Transport of polymer in soils and solute in gels for contaminant remediation and containment

Transport of polymer in soils and

solute in gels for contaminant

Transport of polymer in soils and

solute in gels for contaminant

remediation and containment

PROEFSCHRIFT

Ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof.dr.ir. J.T.Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 14 juni 2004 te 13:30 uur door

Mohamed Ismail Mostafa DARWISH

Master of Science in Civil Engineering, Ain Shams University, Cairo, Egypt

Dit proefschrift is goedgekeurd door de promotor: Prof. Dr. P. K. Currie

Samenstelling promotiecommissie:

Rector Magnificus, Voorzitter

Prof. Dr. P.K. Currie, Technische Universiteit Delft, promotor

Dr. Ir. P.L.J. Zitha, Technische Universiteit Delft, toegevoegd promotor Prof. Dr. R. Kerry Rowe, Queen’s University, Canada

Prof. Dr. Ir. F.B.J. Barends, Technische Universiteit Delft Prof. Dr. Ir. F. Molenkamp, Technische Universiteit Delft Dr. J.R.C. van der Maarel, Leiden University, Leiden Drs. W. van der Zon, GeoDelft, Delft

Prof. Ir. C.P.J.W. van Kruijsdijk, Technische Universiteit Delft, reservelid

The research described in this thesis was performed at the Dietz Laboratory, Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands. The diffusion cell experiments were performed at the laboratory of Civil Engineering, Soil mechanics, Queen’s University, Canada.

To the memory of my father

To my mother, my wife and children

This research work resulted in the following list of

publications:

Mohamed I.M. Darwish, R. Kerry Rowe, J. R. C. van der Maarel, L. Pel,

H. Huinink and P.L.J. Zitha, 2003, Contaminant Containment using

Polymer Gel Barriers, Canadian Geotechnical Journal, Vol. 41, pp.

106-117.

Mohamed I.M. Darwish, J. R. C. van der Maarel, L. Pel, H. Huinink and

P.L.J. Zitha, 2001, Polymer Gel Barriers for Waste Disposal Facilities,

in the book of Geotechnical Engineering: meeting Society’s needs,

edited by K.K.S. Ho and K.S. Li, Balkema Publisher, Vol. 1, ISBN 90

5809 256 9, pp 225-230.

Mohamed I.M. Darwish, J. R. C. van der Maarel, L. Pel, H. Huinink and

P.L.J. Zitha, 2002, Polymer Gel Barriers for Contaminant Containment,

in the book of Environmental Geotechnics, edited by L.G. de Mello and

M. Almeida, Balkema Publisher, Vol. 1, ISBN 90 5809 501 0, pp 77-82.

Mohamed I.M. Darwish, J. E. McCray, P.K. Currie and P.L.J. Zitha,

2003, Polymer-enhanced flushing of DNAPL in stratified media: an

experimental study” Journal of Ground Water Monitoring and

Remediation, Vol. 23, No. 2, pp. 92-101.

Mohamed I.M. Darwish, J. R. C. van der Maarel and P.L.J. Zitha, 2003,

Ionic transport in polyelectrolyte Gels: Model and NMR investigations,

Macromolecules, Vol. 37, pp. 2307-2312.

Zitha, P.L.J., Darwish, M. I. M., Effect of bridging adsorption on the

placement of Gels for water Control, presented at the 1999 SPE Asia

Pacific Improved Oil Recovery Conference held in Kuala Lumpur,

Malaysia, 25–26 October 1999, on CD ROM

Mohamed I.M. Darwish, Pim van Boven, Hans C. Hensens, and P.L.J.

Zitha, 1999, Porous media flow of oil dispersion in polymers, presented

at the SPE annual Technical conference held in Houston, Texas, 3-6

Oct., pp 285-296.

Mohamed I.M. Darwish, P.L.J. Zitha and P.K. Currie, 2000,

Enhancement of the Pump-and-Treat technique using polymers,

presented at the 53

ed

Canadian Geotechnical Conference, Montreal,

15-18 Oct., Canada.

Abstract

Recently geoenvironmental engineering applications have received considerable attention due to the growing awareness of their importance for the environment. There are several remediation techniques to clean-up contaminated sites or to decrease the threat of contaminant on the environment. In this thesis, the focus is on removal and treatment by the pump-and treat technique and on contaminant containment using physical barriers.

Pump-and-treat systems operate by pumping out contaminated ground water to surface and removing the contaminant. In layered soil, the pump-and-treat technique suffers from several drawbacks. One of the important drawbacks is the difficulty of removing the contaminant from the soil layers with relatively lower permeability.

For physical barriers, used for contaminant containment there are several disadvantages of the materials used nowadays. One important disadvantage is the limited attenuation capacity for the solute transport through these barriers.

In this thesis, the use of environmentally friendly polymer solutions and gels to overcome the drawbacks and disadvantages of the present techniques and materials is investigated. The injection of polymer solutions in extraction wells to change the velocity profile, thus favoring efficient contaminant removal, is proposed and evaluated both experimentally and theoretically. The injection at relatively high injection rate that results in polymer chain stretching and the occurrence of polymer bridging adsorption in lower permeability soil layers is proposed. Also the use of polymer gels as barrier or as a layer of composite liner, when mixed with sand, is considered. The transport and sorption of charged polymers (polyelectrolytes) in porous media was studied experimentally by flowing polymer solutions in packs of granular silicon carbide (SiC) powder. Three types of experiments were carried out. First, disk-shaped samples that were aiming at studying the sorption kinetics and adsorption reversibility. Second, single-core experiments, which were conducted mainly to investigate the polymer rheology and the adsorption mechanism. Third, parallel-cores experiments that were conducted to check the enhancement that polymer bridging adsorption can provide to the pump-and-treat remediation technology.

The experiments showed that there is irreversible polymer adsorption due to the injection at relatively high rates, which was attributed to polymer bridging adsorption. The increase in flow resistance due to the injection at relatively high rates is much higher than the increase in adsorption density. The parallel-core experiments show that the polymer injection leads to a considerable decrease of the hydraulic conductivity contrast between the

higher- and lower-permeability layers favoring more efficient contaminant removal from lower-permeability layers. A reasonable agreement between the measured and predicted adsorption density profiles was found, which validate the developed model for charged polymer transport and sorption based on the two types of polymer adsorption namely layer and bridging adsorption.

The transport and sorption of charged solute in charged gels was studied experimentally and theoretically. The ion diffusion in gels was investigated on both microscopic and macroscopic scales using nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), respectively. The gel adsorption capacity was examined using batch experiments. The portioning and diffusion coefficient for ions were measured using conventional diffusion cell experiments and the values were compared with that measured in MRI experiments. The compatibility of gel barrier with leachate was tested utilizing permeation tests. A model was developed that takes into account both geometric and electrostatic obstructions that ions experience while diffusing through charged gels. The validity of this model was evaluated on microscopic and macroscopic scales by comparing it is predicted vales with the NMR and MRI measurements. The comparison showed the validity of the model on both scales. The gel showed reasonable compatibility with the leachate. The positively charged gel was able to retard the chloride transport, which is not retarded by natural clay barriers.

On the basis of this work, it is concluded that environmentally friendly polymers solutions and gels may have an important part to play in soil remediation and contaminant containment. It is recommended that further work is pursued to confirm this conclusion.

Contents

Chapter 1 Introduction 1

1.1 Remediation technologies 1

1.2 Scope and organization of the thesis 3

Chapter 2 Background 5

2.1 Dense Non-Aqueous Phase Liquids (DNAPL) 5

2.2 Municipal solid waste (MSW) 6

2.3 Contaminant transport in soil 6

2.3.1 DNAPL migration into layered soils 7

2.3.2 Transport of miscible species 8

2.4 Soil and groundwater remediation techniques 12

2.4.1 Pump and Treat 12

2.4.2 Contaminant containment 16

Chapter 3 Physical Chemistry of Charged Polymers and Gels 21

3.1 Introduction 21

3.2 Charged polymer solutions 22

3.2.1 The uniqueness of charged polymers properties 22

3.2.2 Mechanical models for polymer molecules 22

3.2.3 Scaling theory of charged polymer solutions 24

3.3 Rheology of charged polymer solutions 26

3.3.1 Types of flow 26

3.3.2 Flow in porous media 28

3.4 Adsorption of charged polymers 32

3.4.1 Adsorption on planar surfaces 32

3.4.2 Adsorption in porous media 34

3.5 Polymer Gels 36

3.5.1 Gel cross-linking 36

3.5.2 Structure of gels 37

3.5.3 Evaluation of gel point 37

3.5.4 Gel swelling and swelling kinetics 38

Chapter 4 Transport and sorption theory 41

4.1 Introduction 41

4.2 Transport and sorption of charged polymers in P.M. 42

4.2.1 Previous work 42

4.2.2 Model development 45

4.2.3 Simplified simulation for the disk-shaped samples 53

4.3 Transport and sorption of ions in charged gels 62 4.3.1 Solute diffusion in charged polymer gel 62 4.3.2 Development of model for ions diffusion in charged gels on

microscopic scale 66

4.3.3 Ions transport and sorption in charged gels 70 Chapter 5 Enhancement of DNAPL flushing from layered soils by

adsorption of charged polymers 73

5.1 Introduction 73

5.2 Experimental technique 74

5.2.1 Polymer solutions 74

5.2.2 Samples and procedure 75

5.3 Results and discussion 79

5.3.1 Disk-shaped samples 79

5.3.2 Single core Experiments 92

5.3.3 Polymer adsorption mechanism 100

5.3.4 Parallel-core experiments 102

5.4 Discussion on Cross-flow 104

Chapter 6 Evaluation of polymer gel as barriers for contaminant

containment 107

6.1 Introduction 107

6.2 Experimental techniques 108

6.2.1 Gel preparation and characterization 108

6.2.2 Batch Experiments 109

6.2.3 Nuclear Magnetic Resonance (NMR) spectroscopy 110

6.2.4 Magnetic Resonance Imaging (MRI) 111

6.2.5 Diffusion cell experiments 113

6.2.6 Leachate-gel barrier compatibility 115

6.3 Results and discussion 118

6.3.1 Gelling Time 118

6.3.2 Batch adsorption 120

6.3.3 Diffusion coefficients 121

6.3.4 Macroscopic diffusion of H+ _{and Na}+ ₁₂₆

6.3.5 Diffusion cell experiments 132

6.3.6 Comparison between diffusion coefficients from MRI and

Diffusion cell experiments 135

6.3.7 Leachate-gel barrier compatibility 136

Chapter 7 Conclusions and Recommendations 141

7.1 Conclusions 141

7.1.1 Charged polymers for the enhancement of DNAPL flushing

from layered subsurface soil 141

7.2 Applications in Geoenvironmental engineering 143

7.2.1 Pump and Treat enhancement 143

7.2.2 Contaminant containment barriers 143

7.3 Recommendations for future work 143

Appendix A Suggested experiments for further evaluation of gel

barriers 145

A.1 Gel Swelling 145

A.1.1 Gel swelling pressure 146

A.2 Gel flexibility and strength 148

A.2.1 Sample preparation and procedure 148

A.2.2 Gel-sand barrier flexibility and strength 148

Nomenclature 151

Reference 155

Acknowledgement 163

About the Author 165

Chapter 1

Introduction

In this chapter, an introduction is given to the role of geoenvironmental

engineering, the challenges facing current remediation technologies and

proposed solutions. The scope and organization of the thesis are

explained.

The scope of this thesis is to investigate the potential use of environmentally safe polymers and gels in geoenvironmental applications. The idea of using polymers and gels originated from the oil industry. In the oil industry, polymers and gels are used extensively for enhanced oil recovery as relative permeability modifiers or as full blocking agents for water shut-off.

In the past few decades there has been immense growth in global population, industrial development, energy use, and civil infrastructure. Growth in one sector often generates problems in other areas. Consequently, debates have intensified on industrialization and associated environmental issues such as waste generation, ecosystem and human health risk assessment, and waste management systems. This was the setting for the birth of

geoenvironmental engineering as an amalgam of principles drawn from a

variety of engineering and applied science fields (Reddi & Inyang, 2000). Solutions to the complex problems confronted by the waste management and environmental restoration industry are currently handled by the

geoenvironmental engineering profession, consisting of geotechnical,

environmental and chemical engineers, geologists, chemists, microbiologists, and soil scientists.

Remediation of contaminated soil and groundwater, which is one of the branches of geoenvironmental engineering, has been in full swing for the last two decades. During this relatively short period, the environmental industry has seen tremendous changes in both strategy and technique.

1.1 Remediation technologies

Remediation technologies for polluted soils can be grouped into one or more of the following options: 1) Natural attenuation, 2) Containment, 3) Removal for subsequent on-site or off-site treatment, 4) In-situ treatment.

Natural attenuation: requires that the natural processes currently

existing in the subsurface continue to provide adequate environmental protection. For example, due to existence of a thick clay layer beneath the disposal site, dissolved pollutants may be naturally attenuated before an unacceptable risk to the environment occurs. Attenuation can be accomplished through the use of sorptive, low-permeability materials, or permeable, but

Chapter 1: Introduction

reactive materials. Chemical attenuation processes include adsorption, precipitation, biological processes, oxidation-reduction reactions, acid-base reactions, and complex formation (Dunn, 1983).

Containment techniques: generally involve creating barriers or

immobilizing pollutants for preventing unacceptable pollutant migration. Techniques such as physical (hydraulic or barriers), chemical (encapsulation of pollutants), thermal (transformation of the polluted soil into solid mass) are used. Waste constituents and moisture can be contained hydraulically through the installation of pore fluid extraction through, gravity-induced drainage or pumping, chemically by encapsulation using stabilizers or physically using containment barriers (Reddi & Inyang, 2000). Hydraulic containment involves the removal of moisture, which may be allowed to drain into constructed ditches, or pumping of water from the soil. The shape of a containment system for wastes plays a significant role with respect to the effectiveness of the system in meeting its design function during the design life. Chemical containment attempts to encapsulate the pollutants directly using organic or inorganic stabilizers, hence reducing the potential leachability. Physical containment, which falls within the scope of this study, involves the installation of physical barriers to attenuate contaminants, and/or change their direction and/or rate of transport in the soil.

Removal and treatment: recovery of non-aqueous phase liquids (NAPLs)

using extraction wells, soil vapor extraction to recover pollutants from the soil gas phase, pump-and-treat to recover dissolved pollutants in ground water. Removal/ excavation of contaminated soil was once the solution for soil remediation. However, because of the high cost of excavation and final disposal in landfills, in addition to the lack of available landfill sites, these disposal methods are becoming increasingly less popular (Mann, et al, 1993).

In-situ treatment: in-situ soil flushing where solubilizing agents can be

injected into the subsurface to dissolve pollutants and flush them out, electrochemical treatment used for soils with low hydraulic conductivity, biological treatment usually used for organically polluted soils.

In this thesis we shall be concerned with a contaminant removal technique (pump-and-treat) and a containment technique using impermeable flow barriers. These techniques are described in more detail in chapter 2.

For the pump-and-treat remediation technology, the most important problem that it faces is the production of substantial amounts of water in order to extract a small amount of contaminant especially under layered soil conditions. The origin and consequences of this problem will be discussed in chapter 2. This thesis proposes that the process can be improved by the injection of a polymer solution in the extraction well. The injection will modify the velocity profile in the extraction well vicinity favoring more efficient removal of the contaminant per volume of water produced.

For contaminant containment using physical barriers, the most important problem facing the technology is the need for environmentally friendly

Chapter 1: Introduction

material that can be used as a barrier and shows compatibility with the contaminant, has sufficient ductility to accommodate expected deformations, has the ability to limit the flux of both anions and cations, and can limit downward, as well as lateral, movement of contaminants. The proposed solution is the use of polymer gel barriers.

1.2 Scope and organization of the thesis

The previously mentioned two applications require understanding of related processes such as transport and sorption of polymer and contaminant in porous media and polymer gels and these have been studied both experimentally and theoretically. Moreover, the required properties for the polymers and gels to cope with the proposed applications such as rheological behavior, compatibility between contaminant and gel, gel swelling and ductility performance, were investigated. The results of those analyses can be utilized in actual applications and suggestions can be made to improve remediation technologies.

The rest of this thesis is divided into 6 chapters. Chapter 2 describes contaminant transport in porous media, pump and treat remediation and containment disadvantages, and proposed solutions using polymers and gels. Chapter 3 presents the physics and chemistry of polymers and gels. In chapter 4, transport and sorption theory and simulations for both charged polymers in porous media and ions in charged gels is explained. Chapter 5 provides details about experimental work and comparison with the simulations for the transport and sorption of charged polymers in porous media. Chapter 6 contains the experiments for ions transport through charged gels and comparison with the simulation results. Chapter 7 presents the main conclusions and recommendations that can be drawn from this work.

Chapter 2

Background

In this chapter, background information is given about contaminant

classification, contaminant transport mechanisms, challenges facing the

Pump-and-Treat and the contaminant containment remediation

techniques. Proposed solutions to the associated problems using

polymer solutions and gels are presented in more detail.

The migration of pollution or leachate from contaminant sources is a serious hazard for the human health, the environment and the integrity of buildings. The movement of pollutants has a profound effect upon its bioavailability. Once a pollutant enters one of the mobile phases, i.e., air or water, it disperses rapidly due to fluid movement. In some cases the contamination poses little risk in the present use of the site but delays its redevelopment until remediation occurs.

In this study, two types of contaminants will be considered with two different remedial measures. Firstly, organic or inorganic-immiscible such as chlorinated solvents, coal tars, pesticides and heavy oil products that are defined as Dense Non-Aqueous Phase Liquids (DNAPL). For this type of contaminant the removal and treatment (pump-and-treat) technique will be considered. Secondly, inorganic-miscible, ion-containing waste materials that cause soil and groundwater pollution, which include: Municipal Solid Wastes (MSW), sewage sludge, storm water run-off, dredged materials, industrial by-products, wastes from mining and smelting operations, filter residues from wastewater treatment and atmospheric emission control, ashes and slags. For this category of contaminants the containment technique, using barriers or liners, will be considered and MSW is chosen as a representative contaminant.

2.1 Dense Non-Aqueous Phase Liquids (DNAPL)

The class of contaminants referred to as Dense Non-Aqueous Phase Liquids (DNAPL’s) present one of the most challenging remediation situations. The DNAPL’s typically have low solubility in water (immiscible) and high interfacial surface tension. As they are denser than water, they tend to move downward in the subsurface, and become trapped in the pore system by surface tension forces. Moreover, they may sit in zones (referred to as ‘pools’) on top of very low permeability layers that are less accessible to groundwater flow, dissolving into the aqueous phase over a long period of time to contribute to long-term groundwater contamination. As a result, DNAPL’s are both difficult to locate and to remove from the subsurface.

Chapter 2: Background

Although immiscible, DNAPL’s tend to be relatively insoluble in water. Unfortunately they are often sufficiently soluble to cause concentrations in ground water to exceed the allowed maximum contaminant level. Consequently, residual and pooled DNAPL will continue to contaminate ground water that makes sufficient contact to dissolve small amounts of DNAPL. The irregular distribution of the entrapped and pooled DNAPL, coupled with natural variations in hydraulic conductivity and capillary properties, makes complete mass removal virtually infeasible.

2.2 Municipal solid waste (MSW)

The composition of average municipal refuse, picked up at the curbside, varies from country to country, and will depend on the local cultural background of the generating community. Municipal solid waste (MSW) consists of everyday items such as product packaging, grass clippings, furniture, clothing, bottles, food scraps, newspapers, appliances, paint, and batteries. Percolation of ground water or rainwater through municipal solid waste storage site, leaches out soluble salts and biodegraded organic products to form a leachate. MSW leachate is a complex liquid, which changes in characteristics as one passes from the early acetic phase of young leachate to the methanogenic phase of older leachate.

There are several MSW management practices, such as source reduction, recycling, and composting that prevent or divert materials from the waste stream. Other practices address those materials that require environmentally safe disposal.

2.3 Contaminant transport in soil

Knowledge of contaminant transport and transfer in soils is crucial in site remediation and waste containment efforts. Two basic elements affecting the transport and fate of contaminants in the subsurface are the properties of the subsurface materials or subsurface environment and the physicochemical and biological properties of the contaminants.

An important distinction is between contaminants that are soluble or miscible in water and those that are insoluble or immiscible in water. The two types of contaminants differ in the way their transport takes place relative to pore water (Reddi & Inyang, 2000). The transport of soluble contaminants is more closely linked to the flow of pore water than that of immiscible contaminants, which is governed by a host of pore-scale and field-scale mechanisms not related to flow of water. Under saturated conditions, dissolved contaminants are transported mainly by advective movement of the bulk fluid resulting from the hydraulic gradients present in the saturated zone. Advective transport is always accompanied by molecular diffusion wherever concentration gradients are present and by mechanical dispersion that results from the tortuosity of the pore system geometry. Sorption processes that act to partition the contaminant between liquid and solid phases may affect

Chapter 2: Background

advective-diffusive transport. Biochemical reactions may also occur, causing precipitation and /or transformations in the chemical form of the contaminant (Rowe et al 1995). In the following section, the focus is on the DNAPL migration into layered soils and on single-phase miscible species transport.

2.3.1 DNAPL migration into layered soils

To consider the enhancement of pump and treat technique, it is important to review DNAPL migration in layered soil. The subsurface migration of DNAPL’s is not only controlled by conventional groundwater transport mechanisms (advection, dispersion and diffusion) but also by geological structures (e.g., fissures, faults and bedding planes), gravity and DNAPL properties. The heterogeneous nature of the subsurface and the physical characteristics of DNAPL’s, make migration unpredictable and difficult to model. For instance, relatively small spills may possess adequate ‘driving force’ to migrate downward through permeable drift deposits into fractured and well-bedded sandstone aquifers. DNAPL migration into soils is controlled substantially by the nature of the release, the DNAPL density, interfacial tension, and viscosity and porous media capillary properties. DNAPL’s will tend to sink below the water table to reach layers of low permeability (e.g., clay lenses, aquitards, and bedrock) where they may be trapped or sit in ‘pools’ as shown in figure (2-1).

While migrating in the soil system, DNAPL chemicals may exist either as pure substance or as solubilized contaminant of its dissolved components. They migrate, in the soil, as volatiles in soil gas, dissolved in ground water, and as a mobile soluble phase (Cohen et al, 1993). The aqueous-phase contaminants dissolved from the DNAPL may be adsorbed to the soil grains and are difficult to recover, even with the use of chemical methods.

Normally, the invasion of DNAPL into the subsurface soil favors its migration within the higher-permeability zones. However, several scenarios are possible where vertical migration of DNAPL into zones of lower permeability could take place. This migration into the lower-permeability layers can be one of two types: a) DNAPL migration into lower-permeability layers, and b) diffusion of dissolved-phase constituents into lower-permeability layers. In the first type, the DNAPL may migrate into the low-permeability layer or zone when the height of the DNAPL column on the top of this layer exceeds the non-wetting phase entry pressure, assuming that the DNAPL is the non-wetting phase. This situation is likely if the permeabilities of both layers are relatively high, and the contrast between the different layers is relatively low (e.g., less than a factor of two or three), which occurs frequently in natural media. Permeability contrasts of this type are termed low to medium for purposes of this study (these terms will be explicitly defined later in this chapter). DNAPL may also enter lower-permeability zones, even clay, through vertical cracks (Kueper et al, 1991).

Chapter 2: Background

Figure (2-1): DNAPL spill in a stratified subsurface leads to the development

of perched and deep DNAPL reservoirs. DNAPL or its dissolved constituents can invade the low permeability layers depending on the site conditions (Newell and Ross, 1992).

DNAPL constituents enter lower-permeability strata by diffusion of dissolved-phase chemicals. This can occur for low or high permeability contrast categories. Moreover, dissolved DNAPL constituents can invade the lower-permeability zones and sorb onto the matrix surface transforming its wettability to DNAPL-wet (Cohen et al., 1993). This further promotes the migration of DNAPL and dissolved constituents into these zones. The use of surfactants to enhance the flushing out of DNAPL can have the adverse effect of breaking up the continuous DNAPL phase and promoting vertical migration into lower-permeability layers (Oostrom et al., 1999; Boving and McCray, 2000).

2.3.2 Transport of miscible species

There are three basic physical mechanisms by which miscible pollutants are transported into the soil environment: advection, diffusion, and dispersion. In what follows the discussion is limited to one dimensional case.

2.3.2.1 Steady advection

Advection is the process by which solutes are transported simultaneously, along with the flowing fluid or solvent (typically water), in response to gradient in total hydraulic head. Thus when dealing with contaminants in groundwater the mass of contaminant transported by advection per unit area per unit time (i.e. mass flux),

J

_advection, is given by:

advection

Chapter 2: Background

where is the soil porosity; u the groundwater velocity (interstitial velocity); the Darcy velocity; the concentration of contaminant at the point and time of interest.

n

v c

2.3.2.2 Diffusion

While advection is associated with the bulk macroscopic ground water movement, diffusion is a molecular-based phenomenon. Diffusion is the process in which a chemical or chemical species migrates in response to a gradient in its concentration or in the chemical potential of the solute.

The fundamental equation for diffusion in soil is Fick’s first law, which for one-dimensional transport can be written as:

diffusion

c

J

D

x

∂

= −

∂

(2-2)

where

J

_diffusion is the diffusion mass flux,

D

is the diffusion coefficient, c

∂ ∂x

e

the concentration gradient. There are two soil properties that affect the diffusion coefficient in saturated soils; namely the effective porosity, , and

tortuosity, e

n

τ

. Thus, the free solution diffusion coefficient, , and the porous media (bulk) diffusion coefficient, have the following correlation: o

D

pm

D

pm e e o T o

D

=

n

τ

D

=

W D

(2-3)

where is the complex tortuosity factor that was defined by Rowe et al. (1995). Thus, the diffusive mass flux in soil is:

T W diffusion e e o T o

c

c

J

n

D

W D

x

x

τ

∂

∂

= −

= −

∂

∂

(2-4)

From mass conservation arguments for transport of non-reactive solutes in soil, we get the following equation:

2 2 T o

c

c

n

W D

t

x

∂

_{= −}

∂

∂

∂

(2-5)

Equation (2-5) is known as Fick’s second law and it describes the temporal and spatial variation of diffusing solute in a porous medium.

2.3.2.3 Dispersion

The dispersion mechanism is associated with bulk fluid movement in the porous medium. Fluid particles that are at one time close together tend to

Chapter 2: Background

move apart or spread. The dispersion mass flux, , is usually modeled as Fickian-type process: dispersion

J

dispersion d

c

J

D

x

∂

= −

∂

(2-6)

where is the mechanical dispersion coefficient which is assumed to be a function of seepage velocity and longitudinal dispersivity and given by: d

D

d l

D

=

n

α

u

β (2-7)

where

α

_l is the longitudinal dispersivity in the transport direction,

β

is a constant ranging from 1.0 to 2.0 (Freeze and Cherry, 1979).

2.3.2.4 Combined advection-diffusion

From equations (2-1) through (2-7), the total mass flux, , is given by:

J

advection diffusion dispersion

J

=

J

+

J

+

J

(2-8) hd

c

J

nu c n D

x

∂

=

−

∂

(2-9)

where

D

_hd is the hydrodynamic dispersion coefficient which is given by:

hd o l

D

=

τ

D

+

α

u

β (2-10)

Thus, from mass conservation, the one-dimensional form of the advection-diffusion equation for non-reactive dissolved constituents in saturated, homogeneous, isotropic materials is:

2 2 hd

c

c

D

u

t

x

∂

∂

∂

=

−

∂

∂

∂

c

x

(2-11)

2.3.2.5 Adsorption isotherms

adsorption is a mechanism by which the contaminant constituents are removed from solution. These processes may include cation exchange, precipitation or organic interaction with solid organic matter in the soil/barrier. If is the mass removed from the solution per unit mass of solid, the models for adsorption can be linear or nonlinear. Here we will consider only the

Chapter 2: Background

nonlinear isotherms since they represent better the sorption in the experiments done in this work:

Nonlinear Langmuir isotherm:

1

m s s

S b c

S

b c

=

+

(2-12)

where is the solid-phase concentration corresponding to all available sorption sites being occupied (m ),

S

c→ ∞

b

_s is a parameter representing the rate of sorption, see figure (2-2). This isotherm represents the case when the system has a maximum adsorption capacity that can be reached.

Nonlinear Freundlich isotherm:

f

N f

S

=

K c

(2-13)

where and are Freundlich isotherm parameters, see figure (2-3). This isotherm represents the case when the system has no maximum adsorption capacity.

f

K

N

_f

For nonlinear adsorption isotherm, secant lines can be used to estimate the partitioning coefficient, , in order to be in the conservative side. The secant lines were based on the following semi-analytical formulation for

(Davidson et al. 1976):

( )

d s

K c

( )

d s

K c

0 ( ) 0 o o N Nac Na c f o Na d s f o c o o S S _{K c} S K c K c c c c 1 N = − − ∆ = = = = ∆ − (2-14)

where the initial concentration of Na

c

_o + _{before exposure of the salt solution to}

the gel.

Figure 2-2. Langmuir isotherm Figure 2-3. Freundlich isotherm

Chapter 2: Background

2.4 Soil and groundwater remediation techniques

There are three active approaches for the prevention or control of subsurface contaminant migration that will immobilize the contaminant and/or render its impact to the environment acceptable. These approaches are: (1) cleanup, destruction, or degradation of the contaminants by implementing some form of remediation technology (e.g. pump-and-treat), (2) containment of the contaminants, and (3) stabilization of the contaminants. In this research the focus will be primarily on the first two approaches. The pump and treat technique and contaminant containment using barriers will be considered.

2.4.1 Pump and Treat

Until the very recent past, almost all groundwater cleanup systems installed involved variations of the technology called “pump and treat” (Suthersan 1997). Pump and treat systems operate by pumping groundwater to the surface, removing the contaminants, and then either recharging the treated water back into the ground or discharging it to a surface water body. However, pumping the contaminated water from the aquifer does not guarantee that all of the contaminants have been removed. Contaminant removal is limited by the behavior of contaminants in the subsurface (a function of contaminant characteristics), site geology and hydrogeology, and extraction system design. Pump and treat systems can be designed to meet two very different objectives: (1) containment, to prevent the contamination from spreading, and (2) restoration, to remove the contaminant mass. In pump and treat systems designed for containment, the extraction rate is generally the minimum rate sufficient to prevent enlargement of contaminated zone. In systems designed for restoration, the pumping rate is generally much larger than that required for containment so that clean water will flush through the contaminated zone at an expedited rate. In all other ways, the two types of systems are identical (Suthersan 1997). In this study, the focus is on the enhancement of the restoration system, in particular the removal of DNAPL or its dissolved constituents trapped in lower permeability layers of layered soils. A typical velocity profile, while pumping the contaminant out via horizontal flushing, is given in figure (2-4).

Chapter 2: Background

Figure (2-4): Expected velocity profile during pump-and-treat due to

heterogeneities in hydraulic conductivity. This velocity profile results in removing the contaminant by mainly advection in high permeability layers and by diffusion in low permeability layers (after Schmelling et al. 1992).

This profile shows higher velocities (capillary number) in the higher-permeability layers as well as lower velocities (capillary number) in the lower-permeability layers. Consequently, the extraction efficiency (contaminant / water ratio) is usually higher in higher-permeability layers than in lower-permeability ones, especially at the beginning of the pumping-out process. Accordingly, diffusion of the soluble DNAPL constituents from low to high permeability layers is a primary mechanism resulting in the so-called tailing and rebound problems (Keely, 1989, U.S. EPA, 1996).

Tailing refers to the progressively slower rate of decline in dissolved contaminant concentration with continued operation of a pump-and-treat system. Rebound is the fairly rapid increase in contaminant concentration that can occur after pumping has been discontinued. This increase may be followed by stabilization of the contaminant concentration at a somewhat lower level (see figure (2-5))

Chapter 2: Background

Figure (2-5): relative concentration of contaminant during pumping on and off

periods showing the tailing and rebound phenomena (U.S.EPA, 1996).

2.4.1.1 Disadvantage of the pump-and-treat technique

A serious disadvantage of the pump-and-treat technique is the production of substantial amounts of wastewater (i.e. the contaminated water that needs to be treated) during the clean-up operation. Most DNAPL chemicals are sparingly soluble and pumped water does not efficiently contact the DNAPL (Kevin et al., 2000), limiting the dissolution of DNAPL components into the aqueous phase. This problem is considerably exacerbated in layered soils with permeability contrast. Thus, large amounts of water must be extracted to remove a significant contaminant mass, which considerably increases the overall costs of the remediation process. In view of water scarcity in many parts of the world, the extraction of large amounts of groundwater to dispose of as secondary wastewater is undesirable. Moreover, the substantial amount of groundwater withdrawal may cause soil settlement, thereby adversely affecting the surrounding buildings.

2.4.1.2 Proposed enhancement for pump-and-treat

Considerable efforts have been devoted to the investigation of the role of different parameters influencing the pumping efficiency resulting in several enhancement techniques. One technique consists of setting the screen over the DNAPL layer only (Schmidtke et al., 1992). Another technique uses the upwelling of DNAPL (Villaume et al., 1983). A third technique combines water flooding with well bore vacuum (Connor et al., 1989). A fourth consists of installing DNAPL-wet filters that are permeable only to DNAPL in the pumping system (Ferry et al., 1986). A fifth is pulsed pumping, i.e., alternating pumping out and resting phases, (Bartow et al, 1995). These techniques have not been proven to significantly improve the efficiency of the pump-and-treat method in layered subsurface systems.

Chapter 2: Background

In this thesis, it is proposed to inject mixtures (BLEND) of equal proportions of cationic and anionic polyacrylamides (hydrophilic polymers) to improve the pump-and-treat efficiency in heterogeneous (layered) subsurface systems, after initial DNAPL removal from higher-permeability layers. The polymer treatment will modify the flow velocities in the different layers, while pumping out, in a way that favors contaminant removal from lower-permeability layers. The process is envisaged as follows; a limited amount of polymer solution is injected into the whole zone of interest. The polymer penetrates deeply into the higher-permeability zones that contain mostly water, and only slightly into the lower-permeability layers where the DNAPL (or its dissolved constituents) are trapped as shown in figure (2-6). On recommencing with pumping, the polymer reduces substantially the flow of water through the higher-permeability zones increasing the flow of water through the lower-permeability zones. Thus, the pumped water will more efficiently mobilize the DNAPL phase and will also increase the DNAPL-water contact time for dissolution. The technique is most appropriate for removing DNAPL or dissolved components from the low-permeability zones after initial DNAPL removal from the high-permeability zones.

DNAPL Polymer injection Pumping out after polymer injection DNAPL

Figure (2-6): Polymer solution penetration in layered soil and pumping out

contaminant after polymer injection.

To understand the underlying mechanism for this process, it is necessary to study the transport and sorption of polymers in layered soils. According to previous studies (Zitha et al., 1998), a flow-induced polymer retention called bridging adsorption can take place. This flow-induced adsorption mechanism is expected to reduce the penetration of the polymer in low-permeability layers containing the DNAPL while enhancing penetration of the polymer in the high-permeability layers. This will consequently divert the

Chapter 2: Background

polymer solution from the lower to higher permeability layers during injection thus reducing even more the permeability of the higher- permeability layers and avoiding reduction in the lower permeability ones.

Given that the polymer solution will penetrate the lower permeability layers, as well, but to a smaller extent, there will be a need to unplug the first part of those layers before subsequent pumping out. Different methods could be used for the unplugging: a) widening the well bore hole diameter, after polymer injection, to get rid of the plugged part of the lower-permeability layers b) heating up the vicinity of near well bore formation using radiation heat technology.

Polymers have been used for the enhancement of oil recovery as water blocking agent (Sorbie, 1991 and Lake, 1989). They have also been used in reducing erosion, sealing of cultivated soil, improving soil stability and clay flocculation (Pefferkorn 1999, Ben-Hur et al., 1992). Additionally, they are applied to eliminate residual concentration of inorganic salts in drinking water by floculation (Elfarissi et al., 1998). Polymer solutions were also used in NAPL recovery by sweep (Giese and Powers, 2002, Martel, 1998). They can therefore be considered environmentally acceptable and can be used in geoenivronmental applications (Osada et al., 2001).

2.4.2 Contaminant containment

In some situations, containment may offer the needed flexibility in the allocation of limited resources and in the choice of alternative, and perhaps more cost-effective remedial measures. Containment also offers the potential to wait for the development of promising cost-effective innovative technologies that are near the application stage but not yet proven or available. The contaminants that need to be contained can be present in the solid, liquid, or gaseous forms. In soil, liquid and gaseous-phase contaminants are usually the focus of control efforts because of their relatively high mobility.

Containment of the contaminant source zone may involve both active and passive control measures. Active control involves manipulation of hydraulic gradients to control the direction of groundwater flow while passive control involves the installation of physical barriers. Subsurface barriers have been used for decades in the construction industry in order to reduce groundwater seepage under, through, or into underground structures or excavations (Xanthakos, 1994). More recently, barrier systems have been employed for contaminant migration control or as an integral component of a hazardous waste site remediation effort (Spooner et al., 1984).

Current containment techniques are largely based on two alternatives: a) costly “brute-force” approaches involving trenching, cut-off curtains and slurry walls and b) cheap clay barriers, which have some disadvantages (Rowe et al 1995) as will be explained later in this chapter.

Containment systems from configuration point of view can be divided as follows; 1) grouted barriers (vertical, horizontal, slant or multidirectional),

Chapter 2: Background

2) landfills, 3) slurry walls (vertical only), 4) drainage trenches and wells, 5) surface impoundments and composite systems. In what follows the first two configurations of the containment systems will be considered in more detail.

2.4.2.1 Grouted barriers

Grout barriers are formed by pumping pore-filling materials into the soil, thereby reducing the rate at which fluids can subsequently travel through the soil. Soil grouts can be divided into two categories: a) particulate grouts and b) chemical grouts. Particulate grouts are composed of portland cement, bentonite, fly ash and/or clay and water, while the chemical grouts are composed of chemical base, catalyst, and water or solvent (Rumer and Ryan, 1995). Particulate or suspension grouts are restricted to coarse-grained sand deposits and are not suitable for sites requiring a deep penetration of the grout. Chemical grouts can penetrate deeper and enable a better control of the material properties such as viscosity and setting time (Bodocsi et al., 1991). Due to this flexibility, injection of chemical grouts can be used in areas where the accessibility required for installation of the other types of barriers is missing (Rumer et al., 1995).

2.4.2.2 Landfills and liners

Land disposal has always been and continues to be the most common form of handling and disposing of various types of waste. Land disposal can occur in the following forms: shallow burial vaults in soil (more commonly known as landfills), deep chambers in rock, deep well injection, surface impoundments or composting. In this thesis we consider primarily the municipal solid waste (MSW) landfills, the most common type.

Landfills are engineered areas where waste is placed into the land with acceptable very low risk. A landfill has a carefully designed and constructed envelope that encapsulates the waste and prevents escape of leachate into the environment. The envelope consists basically of a top cap (or cover) and bottom liner. Each of these two main components in turn comprises a system of barrier and drainage layers as shown in figures (2-7).

Chapter 2: Background

Figure (2-7): Schematic diagram of Municipal Solid Waste landfill

containment system (after Qian et al., 2002).

The liner system is the single most important element of a landfill and consists of a compacted clay layer, geomembrane, geosynthetic clay layer, and/or a combination of these. The liner system is placed on the bottom and lateral sides of a landfill. It acts as a barrier against the advective and diffusive transport of leachate solutes. Its main purpose is to isolate the solid waste and prevent contamination of the surrounding soil and groundwater.

Proper functioning of a liner system is critical to containment effectiveness of a landfill. Considerable attention has been devoted to the development and design of different liner systems with diverse materials. Early liners consisted primarily of a single liner composed of a clay or synthetic polymeric membrane. During the past few decades the trend has been to use composite liner system comprising both clay and synthetic geomembranes together with interspersed drainage layers.

Liners types

a) Compacted clay liners

Compacted clay liners are widely used to line landfills and waste impoundments, to cap new waste disposal units, and to close old waste disposal sites. A well-designed compacted clay liner must have a low permeability to prevent or minimize leachate leakage, enough compatibility with leachate to avoid deterioration during the expected life time, adequate shear strength for stability, and minimal shrinkage potential to prevent desiccation cracking.

b) Geomembranes

Geomembranes, known as a flexible membrane liners, are relatively thin sheets of flexible thermoplast or thermoset polymeric materials. The

Chapter 2: Background

primary function of a geomembrane in landfill engineering is as a liquid and/or vapor barrier. They have shown to reduce drastically the leakage rates in landfill liners but they lack the contaminant attenuation capacity of clays. In addition, the use of geomembrane with an underlying compacted clay liner provides the optimum liner system. This approach is referred to as a composite liner system. These benefits notwithstanding, the introduction of the geomembrane complicates the situation from both a design and a construction viewpoint.

c) Geosynthetic clay liners

Geosynthetic clay liners are thin hydraulic barriers containing approximately 5 kg/m2 _{of bentonite, sandwiched between two geotextiles or}

attached with or adhesive to a geomembrane. They are manufactured in continuous sheets and are installed by unrolling and overlapping the edges and ends of the panels, which are self-sealed, when bentonite hydrates. Geosynthetics provide increased crack resistance under deferential settlement and cycles of wetting/ drying and freezing and thawing.

2.4.2.3 Disadvantages of current landfill liners and chemical grouted

barriers

Composite liners consisting of a geomembrane overlying compacted clay have been widely accepted as part of barrier systems for modern MSW disposal landfills. However, this system suffers from the following drawbacks. Many borrow pits used for construction of clayey barriers demonstrate weathering changes. Thus the mineralogy of the clayey soil barrier may vary significantly (Rowe et al., 1995). Furthermore, ions such as potassium ions (K+_{) fixation by “Vermiculite” causes a significant (about 28%) decrease in}

crystal volume, contract the soil peds, open further the voids of fractures and thus increase the hydraulic conductivity (Rowe et al., 1995). Moreover, due to the fact that natural clays have net negative charge they can adsorb and retard only the positively charged solutes but not the negatively charged solutes. With geomembrane layers, leakage can happen through punctures during construction or operation. This leakage can affect the barrier efficiency and might lead to its malfunction. An assessment of leakage through geomembrane holes, based on combination of theory and analysis of geomembrane case histories has been provided (Giroud et al., 1989) and extended by Rowe (1998).

For chemical grouted barriers, there is currently a lack of barriers made of environmentally friendly material that can limit both lateral and downward movement of contaminants.

For both landfill liners and chemical grouted barriers, there is a need for a construction material that has high adsorption capacity, shows compatibility with the contaminants, and sufficient ductility to accommodate the expected deformations during construction and operation, limits the contaminant diffusive flux, and has acceptable swelling behavior.

Chapter 2: Background

2.4.2.4 Proposed solution

In order to overcome these disadvantages, we propose the use of environmentaly friendly polymer gel mixed with sand as a complementary layer in a composite liner system and the use of gel to form grouted barriers. Since the most important function of containment barriers is to limit the contaminant migration flux out of the contaminated site, attenuating materials, such as polymer gels, can be used to improve the efficiency of the barriers. These materials increase the liner sorption capacity resulting in increasing solute breakthrough time (Evans et al., 1991). Unlike natural clay, polymer gels can be positively charged which make them able to attenuate and retard the anion migration through them. Polymer gels possess high flexbility in terms of chemical composition, charge type and amount of cross-linker added to form the gel etc. This flexbility enables them to fit individual site condition and have better compatibility with the specific contaminant. Polymer gel barriers have viscoelastic properties that enable them to accommodate the expected deformations during construction and operation. Polymer solution viscosity, before gelling, is low enough to make it easy for the injection into soil layers. Gel-sand strength, swelling behaviour and swelling pressure accomodate expected insitu stresses. Finally, polymer solution gelling time can be easily controlled to suit the site conditions.

Chapter 3

Physical Chemistry of Charged Polymers and Gels

A brief review of the physical chemistry of charged polymers and gels is

presented in this chapter, including rheology, adsorption on surfaces,

swelling and gelling behavior.

3.1 Introduction

Linear flexible polymers are long chains obtained by successive covalent bonding of small units called monomers (Sorbie, 1991). Many of the unusual and useful properties of polymers arise from the contiguity of segments joined together to form long chains. Several great scientists pioneered work on their properties: Debye, Kuhn, Kramers, Flory, de Gennes, and others. They constructed the basic ideas; those concerning static properties are summarized by Flory (1971), and those concerning dynamics in various reviews (Ferry, 1970, Stockmayer, 1976).

These flexible chains can be neutral or carrying charges (positive or negative) and in that case they are called polyelectrolytes. The term “polyelectrolyte” is employed for polymer systems consisting of a “macroion” i.e. a macromolecule carrying covalently bound anionic or cationic groups, and low-molecular weight “counterions” (counterions being small ions with a charge sign opposite to that of the molecular charge, which must always be present in equivalent amounts, as imposed by the condition of electroneutrality).

Properties of polyelectrolytes have been studied for more than 60 years, but several of them have not yet found a satisfactory theoretical explanation. In many cases a qualitative understanding is available but a quantitative interpretation is still lacking.

In the recent years the study of polyelectrolytes has seen a revival stimulated by the use of newly available experimental techniques such as NMR and neutron scattering and the introduction of new theoretical concepts such as the new scaling concepts (Mandel, 1993).

Since the study of the properties of any material must begin with the development of an understanding of its properties in the bulk state, in the following we start with the polymer solution properties. In the section for polymer solution properties, scaling theory and rheology of polyelectrolytes are reviewed since they are going to be used in polymer solution and gel characterization in chapters 4 and 6. Mechanical models for polymer molecules that can be used to derive the associated configuration and rheological behavior are discussed briefly in this chapter. Then, adsorption of polymers on planar surfaces and in porous media is discussed since it is going to be used as basis for the theoretical development and for the experimental interpretation of

Chapter 3: Physical chemistry of charged polymers and gels

polymer transport and sorption in chapter 4 and 5, respectively. Moreover, gel cross-linking process, definitions for polymer gel gelling point and swelling kinetics are mentioned in this chapter since they help understanding some of the experimental results in chapter 6.

3.2 Charged polymer solutions

In contrast to the well-established state of the theory of uncharged polymers in solution, the understanding of the behavior of polyelectrolytes is not well-developed (Dautzenberg et al, 1994). This lack of understanding has various reasons. (1) experiments are hampered by specific problems (e.g. aggregation phenomena, extreme purity conditions), so experiments often have observed interesting phenomena, but have not been able to characterize the chain structure well enough. (2) Theoretical, difficulties with the treatment of the long-ranged Coulomb interaction have hindered progress. (3) Simulation studies on polyelectrolytes are expensive in CPU time consumption.

3.2.1 The uniqueness of charged polymers properties

Solutions of polyelectrolytes exhibit a behavior that may differ considerably from that of either uncharged macromolecules or low-molar-mass electrolytes. The origin lies in the combination of properties derived from those long-chain molecules with properties that result from charge interactions. This combination is not a simple superposition, as there is a mutual influence of the characteristics of both types of properties. There are short and long-range interactions along the chain. The short-range interaction contributes to the local stiffness of the chain (i.e. the persistence length in the wormlike model of a chain molecule), and the long-range interaction to the excluded volume effects (i.e. the volume that is not accessible by the monomers due to monomer-monomer and monomer-monomer-solvent long-range interactions). In all cases increasing the concentrations of added salts may moderate the strength of the electrostatic interactions, which results in a screening effect by the small ions. These interactions strongly affect not only the average dimensions of the polyelectrolyte chain but also the dynamics of the chains (Mandel, 1993). Actually, it is the influence of charge interactions on the conformational statistics of the chain, which is directly responsible for some of the characteristic properties of polyelectrolytes.

In solution, the chains behave either like individual statistical coils (i.e., dilute concentration regime) or like a transient network of entangled chains (i.e., semi-dilute regime). There is an overlap concentration, C , at which the solution concentration regime changes from dilute to semi-dilute.

*

3.2.2 Mechanical models for polymer molecules

Since flexible polymers in solution can take a large number of different configurations, their shape and size can be understood and described only statistically. Several mechanical models for polymer molecules have been

Chapter 3: Physical chemistry of charged polymers and gels

introduced (Bird et al. 1987) such as: a) Chain models with fixed bond lengths and bond angles: Flory in 1969 pointed out that bond lengths and angles between adjacent bonds are restricted to quite narrow ranges. Thus, in developing a mechanical model of a polymer molecule the bond length and the angle between bonds were constant and the chain is represented as a set of mass points (beads) joined by massless rods. b) Freely jointed bead-rod chain model: in this model the beads do not represent the atoms of the polymer chain backbone, but some portion of the polymer chain. This model possesses a number of features that are characteristic of polymer molecules such as a large number of internal degrees of freedom and a constant contour length. It can be stretched, oriented, and deformed. c) Freely jointed bead-spring models: in this model a portion of the chain containing several hundred backbone atoms is replaced by a “spring” and the atoms mass is concentrated into beads. This model is simpler than the bead-rod model since it contains no internal constraints. This model is called as the Rouse (1953) or Rouse-Zimm (1956) model and is shown schematically in figure (3-1). Each bead is presumed to experience a drag force as it moves through the solvent and the springs are Hookean.

Figure (3-1): The freely jointed bead-spring chain model formed from

beads and

N 1

N− springs (see Bird et al. 1987).

d) The earlier elastic Dumbbell model (Hermans 1943) that has the same idea (i.e. springs and beads) as the Rouse model but with two beads only and a different expression for the spring forces.

These models are used to derive configurations and associated rheological properties. Expressions for static (e.g. chain size) and dynamic

Chapter 3: Physical chemistry of charged polymers and gels

properties (e.g. intrinsic viscosity and relaxation time) can be derived. For the chain size, the effective hydrodynamic diameter

R

is as follows:

2 1/

;

(

_B

)

R b N

=

b

=

b l

3

(3-1) where is the number of monomers, is the monomer length (i.e. mean bond length) and l is the Bjerrum length. For the polymer solution the intrinsic viscosity,

[

N b

B

]

η

, using the Rouse-Zimm (1956) model, is given by the Flory-Fox equation: 3

[ ]

8

_w

R

M

η

= Φ

(3-2)

where

Φ

is a universal constant (in cgs units takes the value 2.1 ± 0.2 x 1021

dl/mol.cm3_{) and} w

M

is the weight averaged molecular weight. The intrinsic viscosity is the rate of change of polymer viscosity with concentration, at zero concentration. It is a characteristic parameter to identify the capability of a polymer molecule to increase the solvent viscosity. Rouse in 1953 derived an expression for the relaxation time,

τ

_f , defined as the time for the fluid to respond to the changing flow field in the porous medium and got the following:

[ ]

_{s w} f g

M

R T

η η

τ

=

_(3-3)

where

η

_s is the solvent viscosity,

R

_gthe ideal gas constant and is the absolute temperature.

T

3.2.3 Scaling theory of charged polymer solutions

Scaling theory results are used as a guide to characterize various

solution regimes depending on the polymer concentration.

Scaling relations were initially developed for systems near critical points. Many properties in the close neighborhood of the critical temperature

can be expressed as power laws of

c

T

ε

≡

(

T T

−

_c

) /

T

_c with exponents that are

independent of the exact nature of the system considered but determined only by the property considered. These universal critical point exponents are related to the long-range correlations that appear in these systems near the critical points. A correlation length characterizes these systems,

ξ

, which is itself related to the relative deviation from the critical point by:

0

,

)

(

→

≈

_ε

−

_ε

ξ

β (3-4)

Chapter 3: Physical chemistry of charged polymers and gels

where

β

is the universal critical point exponent.

De Gennes (1979) pointed out that at an infinitely dilute solution, the position of the monomeric unit of the macromolecular coil is also correlated over distances of the order of the average dimensions of the coil. Therefore, in the limit of infinitely long chains, long range correlations must also exist for such macromolecules just as in systems near critical points and scaling relations independent of the chain structural details should hold as well. He established, for a flexible macromolecule, the relation between the average square radius of gyration,

R

_gy, and the number of monomeric units, , at infinite dilution in a good solvent and in the limit

N

∞

→

N

as follows: gy R ≈bNβ (3-5)

This average radius of gyration,

R

_gy, is the root mean square distance of the elements of the chain from its center of gravity. In the infinitely dilute solution

R

_gy is thus the analog of the correlation length,

ξ

.

The correlation length must depend on the number of monomers, , and the concentration, C. The scaling of the correlation length has been studied for dilute and semi-dilute concentrations categories, but only for two extreme cases; a) case of no salt added, b) case of abundant amount of added salt (Dobrynin et al, 1995).

N

In this thesis, the interest is in the case of semi-dilute concentration with no salt added where the polyelectrolyte chain is as shown schematically in figure (3-2).

R_g

Figure (3-2): polyelectrolyte chain in semidilute salt-free solution. The chain

is a random walk of correlation blobs, each of which is an extended configuration of electrostatic blobs. (after Dobrynin et al, 1995).

D

is the electrostatic blob size inside which the conformation of macromolecules is almost unperturbed by the quality of the solvent for the neutral polymer.