∆ ARKSlope = = PBCK

PBCK = potential buffer capacity for K+

∆Ko = Exchangeable K in soil (Quantity term)∆K = exchangeable K adsorbed (+) or desorbed (-)Kx = specific adsorbed (inner sphere) K – fixed K

25

∆Kcmol/kg

0

+

-

ARK

Intensity

CompareQuantity of KPotential buffering capacity of K

soil 1soil 2

from Essington 2004

Chemical Adsorption ModelsTriple Layer Model

26

from Essington 2004

from Essington 2004

27

σp = σ0 + σH + σIS + σOS

Permanentcharge

Particlecharge

Variablecharge

Inner spherecharge

Outer spherecharge

Other Chemical Adsorption ModelsSparks – Chapter 5 , p.165

Modified Triple Layer Model σ0 + σH + σIS

Stern VSC-VSP(4-layer model)

σ0 + σH + σIS

More complex models will have better fits but–but they are more complex to work withBetter fit due to “statistics” – more parameters –better statistical fit

Adsorption vs. Surface Precipitation

A and B – low surfacecoverage of metalTrue adsorption

C, D – high surfacecoverage of metalSurface precipitation

C

28

Is it adsorption or precipitation?

Data fitting an adsorption model is not proofthe process is adsorption

Surface precipitation will fit a Langmuir or Freundlich Modelbut spectroscopic study of surface can provide evidence

Surface Loading with Adsorbate

AdsorptionMonolayer

SurfacePrecipitation

MineralPrecipitation

Mineral Kspcontrols ion activity

“unsaturated” conditionsbelow adsorption maxima

Adsorption Isothermcontrols ion activity