Early (pre-DLVO) studies of particle aggregation

Advances in Colloid and Interface Science 170 (2012) 56–67

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Early (pre-DLVO) studies of particle aggregation Brian Vincent School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK

a r t i c l e

i n f o

Available online 27 December 2011 Keywords: Particle aggregation Critical electrolyte concentration Aggregation rate Colloid stability DLVO theory

a b s t r a c t The history of colloid science, from its modern foundations in the mid-nineteenth century, has been strongly concerned with studies of the aggregation of colloidal particles. It was Thomas Graham (1861) who defined the word “colloid” (from the Greek word for glue) for those materials which could not pass through membranes, unlike smaller, truly-dissolved materials. Subsequently, Graham (1864), following earlier studies, principally by Selmi and Faraday, described “the power possessed by salts for destroying colloidal solutions”. Although numerous, quantitative studies of particle aggregation were made in the years that followed, in particular, the determination of minimum electrolyte concentrations for the onset of particle aggregation and aggregation rates, no general theoretical framework emerged to account for these quantitative findings until the middle of the twentieth century. It was during and immediately following the Second World War that two sets of authors, Derjaguin and Landau, in Russia, and Verwey and Overbeek, in the Netherlands, independently came up with the theory that is now universally referred to as the DLVO theory of particle interactions and aggregation. All modern developments of the theory of particle aggregation use the DLVO theory as the keystone. However, the DLVO theory itself was based on a large body of experimental data in regard to particle aggregation obtained over the previous hundred years or so. This article is an attempt to review that body of experimental data and to show how this guided the DLVO authors in their thinking. © 2012 Elsevier B.V. All rights reserved.

1. Introduction A truly pivotal point in the history of colloid science was the emergence, around the time of the Second World War, of a quantitative theory of the stability to aggregation of dispersions of charged colloidal particles. This was based on the concept, originally suggested in 1936 [1], by Hugo Christiaan Hamaker (Fig. 1; from the Philips Laboratories in Eindhoven) that the stability of a colloidal dispersion depends on the interplay of two long-range interparticle forces: repulsive interactions resulting from double layer overlap and attractive van der Waals interactions. Hamaker sketched various possible total potential energy curves, as a function of particle separation, indicating maxima and minima in certain cases, to which conditions for stability and aggregation could be attributed. Quantitative theories of these interactions were developed and published independently by Derjaguin and Landau (Fig. 1) in Russia in 1941[2], and by Verwey and Overbeek (Fig. 1) in the Netherlands in 1948 [3]. Boris Derjaguin was from the USSR Academy of Sciences and Lev Landau from Moscow State University; Evert Johannes Willem Verwey was Director of Research at the Philips Research Laboratories in Eindhoven and Theo Overbeek was professor of physical chemistry in the van't Hoff Laboratory in Utrecht. Together their work forms the basis of what has become

E-mail address: [email protected]. 0001-8686/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.cis.2011.12.003

universally known as the “DLVO” theory of colloid stability. This term was first coined it seems by Samuel Levine. Although, as we shall discuss later, there had been preliminary, separate publications by Derjaguin, Verwey and Overbeek, and their colleagues, in a UK journal (the Transactions of the Faraday Society) in 1940, the war prevented the two groups retaining awareness of each others subsequent work, both whilst the war was in progress and in the immediate aftermath. This led to some discussion [4] as to “priorities” when Derjaguin actually met Overbeek and Verwey for the first time (Landau was not present), at the Discussion meeting of the (UK) Faraday Society in Sheffield in 1954 on “Coagulation and Flocculation”. However, this issue was settled amicably at the meeting [4]. Much of the work in the area subsequently has been concerned with modifications to the basic ideas set out on the DLVO theory, including the introduction of additional types of interactions and its extension to concentrated dispersions, where the concept of pairwiseadditivity breaks down. On the experimental side, over this period, there have been considerable developments in both systems and techniques. There are now much better defined colloidal particles for use in model studies, and a much greater variety of sophisticated techniques available for studying both aggregation processes and the forces between colloidal particles. The reader is simply referred to recent textbooks on colloid science for information on these topics. It is worth noting, however, that the first direct measurements of surface forces were reported at the 1954 Faraday Discussions meeting, again by Overbeek [5] and by Derjaguin [6] and their co-workers. In

B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

Hugo Hamaker

Overbeek, Derjaguin and Verwey (at Portmeirion, Wales, 1968)

57

Lev Landau

Fig. 1. Hugo Hamaker Overbeek, Derjaguin and Verwey Lev Landau (at Portmeirion, Wales, 1968).

many ways that 1954 meeting marked another watershed in the development of colloid science. In this article I take a different perspective. My aim is to review the body of experimental and theoretical work prior to the DLVO theory, upon which the authors of that theory would have based their ideas regarding colloid stability and particle aggregation. In certain cases I shall briefly refer to more recent studies, but only where this helps to clarify an issue. I shall limit discussion, for the most part, to dispersions of solid particles (in the size range from a few nm to a few μm) in liquid media, as it is for these systems that the DLVO theory was primarily intended. The smallest particles in this size range would these days be called “nanoparticles” by many people. Most of the solid particles studied, pre-DLVO were inorganic (e.g. a metal, a metal salt or metal oxide). Some were organic, but I shall, for the most part, only consider here those comprising organic molecules of low molecular weight. I mostly exclude systems where the dispersed species would these days be considered to be macromolecules (e.g. proteins) or assemblies of amphipathic molecules (e.g. surfactant micelles). However, in the early days of colloid science, such distinctions could not usually be made, so some reference to them is inevitable. In addition, one major class of organic colloidal particles, widely used in more modern aggregation studies, namely synthetic polymer (latex) particles, were only really developed after the Second World War, i.e. post-DLVO. (On the other hand, natural rubber latex, originally

Francesco Selmi

discovered in South America, had been known and exploited since the eighteenth century). Finally, in this section, I would add a word on nomenclature, in particular, concerning the use of the words coagulation, flocculation and aggregation. To avoid confusion, except in specific circumstances, I have deliberately used the word aggregation as the generic word, to cover both coagulation and flocculation processes. Some colloid scientists, the first probably being Victor La Mer in 1964 [7], have wished to make a distinction between these two processes; in general, the earlier colloid scientists, whose work is reviewed in this article, such as Herbert Freundlich [8], used the two terms interchangeably. The I.U.P.A.C. publication “Definitions, Terminology and Symbols in Colloid and Surface Chemistry”, compiled by Douglas Everett in 1972 [9], is somewhat indecisive on this particular point. Similar definitions to those given by La Mer are recommended. However, the following statement is also included: “while this distinction has certain advantages, in view of the more general (but not universal) equivalence of the two words, any author who wishes to make a distinction between them should state so clearly in his publication”. 2. Aggregation Phenomena Francesco Selmi (Fig. 2), whilst he was head of chemistry at the University of Modena in Italy, published, during the period 1845–1850 [10],

Michael Faraday Fig. 2. Francesco Selmi Michael Faraday Thomas Graham.

Thomas Graham

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B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

Hans Oscar Schulze

Sir William Bate Hardy

Jean Baptiste Perrin

Fig. 3. Hans Oscar Schulze Sir William Bate Hardy Jean Baptiste Perrin.

the first systematic study of inorganic colloids (including silver chloride, Prussian blue and sulphur) and their aggregation by salts. Michael Faraday (Fig. 2), at the Royal Institution (R.I.) in London, followed this up in 1857 with his classical investigation of the colour changes in gold sols (red to blue), which could be induced on adding salts, leading to particle aggregation [11]. He demonstrated that the gold particles could be stabilised against aggregation by the addition of gelatin. Indeed it is alleged that the gold sol he prepared, which is still on display at the Faraday Museum at the R.I., contains gelatin (it has retained its red colour anyway – after more than 150 years!). Thomas Graham (Fig. 2) in 1864 [12] also noted “the power possessed by salts of destroying colloidal solutions”. At that time Graham was at University College London; he was the founder and first President of the U.K. Chemical Society (the forerunner of the Royal Society of Chemistry) and in 1854 was appointed “Master of the Mint” (a post Newton had occupied some 150 years earlier). Despite these early studies of particle aggregation, colloid science struggled to find a home in the pantheon of the natural sciences until the last years of the nineteenth century. Chemists, physicists and biologists all showed some peripheral interest in the subject, but their work was mostly of a descriptive nature. With the strong development of the relatively new field of physical chemistry in the late nineteenth century, one might have thought that the scene was set for more quantitative investigations of colloidal dispersions. However, probably because colloidal dispersions exhibit only weak colligative properties and low ionic conductivities, the leading luminaries working on the physical chemistry of solutions at that time, such as Wilhelm Ostwald (in Germany), Jacobus van't Hoff (in the Netherlands) and Svante Arrhenius (in Sweden), rather shunned their study. It was left to less well-known persons to lead the way. The first systematic, quantitative studies of the aggregation of colloidal dispersions by salts were made by Hans Oscar Schulze (Fig. 3) in 1882/3 [13,14]. Schulze spent time at the Technical University in Freiberg and then subsequently at the University de Chile in Santiago (where sadly he died at the early age of 39 in 1892). He demonstrated that the “power”, which various salts have in aggregating or precipitating a sol of negatively charged arsenic sulphide particles, is strongly dependant on the valency of the “metal”, but not on that of the “acid” constituent of the salt (these days, for “metal” we would substitute metal ion, for “acid” we would substitute the corresponding anion, e.g. Cl - from HCl). The “coagulative power” (R) of a given metal (i.e. metal ion) was defined by Schulze as “the inverse of the concentration of the salt (in gram molecules per litre) necessary to convert a given hydrosol into a hydrogel”. He established the following empirical ratio, R’: R”: R”’ = 1 : 30 : 1650, where the dashes refer to the valency of the metal (ion).

The trends, regarding the dependence of the “coagulating power” of a given salt, on the metal (ion) valency, found by Schulze, were subsequently broadly confirmed, firstly by the Belgian metallurgist, Eugene Prost in 1887 [15], who used cadmium hydrosulphide sols, and then by Lindler and Picton in 1895 [16], who used antimony sulphide sols. Ernest Linder and Harold Picton (both from University College, London) observed that “a small portion of the coagulating salt was decomposed, the metal being entangled in the coagulum”. In a later paper, in 1905, Lindler and Picton [17] accounted for this in terms of a “chemical reaction” between the metal salt and the colloidal particle, with the metal of the salt being taken up by, and hydrogen being released from, the cadmium hydrosulphide particles to form the corresponding acid in solution. The idea that the metal is somehow “taken up” by the particles had an important bearing on some of the ideas developed later regarding the mechanism of particle coagulation by salts. We will come back to this point. Two seminal papers on the subject of particle aggregation were those by William Bate Hardy (Fig. 3), which were presented to the Royal Society in London in 1900 [18,19]. Hardy, although a strong protagonist for colloid science, was essentially a biologist. He was a professor of physiology in Cambridge and the Biological Secretary of the Royal Society; he received a knighthood in 1925. In the first paper [18], Hardy makes a clear distinction between two basic classes of colloidal particles: what he termed “reversible” and “irreversible” colloids. This distinction depended on whether the sol-to-gel transition, which accompanies aggregation, could be reversed by simply reversing the (thermodynamic) conditions of the system, e.g. temperature. He gives a number of examples of reversible colloids, such as gelatine and agar, which form gels on cooling, but which may be re-dispersed on heating. Examples he quotes of irreversible colloids are gold and the metal hydrosulphides and oxides, for which the state of aggregation cannot be readily reversed. It was the famous French scientist, Jean Baptiste Perrin (Fig. 3; at the Sorbonne), who subsequently, in 1905, [20] introduced the distinction, we would now more readily recognise, namely between hydrophilic and hydrophobic colloids, with the former corresponding to Hardy's “reversible” class of colloids and the latter to his “irreversible” class. In 1909 Perrin used colloidal particles to test Einstein's 1905 theory of diffusion; he was awarded the Nobel Prize for physics in 1926. In his second paper [19], Hardy deals with irreversible colloids, on which we will focus most attention in this article. One of the issues he stressed in this paper is the relationship between the stability of the particles and their surface charge. He acknowledged that others, such as, Lindler and Picton in 1892 [21] and Zsigmondy [22] in 1898 (to whom we shall return), had previously referred to the connection between particle charge and stability to aggregation. The concept that

B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

colloidal particles carry a surface charge had arisen from earlier experiments on electrokinetics, in the mid-nineteenth century, principally by Reuss, Wiedemann and Quinke (see the recent review article by Staffan Wall [23] on the “history of electrokinetic phenomena” for further details). Hardy had already shown (1899) [24] that the direction of movement of certain, what he termed “heat-modified proteids” (modern term: protein) in electrophoresis, depended on whether an acid or alkali was added (i.e. on pH). The proteid dispersions he used were prepared by diluting egg white with water, then filtering and boiling the solution. He deduced that the proteid particles have opposite signs under different pH conditions. His electrophoresis apparatus basically consisted of a U-tube with electrodes attached at each end. Hardy can, therefore, be accredited with introducing the concept of the iso-electric point (i.e.p.). He states in his second 1900 paper [19] that, as the i.e.p. is approached (by adding acid or alkali, as appropriate), the particles become unstable, tending either to aggregate or to precipitate. Which of these two processes dominates depended on a number of factors: (i) the concentration of the particles, (ii) whether the i.e.p. is approached slowly or quickly, and (iii) whether “mechanical agitation” is applied or not. Hardy discusses in this paper the fact that, as the i.e.p. of the proteid particles is approached, the nature of the scattered light changes from blue to white, indicating an increase in particle size. Hardy showed [19] that hydrosols of ferric hydrate are “electropositive”, i.e. positively charged. He found that a small negative charge can be imparted by addition of ammonia. This finding is consistent with the modern picture of the charge reversal of ferric oxide/hydroxide particles on raising the pH above the i.e.p. However, he also found that the cationic hydrosols of ferric hydrate could be aggregated by adding a certain concentration of citric acid and that, if further citric acid was added, the particles become slightly negative and re-stabilised. These citric acid results are, at first sight, odd, since one would have thought one was lowering the pH of the solution. Maybe the observed reversal of charge occurs through specific adsorption of citrate ions? Hardy also showed [19] that silica particles (made by “breaking-up” a silica gel in water) are neutral, but become strongly negative on addition of small amounts of alkali, which is again consistent with the modern picture of the ionisation of surface silanol groups on silica particles on raising the pH. In 1904, Buxton and Teague [25] (who both worked in the Department of Experimental Pathology at the Cornell University Medical School in New York City) were probably the first to demonstrate, using electrophoresis, that the sign of colloidal particles could be reversed in certain cases on adding sufficient electrolyte (rather than by a change in pH), particularly if the ion of opposite charge to the particles was multivalent. They demonstrated this for platinum sols on adding ferric chloride solution. At low concentrations of ferric

Hugo Randolph Kruyt

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chloride the particles remained negative and stable. Above a certain concentration of ferric chloride the particles aggregated. However, at an even higher concentration the platinum particles re-dispersed; in that state the particles were shown to be positive. Furthermore, on adding even more ferric chloride, at some point the particles aggregated again, indicating the onset of a second coagulation region. It was, of course, not appreciated at that time, that many multivalent cations exhibit complex hydration chemistry in aqueous solution, particularly at higher pH values, leading to complex, multi-charged ions which may adsorb strongly onto negative particles. It was Hugo Randolph Kruyt (Fig. 4) and Sjerp Troelstra in 1943 [26] who made the first systematic studies of this latter effect; they produced “stability maps” for silver iodide sols, to which aluminium or thorium nitrate, and either acid or base, were added. Kruyt was Overbeek's immediate predecessor as Professor of Physical Chemistry at Utrecht University. In his 1900 paper [19], Hardy developed the discussion about the stability of charged particles to aggregation a little further. He argued that their stability is dependant on the difference in potential between the solid particles and the fluid. This is probably the first reference to the concept of an electrostatic interfacial potential playing a fundamental role in colloid stability. However, he also states that “the experimental investigation of this question is beset by many difficulties”. Hardy [19] refers specifically to Quinke's theory [27] of the movement of particles in an electric field. It was Georg Quinke [27] who had introduced the concept of “each particle being surrounded by a double layer of electricity”. Jean Perrin in 1904 [28] introduced the term “electokinetic potential”. Freundlich [29] later introduced the symbol ζ for the electrokinetic potential and, henceforth, this potential has become commonly referred to as the “zeta potential”. Herbert Freundlich (1880–1941; Fig. 4), was a contemporary of Richard Zsigmondy (1865–1929; Fig. 5) and Wolfgang Ostwald (1882–1943; Fig. 4). These three can be considered to be the founding fathers of colloid science in Germany; as we shall see, they all contributed to the literature on aggregation. Freundlich, after completing his PhD in Leipzig in 1903, stayed on there as an assistant to Wilhelm Ostwald (Wolfgang's father). He was subsequently appointed a professor at the Institute of Technology in Brunswick (Braunschweig) from 1911 to 1917, and then a professor and assistant director at the Kaiser Wilhelm Institute für Physikalische Chemie in BerlinDahlem, from 1917 to 1933. He then left Germany and travelled first to Britain and worked, as a guest, in F.G. Donnan's laboratory at University College, London (Frederick Donnan had also done his PhD with Wilhelm Ostwald in Leipzig). From 1938 Freundlich was professor of colloid chemistry at the University of Minnesota. The greater part of Hardy's 1900 paper [19] is concerned with a systematic study of the effect of salts on the aggregation of irreversible

Herbert Freundlich

Wolfgang Ostwald

Fig. 4. Hugo Randolph Kruyt Herbert Freundlich Wolfgang Ostwald.

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B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

Richard Zsigmondy

Marian von Smoluchowski

Nikolai Fuchs

Fig. 5. Richard Zsigmondy Marian von Smoluchowski Nikolai Fuchs.

(i.e. hydrophobic) hydrosols. His results were qualitatively consistent with Schulze's earlier findings [13,14]. However, he established a more refined definition for the “coagulative power” of a salt, and he recognised, following Arrhenius [30], that salts spontaneously formed ions in solution. The aggregating ion may be either the negative or the positive ion, but it is always the one of opposite sign to the particles (i.e. what we would now call the “counter-ion”). In his own experimental studies [19] he used a large range of salts, including Al, Cu, Mg, K and Na sulphates, Cu, Ba, Ca and Na chlorides and Cd nitrate. He used the following hydrosols: silica (electronegative), “proteid” (with a “slight trace of added acid”, making it electropositive, or with a “slight trace of added alkali”, making it electronegative), mastic gum (electronegative), gold (electronegative) and ferric hydrate (electropositive). He established the following general empirical relationship (although there were some strong exceptions), R’: R”: R”’ = K : K 2 : K 3, where R is the “coagulating power” of an ion of a given valency (as defined by Schulze – see earlier), and K is the reciprocal of the concentration of the salt containing that ion required to induce the onset of coagulation (ccrit), i.e. K = 1/ ccrit. (Note that a more rigorous definition of ccrit will be considered later in the section on aggregation rates). An alternative way of expressing Hardy's relationship would be: 1

ccrit ¼ ðconst Þz

ð1Þ

where z is the valency of the ion. In deference to the pioneering work of both Shulze and Hardy, in establishing these links between the critical electrolyte concentration for the onset of coagulation and the valency of the coagulating species, such relationships are collectively nowadays known as “Schulze-Hardy” rules, of which several versions have been proposed. (There is an excellent article, published in German in 2006 and available online [31], by Klaus and Margit Beneke, from Kiel: “Hans Oscar Schulze und Sir William Bate Hardy, und die SchulzeHardy Regel”). Hardy suggested [19] that aggregation with added salts occurs when the surface charge of the particles is “neutralised”. Maybe he was drawing the analogy with the concept that some particles (e.g. his “proteid” or ferric oxide particles) can reverse their charge with changes in pH, and therefore at the i.e.p. they have zero charge, and this is where they show the strongest tendency to aggregate. This idea subsequently became a source of some confusion and debate. I shall return to a discussion on this topic in the next section (on aggregation kinetics). Freundlich in 1910 [32] took up Hardy's idea that particles must be “discharged” for coagulation to occur. He attributed this to the adsorption of ions of opposite charge. In his famous 1922 book [33], Freundlich reviewed comparisons that had been made, by himself

and others, of observed ccrit values and directly measured adsorbed amounts of the aggregating species, for various sols. Freundlich had already shown in 1903 [34] that the precipitated coagulum of arsenic trisulphide sols contained some of the aggregating cations (hydrogen ions were liberated at the same time). Later, Thomas Bolan and Joseph Muir (1934) [35], from the University of Edinburgh, and then May Annetts and Lorne Newman (1936) [36], from the University of Toronto, made similar studies on sulphur sols and gold sols, respectively. They determined what fraction of the counter-ions was associated with the (precipitated) particles, and what fraction of the co-ions was in the solution phase. Their results seem to suggest that lower values for ccrit are observed with more strongly adsorbing species. In order to establish a relationship between ccrit and the valency of the coagulating species, Freundlich made use [32] of the generalised form of the adsorption isotherm which bears his name, 1

Γ ¼ acn

ð2Þ

where Γ is the adsorbed amount (in moles per unit area), c is the concentration of the adsorbate species in solution and a and n are constants, which are related to the adsorption capacity and energy, respectively. He assumed that, for a given sol, the number of equivalents (rather than moles) of ions needed to be adsorbed to achieve neutralisation is the same for ions of different valency, z. Hence, using Eq. (2), we may relate ccrit to Γcrit, as follows, leading to Freundlich's version of the Shulze-Hardy rule [32], 1 Γ crit const ¼ acncrit or ccrit ¼ n z z

ð3Þ

The current, generalised version of the Schulze-Hardy rule, derived from the DLVO theory (see e.g. the account by Overbeek, 1980 [37]), states that, ccrit ¼

const zx

ð4Þ

Table 1 Illustrative predictions of the various forms of the Shulze-Hardy relationships referred to in the text, assuming the ccrit value in each case for monovalent ions is 50 mmol L-1. coagulating

Schulze

Hardy

DLVO limiting values

ion

[13,14]

[19]

high potential

low potential

monovalent divalent trivalent

50 1.6 0.03

50 7.0 3.7

50 0.78 0.07

50 12 6.0

B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67 Table 2 Experimental ccrit values (mmol L-1) taken form the work of Wannow [39] for arsenic trisulphide sols on the addition of various metal chloride salts. monovalent

divalent

trivalent

ion

pH

ccrit

ion

pH

ccrit

ion

pH

ccrit

Li Na K Rb Cs

7.1 7.1 7.1 7.0 6.3

58 52 49 42 29

Be Mg Ca Sr Ba

3.7 6.2 6.0 6.0 5.9

0.77 0.90 0.83 0.80 0.77

Al Ce La

5.7 6.0 6.0

0.085 0.098 0.088

where 2 b x b 6, depending on the Stern potential of the particles, with x = 6 in the limit of high Stern potentials. (Ian Metcalfe and Tom Healy, from the University of Melbourne, (1990)[38] have discussed modelling the Schulze-Hardy rule in terms of the charge-regulation approach for the electrostatic interactions, and give a detailed discussion of the x exponent). In passing, it is interesting to note that Eq. (3), due to Freundlich, has a similar form to Eq. (4), with n replacing x. Since n relates to the energy of adsorption of adsorption of the counter ion on the particles concerned, and x to the magnitude of the Stern potential of the particles, there is some correlation between these two parameters, albeit a weak one! Table 1 illustrates the predictions from the various Schulze-Hardy relationships discussed above, based on choosing a value for monovalent ions of 50 mmol L-1. This typical value was based on the experimental data for the ccrit values for monovalent ions obtained by Wannow (from the Deutsche Forschungsinstitut für Textilindustrie, Dresden) in 1939 [39] for the aggregation of arsenic trisulphide sols, shown in Table 2. (Wannow had at one time worked with Wolfgang Ostwald). Given the difficulties faced by Schulze and Hardy in establishing rigorous conditions for the “onset” of aggregation, their own versions of the rule seem to predict values for di- and trivalent coagulating ions, which are more-or-less within the range of the DLVO predictions. It is interesting that Wannow's experimental values (Table 2) agree quite well with the values predicted by the DLVO theory, for the high potential values (Table 1). So far we have not considered any differences in observed ccrit values (for a given sol) for ions of the same valency (i.e. what we would now recognise as specific ion effects). Wannow's results in 1939 [39], shown in Table 2, represent one of the first extensive studies for a range of salts having the same co-ion, and where the pH was controlled. Moreover, he used turbidity measurements to monitor aggregation, rather than just visual observation. For the monovalent cations, Wannow's data show that their effectiveness in coagulating the (negative) arsenic trisulphide particles is: Cs+ >Rb+ >K+ >Na+ >Li +. Earlier authors had noticed similar trends but could not account for them. The concept of “lyotropic sequences” had been first discussed by Franz Hofmeister (then at the University of Prague) in 1888 [40] in relation to the effectiveness of different ions in salting out egg albumin from aqueous solutions. Freundlich in his book (1922) [41], in compiling lists of ccrit values for various sols with a variety of salts from a range of sources, hints that ion hydration effects may be an underlying cause for the occurrence of lyotropic sequences in ccrit values for ions of the same valency. It is interesting that the concept, introduced by Otto Stern (then at the University of Hamburg) in 1924 [42], of the “specific adsorption” of counter-ions in the electrical double layer, was not introduced into theories of colloid stability until the publication of Verwey and Overbeek's treatise [3]. Even these authors raised some slight reservations, as the Stern model involved introducing two new parameters, both difficult to estimate, into the theory of electrical double layer repulsion: the dimensions of specifically adsorbed ions and their adsorption energies. Linder and Picton in 1895 [43] and Freundlich in 1914 [44] made some early studies of the effect of mixtures of electrolytes on the aggregation behaviour of arsenic trisulphide sols, and reported some non-additive effects in certain mixtures, but no clear patterns emerged from their work. Wannow, in 1939 [39], was probably the

61

first person to study mixtures of electrolytes in a rigorous manner. In general, he concluded that mixtures of salts, where the valency of the counter ion was the same (e.g. NaCl + KCl or CaCl2 + BaCl2), resulted in additive behaviour for (negative) arsenic trisulphide particles; some exceptions were observed, e.g. mixtures of LiCl and KCl resulted in synergistic behaviour. However, when mixtures of salts were used, where the valency of the counter-ions was different (e.g. NaCl + CaCl2), then antagonistic behaviour resulted. The effect of varying particle concentration (e.g., the initial particle number concentration, N0) on ccrit values, for many different systems, was studied quite extensively pre-DLVO. Yet no consistent picture emerged from all these studies. Some authors found that ccrit increased with increasing N0, whilst others reported a decrease in ccrit with increasing N0. Some authors subscribed to the so-called “rule of Burton and Bishop” (from the University of Toronto), based on their 1920 paper [45], whereby ccrit values increased with N0 for polyvalent counter-ions, but decreased for monovalent counter-ions. However, other examples were found where all the salts studied in a particular system led either to an increase or a decrease in ccrit with increasing N0. With the benefit of hindsight one would suggest that two effects, which we would now recognise, had not been considered by these early authors. Firstly, in the case of inert electrolytes (i.e. where there is no specific adsorption of ions - mostly the case for monovalent counter-ions – but not always!), then simply by increasing N0 one is also increasing the general background ionic strength, thereby reducing the amount of the inert electrolyte required to reach ccrit. Secondly, in the case of specifically adsorbed counter-ions (more usual with multivalent ions), one is reducing their concentration in solution, through adsorption, on increasing N0, so more will be needed of the added electrolyte in those cases to reach ccrit. There were a number of early studies on the effects of adding organic solvents to aqueous dispersions. Freundlich [46] has reviewed the pre-1920 studies, and concluded that mostly “sensitization” was observed, in that ccrit was lowered in the presence of the organic solvent. He does, however, refer to some early studies by Kruyt and van Duyn (1914) [47] where the opposite trend was observed. Harry Weiser and Guilford Mack (from the Rice Institute in Houston, Texas), in 1930 [48], studied the effect on ccrit of adding low molecular weight alcohols to aqueous dispersions of mercuric sulfide (and indeed water to dispersions of mercuric sulfide in alcohols). Again, in some cases, on adding the organic solvent to the aqueous dispersion, ccrit was found to decrease, but other times to increase. Freundlich [46] suggested that the organic molecules might compete with the adsorbed counter-ions and this would tend to increase ccrit. Wolfgang Ostwald [49] had pointed (1909) out that the dielectric constant (ε) of the medium appears in the equation for the capacity of the electrical double layer at a particle surface; this relates the potential of the particle to its charge. Freundlich, therefore, concluded [46] that, if a critical potential for the onset of aggregation exists, and if ε is lowered on the addition of organic molecules to the aqueous phase, then the corresponding critical particle charge would be decreased. This might be the mechanism by which ccrit is decreased on adding organic molecules. (A proper inclusion of the effect of the dielectric constant of the medium on ccrit would have to await the DLVO theory (see Eq. (4), which summarizes the DLVO expression for ccrit : the “constant” actually contains a term in ε3). Hardly any studies on dispersions in totally non-polar media were carried out pre-DLVO. This is probably because methods for stabilizing such dispersions were poorly understood. Certainly suitable steric stabilizers would have been difficult to find. Systematic studies in this area only began in the early 1950's, and, to start with, mostly in industrial laboratories, such as those of Philips and Shell in the Netherlands. 3. Aggregation rates Early attempts to measure aggregation rates mostly depended on somehow isolating the singlet particles from the aggregates that

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B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

formed, and then determining their mass or number, as a function of time. An early method, used by Paine (from the University of Witwatersrand in South Africa) in 1912 [50], was applied to copper sols. As coagulation proceeded a gel precipitated and the mass of nonprecipitated copper particles was determined periodically by dissolving them in nitric acid and then measuring the excess acid concentration by back titration. However, the most successful of the early methods used for following the aggregation process with time was the ultramicroscope technique introduced by Zsigmondy in 1903 [51]. This technique, which uses dark field-illumination, allowed colloidal particles to be detected and monitored for the first time. Richard Adolf Zsigmondy (Fig. 5) was born in Vienna, but did his PhD in Munich. He subsequently became a professor of physics in Göttingen. He was awarded the Nobel Prize in Chemistry in 1925 for his development of the ultramicroscope. The effect of added salt concentration on the rate of aggregation was first studied by Zsigmondy in 1907 [52]. He simply noted the time taken for a gold sol to turn from red to violet, on adding increasing concentrations of sodium chloride. He found that the time taken decreased with increasing salt concentration, up to about 20 mM salt. Thereafter, the time taken remained invariant with increasing salt concentration (up to ~ 0.5 M sodium chloride). Moreover, Zsigmondy showed that this minimum time taken was independent of the valency of the counter-ions of the salt used. This implies that there is a maximum rate (for a given particle concentration), i.e. a maximum rate constant for aggregation. In this way, Zsigmondy [52] was able to distinguish regions of slow and rapid aggregation. This leads us to consider more carefully the definition of ccrit introduced in the discussion of the Schulze-Hardy rule in the previous section. Some early authors had, somewhat loosely, defined this as the minimum salt concentration required to observe the onset of (slow) aggregation, either visually or from turbidity measurements. More rigorously, and certainly in terms of the DLVO theory, we would now define ccrit as the minimum salt concentration required for the onset of rapid aggregation; there will be some lower, ill-defined, salt concentration where slow aggregation, effectively starts (although this will depend on several factors such as the sol concentration and the observation time!). So one needs to be careful in discussing ccrit values taken from the older literature, where the observation of the onset of slow aggregation, may have been taken as the criterion for defining ccrit. A related question is: what are the electrical properties of the particles at the onsets of slow and rapid aggregation? As we saw in the last section, Hardy suggested [19] that particles must be “neutralised”, prior to aggregation, which led to some confusion. If the particles are neutralised, presumably not only their charge is zero, but also their interfacial potential? On the other hand, Ellis (University of Liverpool) in 1912 [53] and Powis (University of Leeds) in 1915 [54,55] introduced the idea of a critical electrokinetic potential, for the onset of aggregation. They suggested, for a number of systems, that this critical potential was ca. 20–30 mV, for counter-ions of all valencies. There were some exceptions, e.g. for arsenic sulphide sols in the case of K + counter-ions the critical potential was~ 44 mV, although no explanation was offered. This discussion simply relates back to the question of whether one is talking about the onset of (slow) coagulation, per se, or the boundary between slow and rapid coagulation. None of these earlier authors had actually determined aggregation rates, only “critical conditions” for aggregation. At the onset of slow aggregation, it is clear that the particles must still be charged. However, at the onset of rapid aggregation, it might perhaps have been reasonable to make a case for particle discharge, at that time. However, these days we would not accept this condition either, except for systems where a reversal of charge may occur (by potential determining ions or other strongly adsorbing, oppositelycharged species). Particles remain charged, even in the rapid aggregation region, when an inert electrolyte is added.

As we have seen, in his early days Freundlich subscribed to Hardy's concept of particle neutralization, at the critical electrolyte concentration for particle aggregation (ccrit), and this is the position he adopts in his 1922 textbook. Subsequently, however, he revised his view. In 1926 [56], he introduced the concept of “first” and “second” critical potentials, the first corresponding to the onset of slow aggregation, and the second to the onset of rapid aggregation. By 1929 [57], as more experimental data became available, he realized that one cannot make a direct, quantitative link between ccrit and the amount of adsorbed counter-ions at that condition, which is the basis of Eq. (3), the Freundlich version of the Schulze-Hardy rule. Given the seeming failure of Freundlich's adsorption theory of electrolyte-induced aggregation, Wolfang Ostwald took up the challenge. Although he made several visits overseas (the first from 1904 to 1906, in the laboratory of Jacques Loeb in Berkeley), Wolfgang Ostwald spent nearly all his scientific career in Leipzig. Like Hardy, he started his studies in biology. Both Freundlich and Ostwald had very active interests in music. However, they differed as to what area of science the rapidly developing field of “colloids” really belonged. Freundlich always held the view that the subject was traditionally part of chemistry. Ostwald took a broader view, regarding it as a new, stand-alone field of science. His classic textbook, based on a lecture series he had given in North America, and which was published in 1914, was entitled: “the World of Neglected Dimensions” [58]. In 1938 [59] Ostwald presented a paper at the 15th American Chemical Society Colloid Science Symposium in Cambridge, Massachusetts, in which he clearly (and famously!) expressed his frustration with the (then) current theories of colloid stability: “If a professor is obliged to discuss the unsatisfactory conditions of the theory of coagulation for thirty or more years in every term of the academic year, then it may easily happen that he becomes more and more impatient. Either he becomes resigned or he commences to curse. The latter course is, in general, the more fruitful”. So instead Ostwald proposed a new idea: the “activity coefficient” theory of aggregation. The DebyeHückel theory of the activity coefficients of electrolyte solutions had appeared in 1923 [60]. It was formulated in terms of ionic interactions in solution. Ostwald assumed that similar ionic interactions, between the charged particles and the ions in the aqueous medium of a colloidal dispersion, must play a role in determining the onset of rapid particle aggregation. He therefore proposed that the aggregating power of a given electrolyte, at ccrit, should somehow be related to its (mean) activity coefficient in solution at that concentration. However, this theory attracted little support. Two obvious criticisms one might make now are that, firstly, the original Debye-Hückel theory is only applicable to rather dilute solutions of low valency electrolytes; it certainly does not account for the activity coefficients of asymmetric electrolytes containing ions of high valency. Secondly, the charge properties of different types of colloidal particles are not properly accounted for. Nevertheless, both Freundlich and Ostwald's ideas were, in certain aspects, revised by the Yugoslav colloid school, led by Bozo Tezak (Ruder Boskovitch Institute, Zagreb), beginning in the early 1940's [61]. They focussed on the surface charge group - adsorbed counter ion interaction, and related this to Bjerrum's ion-association theory, published in 1926 [62], for the same ion-pairs in solution. Although this approach led to an empirical formulation of the Shulze-Hardy rule, it has also received little support. The first theoretical analysis of the rate of rapid aggregation was made by Marian von Smoluchowski (a theoretical physicist, then working in Krakow in Poland; Fig. 5) in 1916 (sadly, he died in 1917, aged 45)[63]. He had been approached by Zsigmondy to account for the latter's own experimental coagulation rate data, obtained with the ultramicroscope. Around each supposedly spherical particle (thought to be “discharged”) there exists a “sphere of attraction”, upon entering which, a second particle would adhere to the first, irreversibly. The minimum value of the radius (R) of this sphere of attraction was assumed to be the radius (a) of the particle itself. An

B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

understanding of the nature (and hence the range) of the interparticle attractive force was lacking at this time. However, this was not necessary as Smoluchowski based his analysis of particle aggregation rates purely on a consideration of interparticle diffusion. The interaction energy as such was taken to be zero when the centres any two approaching particles were at a separation of greater than 2R, and minus infinity when it was less than 2R. Smoluchowski's derivation of the rapid rate constant for particle aggregation may be found in many standard textbooks on colloids and will not be repeated here. The result he obtained for the rate constant (k) for the disappearance of primary particles is in given in Eq. (5). k ¼ 8πRD

ð5Þ

where D is the diffusion coefficient of the singlet particles. By substituting into Eq. (5), R = a and D = kBT/ 6πηa (the StokesEinstein relationship), one obtains for the half-life (t½) of the aggregation process, i.e. the time taken for the singlet particle number concentration to be reduced to half its initial value (N0), t 1=2 ¼

1 3η ¼ kN0 4kB TN0

ð6Þ

where η is the viscosity of the medium, kB is Boltzmann constant and T is the absolute temperature. One may re-write Eq. (6) in terms of the weight / volume concentration of particles (w): t 1=2 ¼

πa31 ρη kB Tw

ð7Þ

where a1 is the radius of the singlet particles, and ρ is their density. For aqueous dispersions at 20°C, Eq. (6) reduces to,

63

investigated the aggregation time (tagg) for a dispersion of kaolin particles, as a function of their weight concentration using a sedimentation rate method. This involved placing one pan of a weighing balance close to the bottom of the dispersion, and adding weights to the other pan to monitor, with time (t), the weight (Wt) of sediment build-up on the first pan. If the particles are monodispersed and there is no aggregation, then a plot of Wt(t) should be linear; when all the particles have sedimented, the final value of Wt is, of course, related to w. If the particles are polydispersed, or if aggregation occurs, the plot is nonlinear. Odén [66] showed that, for polydispersed (but nonaggregating) particles, the particle size distribution could be deduced from the mathematical form of the Wt(t) plot. For aggregating, but initially monodispersed, particles a value of tagg may be evaluated. The exact definition of tagg, and how this relates to t½ is not entirely clear. Nevertheless, with the kaolin system referred to, he showed that tagg.w was constant, in line with Eq. (7). Using selenium sols and Zsigmondy's ultramicroscope technique, Kruyt and Anton van Arkel (1920) [67] were able to demonstrate, that t½ is inversely proportional to N0 (see Eq. (8)), in agreement with Odén's earlier studies. Another parameter, investigated by Zsigmondy in 1917 [68], and by Arne Westgren (Stockholm University) and Josef Reitstötter (who joined the AGFA company) also in 1917 [69], and then later by Pauli Tuorila (then at the Technische Hochschule in Zürich, but later a professor in Helsinki) in 1926 [70] (all mainly with gold sols), was the ratio R/a, i.e. the radius of the “sphere of attraction” (see earlier) to the actual particle radius. In deriving Eqs. (6) and (7) R/a was set equal to 1. More generally, the rapid aggregation rate constant is given by: k¼

  4kB T R 3η a

ð10Þ

i.e. t½ should only depend on the initial particle number concentration, and not any of the physical properties of the particles themselves. For initial particle concentrations in the rather dilute range used in typical aggregation experiments (say using particle counting or light scattering methods) one would expect t½ to lie in the range seconds to minutes. One of the assumptions implicit in the Smoluchowski theory of rapid aggregation rates is that sufficient time has past, such that the flux of particles towards any one particle has reached a steady state condition. Smoluchowski actually gave a formal derivation of the more exact result for k, without this assumption. Eq. (5) needs in that case to be replaced by Eq. (9) below,

These authors all found R/a to be about 2–3, over a wide range of particle radii (3 to 100 nm). (With hindsight, if one were today to estimate a value for R/a using the Hamaker theory of interparticle van der Waals forces, and a reasonable value for the Hamaker constant one would expect an R/a value of about 3 to 4 [71]). It would seem that, by and large, the Smoluchowski theory of rapid aggregation rates was proven to be sound by these early experimental studies. It is interesting that in these early experimental studies of aggregation kinetics very few authors reported detailed studies of both rapid and slow aggregation rates. When one considers slow aggregation rates, it becomes necessary to take into account the net repulsive forces between the particles. Smoluchowski circumvented this consideration, by simply introducing a semi-empirical correction factor (ξ) into Eqs. (5) or (6), where ξ is the fraction of successful collision between particles in a slow particle aggregation process. Thus, Eq. (6) now reads:

 k ¼ 8πRD 1 þ

t1 ¼

1:85x1011 t 1=2 ¼ N0

ðsÞ

R ðπDt Þ1=2

ð8Þ

 ð9Þ

The correction factor in Eq. (9) becomes insignificant when t > > R 2 /πD, or substituting R = 2a, t > > 8ϕt½, where ϕ is the particle volume fraction of the dispersion. For most typical aggregation experiments, carried out using dilute dispersions (in general, ϕ b 10-5), t is a small fraction of t½. In 1949 Frank Collins and George Kimball, at Columbia University [64], reviewed this, and some of the other, assumptions in Smoluchowski's theory. They concluded that the theory is by and large valid, but they did introduce a modified version which overcomes the problems associated with assuming a particle concentration gradient around any given particle at zero time. An early set of aggregation kinetics data, used to test the validity of Eq. (7), was that by Sven Odén (KTH, Stockholm) [65]. He

=2

1 ζ kN 0

ð11Þ

Some early estimates of ξ, based on t½ measurements, were made by Kruyt and van Arkel in 1920 [67] on selenium sols, as a function of BaCl2 concentration, using the ultramicroscope. They found that ξ was 0.0035, at the lowest BaCl2 concentration studied, and approached 1 with increasing BaCl2 concentration. Tuorila, in 1928 [72], found for dispersions of paraffin oil in water, that ξ depended on the zeta potential of the droplets: the smaller the zeta potential, the smaller was t½ and, therefore, the greater was ξ. It was Nikolai Albertovich Fuchs (USSR Academy of Sciences, Moscow; Fig. 5) in 1934 [73] who first properly accounted for the interparticle forces between particles on their aggregation rate (originally in the context of aerosol particles). Instead of just considering pure diffusion, he considered diffusion in a force field. In

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this way he was able to introduce a stability factor (W) into Eq. (5), i.e. k¼

k0 W

ð12Þ

where k0 is the rapid (diffusion-controlled) rate constant, given by Eq. (5), and W is given by, ∞

W ¼ 2a∫ exp 2a

V dr kT r 2

ð13Þ

where V is the interaction potential as a function of r, the interparticle (centre-centre) separation. V(r) is what the DLVO theory, in due course, provided. Hence, post-DLVO, the Fuchs theory has been used as the basis for interpreting slow aggregation rates. An important development was made around the same time that the DLVO theory was emerging: in 1943, Sjerp Troelstra and Kruyt [74] combined the Smoluchowski theory of aggregation rates with the Rayleigh theory of light scattering by particles. They derived the following equation for the light extinction coefficient, E, as a function of time: 2

E ¼ Kv1 N 0 ð1 þ 2kN 0 t Þ

ð14Þ

Where K is a light scattering function (which depends on the refractive indices of the particles and the medium, and the wavelength of light) and v1 is the volume of the primary particles. From Eq. (14) dE / dt is given by, dE 2 2 ¼ 2Kv1 N0 k dt

ð15Þ

Post-DLVO, Eq. (15) has been widely used to evaluate the aggregation rate constant, k, as a function of electrolyte concentration (ce). Exact calculation of k is difficult as this requires knowledge of the light scattering function, K. However, by combining Eqs. (12) and (15), one may obtain Eq. (16), W¼

ðdE=dt Þ0 ðdE=dt Þ

ð16Þ

where (dE/dt) is the slope of the E(t) plot at a given value of ce and (dE/dt)0 is the slope in the rapid coagulation region. Thus, from a plot of W versus ce, or better as it turns out, log W versus log ce, an accurate value for ccrit may be found. This method, therefore, gives a sound basis for testing the different forms of the Shulze-Hardy rule, which has been a major consideration in this article! (Note that, in practice, it is found experimentally that E is not a linear function of t, simply because the Rayleigh theory of light scattering strictly only applies to very small particles (diameters b one-tenth the wavelength of visible light). Even if the singlet particles fulfill this criterion, doublets and higher aggregates will not in general do so. As a result, experimentally, (dE/ dt) is generally found to decrease with time. To overcome this problem Ron Ottewill and John Sirs (then at the University of Cambridge) [75] suggested using the initial slope of the E(t) plot.) Finally, in this section on aggregation kinetics, we briefly mention some other factors which can affect aggregation rates. The original theory of Smoluchowski was derived for monodisperse particles. Hans Müller (E.T.H., Zürich and then M.I.T.), in 1926 [76,77], extended the theory to polydisperse systems. In the simplest case of bimodal mixtures, the aggregation rate was predicted to depend on both the ratio of the particle radii and the ratio of the particle number concentrations. Generally, aggregation was predicted to be faster in a polydisperse system than an equivalent monodisperse system having the same modal particle radius. Müller's theory was tested by Georg Wiegner and Pauli Tuorila (from the Technische Hochschule in

Zürich) in 1926 [78] with gold sols and reasonable agreement was found. The effect of particle shape on aggregation rates was studied by Wiegner and Edmund Marshall in 1929 [79]. They used rod-shaped particles of vanadium pentoxide (and also benzopurpurin). The aggregation rate for vanadium pentoxide particles was found to be much faster than for equivalent, near-spherical particles. In terms of R/a (see earlier – Eq. (10)) values of up to 100 were found initially. However, as aggregation proceeded, R/a decreased with time. This suggested that in the aggregates the rod-like particles were clustering in parallel bundles, such that their asymmetry diminished. The effect of stirring rate, pre-DLVO, had been well noted. For example, in 1922 Freundlich [80] reported the following observation with arsenic trisulphide sols. If these were allowed to aggregate slowly under quiescent conditions, for say 30 min, such that no apparent visible changes in appearance had occurred, then, if they were at that point stirred, large “flakes” appeared immediately. (This is the process we would now call “orthokinetic aggregation”, as opposed to “perikinetic aggregation” under quiescent conditions). Smoluchowski in his 1917 paper [63] also made a theory for particle aggregation rates in laminar flow. 4. Mixed particle and particle plus polymer systems I will discuss these two topics under the same heading, simply because, prior to Staudinger's pioneering work (1920) [81] in which he established the true, macromolecular nature of materials such as rubber, starch, cellulose and proteins (for which he received the Nobel Prize in Chemistry in 1953), such materials were classified by most organic chemists (even eminent ones like Emil Fischer) as “lyophilic colloids”; their apparent high molecular weights were thought to result from the extensive association of much smaller organic molecules into “particles”. Before Staudinger's proposal was firmly established, three types of processes were distinguished [82] which might result if binary mixtures of “colloids” were made: (i) mutual precipitation; (ii) sensitization; (iii) “protective action”. These were the classical names used, in general, during the period covered by this review; nowadays we would better recognize these terms as, respectively: (1) heteroaggregation; (ii) (polymer) bridging flocculation; (iii) steric stabilization. 4.1. Heteroaggregation/mutual precipitation Linder and Picton [21,83] , in the 1890's, were probably the first persons to notice that when colloidal particles of opposite charge were mixed, in certain proportions, precipitation resulted. Blitz in 1912 [84] made similar observations. Lottermoser and Kurt May (from the Technischen Hochschule in Dresden), in 1932 [85], showed that, in the aggregation of mixtures of particles of opposite charge, the maximum extent of aggregation was achieved when the magnitude of the charges on each set of particles was equal. In the same year, Wiegner [86] studied the kinetics of aggregation of mixtures positive copper hydroxide particles and negative clay particles, and showed that the ratio R/a (see earlier – Eq.(4)) was 65 during the initial stages of heteroaggregation, i.e. much higher than the values of 3–4 quoted earlier for homoaggregation. This suggested the longrange nature of the electrostatic attraction between oppositelycharged particles. 4.2. Bridging flocculation/ sensitization Here, and in the next section, we consider the addition of “colloids”, as they were then described, but which we would now recognize to be macromolecules, to a colloidal dispersion, rather than the mixing of two actual colloidal systems, per se, as in the last section. In general, the macromolecules added would have been much smaller

B. Vincent / Advances in Colloid and Interface Science 170 (2012) 56–67

James William McBain

Irving Langmuir

65

Samuel Levine

Fig. 6. James William McBain Irving Langmuir Samuel Levine.

than the colloidal particles. One needs to distinguish carefully between systems where the added macromolecules are (i) of opposite sign to the particles, or (ii) of the same sign or neutral. The mechanism of the aggregation that results is different in the two cases, even though both types of behaviour have been referred to as “sensitization” in the past. As an example of adding macromolecules of opposite sign, Overbeek in 1938 [87] studied the aggregation of anionic gold particles that resulted from adding certain concentrations of gelatin solution at low pH where the gelatin is cationic; the effect is one of charge neutralization of the gold particles. A related example was reported by another famous colloid scientist of the twentieth century: James William McBain (Fig. 6). McBain was a Canadian, who did his postgraduate studies in Germany; he was appointed to positions first at Bristol University (in 1906) in the UK and then at Stanford University in the US (in 1927). He reported [82] on the addition of dye molecules to a silver iodide sol (clearly of significance in the wet photographic process) [J]. At low concentrations of dye, particle aggregation is induced, but at higher concentrations the particles are again stable. Although McBain does not specifically refer to it, we would now recognize that the dye molecules and the particles are oppositely charged. So this is another example of charge neutralization. Interestingly, in regard to the gold particles plus gelatin system that Overbeek studied, Willem Reinders (Technische Hogeschool, Delft) and Willem Bendien (University of Amsterdam)[88] had previously (1928) made similar studies, but at higher pH values, where the gelatin and the gold particles were now both anionic. They found that aggregation of the gold particles could also be induced, at low concentrations of gelatin, but only if electrolyte were added. Similarly, McBain [82] discussed the effects of adding small amounts of albumin to a ferric hydroxide sol, where both are cationic. The sol remained stable, but if salt was added subsequently, then less salt was needed to induce particle aggregation than without the albumin present. No mechanism was proposed by McBain. However, we would now regard both these studies as examples of polymer bridging flocculation by the adsorbed protein molecules at low coverage; some electrolyte is still need to screen the electrical double layer sufficiently to allow the particles to approach close enough for protein molecules adsorbed on one surface to form “bridges” across to the second surface, but not as high as that needed to cause aggregation into the primary minimum in the DLVO pair potential. At high albumin concentrations, the particle surfaces become fully covered with protein molecules, and the particles are then sterically-stabilized, so much higher concentrations of added electrolyte can be tolerated. This effect is discussed in the next section.

4.3. Steric stabilization/ protective action As mentioned earlier, the “protective action” of adding substances like gelatin to a colloidal dispersion, to prevent or reduce particle aggregation, was first formally recognized by Faraday in 1857 [11], in that case with gold particles. Perhaps the first systematic studies of this effect were those by the German medic from Marburg, Heinrich Bechhold in 1904 [89]. He added gelatin to ferric hydroxide sols, and showed that they could not be flocculated by adding ammonium hydroxide (which presumably not only increased the ionic strength, but also raised the pH, of the solution, thereby reducing the chargedensity of the positive ferric hydroxide particles). Zsigmondy tried to introduce some comparative measure of the effectiveness of an additive in giving protection against aggregation. He introduced in 1901 [90] the “gold number”, which he defined as “the minimum amount (mg) of protective colloid required to prevent any color change in 10 cm 3 of a red gold sol on the addition of 1 cm 3 of a 10% solution of sodium chloride”. Ross Gortner (from Minnesota Agriculture Department) [91] in 1920 produced a list of comparative values for a number of common additives, e.g. gelatin 0.005 to 0.0125; gum arabic 0.10 to 0.125; sodium oleate 2 to 4; dextrin 125 to 150. However, the gold number was not widely adopted and received some early criticism from colleagues like McBain [82]. 5. Pre-DLVO theories of particle interactions and colloid stability Largely because the nature of polymers (including bio-polymers), and certainly their physical chemistry in solution, were not well understood, there was no real attempt, pre-DLVO, to produce quantitative theories regarding the sensitizing or protective action of polymers added to colloidal dispersions. This had to wait until the early 1950's and the first elementary theory of steric interactions by Edward Mackor (from the Shell Laboratory in Amsterdam)[92]. Similarly, the first quantitative theory of the heteroaggregation of mixtures of unequally charged particles (in magnitude or sign) was presented post-DLVO, by Derjaguin, in 1954, at the famous Faraday Discussion meeting in Sheffield, to which I have already referred [93] For single charge-stabilised dispersions, and homoaggregation, the story is different. As we have seen, it had been well established, from electrokinetic studies made from the mid-nineteenth century onwards, that particles in aqueous media carried a surface charge. This led Hardy, Zsigmondy, Freundlich and others to realise that electrostatic repulsion between particles must be a contributing factor to their stability to coagulation, although they themselves were unable to formulate a quantitative theory for this effect. In 1930, David Briggs (from the Sprague Memorial institute in Chicago) [94] attempted to account for the repulsion between charged spheres by simply

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applying Coulomb's law. However, this is incorrect as it ignores the screening effect of the ions, particularly in aqueous media. In 1939, Samuel Levine [95,96](Fig.6), then at the Department of Colloid Science in Cambridge (and subsequently at Manchester University), applied the framework of the linearized form of the DebyeHückel theory [60] of electrolyte solutions to dispersions of charged particles. He predicted the existence of medium-range repulsive forces and longer-range attraction forces between such particles, giving rise to what we would now term a “secondary minimum” in the pair potential. He was also able to predict a strong particle size dependence of the critical electrolyte concentrations (ccrit). It is interesting that the (UK) Faraday Society had been planning to hold a Discussion meeting in Cambridge in September 1939 (the month that the Second World War commenced in Europe), organised by its then President, Sir Eric Rideal, on “The Electrical Double Layer”. It never took place, but discussion comments were invited on the papers that had been submitted and circulated, and these were subsequently published in the Transactions of the Faraday Society in 1940. Many famous physical chemists contributed. Kruyt and Overbeek contributed a paper [97], mainly focussed on the electrical double layer itself, but did make the comment that the exact relationship between the electrophoretic mobility of colloidal particles and their stability to coagulation, as originally pointed out by Hardy [7], was still essentially unresolved. Herman Eilers and J. Korff [98], from the Bataafsche Petroleum Company in Amsterdam, produced a semiempirical theory for electrostatic repulsion, but as this had no real foundations in theory, it has not received much attention. Hamaker and Verwey [99] contributed a paper on the role of forces between particles in electrodeposition. Derjaguin [100] introduced the theory of electrical double layer repulsion based on excess osmotic pressure calculations, and also considered the theory of slow aggregation, incorporating Fuch's approach (see earlier, Eq. (13)). Levine, Derjaguin and Verwey all contributed to the invited, written discussion comments [101] on the submitted papers. The most significant contribution (some seven pages) is from Levine, who attempted to respond to major criticisms of his papers [95,96] by Hamaker [102] and Derjaguin [100]. The first of these criticisms was concerned with the “secondary minimum” in the pair potential predicted by Levine (see earlier) and its role in aggregation, particularly for large particles. Levine points out that A.J. Corkill and Louis Rosenhead (University of Liverpool)[103] had also predicted attraction forces between overlapping double layers for flat, parallel plates, depending on the boundary conditions. This is still very much a live topic of debate these days. The second criticism has to do with Levine's use of internal electrical energy rather than free energy in computing the interactions. Verwey and Overbeek summarize some of the differences in the various approaches made to calculating the magnitude of electrical double layer interactions in the Appendix to their 1948 book [3]. However, the community working on electrical double layer repulsion between charged particles had to wait until the 1954 Faraday Discussion meeting in Sheffield, referred to in the Introduction, before they could actually meet in person to discuss this topic. Even before these quantitative theories for the repulsion between charged particles were proposed, some of the earlier workers in the field posed a very pertinent question: if particles repel each other, then, when they do coagulate, what is the driving force for this process? Georg Bredig (who had worked with Wilhelm Ostwald in Leipzig) in 1901 [104] attributed interparticle attraction to the “reduction in surface tension” of the particles when they aggregate. I suppose we would now restate this as the reduction in total interfacial free energy of the system. Also we would associate this reduction with any decrease in surface area (rather than surface tension, per se) which might accompany aggregation, even though, unless significant coarsening (through Ostwald ripening) or sintering of the particles occurs, this is likely to be negligible! Nevertheless, Perrin (1905) [105] supported and extended Bredig's explanation.

Various later authors proposed that the stability of colloids involves the interplay of surface tension and surface charge effects. This was considered for emulsion droplets by William Lewis (from Liverpool University) in 1932 [106]. Oscar Rice (from the University of California, Berkeley) in 1926 [107], attempted to formulate a thermodynamic basis for particle aggregation, assuming that the process proceeded to some new equilibrium state, where the increase in free energy associated with electrical double layer overlap and the reduction in interfacial free energy just balanced. He dismissed any experimental observations that some aggregation processes appear to be irreversible and attributed such findings to there being insufficient Brownian motion of the larger aggregates. March (from the Institut für theoretische Physik, Innsbruck), in 1928 [108], refuted Rice's claim concerning the reversibility of aggregation processes. As far as he was aware, there were no reported cases of hydrophobic particles reaching an equilibrium state of aggregation in water. In this regard, it is interesting that Edward Burton and May Anettes in 1931 (university of Toronto) [109] studied, using light scattering, the addition of very small amounts of electrolyte (very much less than that to produce irreversible aggregation at ccrit) to arsenic sulphide, gold and other particles, and found that a limited, equilibrium amount of aggregation seemed to occur (This could be what we would now regard as secondary minimum aggregation, but I suspect the particles may have been too small?). March [108] doubted whether electrical repulsion alone between particles was sufficient to provide stability to aggregation. He proposed that “solvation” of the particles gave additional “protective action”. This is fine for hydrophilic particles, but it is less clear how it would play a role for hydrophobic particles. The connection between molecular condensation processes, ascribed to intermolecular attraction forces by Johannes van der Waals (in his PhD thesis, University of Leyden) in 1873 [110], and particle aggregation processes was not made until 1932, when Hartmut Kallmann and Margarete Willstätter (Kaiser Wilhelm institute, Berlin) [111] suggested that the attractive forces between colloidal particles might be of the same nature as the van der Waals forces between molecules. It may seem surprising that it took nearly sixty years for this realisation to be made. Probably the main reason why it was not made is that van der Waals intermolecular forces were known to be weak. Indeed, it was not until after the quantum mechanical theory of dispersion forces was published by Fritz London (University of Berlin) in 1930 [112] that Kallmann and Willstätter were able to make their suggestion. (The dispersion force of attraction between atomic or molecular pairs arises from the mutual lowering in free energy as two fluctuating dipoles approach and start to correlate; for atoms and molecules these oscillating dipoles are associated with the fluctuations in electron density). Kallmann and Willstätter realised that for two colloidal particles the dispersions forces would be additive. On this basis Jan Hendrik de Boer (then at the Philips Labs in Eindhoven, where he stayed until the Second World War) in 1936 [113] calculated the attraction between two semi-infinite, parallel blocks as a function of their separation. Subsequently, Hamaker in 1937 [114] made a similar calculation for two spherical colloidal particles. Irving Langmuir (from the General Electric Company and winner of the Chemistry Nobel Prize for his work in surface chemistry; Fig. 6) had reservations about the long-range nature of the van der Waals interaction between particles. His theory for the repulsive interaction between colloidal particles, set out in his 1938 paper [115], is in line with the DLVO model, but he put forward an alternative explanation for their long-range attraction. He started from the premise that in a dispersion of charged particles, there is mutual attraction between the particles and the ions of opposite sign (the counter ions). He draws the analogy with an expanded sodium chloride crystal, where the mutual attraction of the oppositely charged ions exceeds the mutual repulsion of the similarly charged ions. This being so, based on detailed osmotic pressure arguments, there

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should be a tendency for a dispersion of charged particles to cluster and eventually to separate into two layers: a concentrated phase containing virtually all the particles plus a very dilute phase (mostly electrolyte solution). In the Appendix to their book [3], Verwey and Overbeek discuss Langmuir's approach and claim that it is incorrect. It is interesting, however, that recently a number of theoreticians have challenged Verwey and Overbeek's dismissal of Langmuir's approach and argued that correlations between charged particles and ions can in some circumstances lead to attractive forces, but that discussion is beyond the remit of this current article. Nevertheless, it is a good point on which to end, for it illustrates that debates on the theory of colloid stability are alive and flourishing, some seventy years after DLVO! Acknowledgements I should like to thank Professors Tom Healy (Melbourne University) and Staffan Wall (Gothenburg University) for carefully reading the manuscript and for their helpful comments and suggestions. References [1] H. C. Hamaker, Rec. Trav. Chim., 1936 55 1015; 1937 56 3, 727. [2] Derjaguin BV, Landau L. Acta Physicochim 1941:14 633 URSS. [3] Verwey EJW, Overbeek JThG. Theory of the Stability of Lyophobic Colloids. Amsterdam: Elsevier; 1948. [4] see general discussion, Disc Faraday Soc, 1954 18 180. [5] Overbeek JThG, Sparnaay MJ. Disc Faraday Soc 1954;18:12. [6] Derjaguin BV, Titijevskaia AS, Abriscossova II, Malinka AD. Disc Faraday Soc 1954;18:24. [7] La Mer VK. J Colloid Interface Sci 1964;19:291. [8] H. Freundlich, “Colloid and Capillary Chemistry” (Methuen and co., London, trans. by H.S. Hatfield from the German ed., 1922), 1926 p415. [9] Everett DH. Pure App Chem 1972;31:577. [10] F. Selmi, Nuovi Ann. di Scienze, Naturali di Bologna, Sec II, 1845 IV 146. [11] Faraday M. Phil Trans Royal Soc 1857:145. [12] Graham T. J Chem Soc 1864;17:318. [13] Schulze H. J Prakt Chemie 1882;25:431. [14] Schulze H. J Prakt Chemie 1883;27:320. [15] Prost E. Bull Acad Roy Soc Belg 1887;14:312. [16] Lindler SE, Picton H. J Chem Soc Trans 1895;67:63. [17] Linder SE, Picton H. J Chem Soc Trans 1905;87:1906. [18] Hardy WB. Proc Roy Soc London 1900;66:95. [19] Hardy WB. Proc Roy Soc London 1900;66:110. [20] Perrin JB. J Chim Phys 1905;3:84. [21] Linder SE, Picton H. J Chem Soc Trans 1892;61:148. [22] Zsigmondy RA. Liebigs Ann Chem 1898;29:301. [23] Wall S. Current Opinions in Colloid and. Interface Sci 2010;15:119. [24] Hardy WB. J Physiology 1899;24:288. [25] Buxton BH, Teague O. Z Physik Chemie 1904;57 72, 79. [26] Kruyt HR, Troelstra SA. Kolloidchem Beihefte 1943;54 284, 287. [27] Quincke G. Ann Phys 1861;113:513. [28] Perrin JB. J Chim Phys 1904;2:601. [29] H. Freundlich, “Colloid and Capillary Chemistry” (Methuen and co., London, trans. by H.S. Hatfield from the German ed., 1922), 1926 p241. [30] S.A. Arrhenius, doctoral dissertation, University of Uppsala, 1884. [31] http://www.uni-kiel.de/anorg/lagaly/ group/ klausShiver/schulze.pdf. [32] Freundlich H. Z Physik Chem 1910;73:385. [33] H. Freundlich, “Colloid and Capillary Chemistry” (Methuen and co., London, trans. by H.S. Hatfield from German ed., 1922), 1926 p423. [34] Freundlich H. Z Physik Chem 1903;44:136. [35] Bolam TR, Muir JJ. J Chem Soc 1934:754. [36] Annetts M, Newman L. J Phys Chem 1936;40:187. [37] Overbeek JThG. Pure Appl Chem 1980;52:1151. [38] Metcalfe IM, Healy TW. Faraday Disc Chem Soc 1990;90:335. [39] Wannow HA. Kolloidchem Beih 1939;50:367. [40] Hofmeister F. Arch Exp Path 1888;24:247. [41] H. Freundlich, “Colloid and Capillary Chemistry” (Methuen and co., London, trans. by H.S. Hatfield from German ed., 1922), 1926 p426. [42] Stern O. Z Electrochem 1924;30:508. [43] Linder SE, Picton H. J Chem Soc 1895;67:67. [44] Freundlich H, Pape H. Z Phys Chem 1914;86:458.

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