Orders of Magnitude Reduction of Rapid Coagulation Rate with

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article

Orders of Magnitude Reduction of Rapid Coagulation Rate with Decreasing Size of Silica Nanoparticles Ko Higashitani, Kouta Nakamura, Takuya Shimamura, Tomonori Fukasawa, Katsumi Tsuchiya, and Yasushige Mori Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b00932 • Publication Date (Web): 20 Apr 2017 Downloaded from http://pubs.acs.org on May 5, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Orders of Magnitude Reduction of Rapid Coagulation Rate with Decreasing Size of Silica Nanoparticles

Ko Higashitani1＊, Kouta Nakamura2, Takuya Shimamura2, Tomonori Fukasawa3, Katsumi Tsuchiya2, Yasushige Mori2

1. Department of Chemical Engineering Kyoto University-Katsura, Nishikyo-ku, Kyoto, Japan

2. Department of Chemical Engineering and Materials Science Doshisha University, Kyotanabe, Kyoto, Japan

3. Department of Chemical Engineering Hiroshima University, Higashi Hiroshima, Hiroshima, Japan

* To whom correspondence should be addressed. Ko Higashitani, [email protected]

Keywords: rapid coagulation rate, redution of coagulation rate, nanoparticle, particle size dependence, silica, hydration force, structured layer, low angle light scattering

1

ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The modification of the classical Smoluchowski theory for the rapid coagulation rate of colloidal particles, which takes account of the effect of the squeezing flow between colliding particles, has been widely accepted, because it predicts experimental results adequately. However, it is not clear whether the modified theory, in which the coagulation rate is independent of particle size, is applicable even to nanoparticles in solutions. In the present study, the rapid coagulation rates of silica particles in various 2M chloride and 1M potassium solutions were measured by using a low angle light scattering apparatus, and the dependence of rapid coagulation rate on the particle diameter, Dp, was investigated extensively. It was clearly shown that the rapid coagulation rate of spherical silica particles reduces by the orders of magnitude with decreasing particle size at Dp≦ca.300 nm, while it coincides with the value predicted by the modified theory at Dp≧ca.300 nm. A possible mechanism is proposed and an analytical equation, which predicts the dramatic reduction of rapid coagulation rate with decreasing particle size, is derived.

2


Page 2 of 28

Page 3 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

1. Introduction The basic theory for the Brownian coagulation of hydrophobic spherical colloids was constructed by Smoluchowski, solving the diffusion equation of colliding particles in the medium under the assumption of no redispersion of coagulated particles.1 The results were confirmed later by using the equation of motion on the relative Brownian motion between a pair of spherical particles in solutions.2 According to the Smoluchowski theory, the change in the total number concentration of particles Nt at the initial stage of coagulation of monodisperse spherical particles is given by the following equation. The details of the derivation are found in contemporary books.3-5 t ⁄ = −R S t

(1)

where t is the elapsed time and KRS is the Smoluchowski rate constant for rapid coagulation given by the following equation. R S = 4 /3

(2)

where k is the Boltzmann constant, T is the temperature and µ is the viscosity of medium. It is clear that the value of KRS is independent of particle size and given to be 6.16x10-18 m3/s at T=25℃, provided the viscosity of water is used for µ. Because all the collisions of particles were assumed to result in their coagulation in the derivation of Eq.(2), the coagulation is classified as a rapid coagulation. It is important to note that the electrostatic repulsion and van der Waals attraction between particles, which play the main role in the classical DLVO theory,1,3-5 were not taken into account in the derivation. In order to examine the applicability of the Smoluchowski theory, many attempts have been made to obtain the experimental values of the rapid coagulation rate, KRE,

3


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 28

with various kinds of apparatus, such as, Coulter counter,6,7 low angle light scattering aparatus,8-11 and other light scatting devices.12-18 It is found that most of KRE values obtained are scattering around the half of the magnitude of KRS. However, this discrepancy between KRS and KRE has been successfully explained by introducing the hydrodynamic squeezing flow between colliding particles and adjusting properly the magnitude of Hamaker constant A in the van der Waals attractive potential for equal spheres VAsph, which is expressed by the following equation. sph

A

= −

+

) (

+ ln $

%& ()

(3)

ℎ( is a non-dimensional separation distance, h/a, where h is the separation distance between particle surfaces and a is the particle radius. This gives rise to the modified rate constant of rapid coagulation KRSM expressed by the following equation. 2,19,20 sph

)756 ) ( ℎ(: ()

8 /012 (4A

)*+ = 2 7-3 .9

(4)

Here β is the coefficient for the effect of squeezing flow between colliding spherical particles of equal size. The simplified form of β is given by Honig et al. as follows.20 ; = (6ℎ( + 13ℎ( + 2)/(6ℎ( + 4ℎ()

(5)

This modified theory has been widely accepted,2-5 and is called here the modified Smoluchouski theory. The value of A is often taken to be 8.3x10-21 J for silica particles in water.5,15 Then KRSM is given to be 0.566 KRS(=3.49x10-18 m3/s) by Eqs.(4) and (5), independently of particle size. Recently a numerical approach to the rapid coagulation rate was made without using adjustable parameters.21 It is found that the rapid coagulation rate depends on the particle concentration and the magnitude coincides approximately with that of KRE only in case of dilute colloidal solutions. When the particle concentration increases, the rapid

4


Page 5 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

coagulation rate increases because the multi-collisions among particles of various sizes occur even in the early sate of coagulation, and it could be greater than KRS in solutions of high particle concentration. This dependence of the rapid coagulation rate on the particle concentration coincides with the experimental investigation.22 In the present study, our attention was focused only on the rapid coagulation in dilute solutions, as a fundamental problem of colloids. Because of the approximate coincidence of the values of KRE with those predicted by both the modified Smoluchowski theory and the above-mentioned simulation, it appears that the mechanism of the rapid coagulation in dilute solutions is understood well at least qualitatively, where KRSM is estimated to be independent of the particle size as shown in Eq.(4). Hence much attention has not been paid on the effect of particle size. However, several attempts have been made to examine whether the theory is really applicable even to particles of nanosize or not. Ottewill and Shaw showed for the first time that the dependence of the stability curve on the particle size disagrees with the theoretical prediction, using the polystyrene latex particles of diameter Dp(=2a) =60~423 nm.23 Ludwig and Peschel reported that the value of KRE of silica particles in electrolyte solutions reduces by 7 orders of magnitude with decreasing particle size at Dp≦ca.200 nm.24 Higashitani et al. investigated systematically the low limit of the particle size to which the modified theory is applicable, using silica and latex particles of 14 different nanosizes in various aqueous solutions.10 They concluded that the value of KRE coincides approximately with that of KRSM at Dp≧ca.100 nm, but reduces by three orders of magnitude with decreasing particle size at Dp≦ca.100 nm, and also that KRE depends greatly on the solution pH. Axford showed that the value of KRE of silica particles of Dp=12 nm is three orders of magnitude smaller than that of KRS.25 5


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Kobayashi et al. investigated extensively the size effect of particles by measuring various properties of silica particles of Dp=30, 50 and 80 nm with sophisticated methods.26 They found that the reduction of KRE depends not only on the particle size but also the solution pH in very complicated ways, and concluded that an additional repulsive force must be present between colliding particles in aqueous solutions. Recently Škvarla investigated the stability of silica particles of Dp=50, 150 and 320 nm in KCl solutions from various points of view.27 As for the coagulation rate constant, it was found that the coagulation rate reduces by a few orders of magnitude in the wide range of electrolyte concentration and also depends on the solution pH. Although all these experimental results indicate that the value of KRE reduces by at least a few orders of magnitude with decreasing particle size when Dp is smaller than a few hundred nanometers, any experimental adequacy has not been discussed among the data and no mechanism for the orders of magnitude reduction of KRE has been proposed yet. In the present study, we conduct two series measurements by using a low angle light scattering apparatus to obtain the reliable data for the dependence of KRE on Dp for silica nanoparticles in various chloride and potassium solutions. The results were compared with the data reported previously, and a possible mechanism for the orders of magnitude reduction of KRE with decreasing particle size is proposed.

2. Experimental 2.1.

Materials The pure water used in this study was prepared by a Millipore filtration system

(Direct-Q, Merck Corp., Germany), giving a conductance less than 17.6 MΩ/cm. Two series of electrolyte solutions are prepared: 4M LiCl, NaCl, KCl and CsCl solutions, 6


Page 6 of 28

Page 7 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

and 2M KCl, KI, KNO3, KSCN and KBr solutions (Wako, Japan). After mixing one of these with an equal amount of colloidal solution, the rapid coagulation proceeded in either 2M chloride or 1M potassium solutions. Highly concentrated suspensions of spherical silica particles were kindly supplied by JGC Catalysts and Chemicals Ltd, Japan. The diameters of particles were determined to be 38, 55, 70, 100, 177, 287, 410 nm by the SEM observation. Their zeta potentials were measured in 0.1 mM LiCl solution by using the Zetasizer Nano ZS (Malvern Instruments, UK), and found to be 48.7±2.0 mV at pH=7.0±0.2. Hence, we believe that the surface properties of silica particles used are not too different each other. These suspensions were diluted extensively by pure water to be free from the effect of the multi-scattering in measuring the scattering intensity. The detailed procedures used here are given in the previous paper.10 The total number concentration of particles N0 was determined by the particle size and the dry weight of particles in suspensions. The pH of electrolyte and colloidal solutions were adjusted to be 7.0±0.2 by using 0.1 M HCl solution (Wako, Japan), just before each experiment. All the experiments were conducted in the room temperature of 25±1℃

2.2 Apparatus and Experimental Procedure The low angle light scattering apparatus used is shown schematically in Fig.1. This is the same apparatus employed in the previous study,10 although the He-Ne laser light source of 632 nm wavelength and the photo detector were replaced by new ones. The detecting system was updated such that all the scattered light through the slit of much smaller scattering angle θ between 1.22 and 3.0° than that of the previous experiment was able to be detected at intervals of 0.4 s by the phototube. This raised the detection 7


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 28

sensitivity of scattered light to a large extent. Colloidal and electrolyte solutions were filled in each 5mL syringe respectively, and then injected into the scattering circular cell (the diameter 5mm, the thickness 10 mm) instantaneously through a mixing cock by pushing the syringes strongly at the same speed. The flow of solutions was stopped completely by closing the cock. Then, the change of scattering light intensity was detected as the current intensity generated by the phototube. The coincidence of the initial current intensity with the calibration data of the current intensity vs. particle concentration was checked for all the measurements. Lips and Willis developed a method to determine the value of KRE by measuring the change of the intensity of scattered light at a low angle.8 The importance of this method is that the intensity of scattered light is independent of the shape of aggregates at θ→0, assuming that the Rayleigh-Gans-Debye theory holds.28 Then, the scattered light intensity at time t, I(t), is given by the following equation. >?() − ?(0)A⁄?(0) = 2RE 9

(6)

This equation indicates that the experimental value of rapid coagulation KRE is able to be determined from the slope of the relation of [I(t) - I(0)]/I(0) vs. t, if the value of N0 is known.

3. Results Figure 2 shows the experimental data for the dependence of KRE on the particle size Dp in 2M chloride solutions. It is found that all the values of KRE at Dp≧287 nm are nearly constant and agree with the value given by Eq.(4), KRSM. On the other hand, the values of KRE reduce by 4 orders of magnitude with decreasing particle size at Dp≦287 nm, independently of the kind of cations. Figure 3 shows the data of KRE vs. Dp in 8


Page 9 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

various 1M potassium solutions. All the data overlap approximately with the data in Fig.2, independently of the kind of anions. These data clearly imply that the orders of magnitude reduction of KRE Dp≦ca.300 nm does exit. It seems that the values of KRE at Dp≦70 nm depend slightly on the kind of cations and anions, but this problem will be discussed in the succeeding paper. Our attention in this paper is focused only on the dramatic reduction of KRE with decreasing Dp at Dp≦ca.300 nm.

4. Discussion 4.1 Comparison with the results reported previously The results obtained in this study were compared with those reported elsewhere10, 24-27 in Fig. 4. All the data at Dp≧ca.300 nm coincide well with the value of KRSM predicted by Eq.(4). On the other hand, it is important to note that all the experiments show the orders of magnitude reduction of KRE with decreasing particle size at Dp≦ca.300 nm, although the values do not coincide each other quantitatively. We believe that this disagreement is derived from all sorts of differences in measuring conditions, such as, the measuring methods and procedures, the properties of silica particles (the surface charge, the surface roughness, gelation of surface, etc.), and the medium properties. However, the data obtained in this study agree fairly well with the recent results for 1M KCl solution at pH=6 by Kobayashi et al.26 and those for 0.8M KCl solution at pH=8 by Škvarla27. This implies that the present results given in Figs. 2 and 3 are able to be regarded as reliable. The fact that all the experiments show the orders of magnitude reduction of KRE at Dp≦ca.300 nm implies that there must be a definite mechanism to cause the reduction. In this study, we use the data in Fig.2 as the reference in deriving a possible mechanism. 9


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 28

4.2 A possible mechanism for the reduction of KRE at Dp≦ca.300 nm It is known that the short-range repulsion, which is not accounted for in the classical DLVO theory, acts between silica surfaces in solutions.29,30 There are a few hypotheses for the origin of the repulsion: the layer composed of water molecules and counter ions adsorbed on the surface, the structured layer made of hydrogen bonds between water molecules, the gelation layer of silica at the silica-solution interface, and the roughness of surfaces.30-34 Although the detailed structure of the layers on silica surfaces has not been clarified yet, it is widely accepted that the structured-layer potential for the repulsion between plates in solutions VSLpl is expressed by an exponential decay function. The simplest function is given as follows. pl

SL = 9 exp(-ℎ/G)

(7)

where V0 and λ are arbitrary fitting parameters. According to Israelachvili, V0 is below 3~30 mJ/m2 and λ=0.6~1.1 nm for 1:1 electrolytes in case of hydration force.30 The short-range van der Waals potential between parallel plates is given by pl

A = -A/(12Hℎ )

(8)

Because the contribution of the electrostatic repulsion is negligible in the rapid coagulation, the total interaction potential for parallel plates VTpl is given by the following equation. pl

pl

pl

T = SL + A

(9)

The only way to check the adequacy of this equation is to compare the prediction with experimental data. The potential VTpl is able to be correlated with the interaction force F by F/R =2π VTpl, where F is the force between a plate and a particle of radius R on the cantilever measured by the atomic force microscope (AFM).30 Many measurements of 10


Page 11 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

F/R have been carried out under various conditions, but only a few data were available for silica surfaces in high salt solutions.33,35,36 These data do not necessarily coincide with each other, but the following common features are found. 1) The interaction forces between silica surfaces in high salt solutions have a very shallow minimum; F/R≦ca.0.5 mN/m at the separation distance h=2±1 nm. 2) No strong attractive force acts at h=0, where the van der Waal attractive force must be extremely strong. This implies that there is a gap between the solid surface of silica and the plane at h=0. This gap ∆ is often assumed to be 0.5 nm per surface.30 3) The force curves measured by Donose et al.35 show that the probe particle on the cantilever bounces back along the approaching force curve in retraction. This implies that the layer structure on the surface is, more or less, rubber-like, unless the force between surfaces is strong enough to break the layer at the contact. Now, we tried to find the combination of the arbitrary parameters V0 and λ to satisfy the similar features of force curves given by Valle-Delgado et al.33 and Donose et al.,35 as close as possible. One combination chosen was V0=2 mJ/m2 and λ=0.35 nm, and the gap ∆ per surface was taken to be 0.5 nm, as recommended elsewhere.30 The force curve with this structured-layer potential VSLpl is shown in Fig. 5, as well as the van der Waals force curve and the corresponding total force curve. There are a few theoretical attempts to estimate the structured-layer potential between surfaces in solutions. Valle-Delgado et al. examined extensively which model is the most proper for the force curve between silica surfaces in 1M NaCl solution, and concluded that the Attard-Batchelor model37, in which the structured layer was assumed to be composed of the hydrogen bonds between water molecules, is the most preferable.33 The total force curve given by the Attard-Batchelor model, in which 11


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 28

V0=103 mJ/m2 and λ=0.21 nm for 1M NaCl solution, was shown in Fig. 5 for the sake of comparison. It is clear that both the total force curves are similar each other in terms of the depth and separation distance at their minima, although the repulsion potential by the Attard-Batchelor model seems to be too steep, compared with experimental results.33,35 Once the form of VSLpl is determined, the Derjaguin approximation30 gives rise to the corresponding repulsive force for equal spheres, VSLsph, as follows. sph

SL = HJG9 exp(-ℎ/G)

(10)

Then the total interaction potential between equal spheres is defined by, sph

T

sph

sph

= SL + A

(11)

The viscosity of the structured layer is an important factor to evaluate the coagulation rate. There are various reports about the viscosity of the thin layer on the surface in solutions. Some reports claim that the solvent structuring at surfaces does not affect the liquid viscosity.38,39 On the other hand, there are quite a number of recent reports stating that the viscosity near the hydrophilic surfaces is a few orders of magnitude larger than that of bulk solution.40-43 It is out of scope of the present study to examine the adequacy of the contents of these papers. Nevertheless, it is easy to imagine that the interface between the silica surface and the highly concentrated electrolyte solution will form the complex structure consisting of the gel layer and adsorbed water molecules, ions and hydrated ions. Such a speculation is consistent with the experimental finding that the structured layer behaved rubber-like, as mentioned above.35 We therefore believe that the viscosity of the structured layer is very high at the present experimental situation. If this is the case, it is plausible to assume that the fluid flow cannot penetrate into the layer of h

Orders of Magnitude Reduction of Rapid Coagulation Rate with

Recommend Documents