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Evaluating dispersant stabilization of colloidal suspensions from the scaling behavior of gel rheology and adsorption measurements Fatemeh Khalkhal, Ajay Singh Negi, James Harrison, Casey D Stokes, David L Morgan, and Chinedum O. Osuji Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03343 • Publication Date (Web): 02 Nov 2017 Downloaded from http://pubs.acs.org on November 3, 2017

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Evaluating dispersant stabilization of colloidal suspensions from the scaling behavior of gel rheology and adsorption measurements a

a

b

b

Fatemeh Khalkhal †‡, Ajay Singh Negi †§, James Harrison , Casey D. Stokes , David L. b

Morgan and Chinedum O. Osuji*

a

a

Department of Chemical and Environmental Engineering, Yale University, New Haven, CT

b

Chevron Oronite Company, 100 Chevron Way, Richmond CA 94802. USA

‡ Present address: School of Engineering, San Francisco State University, San Francisco CA 94132 § Present address: Unilever Corporation, Bangalore India. † These authors contributed equally.

KEYWORDS: dispersants; rheology; adsorption isotherms; carbon black;

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ABSTRACT Maintaining suspension stability by effective particle dispersion in systems with attractive interactions can be accomplished by the addition of dispersants that modify the inter-particle potential to provide steric or electrostatic barriers against aggregation. The efficacy of such dispersants is typically considered simply by the modification of suspension rheological properties as a function of the overall added dispersant concentration. Such considerations however do little to reveal the molecular origin of differences in dispersant efficacy as they do not consider differences in surface activity. We combine measured adsorption isotherms with rheological characterization of the elasticity of colloidal gels formed by particle aggregation to provide a more meaningful assessment of dispersant efficacy. The rheological data show the dispersants are effective in reducing particle aggregation while, from the adsorption isotherms, they differ considerably in their surface coverage at constant overall concentrations. When compared at constant dispersant particle surface coverage, the gel rheology shows marked differences across the different dispersants, as opposed to comparisons at constant overall dispersant concentration in the suspensions. In particular, the power-law volume fraction scaling of gel elasticity at constant coverage reveals clear differences in the critical volume fraction for gel formation for the different dispersants. The most efficacious dispersant is that associated with the largest critical volume fraction for gel formation at given surface coverage. This work demonstrates the utility of rheological investigations coupled with accurate determinations of surface coverage to better differentiate dispersant performance, which may improve efforts to engineer new dispersant molecules.


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INTRODUCTION

The physical properties of colloidal suspensions are inherited from their microstructure that is strongly influenced by the relevant processing (flow) conditions1-4, particle concentration, and the nature and strength of applicable colloidal forces.5 Repulsive colloidal interactions provide stabilization against aggregation while attractive forces result in destabilization due to flocculation. Flocculating colloidal dispersions, and gels formed from such, exhibit a wide range of rheological properties such as aging,6-10 shear thickening, formation of vorticity-aligned structures

11-16

, and yielding.17-19 The diversity in the rheological behavior is relevant in the

multiple industrial applications of such materials, in coatings, printing inks, food, biological systems, filtration, oil drilling and engine lubrication.

Starting from an initially stable (i.e. well-dispersed) suspension, increasing the volume fraction of the particles or the attractive forces between them triggers aggregation, and therefore particle cluster formation. As the clusters grow, they develop a self-similar structure.20 At large enough concentrations, the clusters eventually become interconnected and form a percolated spacefilling network, a gel, which exhibits a frequency independent shear modulus. The onset of the formation of an interconnected network appears as a transition from liquid-like (frequency dependent) to solid-like (frequency independent) behavior in the rheological properties.21 At concentrations near the percolation threshold, theory

22-23

predicts the gel modulus scales with

concentration as shown in Equation 1.

G' ~ (φ − φc ) n

(1)


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where φ is the volume concentration of particles, φc is the percolation threshold and n is the power-law index typically spanning between 2 and 4.5 for commonly studied colloidal gels.

The use of colloidal suspensions with attractive interactions is constrained by the potential for particle aggregation due to loss of suspension stability, and the resulting formation of colloidal gels. A widely used approach to control the inter-particle interactions and thus aggregation in colloidal suspensions is the application of dispersing agents, dispersants, that are often also surfactants. Dispersants are typically polymers or small molecules with a polar or apolar “head” that adsorbs to the particle surface and an apolar or polar (i.e opposite polarity to head) “tail” that is soluble in the suspending medium. The net result of the dispersant’s action is to improve the affinity between the suspending medium and the colloidal particle, and to provide a steric or electrostatic barrier against particle aggregation. Dispersant addition to an unstable colloidal suspension results in a return of stability as the dispersant progressively breaks down particulate aggregates by adsorption to particle surfaces, as schematically illustrated in Figure 1. A typical example of such dispersants is polyisobutylene succinimide (PIBSI), which is widely used to prevent aggregation of carbonaceous nanomaterials (e.g. carbon black, asphaltenes, carbon nanotubes).24-25


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Figure 1: A schematic of cluster breakdown and steric stabilization of attractive particles upon the addition of a dispersant.

Adsorption continues until no more dispersant can be taken up by the particle surfaces. At sufficiently high concentrations, dispersant molecules may aggregate or assemble to form micelles. Such micelles have been implicated in an unusual charge-based stabilization of carbon black in non-polar suspending media through their ability to mediate charge exchange between the colloidal particles. 26-28 Eventually, the adsorbed and the non-adsorbed dispersant in solution reach equilibrium and particle dispersion or suspension stability is achieved as a consequence of steric and/or electrostatic barriers against particle aggregation.

Rheological measurements have commonly been used to assess the efficacy of dispersants in reducing colloidal aggregation.29-30 The effect of the dispersant chemical structure as captured by molecular architecture,31-32 the number of secondary amine groups in the polyamine core of PIBSI,24 or the length and backbone structure of the hydrophobic tail33 have been considered, along with dispersant molecular weight

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and suspension temperature.34-35 The common

practice is to consider the properties of the suspension at identical overall concentrations of the added dispersant. However, different dispersants will in general present different surface coverage values at the same overall concentration, reflecting differences in the adsorptiondesorption equilibrium due to differences in molecular structure. As a result, the conventional approach to examine the effect of dispersants on rheological properties at similar overall dispersant concentration results in ambiguity in elaborating the dispersants’ efficacy. This work proposes a potentially more useful approach that combines rheological measurements and adsorption isotherms to examine rheological characteristics of colloidal systems at constant 5 ACS Paragon Plus Environment

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dispersant coverage. The approach enables better differentiation of dispersant efficacy, thereby providing potentially valuable insight for the design of new dispersants with improved properties.

A model attractive colloidal system is provided by the suspension of carbon black particles in a non-polar hydrocarbon fluid. Such suspensions and their resulting gels are of interest as mimics for the performance of entrained soot suspensions in combustion engines, and as prototypical weakly attractive colloidal gels.36 Three model PIBSI-like dispersants are considered. Langmuirmodeled adsorption isotherms are obtained to explore the surface coverage of each dispersant at various overall concentrations. Linear viscoelastic properties are then compared at various dispersant mass concentrations as well as the surface coverage. The effectiveness of the dispersants is quantitatively analyzed by means of the scaling behavior of the linear viscoelastic rheological properties over a range of surface coverage. In particular, it is shown that the dependence of the colloidal gel elasticity on volume fraction of particles reveals marked differences when compared at analogous dispersant surface coverage.

Scaling Analysis of Fractal Colloidal Gel Rheology

Increasing the volume fraction of attractive particles or the interaction potential between particles leads to the formation of clusters. Continued growth and aggregation of such clusters leads to the formation of a colloidal gel – a network of particles with a self-similar or fractal structure. Shih 6 ACS Paragon Plus Environment

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et al.

20

have shown that the elastic modulus of such gels in the strong link regime scales with

particle volume fraction as shown in Equation 2, where G ' denotes the storage modulus (Pa) of the suspensions, d and df are the Euclidian dimension and the fractal dimension, respectively and x is the fractal dimension of individual clusters.

n

G′ ~ φ ~ φ

d+x d −d f

(2)

Similarly, the critical strain which sets the limit for linear viscoelasticity can be approximated by Equation 3. −(

γc ~ φ

−m

~φ

1+ x ) d −d f

(3).

In Equations 2 and 3 it is assumed that the macroscopic elasticity of suspensions originates from the links between flocs (inter-floc links). The fractal dimension of the colloidal gel can be deduced from the power-law exponents in the expressions, and reflects the cluster density with lower fractal dimensions corresponding to more ramified, less dense gels. In the diffusionlimited regime, floc or particle collision always leads to aggregation (i.e. the probability of sticking is unity) and df is about 1.7-1.8. Denser gels are produced in the reaction limited regime, where the sticking probability is less than unity, with df commonly seen to vary between 2.02.2.37

EXPERIMENTAL SECTION


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Materials and Sample Preparation Carbon black with a primary cluster size of 500 nm (composed of irreversibly aggregated 30 nm primary particles) and density of 1.8 g/cm3 was obtained from Cabot (Vulcan X72R). A nonpolar oil (Chevron 100N, a Group II base oil) (with a specific gravity of 0.85-0.87 and viscosity of 36.2 cP at room temperature) was used as the dispersing medium to prepare a master batch of carbon black suspension by 2 min of vortex mixing followed by 30 min sonication and another 2 min of vortex mixing. The master batch was diluted with oil and three different PIBSI-based dispersants (proprietary commercial materials from Chevron) referenced here as A, B, and C to obtain the required samples with constant surface coverage of 0.02 (g/g), 0.04 (g/g) and 0.08 (g/g) following the same mixing procedure. The molecular weights of the dispersants are roughly 30-40K (kg/mol.), 5K and 40-50K, respectively. All measurements were performed at room temperature.

Rheological Characterization Linear viscoelastic (LVE) properties were measured by a strain controlled ARES LS-1 rheometer (TA Instruments). Samples were initially pre-sheared at the rate of 400 s-1 for 600s followed by 1000s rest to ensure a uniform shear history. Strain sweep measurements were performed at a frequency of 10 rad/s, from strain values of 0.01% to 500%. The critical strain for the limit of linearity, γc, was obtained as the strain where the reduced storage modulus (i.e. instantaneous storage modulus relative to the strain independent or plateau storage modulus) was approximately 0.9. Frequency sweeps were performed at a small strain in the linear regime from 100 rad/s to 0.1 rad/s.


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Adsorption Isotherm Measurements Adsorption isotherms were measured by mass-balance by determining the free dispersant concentration in the suspension by FTIR measurements on filtered solutions. FTIR measurements were performed on a Bruker Optics Tensor 27 Spectrometer. The samples were prepared by separation of carbon black from the suspensions containing different quantities of dispersants using a 0.2 µm Polytetrafluoroethylene (PTFE) filter. The FTIR measurements were performed on the filtrate in a liquid cell (Pike Technologies) where the sample was held between two NaCl crystal windows with 1.0 mm spacing. For a quality control, solutions of oil and dispersant (without any carbon black) were passed through the filters and FTIR measurements were performed and compared on the solutions before and after filtration to ensure no selective adsorption of the dispersants on the filter.

RESULTS AND DISCUSSION

Adsorption isotherms extracted from FTIR measurements are plotted in Figure 2. The experimental data points are the average result of 3 or more independent measurements and the error bars show the standard deviation. The experimental data points are well-described by the Langmuir model given by Equation 4 where Γ and Γ are the amount of the dispersant adsorbed at the interface (i.e. the surface coverage) and its maximum value, respectively, K is an equilibrium constant that captures the binding affinity and strongly depends on the enthalpy of adsorption and temperature, and c is the equilibrium concentration of the dispersant in solution 9 ACS Paragon Plus Environment

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(i.e. free dispersant). Equation 5 provides the mass balance that relates the overall dispersant concentration ( ) to the free dispersant concentration , the carbon black content, , and the coverage, Γ.

(4)

1 Γ 1 Γ

(5)

Figure 2. Langmuir adsorption isotherms. The lines show the best fit of the experimental data points using Equation 4.

The adsorption isotherms in Figure 2 reveal the equilibrium between the adsorbed and the free concentrations of the three dispersants. The overall dispersant concentration used to prepare samples varied from 0.5 to 4.0 wt.%, resulting in free dispersant concentrations less than 1 wt.% in all cases, for 4 wt.% carbon black. At relatively low concentrations ( c < 0.1 wt% ), there is little difference in the coverage displayed by different dispersants; by increasing the free 10 ACS Paragon Plus Environment

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concentration, the difference between the isotherms becomes more evident. Eventually, the surface coverage saturates at a different maximum value for each dispersant. By plotting c/Γ versus c, Γmax and K can be obtained from the slope (1/Γmax) and the intercept (1/KΓmax). The fitting parameters are shown in Table 1. Results of statistical analysis of the fitting are provided in Supporting Information (Figure S1).

It is observed that B has the lowest and C has the highest surface coverage at saturation (i.e. Γmax); however, B has the highest binding affinity (K) among the dispersants. From these data we may infer that B has a strong favorable interaction with the carbon black surface, such that the equilibrium is strongly shifted towards adsorption rather than desorption. At low overall concentrations of dispersant, most of B is found on the carbon black surface. In the hypothetical situation that all species had the same ability to prevent aggregation once present at any concentration on the colloid surface, we could reasonably anticipate that B would be a more effective stabilizer at low overall concentrations. At the same time, the colloid surface demonstrates a limited capacity for B, by comparison with species A and C. This may be due to the particular chemistry responsible for the adsorption of the different species to carbon black, and the prevalence of compatible binding sites for the different dispersant. As a consequence, in the same hypothetical situation, if a larger amount of material (i.e. of any species) was needed at the surface to provide stability against aggregation, it may not be possible to achieve such stability with species B due to the limited amount which covers the surface, even at large overall concentrations.


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Table 1. Fitting parameters of Equation 4 for Langmuir adsorption isotherms shown in Figure 2. Dispersant

Γmax(g/g)

K

A

0.240

9.15

B

0.094

19.90

C

0.290

3.09

Although valuable information about the adsorption capacity of the different dispersants can be achieved from the adsorption isotherms, little direct information is provided regarding the dispersants’ efficacy in controlling the inter-particle attractions. On the other hand, rheology can provide valuable information about the microstructure of the suspensions that is controlled by the inter-particle interactions. Rheological measurements were performed to investigate the stabilizing effect of the dispersants on the suspensions microstructure. Following the common approach, linear viscoelastic (LVE) properties of a 4 wt.% carbon black suspension in oil were evaluated at various dispersant concentrations. The results for storage modulus at 10 rad/s are demonstrated in Figure 3 as a function of the inverse of overall dispersant concentration used to formulate the samples.


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Figure 3: Effect of dispersant mass concentration on elastic modulus (at ω = 10 rad/s) in a 4 wt.% suspension. Note that the x-axis is the inverse of the dispersant concentration. The dashed line shows the results without any dispersants.

As shown by the figure data, the storage modulus is almost 100 Pa (as shown by the dashed line) in the absence of the dispersants. The elastic modulus decreases on increasing the dispersant concentration, as a manifestation of reduced inter-particle interactions. At relatively low dispersant concentrations, the suspension containing dispersant C shows a much higher storage modulus while the suspension with dispersant A shows the lowest modulus. The moduli differ by a factor of over two orders of magnitude, suggesting a better ability of A in reducing the interparticle attractions in the suspension. At higher dispersant concentrations, the difference between the moduli across dispersants becomes less distinguishable. On the other hand, from the adsorption isotherms reported in Figure 2, the three dispersants have different surface coverage at similar free concentrations and comparison of their performance at identical overall concentrations may result in misleading conclusions. To address this issue, we extend our analysis to include the comparative LVE results obtained at similar surface coverage. 13 ACS Paragon Plus Environment

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Using the adsorption isotherms in Figure 2 and Langmuir correlation (Equation 4), samples of 4 wt.% carbon black with sufficient quantities of each dispersant were prepared to obtain similar surface coverages for each of the dispersants. A small quantity of each sample was then filtered and the exact amounts of the free concentration and coverage were determined to ensure the prepared suspensions at a certain coverage overlap on the adsorption isotherms within the experimental error. The effect of dispersant on the linear viscoelastic properties of a 4 wt.% carbon black suspension is analyzed at three surface coverages of 0.02 (g/g), 0.04 (g/g) and 0.08 (g/g). The results are reported in Figure 4. In the absence of the dispersants (zero surface coverage), the system displays frequency independent storage and loss moduli,with the storage modulus, G’, well in excess of the loss modulus, G’’. This indicates that a non-relaxing solid-like gel is formed in the absence of dispersants . The viscoelastic moduli decrease at a surface coverage of 0.02 (g/g) dispersant. This decrease is consistent with the notion that the dispersant hinders inter-particle interactions, thereby reducing the interaction energy which leads to the formation of weaker (lower modulus) gels. Further increasing the surface coverage decreases the moduli in all cases. The suspensions containing A and C exhibit a frequency independent storage modulus with G ′ dominating G" typical for solid-like behavior regardless of the surface coverage. On the contrary, a transition from solid-like to liquid-like behavior is observed in case of the B dispersant when the surface coverage increases from 0.04 to 0.08 (g/g). The results reported in this figure reveal that the dispersants affect the rheology, and therefore presumably the microstructure, of the carbon black suspensions in different ways and the dispersant B seems to be able to hinder the inter-particle interactions more significantly and reduce the viscoelastic moduli more drastically by comparison with A and C 14 ACS Paragon Plus Environment

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The results shown in Figure 4 at 4 wt.% carbon black can be further analyzed over an extended range of carbon black concentrations to get more insight into the rheological and therefore microstructural variations at constant surface coverage. In this approach, the scaling behavior of gel elasticity with volume fraction of particles is employed to obtain in-depth knowledge about the stabilizing effect of the dispersants on the microstructure of suspensions. Analyzing the scaling behavior of gel elasticity under the influence of different parameters has been shown to be very helpful in studying the microstructure (i.e. fractal dimension) of carbon-based suspensions38 since the use of light scattering is not feasible in these suspensions. Initially, the suspensions demonstrate a liquid like behavior with G ′′ dominating G ′ at relatively low particle concentrations (the results are not shown here); by increasing the particle concentrations, the suspensions reveal a transition from liquid-like to solid-like behavior with G ′ becoming frequency independent and dominating G ′′ ; the results for elastic modulus are shown in Figure 5 at a single frequency for similar surface coverage of each dispersant.


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Figure 4. Effect of dispersant (A, B and C) on linear viscoelastic results in a 4 wt.% (1.93 vol.%) carbon black suspension and various surface coverage of the dispersants.

For the A and C dispersants, the elastic modulus does not decrease strikingly by increasing the surface coverage and G ′ scales with concentration over a wide range of volume fractions with a 16 ACS Paragon Plus Environment

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lower limit of roughly 1.0 vol.%. Likewise, dispersant B exhibits an analogous scaling behavior at relatively low surface coverage of 0.02 (g/g) and 0.04 (g/g); however, as the surface coverage approaches 0.08 (g/g), it is apparent that the critical concentration shifts to higher values ( ϕ c > 1.5 vol.%) whereas the data originally presented in Figure 3 had masked this now apparent difference in efficiency. The observed scaling behavior of elastic modulus with concentration can be fitted with a slightly modified form of Equation 1 (as shown by solid-lines in Figure 5) shown in Equation 6, where λ is a pre-factor that depends on the inter-particle interaction potential, primary particle size, cluster size and distance between two particles at equilibrium 39.

G' = λ(φ − φc ) n

(6)

The scaling parameters for all three dispersants are reported in Table 2 and will be discussed shortly. Similarly, Figure 6 represents the scaling behavior of G ′ at similar surface coverage across the dispersants. At 0.02 (g/g), the storage moduli for different dispersants almost overlap when plotted against the volume fraction of carbon black particles. By increasing the surface coverage to 0.04 (g/g), the dispersant C produces a slightly higher modulus than A and B at similar volume fractions. The difference between the three dispersants becomes more substantial at higher coverage of 0.08 (g/g). Clear differences can be seen not just in the value of the gel modulus at a given particle volume fraction, but also in the scaling behavior of the modulus with volume fraction, and the critical gel concentrations thereby implied.


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Figure 5. Scaling behavior of frequency independent elastic modulus with carbon black volume concentration at various surface coverages of different dispersants A (top), B (middle) and C (bottom). The lines demonstrate the best fit of the experimental data points with Equation 6.


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Figure 6. Scaling behavior of frequency-independent elastic modulus with carbon black volume concentration for different dispersants at various coverages. The lines demonstrate the best fit of the experimental data points with Equation 6.

Fig. 7 represents the storage modulus of the 4 wt.% carbon black suspensions as a function of dispersant surface coverage. Moduli at a frequency of 1 rad/s were used. The moduli are largely frequency independent, except in the case of 0.08 g/g coverage for dispersant B. In the absence of the dispersants (zero surface coverage), a relatively high storage modulus of ~100 Pa is 19 ACS Paragon Plus Environment

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observed. The storage moduli of the gels diminish upon dispersant addition due to species adsorption on the carbon surface. As the surface coverage approaches 0.08 (g/g), the elasticity decreases drastically. This decrease is most evident in case of dispersant B where the modulus drops by more than three decades. By plotting the data as a function of surface coverage, the differences in the efficacy of the dispersants in mitigating aggregation become readily apparent. It is important to note that the differences in free dispersant concentration at a given surface coverage do not affect the interpretation here – in the regime of concentrations considered, the solution of free dispersant in the suspending medium is a simple Newtonian fluid (free concentrations < 1 wt.%) and therefore does not contribute to the gel elasticity. A representative flow curve for dispersant in oil is shown in Supporting Information (Figure S2).

Fig. 7 Storage modulus of a 4wt% carbon black suspension (at 1 rad/s) as a function of surface coverage for various dispersants. The lines are shown as guides.


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A more quantitative analysis about the effect of the dispersants surface coverage on microstructure can be made by comparing the fitting parameters of the power-law correlation in Equation 6 and the fractal dimensions from Equations 2-3. The results are shown in Table 2. The pre-factor λ is about 40.5 in the absence of the dispersants. Upon the introduction of the dispersants, the pre-factor decreases but doesn’t follow a unique trend in all cases as the coverage is increased (i.e., by increasing coverage, λ decreases in A and C, but increases in the case of B). To analyze the effect of surface coverage on inter-particle interactions using λ more explicitly, complementary techniques should be employed to characterize the cluster size in each case.

The critical concentration for the onset of gel formation ( ϕ c ) is about 0.5 vol.%, in the absence of the dispersants. Upon the adsorption of the dispersant molecules, the attractive interactions between the particles diminish as evident from the slight increase of

ϕ c with surface coverage.

The trend is observed in all three dispersants but is most pronounced in the case of dispersant B where the critical concentration increases from 0.5 vol.% at 0.02 (g/g) coverage to 0.73 vol.% at 0.04 (g/g) coverage. At the highest surface coverage of 0.08 (g/g), the critical concentration could not be robustly determined due to the limited range of particle volume fraction over which the elastic modulus could be reliably measured (i.e. moduli were too low at lower volume fraction) and over which therefore firm data could be fit to the model of Equation 6. Based on the inability to measure an elastic modulus in the lower concentration regime, we conservatively estimate that the critical concentration is larger than 1.5 vol.% for 0.08 g/g. It is clear that the critical concentration at this highest of coverages is substantially larger than for 0.04 g/g as apparent from the concentration dependence of the modulus in Figure 6. 21 ACS Paragon Plus Environment

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These results suggest that in the model attractive colloidal suspensions studied here, dispersant B can more effectively screen the attractive inter-particle interactions at a given surface coverage. Therefore, a larger concentration of particles is required to form a gel, i.e. the critical concentration for gel formation is larger in the presence of B ( ϕ c > 1.5 vol.%). The more efficient performance of dispersant B may be related to its higher binding affinity. A and C show lower gel percolation thresholds, revealing poorer dispersion capabilities by comparison. The critical concentrations reported in this table are comparable with other carbon black suspensions of about 0.8 wt.% (or about 0.4 vol.%) 40 and quite low compared to 3.0 wt.% (~ 1.67 vol.%) in

41

and 7.4 wt.%-16 wt.% (~ 4.1-8.9 vol%) 42 even in the absence of dispersants; this could be due to highly structured carbon black particles used in this study (primary cluster size ~ 500 nm). In some cases, e.g. at 0.04 (g/g), A has an even lower percolation threshold (0.43 vol.%) compared to the case without any dispersants (0.51 vol.%). This is likely simply the result of uncertainty associated with the data fitting to extract the critical concentration.

Table 2. Fitting parameters of Equation 6 and Equations 2-3 in Figures 5-6. Dispersant

Γ(g/g)

λ (pre-factor)

φc (vol %)

n

m

df

none

0.00

40.50

0.51

3.40

1.50

1.95

A

0.02

15.49

0.60

4.17

2.28

1.94

A

0.04

5.25

0.43

4.70

1.71

2.33

A

0.08

1.55

0.69

4.72

2.38

2.14


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B

0.02

5.62

0.50

4.85

2.76

2.04

B

0.04

11.75

0.73

4.10

2.03

2.03

B

0.08

23.44

> 1.5

-

-

-

C

0.02

20.89

0.65

4.04

2.38

1.79

C

0.04

17.38

0.50

3.93

2.50

1.60

C

0.08

5.50

0.50

4.50

2.53

1.98

Similarly, the power-law exponents for the storage modulus (n) from Equation 2 and the critical strain for the limit of linearity (m) from Equation 3 are reported in Table 2, from which the fractal dimensions can be estimated. In the absence of the dispersants, the carbon black agglomerates in oil demonstrate a fractal dimension of 1.95. The estimated fractal dimensions do not change significantly on dispersant addition; in case of C, the fractal dimension remains within the range of 1.60 to 1.98. The fractal dimensions given in Table 2 are comparable with previously reported values in literature of about 2.06-2.22.

42

and 1.75-2.15

43

in other carbon

black suspensions. In the case of dispersant B at 0.08 (g/g) coverage, due to the strong reduction in gel elasticity, moduli at lower particle volume fractions could not be reliably measured and therefore a power-law exponent could not be reasonably deduced over the standardized range of particle volume fractions considered. As a result the exponents (n) and (m) and consequently df are not reported for this coverage.

Our results show that the comparison of LVE data at similar overall dispersant concentrations can be misleading since different dispersants will in general exhibit different surface coverage at 23 ACS Paragon Plus Environment

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the same overall concentrations. This is evident by comparing the results from Figure 3 and Figures 5-7; in the former, dispersant A produces the lowest elasticity gels at a fixed overall dispersant concentration, when compared at low concentrations. At high dispersant concentrations, the results mask the differences among the gels (all low modulus) and make the comparison of dispersant efficacy difficult. On the other hand, from the comparison of the scaling of elasticity at similar surface coverage (Figures 5-7 and Table 2), it is clear that dispersant B is the most efficacious at reducing the attractive inter-particle interactions and stabilizing the suspension microstructure per unit mass present at the particle surface. This stabilization is manifested by the significant increase of the critical volume fraction for gel formation from 0.51 vol.% in the absence of dispersants to more than 1.5 vol.% at 0.08 (g/g) coverage. This contrasts strongly with A and C for which there is no significant change in the critical volume fraction with coverage.

CONCLUSIONS

In summary, this work presents an in-depth study that examines the efficacy of different dispersants by comparing the scaling behavior of LVE properties of colloidal carbon black gels in the presence of the dispersants. Robust adsorption isotherms were obtained from FTIR measurements that indicate the dispersants display different surface coverage at similar overall concentrations. Correspondingly, more consistent outcomes describing the efficacy of dispersants can be achieved by comparing the rheological properties at similar surface coverage as an alternative to similar overall concentration. Quantitative analysis of the scaling behavior of


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gel modulus with volume fraction of particles reveal a striking decrease in the onset of gel formation by increasing the dispersant surface coverage. The results reported in this work highlight the importance of rheological investigations in combination with precise determination of adsorption isotherms in designing novel dispersants.

AUTHOR INFORMATION Corresponding Author *[email protected] Author Contributions F.K. and A.N. contributed equally to this work. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENTS This work was supported by ACS PRF (56324-ND9) and by Chevron Oronite Company. Facilities use was supported by NSF (DMR-1119826) and the Yale Institute for Nano and Quantum Engineering (YINQE).

SUPPORTING INFORMATION Statistical analysis of adsorption isotherm data and flow curve for dispersant solution are included in Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. 25 ACS Paragon Plus Environment

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