Colloid Chemistry · 2019. 4. 1. · Silvia Gross –Chimica dei ... (A, y 0, electrolyte nature...

Silvia Gross – Chimica dei Colloidi – Laurea Triennale in Chimica

Istituto di Scienze e Tecnologie Molecolari

ISTM-CNR, Università degli Studi di Padova

e-mail: [email protected]

Silvia Gross

La chimica moderna e la sua comunicazione

Dipartimento di Scienze Chimiche

Università degli Studi di Padova

e-mail: [email protected]

http://www.chimica.unipd.it/silvia.gross/

Silvia Gross

Colloid Chemistry


Colloid stability and DLVO theory

Understanding and controlling stability and structure (= spatial

organisation of the colloidal particles) of dispersion:

- Nature and origin of interparticles interactions (attractive, repulsive)

- Derivation of classical theory on colloid stability DLVO

- Effect of solution chemistry (A, y0, electrolyte nature and concentration) on

interparticles interaction energies (see vdW and electrostatic interactions):

- critical coagulation concentration (of electrolyte)

- Schulze-Hardy rule (effect of electrolyte valence)

- Effect of interparticles interactions on coagulation in dilute dispersions and on

structure of dispersion

- Quantitative determination of stability of a dispersion against coagulation (stability

ratio, W) (Smoluchowski and Fuchs theories of colloid stability)

- Develop quantitative relationship between stability and interparticle forces

- Theory of rapid and slow coagulation


Concept of colloidal stability

Colloidal stability relates to the physical state of the system: it is

stable if it remains well dispersed

Colloidally stable means that the particles do not aggregate at a

significant rate: the precise connotation depends on the type of

aggregation under consideration.

http://old.iupac.org/reports/2001/colloid_2001/manual_of_s_and_t/no

de35.html


Collod stability

Stability: ability of a dispersion to resist coagulation

Aggregation is the process or the result of the formation of aggregates.

When a sol is colloidally unstable (i.e. the rate of aggregation is not

negligible) the formation of aggregates is called coagulation or

flocculation.

coagulation, implying the formation of compact aggregates, leading to

the macroscopic separation of a coagulum;

flocculation, implying the formation of a loose or open network which may

or may not separate macroscopically. In many contexts the loose

structure formed in this way is called a floc.

http://old.iupac.org/goldbook/C01119.pdf


Stability of colloidal dispersion

van der Walls: attractive forces and typically high intensity at short distances

→ if not counterbalanced: unstable dispersion and coagulation

Protection against vdW attraction provided through two main mechanisms:

1. Polymer-induced (steric) stability: suitable polymer/surfactant

adsorbed on particle surface; may also provide repulsive force, partially

due to pure steric effects (polymers chains overlap).

2. Electrostatic stability: electrostatic repulsive force deriving from

particles becoming charged (overlap of the electrical double layer):

understanding how it depends from experimental parameters


Stability of colloidal dispersion

1. Polymer-induced (steric) stability: suitable polymer/surfactant

adsorbed on particle surface; may also provide repulsive force, partially

due to pure steric effects (polymers chains overlap).

- interaction polymer-dispersing medium

- configurational freedom of polymers

- analytical methods needed to be developed

- thermodynamic picture of steric stabilisation only accounting of:

- excluded volume of polymer chains

- elastic contributions determining interactions between polymer layers


Stability of colloidal dispersion:

kinetics or thermodynamics?

barrier along the path

to coagulation

coagulation

Kinetic stability: consequence of a

energy barrier against collision and

eventually coagulation (favoured,

thermodynamically, by reduction of

DG)

But: Interaction energy barrier >> kBT

Thermodynamic stability

Example: related to the possibility of

the particle to assembly to give

ordered networks or association

colloids


Stability of colloidal dispersion:

kinetics or thermodynamics?

Thermodynamics: what the equilibrium state will be

Kinetics: if that equilibrium state will be reached and how fast

Examples:

- Formation of micelles from surfactants at given concentration:

thermodynamics driven

- Lyophobic colloids (clays, silica dispersion) thermodynamically

unstable, kinetically stable (if potential and/or surface charges are

enough large)

→ see DLVO: classical theory of electrostatic stability of colloids

→ in colloid science many dynamic processes and variables

(buoyancy, flow, diffusion, sedimentation)


Colloid stability and DLVO theory

Quantitative relationship between interparticle forces and colloid stability:

Understanding relationship between interparticle forces and microstructure* of

dispersion (average distance, size and size distribution etc.)

*structure= spatial organisation of collodal particles


Interplay interparticle forces/structure

Microstructure & stability determine quality, processability and properties of

colloidal systems.

Effect of:

- Interparticle forces

- Concentration

on structure of dispersions

Analysed example: microstructure (local arrangement of particles) in a

monodisperse colloid as a function of particles concentration


Correlation between

interparticle forces and

corresponding microstructure)

in monodisperse colloid

1. Overall interparticle forces

dominated by strong

repulsion (TD stability)


dominated by strong

attraction

3. Intermediate situation

Volume fraction= fraction of the volume

of the system occupied = n4/3pa3

2

1

3




dominated by strong

repulsion (1)

surface charge large

strongly overall repulsive forces

extended over large distances (k-1)

thermodynamic stable dispersion

particles can assembly in ordered

crystalline structures even at very

low volume fractions (f= nvp< 0.001)

type of crystalline structure:

concentration and k-1

large k-1: body centered cubic structure

small k-1: face centered cubic structure

2

1

3



atom packing/crystalline structures


Overall interparticle forces

dominated by strong

attraction (2)

Dispersion becomes

thermodynamically and

kinetically unstable:

Aggregated interconnetcted

networks (gel) with loose

fractal structure with strong

vdW interparticle “bonds”2

1

3



Gels

Gel

Non-fluid colloidal network or polymer network that is expanded throughout its whole volume by

a fluid.

http://goldbook.iupac.org/CT07563.html

http://goldbook.iupac.org/P04742.html



dominated by strong

repulsion


dominated by strong

attraction


2

1

3




dominated by strong

repulsion


dominated by strong

attraction


2

1

3


Repulsion/attraction of comparable

magnitude, system microstucture more

sensitive to changes in relative

contributions

Aggregation in secondary/primary minima

Dense and more efficient packing are

possible (e.g. ceramics processing)

Solution chemistry and surface chemistry

allows tuning


DLVO theory (ca. 1940)

B.V. Derjaguin, L.D. Landau, Theory of Stability

of Strongly Charged Lyophobic Sols and

Adhesion of Strongly Charged Particles in

Solutions of Electrolytes, Acta Physicochim.

URSS 14 (1941) 633-662.

E.J.W. Verwey, J.Th.G. Overbeek, Theory of

Stability of Lyophobic Colloids, Elsevier,

Amsterdam, 1948.


DLVO theory


DLVO theory (ca. 1940)

Assumption 1 (approximation → see further “non-DLVO” forces)

Colloidal stability determined by a balance between:

- electrostatic repulsion

- van der Walls attraction

further contributions (”non-DLVO” forces, e.g. depletion interactions) neglected

Assumption 2

Additivity of the two contributions

Assumption 3

Even distribution of particles and ions in the dispersion


0

B

B

exp( x)

[exp(ze / 2k T) 1]

[exp(ze / 2k T) 1]

k

DLVO theory

Poisson-Boltzmann without limitations of DH

approximation → development of Gouy-Chapman

theory for EDL: derivation of an equation

describing variation in potential with distance

from the surface for diffuse double layer without

the simplifying DH approximation of low potential:

1 2

Bne 0

2212t 64k Tn ex

A( )( d1

d)2

p

p

k k

Case: two interacting parallel planes at a distance d

Vnet (d) = VR(d) + VA(d)

n∞ = bulk ions concentration

repulsion potential assuming:

- interacting planes

- not DH approximation (Gouy-Chapman)

- superposition approximation

- Taylor series

(interacting planes, d)


DLVO theory (interacting planes, d)

The secondary minimum could cause

flocculation/reversible coagulation

The primary minimum is the reason for

coagulation in most cases

1 2 2t

212ne B 0

A64k Tn exp( ) ( )d

12d

k p

k

Height of potential barrier determined by VR

Potential barrier can be lowered by:

- increasing electrolyte concentration (decrease

of k1)

- decreasing surface potential2

0

Unstability if barrier < several kBT

VR(d) VA(d)

Shape of curves: physical & geometrical

factors

12

1 0

2 2

r

i i

i

kT

e z n

k


DLVO theory

General conclusions:

1. The higher potential at surface (and through the EDL, inner limit of the

diffuse part), the higher the repulsion

2. The lower the concentration of electrolytes, the longer the distance

from the surface before the repulsion drops significantly (k-1)

3. The larger the Hamaker constant, the larger the attraction between

macroscopic bodies

1 2 2t

212ne B 0

A64k Tn exp( ) ( )d

12d

k p

k


DLVO theory


1. The higher potential at surface (and through the EDL), the higher the

repulsion




macroscopic bodies

1 21t

22ne B

2

0

A64k Tn exp( ) ( )d

12d

k p

k


DLVO theory: effect of the potential

0 (case flat blocks): Gouy-Chapman

0

B0

B

0

0

0

0[exp(ze / 2k T) 1]

[exp(ze / 2k T) 1]

1

for large values of 𝛹0

Potential of the inner limit of the diffuse part of EDL

(not the «surface»)

𝛹0 𝛹0→ sensitivity to the value of decreses as increases



0 (case flat blocks)

y0

Adjustable through the concentration of

potential determining ions

Value affected by specific adsorbtion

phenomena

More correct to refer to “inner limit of the

diffuse double layer” instead of “on the

surface”

→ zeta potential is the lower limit for y0



0 (case flat blocks)

Plot of net /kBT

versus d for flat blocks

Different values of 0

Electrolyte z:z = 1:1, 0.093 M

Constant value of k = 109 m-1

Constant value of A= 2*10-19 J

0

1 2212net B

2 A64k Tn exp( d) ( )d

12

k k p

y0

increase in barrier = repulsion

potential can be tuned by p.d.i.

Large values of 0 0 1


Inert and potential determining ions

potential-determining (p.d.) ions

Species which by virtue of their electron distribution between the solid and liquid phase (or by

their equilibrium with electrons in the solid) determine the difference in potential between

these phases. This definition requires that adsorbed p.d. ions are part of the adsorbent and

belong to the category of surface ions (http://goldbook.iupac.org/P04776.html)

Es: Ag+ and I- ions in AgI sols, H+ in oxides (potential pH-determined)

inert (indifferent) ions

They do not change the charge density at the surface of the particles, but may influence the

interfacial potential difference by virtue of their local distribution (e.g. NaNO3)

http://goldbook.iupac.org/A00153.html

http://goldbook.iupac.org/S06180.html

http://goldbook.iupac.org/P04776.html


DLVO theory: surface charge density

DLVO potentials at constant salt concentration with varying surface charge density

Picture:

Courtesy Prof. Peter Lang,

Forschungszentrum Jülich,

Germany


DLVO theory



repulsion




macroscopic bodies

1 2 2t

212ne B 0

A64k Tn exp( ) ( )d

12d

k p

k

(interacting planes)


DLVO theory: electrolyte

concentration

1/ 2

1 0 r

i

B

2 2

A i

i

k T

1000e N z M

k

most «tunable» parameter from the experimental point of view

charge/valence of the electrolyte

concentration of the electrolyte



concentration

DLVO potentials at constant

surface charge density with

varying electrolyte concentration

Picture:



Germany

1/ 2

1 0 r B

2 2

A i i

i

1

1/ 2

k T

1000e N z M

1

zM

k

k



concentration

1/ 2

1 0 r

i

B

2 2

A i

i

k T

1000e N z M

k

we concentrate on M


DLVO theory: effect of the electrolyte

(case spheres of equal r = 100 nm)

Constant value of 0 = 25.7 mV

Radius (equal) of spheres = 100 nm

Constant value of A= 2*10-19 J

Different values of k (concentration

10-3 to 10-2)

1/ 2

1 0 r B

2 2

A i i

i

1

1/ 2

k T

1000e N z M

1

zM

k

k

k

k1


DLVO theory



repulsion




macroscopic bodies

1 2 212net B 0

2A64k Tn exp( ) ( )

12d d

k p

k


DLVO theory: effect of Hamaker

constant

Plot of net /kBT

versus d for flat blocks

Constant value of 0 = 103 mV

Constant value of k = 109 m-1 = k-1 = 1 nm

Different values of A 212

1 2 2t

212ne B 0

A64k Tn exp( ) ( )d

12d

k p

k

Energy barrier decreases, secondary minimum depth

increases with increasing A

Lowest degree control (chemical nature of the

phases)


DLVO theory: actual values

Contributions to the total interaction energy between two spheres

Picture:



Germany

kBT scala

kBT at 298 K = 4.11 *10-21 J


Critical Coagulation Concentration

Experimental starting point:

addition of an indifferent (i.e. not potential determining)

electrolyte to a lyophobic colloid can cause coagulation


DLVO theory


1. The higher potential at surface (and through the EDL, inner limit of the

diffuse part), the higher the repulsion




macroscopic bodies

1 2 2t

212ne B 0

A64k Tn exp( ) ( )d

12d

k p

k



Sharply defined concentration of the electrolyte

needed to induce coagulation (settling out of the dispersed

phase)

Critical coagulation concentration (CCC)

Experimental determination:

1. test tubes of the colloidal suspension with increasing

electrolyte concentration

2. addition of water and electrolyte (dilution being constant)

3. mixing/waiting an arbitrary but consistent lenght of time

4. visual/microscopic inspection of the tube (settling out of

the coagulum)

the highest concentration that leaves the colloid unchanged

and the lowest determining coagulation brackets the CCC



Actual concentration of electrolyte at CCC affected by:

a) time allowed to elapse after electrolyte addition

b) polydispersity of the sample

c) potential at the surface

d) the value of Hamaker constant

e) the valence of the ions of the electrolyte

Typically (a)-(d) remain constant, so CCC can be used for a quantitative

measure of the effect of the valence of the ions (Schulze-Hardy rule)



Actual values of concentrations: array of different (and partially unknown) parameters

Relative values of concentrations: valence of the counterions: generalisation possible: SH rule


Schulze-Hardy rule (1900)

Generalization about the effect of electrolyte

It is the valence of the ion of opposite charge with respect to the surface of

the colloid which has the prevailing effect on colloid stability (regadless the

nature of the ion with the same charge as the surfcae).

Definition of Schulze-Hardy Rule by IUPAC

The generalization that the critical coagulation concentration for a typical lyophobic sol is extremely

sensitive to the valence of the counter-ions (high valence gives a low critical coagulation

concentration).

http://goldbook.iupac.org/S05501.html

H. O. Schulze (1853–1892), Sir W. B. Hardy (1864–1934)



stable

coagulate

can we translate it into a qualitative

relationship?

value of k for which the barrier becomes 0?



Derivation of SH rule

We assume: border stability/unstability at k values corresponding to energy

barrier = 0 (kBT units)

Maximum in the potential energy occurs at zero means

net = 0 at d = dm (location at the maximum of the potential)

and

dnet/dd = 0 at d = dm



Derivation of SH rule

since holds: 1 2 2212net B 0

A64k Tn exp( d) ( )d

12

k k p

1 2 2212B 0 m m

A64k Tn exp( d ) ( )d

12

k k p

net = 0 at d = dm

dnet/dd = 0 at d = dm

2 3212B 0 m m

A64k Tn exp( d ) 2( )d

12

k p

conditions of zero barrier are satisfied for:



Derivation of SH rule (looking for dependence of CCC from valence)

since holds: 1 2 2212net B 0

A64k Tn exp( d) ( )d

12

k k p

1 2 2212B 0 m m

A64k Tn exp( d ) ( )d

12

k k p

net = 0 at d = dm

dnet/dd = 0 at d = dm2 3212

B 0 m m


12

k p

1

m2 dk from which we obtain

we have obtained:

1

mdk case: spherical particles:

criterion for stability



Derivation of SH rule: dependence of CCC from valence

since holds:

3n k

1

m2 dk

(neglected the dependence of on z) we obtain:

and

0

2 2

i i

i

0 r B

e z n

k T

k

1/2

3 3/ 2n z n

since holds:

and6

1c

z

2 3212B 0 m m


12

k p


Rules of thumb for the calculation of

k for different types of electrolytes.

The salt concentration, c has to be

introduced in the unit mol/L

2 3

6 6

1 1 1 1Na : Mg : Al CCC 1: : 1: :

2 3 64 729



2 3

6 6

1 1 1 1Na : Mg : Al CCC 1: : 1: :

2 3 64 729



“Inverse” Schulze-Hardy rule (2015)



Schulze-Hardy Rule CCC ≈ 1/z6

Inverse Schulze-Hardy Rule CCC ≈ 1/z

EXPERIMENTAL

Polystyrene latex 300 nm diameter

Amidine and sulphate groups functionalisation

Dispersed in salt solutions 10 mg/L

Different multivalent electrolytes

Evolution followed by DLS

Typically positively charged particles coagulated by multivalent anions and viceversa

Multivalent ions are the co-ions (same sign as the colloidal particles)


CCC: summary

- Ions opposite in charge with respect to the surface: predominant

role in EDL (basic statment of Schulze-Hardy rule, SHR)

- In the Gouy-Chapman theory, a Boltzmann factor introduced to

describe relative concentration of ions in EDL with respect to bulk

ni/ni∞ = exp (-zi·e·y /kBT)

Ions having the same charge as the surface

exponent is negative → (Coulombic repulsion of the ions from the surface)

→ ions with same charge as the surface present a lower concentration in

EDL (ni) than in the bulk (ni∞)

Oppositely charged ions: concentration increased in EDL

→ only counterions contribute to the diffuse double layer at CCC


CCC: summary

- The valence chiefly determine the CCC (Schulze-Hardy rule)

- Small difference in ions with same valency: to coagulate:

As2S3 sol: 0.058 M of Li+ and 0.051 M of Na+

AgI sol: 0.165 M of Li+ and 0.140 M of Na+

- Li+ less effective than Na+ in coagulation

Effectiveness to promote coaugulation

- Cs+ > Rb+ > NH4+ > K+ > Na+ > Li+

- F- > Cl-> Br-> NO3-> I- >SCN-


strength of specific adsorbtion

I- >SCN->Br->Cl->OH->F-

N(C2H5)4+ > N(CH3) 5

+ > Tl+> Cs+> Na+

Specific adsorption enhanced by larger size (= larger polarizability)

and lower hydration

→ The stronger the specific adsorption, the lower the effectiveness in

determining coagulation


DLVO theory: summary

additional approximations introduced, but:

- effective and versatile tool for understanding colloid stability

- quantitative theoretical analysis well matching with experimental

outputs

- threshold of stability in terms of

(a) valence and

(b) concentration of added indifferent electrolyte easily measured

Colloid Chemistry · 2019. 4. 1. · Silvia Gross –Chimica dei ... (A, y 0, electrolyte nature...

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Transcript of Colloid Chemistry · 2019. 4. 1. · Silvia Gross –Chimica dei ... (A, y 0, electrolyte nature...