Layer-by-layer Adsorption: Factors Affecting the Choice of Substrates and Polymers

Iuliia S Elizarova*1 and Paul F Luckham2

1 Department of Materials, Imperial College London, Prince Consort Road, Royal School of Mines, London SW7 2BP, UK

2Department of Chemical Engineering and Chemical Technology, Imperial College London, Prince Consort Road, London SW7 2AZ,

UK

Highlights

Materials and mechanisms of the electrostatic layer-by-layer procedure are examined

The electrostatic layer-by-layer procedure is a process consisting of distinct stages

Each stage (adsorption of the first layer, second layer, multi-layering) is specific

Understanding of the underlying mechanisms serves as a guide to the technique

Abstract

The electrostatic layer-by-layer technique for fabrication of multi-layered structures of various sizes and

shapes using flat and colloidal templates coupled with polyelectrolyte layer-forming materials has attracted

significant interest amongst both academic and industrial researchers due to its versatility and relative

simplicity of the procedures involved in its execution. Fabrication of the multi-layered structures using the

electrostatic layer-by-layer method involves several distinct stages each of which holds great importance

when considering the production of a high-quality product. These stages include selection of materials (both

template and a pair of construction polyelectrolytes), adsorption of the first polyelectrolyte layer onto the

selected templates, formation of the second layer comprised of the oppositely charged polyelectrolyte and

guided by the interactions between the two chosen polyelectrolytes, and multi-layering, where a selected

number of layers are produced, and which is conditioned by both intrinsic properties of the involved

construction materials and external fabrication conditions such as temperature, pH and ionic strength. The

current review summarises the most important aspects of each stage mentioned above and gives examples of

the materials suitable for utilization of the technique and describes the underlying physics involved.

Introduction

Layer-by-layer assembly is a highly versatile, reproducible, efficient and simple technique for the fabrication

of multi-layered films with easily controlled and tuneable properties (thickness, composition, structure,

functions) on and around the selected substrate of any type and shape. This technique can be executed through

a variety of approaches based on different mechanisms, including electrostatic interactions, hydrophobic

interactions, hydrogen bonding, charge-transfer interactions, biologically specific interactions, coordination

chemistry, covalent bonding, stereocomplexation and surface sol-gel process [1].

Electrostatically-driven layer-by-layer was the original multi-layering procedure introduced by Iler [2] in the

very first paper regarding the subject in 1966. The study described a solution-based deposition of alternating

layers of negatively charged silica and positively charged boehmite particles onto a flat glass substrate. The

next study concerning this technique was reported by Decher 25 years later, in 1991, and described layer-by-

layer deposition of oppositely charged molecules (polyelectrolytes) onto charged flat substrates [3, 4]. Among

others, the electrostatic layer-by-layer technique has been used extensively in research ever since the latter

study was published (Figure 1), resulting in the development of the well-established conventional layer-by-

layer procedure.

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Figure 1 – Growth of the Number of the Layer-by-layer Related Publications (Web of Science Search 2018).

This procedure involves immersing (for flat surfaces) or mixing (for colloidal templates) the substrate material

with a dilute polyelectrolyte solution, waiting for polyelectrolyte to adsorb, washing the freshly-layered

substrate(s) to remove excess polyelectrolyte and repeating these steps for each following layer to be

fabricated. A schematic of the process is presented in Figure 2.

Figure 2 – Conventional electrostatic layer-by-layer assembly on (a) flat substrate and (b) colloidal substrates

(illustration adapted from [5] with permission of The Royal Society of Chemistry).

Electrostatic interactions, which allow for such consecutive deposition of charged materials, is by far the most

widely-used and studied mechanism within the layer-by-layer research area and is considered to be one of the

most important types of interaction in processes when both participating materials (substrate/layering

material) are charged [1]. The existing wide usage and the versatility of the technique facilitates its further

development and increasingly attracts new research interest; it is, therefore, necessary to have an in-depth

discussion of the theory behind the relevant aspects of the procedure, such as the choice of materials and their

properties, as well as the mechanisms involved in the multi-layering process. The outcomes of such a

discussion are presented in the current review and can be used as a starting manual for the goal-based

implementation of the technique. This review starts with a description of desired properties of the construction

materials – templates (flat surfaces and colloidal substrates such as particles, emulsions and liposomes) and

polyelectrolytes which are relevant to the layer-by-layer procedure. It continues with a detailed examination of

the underlying mechanisms and influential factors behind the electrostatic layer-by-layer assembly, including

adsorption of polyelectrolyte onto a solid surface, polyelectrolyte-polyelectrolyte interactions and,

consecutively, polyelectrolyte multi-layering.

Current review focuses on the fundamentals of the layer-by-layer procedure and does not describe the

techniques and methods of its implementation. Such methods and techniques can be found in the extensive

review by Guzmán et al [6].

1. Electrostatic layer-by-layer construction materials

Two functional components involved in the electrostatic layer-by-layer assembly are a charged template

material and two oppositely charged coating materials (polyelectrolytes).

1.1 Template materials

Templates of any shape and size are generally suitable for the electrostatic layer-by-layer process with the

only requirement of having a surface charge, therefore, a wide range of materials can be used as a core

structure for fabrication of multi-layers, including flat substrates, micro- and nano-scale soft and hard

colloidal templates.

1.1.1 Flat substrates

The use of flat substrates as “foundations” for the film build-up in multi-layering experiments was first

described in several of the original electrostatic layer-by-layer assembly studies by Decher [3, 4]. A planar

substrate geometry allows for the creation of flat polymer films with tunable thickness the area of which is

only limited by the fabrication methods (for example, the size of the polyelectrolyte solution container that is

used in the conventional dipping layer-by-layer procedure). Depending on the morphology of the selected

substrate, the resulting films can be of various surface geometries – smooth, wavy, porous or even patterned,

therefore, the term “planar” is used very generally and applies to any substrate that produces, technically, a

three-dimensional structure, but with low height-to-width aspect ratio.

The choice of material that can be used as a flat substrate for the layer-by-layer assembly is mainly guided by

application considerations which can be classified into two large groups. The first group requires so-called

“free-standing” multi-layered films that must be separated from substrates before being used for different

purposes. The second group, in contrast, utilises the layer-by-layer procedure to coat the substrate of interest

with a goal of providing various functionalities.

Free-standing polyelectrolyte multi-layered films can be obtained using two approaches. The first approach

utilises sacrificial substrates such as cellulose acetate [7, 8, 9] or polystyrene [10] that are deposited onto

various surfaces (for example, gold-coated glass) to act as a dissolvable precursor. Once the desired number of

layers is achieved, the multi-layered substrate is immersed in an appropriate solvent that only affects the

precursor and not the polyelectrolyte layers (for example, cellulose acetate is most commonly dissolved using

acetone, polystyrene – using tetrahydrofuran). The second approach does not rely on any anchor layer and

utilises properties of the substrate itself. Readily detachable polyelectrolyte films can be assembled using

hydrophilic surfaces. For example, one study reported using hydrophilic silicone as a base for the layer-by-

layer film construction in which the resulting film can be detached by simply immersing it in water [11]. This

preparation method does not require any additional film treatment steps to ensure its stability. Other studies

describe fabrication of films based on hydrophobic substrates such as propylene [12, 13] and Teflon (pre-

coated with polyethylene glycol and poly(acrylic acid)) [12, 14]; such films can be easily detached from a

substrate when dried, however, post-layer-by-layer cross-linking is required to keep the film stable and to

detach it without introducing any defects [11].

Fabrication of polyelectrolyte and composite colloid coatings using the layer-by-layer procedure has found its

applications in biomedicine, sensoring, optics, microelectronics and other industries. Layer-by-layer films can

provide further functionality in addition to the properties of the material to be coated by utilising intrinsic

properties of polyelectrolytes themselves, or by introducing additional agents into films. The material in need

of a multi-layered coating in such cases itself acts as a substrate. A good variety of examples can be found in

the area of biomaterials. One study concerning the coagulation of human blood on multi-layered

chitosan/dextran sulfate films used a cell culture plastic disk made of poly(ethyleneterephthalate) as a film-

base [15]; the multi-layered disks were then used for experiments without detachment. Another study reported

using treated poly(L-lactic acid), which is a biocompatible polymer that is widely used in orthopaedics, as a

positively-charged substrate for collagen/heparin multi-layers that are intended for regulation of bone cellular

functions (positive charge on the PLLA substrates is obtained by aminolysis process) [16]. Poly(sodium-4-

styrenesulfonate)/poly(allylamine hydrochloride) multi-layered membranes that contained inter-layer

additions of antibiotic drug (metronidazole) were fabricated on synthetic biocompatible aminolysed poly(D,

L-lactide-co-glycolide) supports to be used as a controlled drug delivery system in the treatment of dental and

periodontal infections[17]. Alongside with polymers, biocompatible metals have been used widely in the

medical field, and may also need surface modification. For example, one study reports the coating ZEK100 (a

magnesium alloy), which is used for fixation of fractured bones, with alginate and chitosan; the alloy required

pre-layering treatment and a precursor layer to be suitable for the coating procedure [18]. Another widely used

biomedical material that has been successfully coated with polyethyleneimine/poly(sodium-4-

styrenesulfonate) multi-layers with a goal of controlling cellular adhesion is silicone rubber [19]. Additional

information about layer-by-layer coatings that are used in biomedical applications, including polyelectrolyte

data and further details about substrates described above is well presented in the article by Lvov [20].

Another area that benefits from the layer-by-layer coatings is optics. One study reports anti-reflective coatings

fabricated using alternating layers of silica nano-particles, poly(diallyldi-methylammoniumchloride) and

poly(sodium p-styrenesulfonate) on glass substrates [21]. Glass substrates have also been used for creating

light-emitting devices based on poly(allylamine hydrochloride)-evans blue/poly(acrylic acid) polyelectrolyte

pair [22]. Other application examples include microelectronics (with poly(dimethylsiloxane) elastomers [23]

as the most commonly used substrates), packaging (poly(lactic acid) substrates) [24] and fabrics (silk

substrates) [25].

1.1.2 Colloidal substrates

The layer-by-layer procedure is capable of multi-layering of not only flat surfaces but other substrate

geometries as well, including variously-shaped colloidal particles with different surface morphologies [1]

(hard templates), emulsions [26, 27, 28, 29, 30] and liposomes [31, 32] (soft templates). Such substrates

generally serve as templates for fabrication of multi-layered containers (capsules) that can be used for various

purposes, such as controlled drug delivery and release, extrinsic self-healing materials, separation systems and

other applications that might utilise encapsulated substances [33, 34].

1.1.2.1 Particles

One of the main requirements for the template particles in terms of the layer-by-layer methodology is their

stability in aqueous suspensions. When using stable templates, the possibility of multi-layering-induced

aggregation is decreased (especially during the deposition of the first polyelectrolyte layer – stable particles

are less likely to be coated as an aggregate), which provides uniformity of the fabricated polyelectrolyte

shells. Particles in any suspension are influenced by van der Waals forces which promote attractive

interactions that lead to aggregation, both reversible and irreversible, meaning that in the absence of any

opposite particle interactions within the system, the stability of the particles cannot be achieved. Such

opposite interactions can be introduced by charging the surface of the particles; if particles are charged, they

experience a repulsive electrostatic inter-particle force which prevents them from coming into contact [35].

Since another crucial requirement for particles as a part of the electrostatic layer-by-layer process is the

presence of charge on their surface, charge-induced stabilisation strategies are considered to be of a high

importance.

Colloidal particles immersed in a liquid can obtain surface charge via four general mechanisms [35, 36]:

1) Dissolution of Constituent Ions

In cases when solids have limited solubility in water one of the ionic species that the solid is composed of has

a greater probability of migrating into the liquid phase. Such unequal dissolution creates the excess of

counter-ions on the surface of the solid particles which results in their either negative or positive surface

charge. The most known example of solids that are susceptible to partial dissolution is silver iodide. It has

very low solubility in water (10-16 mol∙L-1 at room temperature [36]) with silver ions Ag+ having a greater

tendency to move into aqueous phase than iodide I -, resulting in negatively charged particles. Surface charge

can be manipulated by changing the relative concentrations of ions by adding, for example, either AgNO3 or

NaI, which makes it is possible to manipulate the surface charge and make it positive in the case of AgNO3.

On the transition from a negative to a positive charge, another surface condition can be achieved, which is

called the point of zero charge (pzc), where the net surface charge of the particles is zero. The point of zero

charge is generally achieved when the excess concentration of certain ions (in the current example, Ag+) in

solution mitigates their tendency to migrate from the solid surface into water thus creating a balance that

results in the zero net surface charge.

2) Ionisation of Surface Groups

Particles that have acidic or basic surface groups can release or acquire protons (H+) as a result of the change

in the pH of the medium solution. Surface charge, in this case, is induced by the ionisation of such surface

groups.

Two important examples of surfaces that can be charged by manipulating of the pH are biological surfaces

(usually contain surface proteins that consist of carboxylic (COOH) and amine (NH2) groups, Table 1) and

metal oxides (which produce ionizable amphoteric surface groups when exposed to water, Tables 2 and 3).

Table 1 – Biological surfaces – examples of conditions for ionisation of surface groups

Low pH No dissociation of COOH groups, surface remains uncharged;

NH2 groups are protonated, surface acquires positive charge.

Characteristic pH Point of zero charge, the number of dissociated COOH groups is in balance with the number of

protonated NH2 groups (balance depends on the number and type of surface groups; for most

biological surfaces at pH 4-5 [36]).

High pH No dissociation of NH2 groups, surface remains uncharged;

COOH groups are protonated, surface acquires negative charge.

Table 2 – Metallic oxide surfaces – examples of conditions for ionisation of surface groups

Low pH M-OH2+, positive surface charge;

pH < 5.8 Ti-OH + H+ → Ti-OH2+

Characteristic pH MOH, point of zero charge (isoelectric point);

depends on the crystalline form of oxide, origin, preparation, impurities; a rough guide for some

widely used materials can be found in Table 3.

High pH M-O-, negative surface charge;

pH > 5.8 Ti-OH + OH- → Ti-O- + H2O

Table 3 – The point of zero charge as a function of pH for common metal oxides [37].

Oxide SiO2 TiO2 Fe2O3 Al2O3 MgO

pzc 2 6 8 9 12

It should be noted that not only surfaces that contain two types of surface groups can change their ionisation

degree; one surface group can also undergo ionisation change resulting in a stronger or weaker surface charge

but with no charge reversal. The trend of the surface becoming less negative with a decrease of the pH stays

the same.

3) Isomorphous substitution

A process when one atom substitutes another in the crystal structure without a significant structural change is

called isomorphous substitution. For such substitution to happen, the participating atoms should have similar

ionic radii and valence state [38]. Most known materials that undergo this process are clays. Kaolinite, for

example, consists of alternating layers of tetrahedral silica and octahedral alumina which share apical

oxygens; bilayers are bound together by van der Waals forces and hydrogen bonding. When Si4+ gets

substituted by Al3+ the lattice acquires a residual negative charge. Much like metal oxides, the same negatively

charged kaolinite particles can acquire a positive charge at low pH conditions; as a result, the combined effect

of a positive charge and negative faces charge can result in edge-to-face aggregation of particles [36].

4) Ion adsorption

In cases when particles do not have any ionisable surface groups (2) and cannot be ionised in their bulk form

(1) their surface can be charged by adsorption of ionic species from the medium solution. Adsorption of ions

onto neutral surfaces must involve other interactions favourable to electrostatic interactions and is called

specific adsorption [36]. The most well-known example of this charging mechanism is an adsorption of an

ionic surfactant. Surfactants consist of a hydrophilic head, which is ionisable, and a hydrophobic tail which

attaches to the surface of the particle to minimise its contact with water. This results in either negative or

positive surface charge provided by the hydrophilic heads “floating” around the particle. A well-known

example where ion adsorption-induced surface charge is utilised are inks where mixtures of surfactants are

used as dispersants; carbon black, for instance, can be easily suspended in water if treated with anionic

surfactant [35].

When charged and placed into water, particles acquire a two-layered charge structure: an electric double layer,

also referred to as the “Stern layer”, and a “diffuse layer” of weakly associated ions (Figure 11). The potential

of the surface layer (e.g. of the particle itself) is defined by potential-determining ions, species which by virtue

of their electron distribution between the solid and liquid phase determine the difference in potential between

these phases (IUPAC). Examples of such ions include the aforementioned Ag+ and I- ions (1) since surface

charge changes on addition of either ion type; as for materials with ionisable groups, protons strictly speaking

cannot be considered potential-determining ions from the thermodynamic point of view, however, they do

show the change of the surface charge with a change of pH [36].

1.1.2.1.1 Examples of commonly used template particles

Depending on the application, core particles might be used for the production of non-loaded hollow capsules

where they are used without any treatment and removed on completion of the layer-by-layer procedure to

produce capsule shells for post-loading [39, 40, 41, 42] or may serve as a cargo loading base where substance

of interest (both molecules and nanoparticles [43]) is attached to the sacrificial or non-sacrificial particle

before being encapsulated (for example, porous particles provide high loading efficiency) [44, 45, 46, 47, 48].

Some of the most used template particles and their layer-by-layer relevant characteristics are presented in

Table 4.

Table 4 – Common colloid layer-by-layer templates

ParticleSize, µm

General polydispersity

Surface charge Solvent required to remove core

Non-porousPolystyrene

0.1 – 5 [43]Monodisperse

[49]

Negative [50, 51]

Tetrahydrofuran [43, 50, 52]

Melamine formaldehyde

Positive [40, 53]

Hydrochloric acid [40, 53], generally can be decomposed under

acidic conditions [43]Silica Negative [39,

54, 55]Hydrofluoric acid [39, 43, 49]

Gold nanoparticles

0.01-0.04 [56, 57, 58, 59]

Monodisperse [56, 57, 58, 59]

Negative [56, 57, 58, 59]

Potassium cyanide solution [56, 57, 58, 59]

PorousMesoporous silica

Available in both micro and nano-range [60];

≤0.2 µm desirable sizes for medical

applications [61], all other applications utilize 1-5µm [60]

Moderately polydisperse and

monodisperse [60]

Negative [61] Hydrofluoric acid [39, 43, 49]

Calcium carbonate

3-5 [62, 63, 64, 65, 66], 0.4-0.9 [67]

Polydisperse [49]Negative [62,

65]Ethylenediaminetetraacetic acid

[62, 65, 66]

1.1.2.2 Emulsions

Emulsions, which are dispersions of one liquid immiscible in a second liquid continuous phase, can also be

used as templates for the electrostatic layer-by-layer procedure. These systems can be classified by their type

(oil-in-water and water-in-oil) and size as micro-emulsions (< 100 nm), mini-emulsions, or nano-emulsions

(100 nm – 1 µm) and macro-emulsions (>1 µm), although the size classification is very general. A more

rigorous way to classify emulsions is with regard to their thermodynamic stability using the following

equation:

∆ G form=∆ A γ12−T ∆ Sconf (1)

where ∆Gform is the associated free energy of droplet formation, ∆A is a change in the interfacial area, γ12 is the

interfacial tension between phases 1 and 2 at the temperature T, and ∆Sconf is the configurational entropy

change which can be approximated as

∆ Sconf=−nk b∙[ ln (φ)+{(1−φ )

φ}∙ ln(1−φ)] (2)

where n is the number of droplets, kb is the Boltzmann constant, φ is the volume fraction of the dispersed

phase.

Micro-emulsions are formed when ∆Gform is negative – this means they are thermodynamically stable and form

spontaneously (in conditions of low interfacial tension, ∆Sconf > ∆Aγ12). If the value ∆Gform is positive (∆Sconf <<

∆Aγ12), meaning that emulsions are not formed spontaneously and work is required, emulsions are not

thermodynamically stable. This applies to macro-emulsions.

In mini-emulsions ∆Sconf < ∆Aγ12 resulting in still positive ∆Gform, however, those two values are much closer in

magnitude than in the case of macro-emulsions [35].

To act as layer-by-layer templates, much like particles, emulsions must be stable (e.g. droplet coalescence

must be minimised) and have a surface charge. Stability of emulsions can be achieved by increasing

electrostatic or steric (or a combination of both) repulsions to counteract van der Waals forces; for the same

reasons, as for particles, electrostatic stabilisation is more applicable and therefore will be discussed below.

Only oil-in-water emulsions are considered since the electrostatic layer-by-layer is a water solution based

process.

Electrostatic repulsion can be introduced by adsorption of an ionic surfactant onto surfaces of droplets [68].

Surfactant heads assemble at the interface and produce a surface charge that leads to the formation of an

electric double layer (essentially, the same structure is formed as in particle-in-water case) on the droplets;

when these droplets approach one another the overlap of the formed double layers creates a mutual repulsion.

The droplet of any liquid phase immiscible in water and stabilised by an ionic surfactant can be used as a

template for the layer-by-layer procedure. Some of the most used ionic surfactants when producing liquid core

layer-by-layer structures are anionic sodium docusate salt (AOT) [69, 70] and sodium dodecyl sulfate [28, 71,

72], cationic dioctadecyldimethylammonium bromide (DODAB) [29]. Other suitable ionic surfactants are

presented in Table 5 [73].

Table 5 – Commonly used ionic surfactants

Anionic (1) carboxylates: alkyl carboxylates-fatty acid salts; carboxylate fluoro-surfactants;(2) sulfates: alkyl sulfates (sodium lauryl sulfate); alkyl ether sulfates (sodium laureth sulfate);(3) sulfonates: docusates (dioctyl sodium sulfosuccinate); alkyl benzene sulfonates;(4) phosphate esters: alkyl aryl ether phosphates; alkyl ether phosphates.

Zwitterionic (amphoteric, charge depends on pH)

(1) RN+H2CH2COO-;(2) RN+(CH3)2CH2CHSO3

-;(3) Phospholipids: Phosphatidylcholine (Lecithin) [74].

Cationic (1) RN+H3Cl- (salt of a long-chain amine);(2) RN+(CH3)3Cl- (quaternary ammonium chloride – quats);(3) Ester – quats;Benzyldimethylhexade cylammonium chloride [34].

Once emulsified with an appropriate surfactant, emulsion droplets can serve as templates for the layer-by-

layer procedure which is to be started with a polyelectrolyte of the opposite to the selected surfactant charge.

1.1.2.3 Liposomes

Artificial spherical vesicles with an aqueous core embedded into one or multiple phospholipid bilayers or

lamellae are called liposomes [75]. Phospholipids are the main construction components for the outer part of

liposomes called the membrane. Another important element of the structure is cholesterol which acts as an

additive and fills up empty spaces between the phospholipids in the membrane. Cholesterol promotes a

stronger bond of the bilayer enhancing its stability. Liposomes can be prepared in different sizes (0.025 – 2.5

µm [76]), can contain a different number of bilayers and can be either charged (anionic or cationic) or neutral.

Other classifications available based on functionality – liposomes are classified as conventional, stealth,

ligand-targeted, long-release, triggered-release, most of which are properties relevant to drug-delivery

applications [75].

Liposome charge and stability are the most important characteristics in the scope of the layer-by-layer

process, the same as for particles and emulsions. Stability of liposomes is a complex phenomenon consisting

of physical, chemical and biological aspects. Physical stability is of the most practical interest since it largely

defines liposome shelf-live; processes such as aggregation and coalescence that are common for all colloidal

systems affect liposomes as well. Aggregation in liposomes, although in most cases reversible, can lead to

their irreversible coalescence, therefore, increasing their size, which normally is an undesirable outcome [77].

Liposome stability can be enhanced in the same ways as for all other colloids – by the introduction of either

steric or electrostatic repulsion. As in the case of particles and emulsions, electrostatic stabilisation of

liposomes is desired if they are to be used as the layer-by-layer templates.

Different types of liposomes can be prepared using a variety of conventional and novel methods [75]. For

example, both neutral and charged liposomes of the same size distribution can be fabricated by using the

traditional solvent injection method that involves dissolving the constructive phospholipids in an organic

solvent (most commonly ethanol or ether) followed by injection of the resulting mixture into an aqueous

buffer which results in spontaneous formation of vesicles [75, 78]. Depending on the charge of the lipids used

for fabrication, liposomes of corresponding surface charge can be produced. Examples can be found in Table

6 (reproduced from [78] with permission by Attribution 4.0 International (CC BY 4.0) licence), where PC is

soybean phosphatidylcholine, Chol is cholesterol, CHEMS-PEG is a PEGylated cholesterol derivative,

CHEMS is cholesterol hemisuccinate (anionic) and Chol-NH2 is N1-cholesteryloxycarbonyl-1, 2-

diaminoethane (cationic).

Table 6 – Fabrication of liposomes and corresponding characteristics

Formulation Molecular ratio Particle size, nm Zeta potential, mV

PC/Chol/CHEMS-PEG 40/17/3 249.3 ± 12.3 -9.6 ± 0.4 (neutral)

PC/Chol/CHEMS/CHEMS-PEG 40/8.5/8.5/3 275.3 ± 10.6 -31.2 ± 0.9 (anionic)

PC/Chol/Chol-NH2/CHEMS-PEG 40/8.5/8.5/3 271.6 ± 13.8 39.6 ±1.2 (cationic)

1.2 Polyelectrolytes

Polymers that contain ionisable groups along their chain structures that can dissociate in polar solvents (most

commonly water) into charged chains, macroions and small counterions are called polyelectrolytes [79]. A

schematic representation of the structure acquired by polyelectrolytes in solution is shown in Figure 3.

Figure 3 – Schematic representation of a polyelectrolyte in solution

In the electrostatic layer-by-layer procedure these materials represent fundamental construction elements

along with substrates of choice (flat surfaces, particles, emulsion droplets etc.) which are used for the

fabrication of multi-layered films/shells on the selected template. To understand interactions between

templates and polyelectrolytes, as well as polyelectrolyte-polyelectrolyte interactions that allow for the

formation of multi-layered structures, classifications and properties of these polymers should be discussed,

being fundamentals for all underlying layer-by-layer mechanisms.

Polyelectrolytes can be classified by two primary functional attributes: dissociation degree (the fraction of an

original number of polyelectrolyte molecules dissociated once placed in a solvent) and nature of the

counterions produced into solution [80]. A simplified classification diagram is presented in Figure 4.

Figure 4 – Classification of polyelectrolytes

Polyelectrolytes can be also classified based on positions of their functional groups into integral and pendant

types (Figure 5).

Figure 5 – Classification of polyelectrolytes (from left to right): integral type polycation, pendant type

polyanion, integral type polyampholyte.

The specific character of the interactions of the macro-ion with counter-ions in polyelectrolyte solutions is one

of the defining aspects of these materials that differentiate them from simple electrolytes. One of the methods

used for the assessment of ion activity within polyelectrolyte solutions is potentiometry, which allows not

only for the determination of the number of functional groups but also gains the acidity constants that are

directly related to the degree of dissociation (an indicator of polyelectrolyte strength). Potentiometry is usually

carried out in form of titrations accompanied by measurements of H+-ions activity as a function of pH change

using a reference electrode. Polyacids may be titrated with hydroxides, polybases – with acids.

Polyelectrolytes dissociate differently from non-polymer materials, which can be illustrated by an example

comparison of a weak acid and a weak polyacid dissociation during potentiometric titrations [80].

For a weak acid HA, the dissociation constant Ka can be defined as follows:

K a=¿¿ (3)

where [H+], [A-] and [HA] are concentrations of [H+], [A-] and HA respectively.

This expression can be transformed into a more practically used value pKa as

pK a=−log10 K a=pH−log10 ¿¿¿ (4)

By introducing the degree of neutralisation of acid by a titrant α 'which is directly related to [A-], pKa can be

calculated using Henderson-Hasselbalch equation:

pK a=pH + log10(1−α')

α ' (5)

Let us now consider the ionisation equilibrium in a solution of a weak polyacid which has N ionisable groups

per macromolecule. If each monomer contains one ionisable group, then N is also equal to the degree of

polymerisation; the dissociation degree of such a system is strictly speaking defined by N different

dissociation constants. When a titration is performed on such materials the increase in the neutralisation

degree results in an increase of the charge density on the polymer chain producing an additional electrostatic

attraction that affects yet non-detached counter-ions; pKa values of different functional groups change during

the process of titration [81]. This additional attraction results in a necessity of an additional work ∆Gel to

detach a proton from a polymer chain, which is defined as

∆ Gel=N A eψ (6)

where NA is the Avogadro constant, e is the elementary charge, and ψ is the electrostatic potential on the

surface of the polyelectrolyte.

The degree of dissociation α for polyelectrolyte can be calculated from the degree of neutralization

α=α'+CH +¿

CPE¿ (7)

where CH+¿¿ is a molar concentration of H+ ions and CPE is a molar concentration of the polyelectrolyte

segments.

Taking into account the extra work for ion separation and a newly-defined degree of dissociation α we can

relate the apparent acidity constant p Kapp(PE ) to the intrinsic acidity constant p Ka0

p Kapp(PE )=p Ka0+0.4343

∆ Gel

RT (8)

which can be found from the correlation with the potentiometric pH so that the Henderson-Hasselbalch

equation becomes

pH=p Ka0− log10

(1−α)α

+0.4343∆ Gel

RT

(9)

Experimentally p Kapp(PE ) can be found by performing titrations and plotting the differential curve in

coordinates of ∆ pH as a function of titrant concentration (per unit of polyelectrolyte mass), where ∆ pH is

the change of pH per addition of unit of titrant. The maximum on the resulting curve corresponds to the

concentration of the functional groups (equivalent point, Figure 6a). After the titration curve is obtained the

degree of neutralization a ' of each point on the curve is calculated and a pH=f ( log10a'

(1−a')) curve is

constructed which allows for determination of p Kapp(PE ) at half-neutralisation (α '=0.5) using a modified

Henderson-Hasselbalch equation:

p Kapp(PE )=pH−m ∙ log10α '

(1−α' ) (10)

where m can be found as a slope of the aforementioned curve and is a characteristic for electrostatic

interactions between polyelectrolyte functional groups (Figure 6b). The maximum acidity of the polycation or

maximum basicity of polyanion is achieved at α '=0, correspondingly both are a minimum at α ' → 1. Half-

neutralisation point of α '=0.5 is significant because it allows for the determination of an intrinsic intrinsic

p Ka0 value under conditions where the electrostatic interaction of the polymer chain and counterions is

screened by the presence of low molecular salts [80]: m∙ log10α '

( 1−α ' )=0, meaning p Ka

0=pH (α¿¿ '=0.5)¿.

All these differences between the dissociation behaviour of low molecular acids and polyacids can be clearly

seen from their titration curves (Figure 6c). It can be observed that polyacid behaves as a weaker acid in

comparison to its low molecular analogue, even though they consist of the same ionisable groups. Due to the

increasing electrostatic chain-counter-ion interaction that accompanies dissociation of a polyacid, it behaves

as a weaker acid. If a low molecular weight electrolyte is added to the polyacid solution, its ions screen the

charge of a chain and the titration curve becomes more like that of a low-molecular acid.

(a) (b) (c)

Figure 6 – Potentiometric titration curves [81]

The behaviour of polyelectrolytes in solutions is most often explained in terms of “Counterion Binding

Theory” of Manning [82]. The main concept of this theory is that there is a certain critical value of charge

density that can exist on the polyelectrolyte chain that, if exceeded, leads to condensation of counter-ions onto

the chain in order to lower its charge. In this theory, the polyelectrolyte is simplified to a form of an infinitely

long chain which has uniformly-spread charges attached to it (each charge is separated from another by the

length b). The characteristic dimensionless value for linear charge density of such polyelectrolyte chain ε is

then defined as

ε= q2

ϵ kbTb (11)

where q is the protonic charge, ϵ is the dielectric constant of a solvent, k b is Boltzmann’s constant, T is the

temperature, b is the average linear charge (univalent groups) spacing.

The theory postulates that ε cannot be greater than 1; if ε>1 a fraction of counterions electrostatically

“condense” onto the chain to lower its charge density to a maximum value ε=1. Other counterions generate

an “counterion atmosphere” around the polyelectrolyte chain that behaves according to Debye–Hückel theory

(which in simplified form states that each ion in solution polarises its environment and creates an “cloud” of

oppositely-charged ions around it) [82]. The mechanisms of such “condensation” and an overall applicability

of this theory is still debated, although it is considered to be a main polyelectrolyte solutions theory.

Another widely accepted theory of polyelectrolyte behaviour in solutions is based on so-called “electrostatic

blob” model [83] built around polymer scaling theory. It suggests that a weakly charged polyelectrolyte chain

can be presented in a form of chain of electrostatic blobs (Figure 7) of a size defined as

ε el a(f 2 lb

a)−1

3 (12)

where a is a size of a monomer, f is a fraction of charged monomers within polyelectrolyte chain,

lb=e2

4 πϵ kb T is the Bjerrum length (the separation distance at which the electrostatic interaction between two

elementary charges is comparable to the thermal energy scale kBT; e is the elementary charge, ϵ is the

dielectric constant of water).

Figure 7 – Electrostatic blob model

Each blob contains gel ( f 2lb

a )−23 monomers, and the length R of the resulting chain containing N monomers

in absence of added salt can be expressed [84] as

R Na( 1a )

13 ( ln N

3)

13

(13)

In the presence of added salt, the chain becomes less elongated due to the screening of polyelectrolyte charge

by the salt ions; the screening effect can be characterised by the Debye screening length

κ−1=(8 πnlb)−12 (14)

If this screening length is smaller than the size of a chain, the chain becomes less elongated which leads to

bending; the influence of this effect is addressed in terms of a persistent length lp, which is a length of a chain

over which it remains in a stretched geometry [83]. This parameter is theorised to decrease with salt

concentration as a function of κ−1or κ−2 in different theories; at very high added salt concentrations the

electrostatic interaction within polyelectrolyte chain becomes short-range.

In the case of more concentrated solutions, the blob model predicts strong chain-chain interactions and their

overlap, which allows treating such solution as a disordered and isotropic liquid with a presence of local chain

order as shown in Figure 7.

Other theories include the extended “Scaling Theory” by A. Dobrynin [85] and Poisson-Boltzmann approach

by M. Fuoss [86].

1.2.1 Examples of commonly used polyelectrolytes

As previously mentioned, polyelectrolytes can be classified into polyacids, polybases, polyampholytes and

polysalts. Another classification can be introduced by derivation origins – natural and synthetic. Some of the

examples of the polyelectrolytes of aforementioned classifications that has been used as construction materials

for the electrostatic layer-by-layer multilayering (on spherical templates) are presented in Table 7.

Table 7 – Common polyelectrolytes used for the electrostatic layer-by-layer assembly

CationicAbbreviation Origins

Poly(allylamine hydrochloride) [39, 42, 87, 88] PAH

Synthetic

Poly(diallyldimethylammonium chloride) [34, 42, 52, 89, 90, 69] PDADMAC

Poly(vinyl benzyl tri-methylammonium chloride) [91] PVBTAC

Poly(N-ethyl-4-vinylpyridinium bromide) [92] PEVP

Poly-L-lysine [52, 93, 94, 95] (originates from amino acid precursor) PLL

Poly-L-arginine [96, 97, 98] (originates from amino acid precursor) -

Chitosan [46, 99, 100] - Natural

AnionicPoly(sodium 4-styrenesulfonate) [39, 90, 69, 98, 101] PSS

SyntheticPoly(acrylic acid) [45, 102] PAA

Poly(vinyl sulfate) [103, 104, 105] PVS

Poly(vinylsulfonic acid) [106] PVSA

Carrageenan [52, 107] -

NaturalCarboxymethyl cellulose [88] CMC

Hyaluronic acid [46, 87, 93, 108] HA

Alginic acid (sodium alginate) [69, 109, 110, 111] AA

2. Underlying mechanisms of the electrostatic layer-by-layer assembly

The layer-by-layer assembly is a procedure that involves three distinct stages: adsorption of a polyelectrolyte

onto a substrate (polyelectrolyte at interface, first layer formation), adsorption of a second polyelectrolyte

layer (formation of the polyelectrolyte complex) and multi-layering (fabrication of more than two layers).

Each of these stages has unique underlying mechanisms and specifics which are discussed in the section

below.

2.1 Adsorption of polyelectrolyte onto a solid surface (polyelectrolyte at interface)

Let us consider a solid surface that possesses an electric charge eσ per unit area. This charge creates an

electric field closely around this surface which can be expressed as [83]

E=(kb T

e)(4 πσ lb) (15)

where lb is the Bjerrum length.

The electric field decays with the distance from the surface due to the screening effects induced by counter-

ions or by added salt ions if those are present [83]. If the decay trend is only influenced by counterions, which

exist in a proximity to the surface λ=1

2 πσ lb , the field can be defined by the following expression

E≅ 2z+ λ (16)

where z is any given distance from the surface.

In presence of the added salt, screening is mostly due to the added salt ions and the field decays as

E≅ 2λ

exp−κ z (17)

Polyelectrolyte chains in solutions of low added salt concentration, i.e. in conditions of low ionic strength,

adsorb onto the surface of the opposite charge due to electrostatic attraction; the condition for the

polyelectrolyte to be confined at the distance δ from the surface is the sufficient enough surface charge that is

able to move polyelectrolyte chain to a distance δ < λ. The relation between δ, polyelectrolyte properties and

the electrostatic force can be expressed as

δ ( a2

fσ lb)

13 (18)

By adding more salt into such solutions polyelectrolyte adsorption structure does not change unless δ, which

can be also described as the chain thickness, is larger than the Debye screening length. Once this condition is

no longer in place and if there is no short-range non-electrostatic interaction between the polyelectrolyte and

the surface, the chain desorbs [83].

Besides this general principle, adsorption of polyelectrolytes onto solid surfaces has a range of properties and

characteristic aspects that are important in terms of the electrostatic layer-by-layer assembly.

2.2 The nature of the adsorption process

Firstly, the nature of the polyelectrolyte adsorption process is essentially irreversible regardless of the

geometry of the selected substrate [112]. The process of adsorption includes two stages: at the first stage the

mass of the adsorbed polyelectrolyte increases linearly with time (indicating the rapid character of

adsorption), while the second stage is represented by a plateau indicating the saturation point at which no

more polyelectrolyte can be adsorbed to the surface even if some of it is still present in solution. Many studies

report that once coated, both flat [112, 113, 114, 115, 116] and particulate [112, 117, 118] substrates, if then

exposed to a polyelectrolyte-free solution containing low-molecular electrolytes, do not experience any

desorption which is evidence of the irreversibility of the adsorption process. There are, however, minor

exceptions from this behaviour – several studies have reported partial desorption of low molecular weight

polyelectrolytes; some high molecular weight polyelectrolytes have also been reported to desorb, however, the

desorption was induced by additional changes introduced in polyelectrolyte solutions =[112]=[112].

The polyelectrolyte adsorption process is most commonly described in terms of classical Random Sequential

Adsorption (RSA) model. This model is used for the explanation of adsorption of colloidal particles, proteins

and polyelectrolytes where all of these systems are modelled as circular disks that can adsorb to surfaces at

random empty locations with no permitted deposition overlap [112]. Taking these conditions into account, the

maximum achievable coverage (jamming limit) can only be θj ≅ 0.55 which is less than the regular hexagonal

packing (0.91). In relation to the number density of polyelectrolyte molecules Г, the surface coverage can be

expressed as

θ=π a2 Г (19)

where a is the radius of gyration of the polyelectrolyte.

The adsorption process can be approximated kinetically as

d Гdt

=ka cB(Г )

(20)

where d Гdt is the change of the adsorbed number density with time, ka is the polyelectrolyte adsorption rate

constant, c is the number concentration of the polyelectrolyte molecules in solution and B(Г) the so-called

blocking function that describes the available surface area

( Г )={1−ГГ 0

, for Г <Г0

0 , for Г ≥ Г 0

(21)

where Г0 is the adsorbed number density at saturation point (at the jamming limit) [112].

2.3 Characteristic phenomena of the polyelectrolyte adsorption process

The main properties of the adsorbed polyelectrolyte layer are the adsorbed mass, the morphology and the

distribution of charge (surface charge reversal upon the adsorption event). These properties and the conditions

that stipulate them are discussed below.

The adsorbed mass is the amount of the polyelectrolyte that is adsorbed onto a substrate surface while under

the influence of various parameters which include characteristics of the polyelectrolyte (for example,

molecular weight), the substrate (charge density) and the composition of adsorption medium solution

(concentration of added low-molecular weight electrolyte). General trends for the dependency of the

aforementioned factors on the adsorbed mass are summarised in Table 8 below.

Table 8 – Factors defining the adsorbed polyelectrolyte mass

Component Characteristic Influence on the adsorbed mass

Polyelectrolyte Molecular weight [112](at saturation conditions)

Linear polyelectrolytes: weak adsorbed mass – molecular weight dependency, can be described in terms of the RSA model asГ∝M−2 α f (22)where Г is the number density of polyelectrolyte molecules, M is the molecular mass, α f is the Flory exponent in the range 0.5-0.6.

Dendric or branched polyelectrolytes: stronger dependency due to α f being smaller in comparison to one of linear polyelectrolytes (the adsorbed mass increases with the increase of molecular weight)

Charge density [112, 114]

The adsorbed mass increases with the decrease of the charge density (the maximum of the mass can be achieved at very low charge densities). In the absence of the added salt, polyelectrolyte-polyelectrolyte repulsion is long-ranged and affects the coverage of the substrate (less material is needed to saturate the surface).This calls for modification of the RSA model as follows:1 – repulsion between electric double layer polyelectrolyte coils can be accounted by increasing the radius of the “disk” to an “effective radius” aeff

2 – modified surface coverage θ=θ j(aa eff

)2

3 – the interactions between two polyelectrolyte coils are expressed as

u (r )=kb T lb Zeff (eκ a

1+κ a)

2 e−κ r

r (23)

with r being the distance between centres of RSA “disks”

4 – the effective charge is given as Zeff=alb

(4 κ a+6), where lb is the

Bjerrum length and κ−1 is the Debye screening length

With an assumption that interaction energy between two polyelectrolyte coils would be in order of thermal energy u(2aeff )≅ kbT the “effective radius” can be estimated; analysis of the equation (23) in this case shows that the decrease of Zeff leads to the smaller aeff meaning a larger number of “disks”, i.e. polyelectrolyte mass is adsorbed.

Substrate Charge density [112, 116]

The adsorbed mass increases with the increase of the charge density.

This trend can be explained in terms of the modified RSA model proposed for polyelectrolytes above. Qualitatively, the higher the substrate charge density is the more counter-ions accumulated in the vicinity to the surface. A larger amount of surface counter-ions provides larger screening effects onto approaching polyelectrolyte chains resulting in the reduction of mutual repulsion, and, consequently, in the larger adsorbed mass.

Adsorption medium composition

Monovalent electrolyte concentration (added salt) [112, 116, 119, 120]

The adsorbed mass increases with the increase in added salt concentration. The 4-times increase in salt concentration results in 2 to 4 times increase in mass uptake.

The trend of the increasing adsorbed mass, in this case, can be understood using the same modified RSA model described above (polyelectrolyte charge density section). To recap briefly, since polyelectrolyte coils in aqueous solutions obtain electric double layer structure around them they repel each other increasing the aeff “disk” radius resulting in smaller adsorbed mass. However, introduction of monovalent salt provides screening of the long-ranged repulsion resulting in aeff decrease and higher mass uptake.

The reverse trend is only observed for very weak polyelectrolytes and very high salt concentrations. RSA model is not able to predict adsorption maximum in such cases since strong screening will prevent weak polyelectrolytes from adsorption due to decreased electrostatic attraction becoming smaller than thermal motion. If there are no other forces present polyelectrolyte will not adsorb.

The morphology of the adsorbed polyelectrolyte films can be generally described as laterally heterogeneous,

meaning that polyelectrolyte chains adsorb onto the surface individually. This morphology type can be

confirmed both theoretically, in terms of RSA model, and experimentally by using various techniques; among

others, Atomic Force Microscopy (AFM) provides the most conclusive evidence for the formation of the

aforementioned type of structure.

The RSA model described in the current section and Table 8 suggests [112] that polyelectrolyte chains adsorb

onto the substrate one by one at certain separation distances defined by the mutual electrostatic repulsion. The

chains are also flattened by strong attractive forces between the polyelectrolyte and the substrate, which leads

to the formation of very thin films (just a few nm [119, 120] thick while the typical diameter of a

polyelectrolyte chain is 20-100 nm). One of the factors that have an affect on both thickness and

morphological features of the adsorbed films is, as in the case with the adsorbed mass, the presence of added

salt in the adsorption medium. The thickness of the polyelectrolyte films depends on the added salt

concentration in the same way as the adsorbed mass does – it increases as more salt is added into solution

(adsorbed mass behaviour reasoning applies). High salt concentrations lead to the formation of swollen and

porous films [112].

Experimental AFM images supporting theoretical laterally heterogeneous morphology of polyelectrolyte films

are presented in Figure 8. It can be observed that even though the adsorbed layers are saturated, well-defined

polyelectrolyte chains are separated by an unoccupied space which is not and will not be filled in due to the

repulsive forces between the chains.

Figure 8 – AFM images of saturated polyelectrolyte layers of (a) - dendritic PAMAM layered on mica at

pH 4.0 with no added salt; (b) -- PSS layered on amidine latex particles in solution containing 1 mM

monovalent electrolyte [112] – Published by The Royal Society of Chemistry.

The process of adsorption of the polyelectrolyte onto the oppositely charged substrate is characterised by the

reversal of charge on the surface of the substrate. This process, which is also referred to as overcharging,

occurs in a “build-up” regime, meaning that at low polyelectrolyte concentrations the substrate keeps it charge

sign despite partial polyelectrolyte adsorption; the surface potential, however, decreases until a certain amount

of polyelectrolyte is adsorbed that compensates the substrate charge leading to surface neutralisation; if more

polyelectrolyte is added, the accumulation of polyelectrolyte-induced charge (opposite to one of the substrate)

continues until the saturation point is reached. In this regard, the adsorption process can produce unsaturated

films where all of the available polyelectrolyte chains are adsorbed onto the surface, but the saturation point is

not reached, or it can produce saturated films where even in the presence of excess polyelectrolyte no more

chains can be attached to the surface. The overcharging process can be theoretically described using the linear

superposition relationship model [118]

σ=σ 0+q Zeff Г (24)

where σ is the resulting charge density, σ 0 is the surface charge density of the bare substrate, Zeff is the

polyelectrolyte effective charge and Г is the number density of polyelectrolyte molecules.

The charge reversal process is observed both experimentally [121] and theoretically [112] in Figure 9. It can

be seen that the linear superposition relationship provides a good fit for experimental data.

Figure 9 – Overcharging process (a) deposition of PSS onto latex particles as measured by electrophoresis

and AFM (b) calculations based on linear superposition relationship model [112]. – Published by The

Royal Society of Chemistry.

It should be noted that neutralisation point can be achieved stoichiometrically, i.e. when polyelectrolyte

neutralises the substrate charge exactly, and super-stoichiometrically where polyelectrolyte counterions

significantly participate in the charge balance. The latter is characteristic to weakly charged polyelectrolytes

[112]; a higher dose of such polyelectrolyte is required to neutralise a given surface [112, 122]. The opposite

of that is also true – less given polyelectrolyte is needed to neutralise a surface with a smaller charge [112,

123].

The charge density profiles of the surface with an adsorbed polyelectrolyte layer in comparison to the bare

charged surface are presented in Figure 10. This surface charge density can be approximated using the Gouy-

Chapman relationship

σ=2 kbTϵ ϵ 0 κ

esinh (

q ψD

2k bT) (25)

where ψ D the potential of the diffuse layer (the layer of weakly associated ions around the surface), e is the

elementary charge, ϵ is the dielectric constant of the liquid.

The presented profiles indicate that the surface with an adsorbed saturated polyelectrolyte layer behaves much

like a bare surface with the only difference in a charge sign. Both surfaces generate a diffuse layer of attracted

counter-ions and depleted co-ions [112].

Figure 10 – Charge density profiles (schematic) – (a) bare surface; (b) surface coated with polyelectrolyte

of the opposite charge [112]. – Published by The Royal Society of Chemistry.

The degree of surface saturation plays an important role in interactions between both bare and coated with

polyelectrolytes particles. These interactions define the stability of the particles in dispersions (i.e. their

resistance to aggregation) which is, as stated before, one of the fundamental requirements of the layer-by-layer

multi-layering. The stability of the particles in aqueous dispersions can be addressed in terms of a balance of

attractive and repulsive forces between the particles, which is a basis for DLVO theory (named after its

authors, Derjaguin and Landau, Verwey and Overbeek). This theory describes [124] colloidal stability as a

competition between attractive van der Waals force which depends on the distance r between the particles of

radius R as

U vdW (r )=−A12 π

( Rr

)2

(26)

where A is the Hamaker constant (depends on number densities of interacting particles) [125], and repulsive

electrostatic force which also depends on the distance r as

U E (r )=4 πεap

2+ rap

ψ02 e−κr

(27)

where ψ0 is an electric potential on the surface of the particle, ap is a diameter of the particle, κ is the Debye –

Hückel constant

κ=¿ (28)

where e is the elementary charge, n0i is the concentration of i-ions near the particle, zi is the valence of i-ions,

ε is the dielectric constant of a solvent. The inverse to Debye – Hückel constant is called the Debye length

(screening or decay length).

The resulting balanced particle interaction can be expressed as a sum of attractive and repulsive forces as

U=U vdW+U E (29)

The influence of the balance between the forces on the stability of the particles can be visualised if U is

plotted as a function of r. The electric double layer structure which charged particle obtains is aqueous

solutions is presented in Figure 11 (a) as well as the interactions of two such particles in terms of DLVO

theory (b).

Figure 11 – DLVO theory: (a) – dispersed particle in aqueous solution (Stern layer – a layer of strongly

electrostatically bound oppositely charged ions; slipping plane – the boundary between the diffuse layer (of

weakly associated ions) and the medium potential at which is measured to determine stability of dispersions

(ζ-potential)); (b) force balance interactions between particles as a function of interparticle distance.

As can be seen from the U(r) graph, there are three “potential zones” that characterise particles behaviour.

Zone I is the potential well where an attractive force is dominant, zone II is the barrier that prevents particles

from aggregation, zone III is also an attractive potential well. When particles migrate towards each other, they

go through these “zones” in the reverse order, III→II→I. The relative positions of particles (whether they stay

at the distance within III, II or I) can be determined using the following general rules (with 32

k bT being an

average thermal energy of the particle) [126]:

1) – max (U ¿¿ II)≫ 32

kb T ¿ and min|U III|≤32

kb T– particles have enough energy go beyond zone III

but are not able to overcome the barrier II – dispersion is stable;

2) – max (U ¿¿ II)< 32

kbT ¿ and min|U III|<32

kb T– particles have enough energy go beyond zone III

and to overcome the barrier II – dispersion aggregates;

3) – max (U ¿¿ II)≫ 32

kb T ¿ and |min U III|≪32

kb T– particles enter zone III and are not able to

escape it, which results in connected dispersions (an example for such systems is gels).

Let us now compare interaction forces and aggregation stability for two types of particles – with a saturated

and unsaturated layer of adsorbed polyelectrolyte. The comparison of the forces is presented in Table 9 below.

Table 9 – Forces within coated colloid particle dispersions

Particles with saturated polyelectrolyte layer Particles with unsaturated polyelectrolyte layerForces Behave in terms of DLVO theory; thin

and highly charged polyelectrolyte layer produces surfaces interactions which are dominated by electrostatic repulsion [112, 127, 128, 129] (much like between uncoated particles).

Deviations from DLVO theory may be observed at short distances and are attributed to steric repulsion [130, 131] (entropic effect due to conformational entropy of polymer chains), patch-charge attraction [118, 121] (driven by lateral heterogeneity of the adsorbed layer; charged patches obtain preferential orientations in proximity to oppositely charged patches [112]), polyelectrolyte bridging [127, 132] (adsorption of polyelectrolyte chains of one layered surface onto another closely-located surface at the event of enough proximity [112]). These forces have a relatively minor impact.

Particles with homogeneous unsaturated polyelectrolyte layers behave in terms of DLVO theory. Since ``unsaturated" layer means that adsorption process is stopped for analysis at some point of overcharging process, forces between particles can be categorised by stages: electrostatic repulsion at pre-neutralisation adsorption (decreasing with the increase in amount of adsorbed polyelectrolyte), van der Waals attraction at neutralisation point, and electrostatic repulsion beyond neutralisation (increasing until saturation point) [112].

Particles with heterogeneous unsaturated polyelectrolyte layers experience additional, non-DLVO forces (same as saturated layer particles, but more pronounce) the most influential being patch-charge attraction force. Interaction force equation, in this case, is expanded with an extra addend [112, 121](30) U =U vdW+U E+U pcThis force is stronger than van der Waals force of the same segment and is assumed to be exponential(31) U pc=−A e−eh

The origin of this force is, as has already been stated, lateral heterogeneity of the adsorbed layer that leads to preferential orientations of charged patches [112]. The decay length for this force can be expressed as [133]

(32) q−1=κ2+( 2 πb l

)2

where bl is the spacing in patch “lattice”, κ−1 is the Debye length. At low added salt concentrations the decay is driven by spacing, at high concentrations it is screened as an electrostatic force [112].

Theory predicts two aggregation regimes: the fast regime (diffusion controlled aggregation, typical for high

added salt concentration and small charge densities) and the slow regime (characteristic for systems with high

UII barrier (Figure 11): low added salt concentration or large charge densities). The transition point between

the slow and the fast regime is called “Critical Coagulation Concentration” or CCC. The rate of aggregation is

generally reported as the stability ratio [134]

W =k fast

k (33)

where kfast is the aggregation rate in the fast regime of the chosen reference system, k is the rate for the system

of interest.

The stability ratio increases with the slowdown of the aggregation process [112]. The comparison of the

aggregation behaviour of particles with a saturated and unsaturated layer of adsorbed polyelectrolyte is

presented in Table 10.

Table 10 – Aggregation behaviour of coated colloid particle dispersions

Particles with saturated polyelectrolyte layer Particles with unsaturated polyelectrolyte layer

Aggregation behaviour

Both fast and slow aggregation regimes are possible [112, 135].The fast regime is in place at high added salt concentrations, W =const≅ 1

In the slow regime W increases with the decrease in added salt concentration.

Saturated films typically have high charge density meaning that CCC point is shifted to higher salt concentrations.

Deviation from the behaviour described by DLVO, which predicts a stronger dependency of W with a salt concentration that it is in experiments, is most likely related [136] to lateral charge-patch attractions mentioned in Table 8 above.

Aggregation trend in particles with homogeneous unsaturated polyelectrolyte layers is in agreement with DLVO theory and forces described in Table 8 (main reason for the agreement being the homogeneity of the film). Dispersion is stable at low polyelectrolyte coverage (above neutralisation), followed by the decrease of the stability ratio on the way to neutralisation point where it reaches W =1beyond which dispersion is stable again. Deviation from experimental data is again observed in DLVO predictions at high salt levels possibly due to other non-DLVO contributions [112].

Aggregation of particles with heterogeneous unsaturated polyelectrolyte layers is influenced by the molecular mass of the adsorbed polyelectrolyte due to pronounce non-DLVO patch-charge interaction forces introduced by lateral heterogeneity. The larger is the molecular weight, the larger is the size of charge patches meaning that patch-charge attraction force becomes more long-range. The stability ratio decreases with the decrease of added salt concentration; this effect becomes quite major with a simultaneous increase in molecular weight [112].

2.4 Polyelectrolyte interactions and multilayering

2.4.1 Complexation of polyelectrolytes in solutions

When solutions of two oppositely charged polyelectrolytes are mixed poly-ions tend to form polyelectrolyte

complexes, which are dense phases that separate from the medium [83]. Formation of such complexes is

mainly driven by electrostatic interactions between polyelectrolyte chains; other interactions that can be

involved in this process include hydrogen bonding, van der Waals, hydrophobic and dipole interactions [80].

Polyelectrolyte-polyelectrolyte interactions in the absence of any other phase (particles, droplets), strictly

speaking, are not a part of the electrostatic layer-by-layer procedure on their own. The description of such

interactions, however, cannot be excluded, since, firstly, it is believed that polyelectrolytes within multi-layers

exhibit local behaviour identical to complexes formed by the same polyelectrolytes in bulk [137], and

secondly, in conditions of polyelectrolytes excess (which, in the conventional layer-by-layer procedure, can

happen as a result of incomplete washing steps) the fabrication of multi-layers on templates might be affected

by formation of polyelectrolyte complexes in solution.

Polyelectrolyte complexes can be generally divided into stoichiometric and non-stoichiometric depending on

the difference in molecular weights of the participating polymers.

Polyelectrolytes composed with weakly charged ionic groups and with a large difference in molecular

weights, if mixed in non-stoichiometric ratio, produce water-soluble sequential complexes with the structure

presented in Figure 12 (c) [80]. The “guest” polyelectrolyte, which in this structure is a short chain polymer

(with a much lower molecular weight), is able to migrate along the “host”, high molecular weight polymer

chain. The water-soluble character for these complexes is possible up to some critical guest/host concentration

ratio, which, when exceeded, leads to the formation of insoluble complexes co-existing with soluble ones

[80].

If polyelectrolytes with similar molecular weights are mixed the resulting complexes are generally

characterised by 1:1 stoichiometry and are formed as ladders (fixed ionic cross-links) or chaotic scrambled-

egg structures (Figure 12 (a) and (b)) [80].

Figure 12 – Stoichiometric (a and b) and non-stoichiometric (c) polyelectrolyte complexes

This classification approach, though phenomenologically correct, is rather simplified. Complexation of

polyelectrolytes in solutions can be described more comprehensively by using phase diagrams, which can

predict the formation of complexes of different shapes at different conditions (concentration ratios, added salt,

pH and others).

The simplest case of polyelectrolyte complexation diagrams is encountered when both participating polymers

have the same large molecular weights Mw, same fraction of charged groups f, and the same concentrations c.

Under these conditions, polyelectrolytes form dense complexes in water easily and their critical complex

formation concentrations are low [83]. Generally, when two polyelectrolyte solutions are mixed, there are two

possible outcomes: solution separates into two parts each containing one polyion species, or polyelectrolyte

complexes are formed. Polyelectrolyte mixture behaviour route is determined by the fraction of charged

groups in both polymers. When f is low, the interaction between polyelectrolytes becomes much like the

interaction between uncharged polymers and is dominated by low mixing entropy (order of 1/N where N is the

number of monomers per chain) which causes solution segregation. The parameter that is used to characterise

the degree of such repulsive polymer mismatch is called the Flory-Huggins parameter χ [138]; it is used in

the calculation of the free energy of complex formation (enthalpic), and generally, if positive, means that the

selected polymer pair is incompatible and will phase separate in solution [139]. When f is high

polyelectrolytes form complexes due to the attractive electrostatic interactions that dominate over entropic

chain repulsion [83]. The diagrams for both low and high f cases are presented in Figure 13.

Figure 13 – Typical phase diagrams for (a) low charge density polyelectrolyte solutions (b) high charge

density solutions. The thick lines indicate co-existing phases. Reproduced from [139] with permission of

Springer.

The concentration of monomers inside the polyelectrolyte complex is influenced by electrostatic interactions

as follows:

ccf 2

a2nw43 (1− f 2

n32 lb

12 a2 w

23 )∗¿

(34)

where a is the size of a monomer, n is the concentration of counterions, w is the calculational coefficient of

the order of monomer volume a3, lb is the Bjerrum length.

* This formula was derived in terms of the Random Phase Approximation (a generalisation of the Debye –

Hückel theory of strong electrolytes) and Mean Field Theory combined. Details for approximations and a full

list of equations can be found elsewhere [139].

More complex charge density-volume fraction polyelectrolyte complexation phase diagrams have been

developed by Oskolkov and Potemkin [140]. They show the formation of different types of complexes

between N linear flexible poly-ion molecules, where N=N +¿¿ (number of polycations) +N−¿¿ (number of

polyanions) and were built for systems with slight asymmetry of charge, meaning that all polyelectrolyte

molecules have the same length and same absolute charge density, but the number of charged chains in

polycation and polyanion molecules is different, N+¿>N−¿ ¿¿. This asymmetry of charge is represented as an

asymmetry parameter Aasexpressed as

Aas=N+¿− N−¿

N≪1¿

¿

(35)

Each molecule consists of m segments, each segment has the size aand a small fraction of charged groups

f =1σ

≪1. Counterions coming from polyelectrolyte chains themselves are treated as non-influential; the only

“excess” counterions are produced from N+¿−N−¿¿ ¿ symmetry [140].

Diagrams are built by equating the chemical potentials of the phases, μi (ф1 )=μ j ( ф2) and osmotic pressures

π i ( ф1)=π j (ф2 ) where i, j = polycation + globules, spheres, cylinders, lamellae and macrophase (precipitated

globules). Chemical potentials and osmotic pressures are calculated as

μi (ф )=∂ F i

∂ ф, π i (ф )=ф μ i ( ф)−Fi (36)

where F i is a free energy which is calculated by using different formulae for different diagram regions

(different phases) [140].

The resulting diagram is presented in Figure 14 and shows the regions of stability for various complexes. The

lined regions correspond to co-existence of the connected phases.

Figure 14 – Complexation phase diagrams for polyelectrolyte with asymmetric charges. Reprinted [140] with

permission – Copyright 2017 American Chemical Society.

2.4.2 Polyelectrolyte multilayering

Formation of polyelectrolyte multi-layers, as mentioned before, includes adsorption of the first polyelectrolyte

layer onto a substrate, adsorption of the second layer via complexation and further polycation-polyanion

complexation based layering steps. This procedure, up to the 3rd layer (which can be extrapolated to explain

all consecutive layers), is well presented in the widely-accepted theory developed by J.F. Joanny and M.

Castelnovo [83] which describes layer-by-layer polyelectrolyte deposition based on electrostatics and can be

summarised into an example-based diagram presented below (Figure 15). This theory is mostly applicable for

weakly charged polyelectrolytes and is built on following assumptions: polymers have the same large

molecular weights M w, same fraction of charged groups f , and the same concentrations c.

Note: in formulas included in the Figure 15 a is the size of a polyelectrolyte monomer, n is the concentration

of counterions, w is the calculational coefficient of the order of monomer volume a3, lb is the Bjerrum length,

f is the fraction of charged groups.

At low added salt concentrations, the growth of polyelectrolyte multilayers can be described by two regimes –

linear, where the thickness increment is constant for each deposited bilayer, and exponential, in which

thickness increment increases with the number of layers [1, 141]. Any multilayer assembled via the

electrostatic layer-by-layer procedure can be characterised by a general growth profile that contains both

linear and exponential parts with a switch point where the transition from one regime to another occurs

(Figure 16A). If the film grows linearly, the exponential part of the profile is short and almost cannot be

distinguished; exponential growing films have a large well pronounced exponential part of the profile [141].

Figure 15 – Polyelectrolyte multilayering in terms of theory by J.F. Joanny and M. Castelnovo [83].

One of the most important aspects of these profiles is the switch point, and how the switch from one growth

regime to another can be induced.

The switch from exponential to linear growth can be explained by two growth regime models – the

“roughness” model and the “diffusion” model.

The “roughness” model (Figure 16B) describes the formation of multi-layers starting from formation of

isolated islands, which grow in height and diameter with the number of layers leading to the exponential

increase in covered surface area [141]. These isolated islands grow up to a point of coagulation with the

neighbouring islands producing at multi-layer that then grows linearly. This model provides an explanation

for the deviation from linear growth for the first several layers in films that have a pronounced linear growth

regime otherwise [141].

Figure 16 – A – Growth profile of HA/PLL multi-layer showing a switch from exponential to linear growth

regimes. B – Scheme of “roughness” model representing a coalescence of initially formed islands at the

switch point during the multi-layer build-up. C – Scheme of “diffusion" model representing a formation of

restructuring zone (polymer diffusion is restricted) underneath the diffusion zone at the switch point.

Reprinted [141] with permission from Elsevier.

The “diffusion" model describes the growth of multilayers based on the possibility of diffusion of component

polyelectrolyte chains in and out of the fabricated multi-layer [141, 142]. If polyelectrolyte chains are not able

to diffuse into the multilayer the film grows linearly, otherwise – exponentially. In the process of adsorption

of the oppositely charged polyelectrolyte, the excess amount of the polyelectrolyte within the film moves to

the interface and produces complexes with the newly adsorbing oppositely charged polyelectrolyte. In this

case, the increase in the multi-layer thickness leads to the increase in polymer uptake of the each freshly

adsorbed layer – the growth is exponential. Within this model, the switch from exponential to linear regimes

can be explained by the formation of so-called “forbidden zone”, or “restructuring” zone within the multi-

layer that forms between the first several layers and the outer layers. This zone is formed with the increase in

a number of polyelectrolyte layers and is a consequence of the relative rearrangement of the polyelectrolyte

chains within the multi-layer; such rearrangement takes place close to substrate creating the structure

impenetrable to polyelectrolyte chain diffusion, leading to the switch to the linear growth regime [1, 141,

142]. This model provides a good fit for experiments with polyelectrolytes of high molecular weight but does

not explain low molecular weight multilayer growth behaviour which still switches from exponential to linear

even though short chain polyelectrolytes are able to diffuse into the multi-layer easily [143]. The possible

solution for this contradiction is that low molecular weight polyelectrolytes can diffuse out of the multilayer

completely and form complexes outside the film thus removing the excess polymer that could have led to the

exponential growth maintenance [143]. Another possible cause is the formation of an electrostatic barrier on

top of the film that prevents mobile polyelectrolyte chains from diffusing through the surface (meaning that

excess polyelectrolyte would be trapped within the multi-layer) [141].

Since complexation of polyelectrolytes is mostly driven by electrostatic interactions, it is assumed that linear

multilayer growth is common for polyelectrolyte complexes with intrinsically-induced charge compensation

(strong polyelectrolytes), while exponential growth is based on both intrinsic and extrinsic charge

compensation types [141] (weaker polyelectrolytes). The comparison of outcome multi-layers for both growth

regimes is shown in Figure 17.

Figure 17 – Linearly and exponentially grown multi-layers. Adapted [141] with permission from Elsevier.

Growth regimes can be induced/prevented by external factors such as temperature, pH and added salt content

of the multi-layering medium. The effects of these factors are summarised in Table 11.

Table 11 – Factors influencing polyelectrolyte multilayer growth regime

Factor Effect on growth regimeTemperature Polyelectrolyte complexation occurs spontaneously when the change in associated free Gibbs

energy ∆ G is negative

(37) ∆ G=∆ H−T ∆ S

Free Gibbs energy contains two contributions, enthalpic ∆ H and entropic T ∆ S.

As it has been mentioned earlier, polyelectrolyte complex formation is influenced by entropy, which is, if low, prevents weakly charged polyelectrolytes from the complex formation. Interaction of oppositely charged polyelectrolytes leads to some of the counterions escaping into a solution which causes the increase in entropy [144] and favours complex formation [141, 145] and thus to linear multilayer growth.

Enthalpy, which is equal to the heat exchanged by the system (in this case, polyelectrolyte complex at its formation) and its surrounding medium, plays important role in multilayer growth regime outcome as well. It is also the only parameter that can be measured directly by calorific experiments [144]. Linearly growing films are produced if the complexation process is exothermic (∆ H ≤−1000 J ∙mol−1) with negative change in enthalpy (positive in entropy); endothermic complexation accompanied by counteractive positive gain both in enthalpy (∆ H ≥−500 J ∙mol−1) and entropy leads to exponentially growing multilayers.

Thus, the temperature has a larger effect on exponentially growing films: the pronounced increase in multilayer thickness with increase in temperature [141] is observed, while linearly growing films show no or a very small thickness increase [144].

pH The changes in pH of the complexation medium result in changes in polyelectrolyte multilayer growth mechanism since pH can be used to alter the density of charged groups (in weak polyelectrolytes) leading to strengthening or weakening of polyelectrolyte interactions.

General growth regime-pH dependency trend was clearly illustrated by Peter Bieker and Monika Schönhoff [146] who have reported growth behaviour of PAH/PAA multilayers at five different pH values and have got the following results:

pH Influence on polyelectrolyte Growth regime

3-4.5 PAA (acid) 50% charged, PAH (base) nearly fully charged

Linear, rigid asymmetric film.

4.5-6 Increase in PAA charge density, decrease in PAH

Exponential, 4.5 switch point, rigid but not compact film (allows for diffusion of chains into multilayer).

6.5-7.5 Both PAA and PAH are nearly fully charged

Linear as both polymers behave like strong polyelectrolytes with strong polyion interaction (no interlayer diffusion allowed). Symmetric film.

8-10 Further increase in PAA charge density, decrease in PAH

Exponential (same behaviour as pH 4.5-6 regime, non-compact multilayer with allowed diffusion)

10-12 PAA is nearly fully charged, PAH very weakly charged

Linear, rigid asymmetric film.

Therefore, when one or both of polyelectrolytes are fully charged (which can be accomplished by tuning the pH of the solution) one can expect linear film growth due to strong electrostatic interactions; otherwise, exponential growth is observed [1, 146].

It should also be noted that the stability of the resulting film can be affected by the pH

variation. In both flat [Hoogeveen, Cohen Stuart, Fleer] and spherical [DOI: 10.1021/la049934h] multi-layered films, fabricated using at least one weak polyelectrolyte, noticeable softening of the structures is observed under the pH change. It has also been shown that the number of layers, or, from another perspective, type of the outer layer, changes the response of the film to the medium change [Hoogeveen, Cohen Stuart, Fleer]. Partial pH-induced desorption occurs in case of the top layer being composed of a weak polyelectrolyte (odd number of layers), while strong polyelectrolyte layer on the top traps weak polyelectrolyte layers enough to make the structure stable [Hoogeveen, Cohen Stuart, Fleer]. pH-induced softening is believed to be the consequence of the change in the charge density of weak polyelectrolytes caused by the presence of the titrable groups that can be protonated/deprotonated by the pH-changing agent thus influencing the number of charges present on the polymer molecules [Simulation of weak polyelectrolytes:A comparison between the constant pHand the reaction ensemble method]. Impact of the pH on dissociation behaviour of polyelectrolytes is formalised in section 1.2.

The stability of the films assembled using a pair of strong polyelectrolytes is not affected by the pH.

Ionic strength (added salt content)

Additional counterions (added salt) introduced into complexation medium screen polyelectrolyte charges which results in reduced number density of complexed polyion pairs within the multilayer. This leads to non-compact films and facilitates the diffusion of polyelectrolyte chains into the multilayer resulting in exponential growth regime. By introducing additional salt ions one can switch growth regime from linear to exponential and grow thicker films [141]. The effect of salt concentration onto growth regimes and the behaviour of the resulting films are summarised in the picture below (Reprinted [141] with permission from Elsevier).

In both flat [Hoogeveen, Cohen Stuart, Fleer] and spherical [DOI: 10.1021/la049934h] multi-layered films,

fabricated using at least one weak polyelectrolyte, noticeable softening of the structures is observed under the

pH change. It has also been shown that the number of layers, or, from another perspective, type of the outer

layer, changes the response of the film to the medium change [Hoogeveen, Cohen Stuart, Fleer]. Partial pH-

induced desorption occurs in case of the top layer being composed of a weak polyelectrolyte (odd number of

layers), while strong polyelectrolyte layer on the top traps weak polyelectrolyte layers enough to make the

structure stable [Hoogeveen, Cohen Stuart, Fleer]. pH-induced softening is believed to be the consequence of

the change in the charge density of weak polyelectrolytes caused by the presence of the titrable groups that

can be protonated/deprotonated. The stability of the films assembled using a pair of strong polyelectrolytes is

not affected by the pH or the ionic strength.

Conclusion

A wide range of multi-layered structures can be fabricated using the electrostatic layer-by-layer method,

making it a very important production technique for a number of industries including medical, cosmetics,

wastewater treatment, and any other area that involves using encapsulated or layered materials. In this review,

we have comprised a summative description of the current understanding of the materials (templates and

polyelectrolytes) and processes involved in the layer-by-layer procedure, including polyelectrolyte adsorption

process (polyelectrolyte behaviour at the interface, characterised by such parameters as

completion/incompletion (saturation/unsaturation) of the layer, adsorbed mass and morphology of the formed

layer), interactions between polyelectrolytes and the external factors that control them (temperature, pH, ionic

strength), as well as the impact of the interactions themselves on the multi-layering process outcomes

(polyelectrolyte complexation). We have also presented a list of construction materials that can be and have

been successfully used with the layer-by-layer procedure for fabrication of a wide range of structures of

different sizes and structures. This review, thus, can serve as a starting guide for working with the electrostatic

layer-by-layer method and is a reference for selection of the materials and conditions of the multi-layering

procedure for the desired production outcome.

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