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Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose
Accepted Manuscript Title: Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose Authors: Alexandar M. Zhivkov, Rosen P. Hristov PII: DOI: Reference:
S0927-7757(17)30599-X http://dx.doi.org/doi:10.1016/j.colsurfa.2017.06.037 COLSUA 21724
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
27-3-2017 12-6-2017 13-6-2017
Please cite this article as: Alexandar M.Zhivkov, Rosen P.Hristov, Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose, Colloids and Surfaces A: Physicochemical and Engineering Aspectshttp://dx.doi.org/10.1016/j.colsurfa.2017.06.037 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
2
>Crp = 0
CCMC
Mobility
1
0
pH 4.5
pH 6.0 -1
>Crp
-2 0.4
0.6
0.8
1.0
10 20 30 40 50
CMC concentration
Highlights
Stability of alumina suspension with added (carboxymethyl)cellulose
Methods: electric light scattering and micro-electrophoreses
Electric polarizability, electrophoretic mobility and relaxation time
pH-dependent aggregation by polymer bridging at the recharging point
1
Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose
Alexandar M. Zhivkov and Rosen P. Hristov Institute of Physical Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 11, Sofia 1113, Bulgaria
Corresponding author; E-mail: [email protected]; Phone: +359 897 345 013
Abstract
The influence of the counterion condensation on the colloid stability of alumina suspension with added carboxymethylcellulose (CMC) is investigated by electric light scattering and microelectrophoresis. The electrophoretic mobility and the interface ion polarizability are used as criteria for the effective charge of CMC-alumina particles. The light scattering intensity I0 and the field-strength dependence (E2) of the relaxation time are used as criteria for aggregation. The polymer-concentration dependences (CCMC), (CCMC) and I0(CCMC) under and above the recharging point are measured at different degrees of proton dissociation and fraction of counterions condensed on the adsorbed polyelectrolyte chains: 1/2, = 0 at pH 4.5, and 1, 1/3 at pH 6.0. The results show out that the colloid stability is conditioned by the effective charge of CMC-alumina particles determined by the surface charge, the dissociated carboxylic groups of CMC chains and the condensed counterions. The particle aggregation about the recharging point (at 1:50 CMC/alumina) is explained with hetero-coagulation by polyelectrolyte chain bridging conditioned by the reduced total charge, surface charge-patches, low surface occupation and the high rigidity of CMC chains.
Key Words: Alumina particles; Carboxymethyl cellulose; Polyelectrolytes; Counterion condensation; Polymer adsorption; Polymer flocculants; Hetero-flocculation; Electric light scattering; Microelectrophoresis.
1. Introduction The electrostatic adsorption of polyelectrolytes on oppositely charged colloid particles is widely used for stabilization or flocculation of aqueous suspensions in biomedical, pharmaceutical
2
and industrial technologies. The interparticle interactions depend on the surface charge density and the quantity, net charge, flexibility and distribution of the adsorbed polyelectrolyte chains [1, 2]. We study the suspension stability of metal-oxide particles with adsorbed semiflexible polyelectrolytes; the rotational diffusion coefficient and the light scattering intensity are used as criteria for particle aggregation. In several consecutive works we investigate aqueous suspension of alumina (-Al2O3) particles with added (carboxymethyl)cellulose (CMC); the both substances are industrially produced and widely used in different technological processes. CMC is a weak polyelectrolyte with semiflexible chain [3]. It is chemical derivate of the cellulose (linear polymer composed of glucose rings) with covalently attached CH3COOH groups to the chain backbone which rigidity is determined by the impossibility of rotation between the neighbour glucose units; the measure for the chain rigidity is the high persistent length lp 17 nm [4]. The charge density of CMC is pH dependent due to dissociation of the carboxylic groups which dissociation degree [COO/COOH] increases from 0.2 at pH 3 to 1 at pH 6 in aqueous solution with low ionic strength; the apparent dissociation constant Ka() is function of : pKa = pH log[(1)]. At increasing polymer concentration the total particle charge decreases up to zero and then increases with opposite sign; i.e. overequivalent adsorption appears above the recharging point Crp. That is accompanied with change of the anion/cation ratio (counterions to the alumina surface and to the adsorbed CMC chains, respectively). As an indicator for this ratio we use the electrophoretic mobility and electric polarizability ; the employed methods are microelectrophoresis and electric light scattering. In the previous works [5, 6, 7] we have investigated the polymer-concentration dependences (CCMC) and (CCMC) at maximal charge of CMC chins when a fraction of Na+ counterions are electrostatically adsorbed (condensed) on the polyelectrolyte chins [8, 9]. The counterion condensation reduces the effective charge because of formation of [COONa] group-ion pairs; i.e. the net charge is determined by the difference of the structural charge (COO groups) and the condensed ion fraction [COONa][COO]. In this work we distinguish the contribution of the structural and the net charges to the colloid stability of CMC-alumina suspension. For that we investigate (CCMC) and (CCMC) at two (pH) where the different linear charge density determines presence or absence of counterion condensation. We designate the counterions to CMC-alumina as follows: condensed anions (immobile during the existence of the ion-group pairs), loosely bound anions (movable along the adsorbed polyelectrolyte chains) and diffuse cations (counterions to the particle surface); only the last two kinds of counterions contribute to the polarizability in kilohertz electric field [6]. The different
3
mobility and charge sign of the counterions allows distinguishing the structural and net charges by (CCMC) and (CCMC) and their influence on the colloid stability of CMC-alumina suspension. The results show out that the counterion condensation equalizes the total charge of the CMC-alumina particle in the range pH 4–6 where the charge of Al2O3 surface is maximal. Aqueous suspension with 50 g/m3 alumina is stable at high or low polymer concentration but rapid aggregation appears at 1 g/m3 CMC. The results should be useful to stabilize alumina suspensions by polyelectrolytes. In particular, such necessity appears when use dispersed aluminum oxides as activators at fritting of ceramics from high-melting compounds as nitrides and borides. In such cases the uniformly distribution of the alumina nanoparticles is very important for the mechanical properties of the products; that requires avoiding coagulation in the suspension used for slip forming [10]. The colloid stability is important when using alumina nanoparticles in medicine and pharmacy as adjuvant for vaccines, in particular as an antigen carrier for anticancer vaccine [11].
2. Materials and methods 2.1. Materials The used polyelectrolyte was sodium salt of carboxymethyl cellulose (NaCMC, Hercules) with degree of substitution DS = 1.2 (on average 80% of the glucose units have one, and 20% two CH2COONa+) and mean-weight molar mass Mw = 250 kg/mol. This mass corresponds to CMC chain with 952 monomer units and contour length Lc 490 nm [3=]. Alumina particles (γ -Al2O3, Degussa) with total surface 200 m2/g were used as adsorbent. The particles are stable aggregates of 20 nm spheroidal nanoparticles (irreversibly coalesced in the process of synthesis by pyrolysis) with irregular form and average size 0.3 m. As metal-oxide its surface charge is pH dependent [12]; the point of zero charge of Al2O3 surface is pH 7.59.5 [13, 14]. The suspension was prepared by dispergating alumina powder the particles in triple distilled water, 1 min ultrasound treatment (Techpan, Poland, 20 kHz) and mixing of equal volumes of the suspension and water solution of NaCMC, both with pH 4.5 or pH 6.0, followed by continuous stirring for 30 min; the final concentration was 0.05 g/dm3 -Al2O3. NaCl was added to the suspension at pH 6.0 to equalize the ionic strength Iion = 2.5104 mol/dm3 to that at pH 4.5. The pH was controlled before and after the electro-optical measurements; the difference did not exceed ±0.1 pH units. The electrooptical and electrophoretic measurements started about 1 hour after mixing of the alumina suspension and CMC solution; this time is enough for complete adsorption [7=].
2.2. Electrophoresis
4
According to Smoluchowski-Hückel-Henry’s equation [15] the electrophoretic mobility = (0/)f(a) is determined by the electrokinetic potential , bulk viscosity , dielectric permittivity 0. The function f(a) depends on the form, orientation and dimensionless size a of particles with long size a and thickness of the electric double layer (EDL); in case of spherical dielectric particles f(a) = 2/3 – 1 in the range a 1 – 100. Mark II apparatus (Rank Brothers, UK) with a flat quartz cell and dark field optical microscope was used. The time t for which chosen particles migrate on fixed distance lel was measured in a direct electric field with intensity E = 10 V/cm at alternately changing the polarity for a set of 20+20 particles in the two stationary planes where the electroosmotic flow is zero. The averaged value t and the standard deviation are calculated for each plain separately (the difference is about 1%) and the mean values are used to calculate the mobility = leltE. The practically does not depend on the non-adsorbed CMC because it’s inclement to the bulk viscosity is negligible.
2.3. Electric light scattering The intensity I0 of a light with wavelength 0 incoherently scattered by a suspension of particles with refractive index n1, mass M and size L, which are dispersed in a medium with refractive index n0, increases lineally with particle number concentration until they scatter as independent particles [16]. The intensity I at scattering angle depends on M, the relative refractive index n = n1n0 and also on the particle form and relative size L/ (where = 0n0 is the wavelength in the bulk) when L/ 1/20 [17]. In the Rayleigh–Debye–Gans theory the light scattering intensity I0 at random particle orientation is expressed by the function of internal interference P(θ) (called also form-factor): I0 = kcHMP(θ) ,
(1)
where k is the apparatus constant determined by the scattering volume and the solid angle of the photoreceiver; c is the weight concentration of the dispersed substance; and H is the optical constant of the suspension (defined by 0, n0 and n1) [18]. The electric field induced by metal electrodes causes electrooptical effect (EOE) because of orientation of the particles. The electric light scattering (ELS) is defined as ΔII0 = (IEI0 ) 1, where IE and I0 are intensities at presence and absence of electric field. The EOE is determined by the change of the internal light interference because of altered position of the particle’s optical electrons which oscillation is the primary cause of the light scattering. The EOE can be expressed by the functions P(θ, E) and P(θ) at presence and absence of electric field, respectively at certain
5
orientational degree at moment t after switching on/off the field and at random orientation of the particles of the ensemble [19]: It/I0 = [P(θ, E) P(θ )] − 1 = [A(KL) P(θ)] × (γ, E, T, t) ,
(2)
where A(KL) is optical function determined by the particle geometry (form and size); KL = 2π (L/λ) sin(θ2). At given A(KL) the EOE value It/I0 is determined by the orientational function
(γ, E, T, t) (increasing from 0 at random orientation to 1 at full orientation) which expresses the average orientation of the particles with electric polarizability γ in electric field with strength E at temperature T. At steady-state EOE Is the averaged degree of orientation depends only the ratio of the orientational energy γE2 to the energy of random motion kT; the γE2 = γEE in field E is determined by the induced dipole moment γE. At low degree of orientation (when γE2kT) the (γ, E, T) is a linear function of E2; then the initial slope [Is/I0E2]E0 (reduced EOE) is proportional to the polarizability : [IsI0]E0 = [A(KL) / P( (E2 15kT) .
(3)
In the process of particle orientation/disorientation the internal interference function P(,) alters its value with the time t. The transient EOE It at moment t after field switching off is: ItI0 = [A(KL) / P( (γ, E, , t= (IsI0) exp(t /) ,
(4)
where the relaxation time = 16Dr (the time for e-fold decreasing of It starting form the steadystate value Is) is defined by the rotational diffusion coefficient Dr kTL3 which is determined by the particle geometry (form and size L) and the medium viscosity 0 at temperature T. The EOE decay in the case of a monodisperse suspension is mono-exponential for particles with axial symmetry and polyexponential in case of polydisperse suspension. The I0 and I were measured at angle = 90 in electrooptical cell with interelectrode distance 2.6 mm by computerized home-made apparatus [7=] using sinusoidal voltage up to 140 V with frequency 1 Hz, generated by Wavetek-185 functional generator and amplified by Krohn-Hite7500 amplifier. The reproducibility (estimated as deviation from the averaged values) was better than ±5% for the steady-state EOE Is/I0 and ±7% for the relaxation time in the case of given suspension. The reproducibility of different series of suspensions prepared at the same conditions from the same stock (alumina suspension and CMC solution) was in the frame of ±10%.
3. Results The investigation is done in two stages. The aim of the first is to find two pH values where there are or not counterion condensation on the CMC chain but the charge density of the alumina
6
particles is the same. A concomitant purpose is to estimate the charge densities of the alumina surface and the adsorbed polyelectrolyte chains which determine the fractions of the diffuse, loosely bound and condensed counterions. The second part of the results presents the polymerconcentration dependences of the electrophoretic mobility (CCMC), electric polarizability (CCMC), and colloid stability at the two chosen pH values.
3.1. Surface charge density of bare alumina particles To condition electrostatic adsorption of the negatively charged CMC chains, pH must be in the acid range where the alumina surface is positively charged. The 0(pH) dependence (Fig. 1) allowed choosing pH 4.5 and pH 6.0 as the most appropriate; at these pH the mobility values are practically equal: 0 = 1.8 (m/s)/(V/cm) at ionic strength Iion = 1 mol/m3. The result is in agreement with the older data: 0(pH) has a plateau in the range pH 46 [20].
40
2.0
1 20
1.0
0 . 10
8
1.7
2
0 [mV]
30
1.8
2 -1
-1
[m s V ]
1.5
10
0.5
1.6 0.0
0
C
1/2
1 NaCl
2
0
3
3 1/2
[mol/m ]
-0.5 4
5
6
7
8
9
pH
Fig. 1. pH-dependence of the electrophoretic mobility 0 (left ordinate) and the electrokinetic potential 0 (right ordinate) of bare -Al2O3 particles in aqueous suspension with ionic strength Iion = 1 mol/m3. The pH is adjusted by HCl or NaOH, the Iion = 0.25 mol/m3 is equalized by adding of NaCl. The 0 is calculated from 0 by Henry equation with correction factor f(a) = 0.72. Insert: Electrophoretic mobility 0 vs. square root of NaCl concentration at pH 5.25.
7
40
0 [mV]
2
4
36 6
2
32
0 [mC/m ]
8
1
4 28 2
3
24
0 0.0
0.5
1.0
1.5
C
1/2
2.0
2.5
3.0
1/2
NaCl
[mmol/L]
Fig. 2. The electrokinetic potential 0 (left ordinate, lines 1–3) and the surface charge density 0 (right ordinate, curve 4) of bare -Al2O3 particles in aqueous suspension vs. square root of NaCl concentration CNaCl = 0.25–10 mol/m3. The 0 is calculated from the 0 measured at pH 5.5 at Henry correction factor f(a) for dielectric spheres with radius a = 10 nm (line 1), 30 nm (line 2) and 150 nm (line 3). The surface charge density 0 (curve 4) is calculated for spherical particles with diameter 2a = 60 nm. The calculation of the electrokinetic potential of submicron particles with size 2a at thickness of the electric double layer (EDL) = 9.6 nm (Iion = 1 mol/m3) requires employing Henry equation 0 = (0/)f(a) instead Hückel (f(a) = 2/3) or Smoluchowski (f(a) = 1) ones; for dielectric spheres the value of f(a) increases from 0.67 to 0.98 in the range a = 1 – 100. Considering that the alumina particles are aggregates of 20 nm nanoparticles with irregular form and average size 300 nm, we have to approximate them to sphere and calculate f(a) with a in the range 10–150 nm. To choose the diameter 2a we use the dependence of 0 on the ionic strength Iion (Fig. 1, Insert) which shows false plateau at NaCl concentration CNaCl 1 mol/m3 because the f(a) diminishes with increasing of from 9.6 nm to 19.3 nm (Iion = 1–0.25 mol/m3). The calculated shows (Fig. 2) that the ion-concentration dependence (CNaCl)1/2 has nonlinear deviation at both 2a = 20 nm (line 1) and 300 nm (line 3), it is linear at 2a = 60 nm (line 2). That allows as to use a = 30 nm at which f(a) = 0.72 (a/ = 3.1 at Iion = 1 mol/m3). Then Henry’s equation gives = 35 mV at 0 = 1.80108 m2s1V1 in the range pH 4–6. The Gouy-Chapman theory (flat EDL) gives surface charge density 0 = 3.0103 Cm2 (1.9 elementary charges per 100 nm2 or 53 nm2 per charge) at Iion = 1 mol/m3. The average distance between two neighbour charged centers is equal to 7.8 nm, assuming that the surface charge is arranged as a hexagonal lattice [19]. At Iion = 10 mol/m3 the measured mobility is 0 = 1.59108
8
m2s1V1, accordingly f(a) = 0.84, = 27 mV, and 0 = 7.0103 Cm2 (4.3 charges per 100 nm2).
3.2. Linear charge density of free CMC chains At degree of substitution DS = 1.20 the average distance between the COOH groups is b0 = 0.43 nm [3=]. The degree of dissociation 0.5 and 0.95 determines the average distance between COO groups b1 = b0 0.86 nm and 0.45 nm, and the linear charge density (the ionized groups to the contour length) b11 = b0 1.17 nm1 and 2.21 nm1, respectively at pH 4.5 and pH 6.0. The dimensionless charge parameter lB/b1 (determined by the linear charge density and the Bjerrum length lB 0.712 nm at 20C) has values 0.83 and 1.58, respectively at pH 4.5 and pH 6.0. According to the Manning’s theory counterion condensation appears when >1 and the fraction of the condensed ions is = 11 [21]. So, at pH 4.5 there is not condensation but at pH 6.0 condensation of Na+ on COO groups appears and = 0.37. I.e. at pH 6.0 about 1/3 of the dissociated carboxylic groups are neutralized forming COONa+ group-ion pairs, and the effective linear charge density is equal to (1)b1 = b0 1.40 nm1; the 2/3 of COO groups have effective negative charge equal to that of the loosely bound Na+ counterions. The ratio of the net charges at pH 6.0 to pH 4.5 is equal to 1.40 1.17 = 1.20; i.e. the effective charge density at pH 6.0 is only 20% higher than at pH 4.5 although the fraction of dissociated carboxylic groups is almost two times higher.
3.3. Electrophoretic mobility of CMC-alumina particles The polymer-concentration dependence (CCMC) (Fig. 3) shows that the electrophoretic mobility of the alumina particles decreases with polymer concentration CCMC down to the recharging point Crp 0.9 mg/dm3 CMC and then its absolute value increases reaching plateau at CCMC > 30 mg/dm3. The change of sign shows out overequivalent adsorption of the negative CMC chains on the positive alumina particles. The linearity of (CCMC) in the region of Crp indicates that all added CMC chains are adsorbed on the particles at low CCMC [7].
9
. 10
8
2 1
1
[m s V ]
2
1
0
pH 4.5 -1
pH 6.0 -2 0.0
0.3
0.6
0.9
10
20
30
40
50
CCMC, mg/L
Fig. 3. Electrophoretic mobility of CMC-alumina particles vs. NaCMC concentration CCMC at pH 4.5 (▼) and pH 6.0 (▲) at ionic strength Iion = 0.25 mol/m3. The mobility reduction at CMC adsorption is caused by both chain charge and the hydrodynamic friction; the last is absent at = 0. That allows comparing the charge densities at the two pH using Crp values (CMC concentrations where the particle charge is equal to that of the adsorbed chains). Fig. 3 shows out that the ratio (Crp)pH4Crp)pH6 is about 1.1; this value corresponds approximately to the calculated 1.2 ratio of the net charge densities for free CMC chains at pH 6.0 and pH 4.5 (section 3.2). This result reveals that the [COONa+] group-ion pairs are not destroyed after adsorption of the polyelectrolyte chain on the particle surface; in case of full decondensation Crp at pH 6.0 ( 1) should be two times smaller than at pH 4.5 ( 1/2). So, the negative charge added to the positive particle surface by every adsorbed CMC chain is determined by the dissociation degree 0.5 at pH 4.5 or by the fraction of effectively charged carboxylic groups 1 0.6 at pH 6.0; that leads to near courses of (CCMC) curves at the two pH.
3.4. Kilohertz polarizability of CMC-alumina particles Inserts in Figs. 3, 4 show the field-strength dependences IsI0 = f(E2) at CCMC under and above the recharging point Crp. At these CCMC particle aggregation does nor appear (section 3.5); that means that the optical functions in Eqs. (2, 3) remain unchanged. The linearity of Is(E2) verify that the orientational energy is low compared to the thermal one (E2kT), so the line slope (reduced EOE) is proportional to the polarizability: (IsI0E2)E0 (const ). The bare particles (Fig. 4, lines 1) have equal values at the two pH; that is in agreement with the pH-independent surface charge in the range pH 46 (section 3.1).
10
pH 6.0
12
3 9
2
[(Is / I0) / E ] . 10
Is / I0 [%]
4
11
2
2
[m / V ]
pH 4.5 5
2 1
6
2
3 2
0
0 0.0
1
E . 10 0
10
0.2
-8
20
2
2
[V /m ] 30
0.4
0.6
0.8
1.0
CCMC [mg/L]
Fig. 4. Reduced EOE vs. NaCMC concentration CCMC under recharging point at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3 equalized by NaCl. Insert. Steady-state electrooptical effect IsI0 in sinusoidal electric field with frequency = 1 kHz vs. squared field strength E2 for bare -Al2O3 particles (lines 1) and at presence of NaCMC with concentration CCMC = 0.7 mg/dm3 (lines 2) at the same pH and Iion. Fig. 4 shows polymer-concentration dependence (CCMC) of the polarizability (in relative units) under Crp. The both (CCMC) curves have two regions: almost independent on CCMC and strongly decreasing. The linearity of the last shows out that the polarizability reducing (owing to the opposite charge and hydrodynamic friction added to the particle surface) is proportional to the quantity of the adsorbed CMC chains and that their charge do not depends on the degree of surface occupation in the range CCMC Crp. The difference between values at the two pH corresponds to the net charge density likewise that of the mobility . Above the recharging point (Fig. 5) the values also correspond approximately to the net charge density of the adsorbed CMC chains but in this CCMC range the difference at the two pH is smaller owing to higher adsorption at pH 4.5.
11
pH 6.0 pH 4.5
3
Is / I0 [%]
12 9
2
2
[(I / I0) / E ] .10
11
2
2
[m / V ]
4
6
1
3 2
0
0 0
10
E . 10
-8
2
2
[V /m ]
0
10
20
30
20
30
40
50
CCMC [mg/L]
Fig. 5. Reduced EOE vs. NaCMC concentration CCMC above the recharging point at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3. Insert. Field-strength dependence IsI0 = f(E2) at = 1 kHz for alumina particles at CCMC = 40 mg/dm3 at the same pH and Iion. The nearness of the (CCMC) curves values at the two pH (in the CMC range under and above Crp) reveals that the interface polarizability of CMC-alumina particles is due to the mobile counterions (diffuse Cl and loosely bound Na+) but the condensed Na+ do not participate remaining immobile in the applied kilohertz electric field with moderate strength.
3.5. Aggregation stability The increasing light scattering intensity I0 is indication for growing of the particle mass M (Eq. 1). The polymer-concentration dependences I0(CCMC) show out that particle aggregation appears in narrow CCMC range (Fig. 6, the I0 values are out of the scale at the recharging point Crp 0.9 mg/dm3). At Crp the suspension instability rapidly increases with the time up to visible turbidity followed by flocculation.
12
1.6
pH 6.0
1.5
pH 4.5
[rel. un.]
1.4 1.3
I0
1.2
2
1.1
1 1.0 0.0
0.3
0.6
0.9
10
20
30
40
50
CCMC [mg/L]
Fig. 6. Dependence of the light scattering intensity I0 (in relative units) on the polymer concentration CCMC at pH 4.5 (▼) and pH 6.0 (▲) under (line 1) and above (line 2) the recharging point at Iion = 0.25 mol/m3. The low I0 values are indication for absence of noticeable aggregation at CCMC Crp2 (line 1) and CCMC 5Crp (line 2). The suspension stability in the lower range can be explained with enough strong electrostatic repulsion between the positively charged particles (Fig. 3). But the absence of aggregation in the higher range is impressive because the total charge pass zero value in the process of recharging by adsorption of the negative CMC chains on the positive alumina surface. The fact can be explained with the faster polyelectrolyte adsorption compared to the relatively slow particle collision: the kinetics of the two processes is determined by the strongly different translational diffusion coefficients of the polymer random coil and the colloid particles. The slight increasing of I0 with CCMC could be ascribed to the adsorbed CMC but this is precarious inference because the increment M is too small compared to the large particle mass M. An alternative explanation is appearance of a small fraction of aggregates to which I0 cM is not enough sensitive. That is why we use the field-strength dependence (E2) of the relaxation time (Eq. 4) as a more sensitive criterion; at polydisperse suspension (E2) is curve and its curvature strongly increases at particle aggregation. Fig. 7 shows (E2) dependences for suspensions of bare alumina particles (curve 1) and with added CMC at saturated adsorption (curve 2). The (E2) reflects the degree of orientation (γ, E presented by the field dependence (IsI0)(E2) (curve 3). The near forms of the curves 1 and 2 show out absence of significant aggregate fraction which could be appear at passing over zero total charge at CMC adsorption; in the opposite case the curvature of the curve 2 should be significantly increased. The fact that the values practically coincide at the two pH confirms that the colloid
13
stability is pH-independent at high CCMC. The increment = 0 (lift of the curve 2 above the curve 1) is caused by the hydrodynamic friction of the adsorbed CMC chains, additional to that of the bare particle surface. The inference flows from the fact that the is almost the same at increasing degrees of particle orientation (E2) (curve 3); in the case of aggregation the should decrease with E2 (the curve 2 should approach the curve 1) owing to increasing contribution of the faster single particles.
5
[%]
20
4 15
2 3
Is / I0
[ms]
3
10
2
5
1
0 0
5
10
15 2
20 -8
E . 10
2
25
30
2
[V /m ]
Fig. 7. Relaxation time (left ordinate; curves 1, 2) and steady-state EOE IsI0 (right ordinate; curve 3) vs. squared field strength E2 in -Al2O3 suspension at absence of polymer (curves 1, 3) and at CMC concentration 30 mg/dm3 (curve 2) at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3. So, the (E2) dependence confirms the inference obtained by I0(CCMC) that addition of CMC to the alumina suspension does not lead to noticeable aggregation when CCMC is significantly above Crp. The coincidence of I0 and values at the two pH shows out that the colloid stability is pHindependent at enough high total charge: positive at low CCMC or negative at high CCMC. The aggregation near Crp is pH-dependent; the small difference at pH 4.5 and pH 6.0 is indirect indication that the total charge of CMC-alumina particles is determined by the net charge of adsorbed polyelectrolyte chins, not by their two times different structural charge.
4. Discussion 4.1. Static and electric light scattering To investigate the suspension stability we employ static light scattering and electrooptical criteria for particle aggregation. The using of I0(CCMC) is based on the dependence I0 NM2P() cMP() for light scattering of N particles (single or aggregates at chaotic orientation) with mass M in suspension with weight concentration c of the dispersed substance (Eq. 1). In the process of aggregation I0 increases because of the growing M (accompanied by reducing of N at constant c).
14
The aggregate size L (synchronously growing with M) has the opposite effect on I0 because P() P(, L/) has tendency to diminish its value with the relative size L/ but the dependence I0(L) is relatively weak (at = 90 when L is commeasurable with ) compared to that of I0(M). So, I0 is reliable criterion for aggregation of alumina particles with L 0.3 m suspended in aqueous medium in the visible range where = 0n0 0.30.6 m. An advantage of I0 is that it is applicable to particle with size and form (including spherical) which can not be oriented in electric field. On the other hand I0 cM is not sensitive to the small fraction of aggregates because it reflects the averaged mass M of all particles in the ensemble. To overcome this disadvantage of I0 we combining it with the relaxation time L3 which is very sensitive to the particle size L. However is not very sensitive to small fraction of aggregates as well; that is why we use its field-strength dependence (E2) as a criterion for polydispersity. The (E2) is based on the strong dependence L23 of the polarizability on the long particle size L; that leads to higher degree of orientation (γ, E2of the bigger particles in comparison to smaller ones. The relative contribution of the aggregates to I(E2) diminishes with E2 owing to increasing orientation of the small particles; accordingly decreases with E2. In the case of polydisperse suspension the form of (E2) is curve which curvature strongly increases at particle aggregation.
4.2. Alumina surface charge density The electric charge of oxide/water surfaces is caused by dissociation of amphoteric MOH groups, adsorption of the potential-determining H2O+ and OH ions, and physical adsorption of [Mz+(OH)z1]+ and [Mz+(OH)z+1] hydroxide complexes [22]. The electric properties of alumina particles are determined by ionization (AlOH2+ AlOH + H+ and AlOH AlO + H+) of the amphoteric AlOH groups. That allows describing the alumina surface as diprotic acid with intrinsic constants pK1 = 7.9 and pK2 = 9.1, respectively; the surface density of the exchange capacity (the sum [AlOH] + [AlOH2+] + [AlO]) is one functional group per 1.6 nm2 [20]. The strongly hydrated gelatinous surface layer causes shift of the shear plain (reducing of -potential), weak dependence of on the ‘surface’ charge density , and much less electrokinetic charge density ek as compared with pt obtained by potentiometric titration: ek pt5. The high potential in the boundary layer alters the local concentration of H2O+ and OH ions; therefore their replacement with Na+ and Cl (indifferent ions) increases pt and ek. The electric properties of metal oxides strongly depend on the method of synthesis, crystalline modification, impurities, and degree of hydratation. We have used -Al2O3 particles
15
(synthesized by the same method of flame pyrolysis of AlCl3) which have the same 0, pHiep 8.5 and plateau of 0(pH) at pH 4–6 (Fig. 1) as those in Ref. [20]. In electrooptical experiment the ionic strength Iion is kept constant by addition of NaCl (to avoid influence of Iion on ); that leads to different OHCl ratio of the counterions (CNaCl = 0 at pH 4.5 and 0.25 mol/m3 at pH 6.0). The plateau of 0(pH) dependence at pH-lowering (Fig. 1, curve 1) from pH 6 to pH 4 we explain with increasing difference in the local concentrations of H2O+ and OH (compared to the bulk) and exchange of Cl counterions with OH. The high charge density in the boundary layer leads to strong dependence of 0 on CNaCl (Fig. 2, curve 4): the electrokinetic charge increases from 0 = 1.6 to 13.3 mC/m2 in the range CNaCl = 0.25–50 mol/m3.
4.3. Chain/particle charge ratio The electrophoretically measured total charge of CMC-alumina particles allows estimating the average number of polyelectrolyte chains adsorbed on a colloid particle. That can be done correctly at absence of hydrodynamic friction: the zero electrokinetic charge at Crp ( = 0) reflects the charge equality of the positive alumina surface and the negative CMC chains. Assuming that alumina particles (aggregates of 20 nm nanoparticles) have form of oblong ellipsoid with long axis 300 nm and axes ratio 1.5, the envelope surface (hexagonally packed semispheres) of one particle has area S = 0.27 m2 and 2100 positive charges at pH 4–6 (section 3.1). The used CMC has chain contour length Lc = 490 nm (an average value owing the polymer polydispersity), linear charge density 1.17 nm1 or 1.40 nm1 (section 3.2), and 573 or 685 net charges at pH 4.5 and pH 6.0, respectively. Accordingly, at CCMC = Crp the particle charge is neutralized by 3.7 or 3.1 CMC chains; these values are minimal because the estimation takes into account only the envelope surface of a particle with regular form. According it the occupied surface is only 2 % (3 % at S = 0.17 m2 of the ellipsoid with smooth surface) assuming that one adsorbed CMC chain occupy area equal to the radius of gyration Rg = 44 nm of the random coil [3]. At the last assumption the average 2D net charge density of a dome (the projection of the negative polymer charges on the positive particle surface) is 37 negative charges per 100 nm2; i.e. 47 (pH 4.5) or 56 (pH 6.0) times higher than that of the bare alumina surface. The above estimations mean that the probability that a given particle can be rigorous neutral is vanishingly small: it is still positively or already negatively charged owing to the stepwise adsorption of large polyelectrolyte chains bearing about 6–7 hundred negative charges. It can be supposed that at Crp in the suspension there are CMC-alumina particles with both negative and positive charge, and that stimulates the aggregation, together with the reduced total charge. But the experiment does not confirm these suppositions: about Crp all CMC-alumina particles are either
16
positive or negative and the mobility of the single particles is not drastically different, although the dispersion of is in order of magnitude higher than for bare particles (Fig.3). So, the above estimated number of adsorbed CMC chains is actually much higher because the real surface area is several times larger owing to the irregular form of the alumina particles and the effective potential on the bare particle surface is induced not only by the outer charge centers but also by that ones lying under the envelope surface on a depth commensurable with the EDL thickness 20 nm. Nevertheless, it is obvious that the CMC-alumina surface is strongly unhomogeneous: a relatively small number of strongly charged negative domes are disposed on spacious positive area with low charge density. The seeming independence of the mobility and polarizability on the polymer concentration at low CCMC (Figs. 3 and 4 at CCMC 0.5 mg/dm3) is analogical to those of polyvalent inorganic or small organic ions. The reasons for this phenomenon could not be absence of CMC in the medium owing to its adsorption on the laboratory ware because the both polyelectrolyte chains and the glass surface are negatively charged and strongly hydrated. Another possibility is predominant CMC adsorption on the particle aggregates which are disregarded at the electrophoretic measurements and contribute relatively less to EOE owing to the small anisodiametricity. Additional investigations are required to explain the observed low-concentration plateaus of (CCMC) and (CCMC) dependences.
4.4. Polyelectrolyte induced aggregation The alumina suspension is stable at presence of CMC with low or high concentration; i.e. in the two CCMC ranges where the electrostatic repulsion is enough strong as it follows from the comparison of (CCMC) and I0(CCMC) (Figs. 2, 5). On the other hand at Crp rapid turbidity appears which is indication for fast coagulation; i.e. in the point of zero total charge the aggregation is rather diffusion limited. In contrast, at absence of polymer the alumina suspension is practically stable (during the measurements at the low particle concentration and the low ionic strength used in the experiment) even in the isoelectric point (Fig. 1, 0 = 0); the fact is in accordance with earlier observations [23]. The high colloid stability of aqueous suspension of oxides and hydroxides is determined by the strongly hydrated boundary layer which increases the thermodynamic stability by decreasing of the surface pressure [24] and determines the structural component in the extended DLVO theory [25]. In the case of bare alumina particles additional factor is their irregular form and uneven surface which do not allow forming of enough contact area at Brownian collisions. As result the threshold of coagulation strongly increases up to molar concentrations of indifferent electrolyte (1.8 mol/dm3 NaCl [26], which is 4 orders of magnitude higher than in our experiment).
17
The contrast of the suspension behaviour at presence or absence of CMC reveals that the particle aggregation is result of interparticle polymer bridging: a chain adsorbed on one particle contacts with a bare surface area of the approaching particle. This process is conditioned by: (a) the oppositely charged polyelectrolyte and particle surface; (b) strongly heterogeneous distribution of the surface charge of CMC-alumina particle (charge patches); (c) 3D-conformation of the adsorbed polymer chains which form domes because of the high rigidity of CMC chain; and (d) the small area occupied by the adsorbed CMC chins (owing to their small number and the random coil conformation before adsorption). Due to the chain semi-rigidity the CMC domes protrude above the particle surface and conditions by that the aggregation by chain bridging, in difference from the case of flexible polyelectrolytes where the charge-patch mechanism of the polymeric heteroflocculation of big colloid particles dominates [1]. The strong charge inhomogeneity of CMC-alumina particles raises a question: why the recharged particles do not aggregate at CCMC 5Crp (Figs. 5, 6) although on the surface there are enough bare areas which could connect a polyelectrolyte chains already adsorbed on an approaching particle? We explain that with two factors: (a) the low ionic strength Iion used in our experiments; and (b) the relatively fast rotational diffusion compared to the translational one. The second factor leads to averaging of the electrostatic potential for time at which two neighbour particles can approach on distance allowing polymer bridging. As combination of the two factors, the resulting electrostatic repulsion is enough strong (on distance relatively long in comparison with the prominent polymer domes) to prevent particle aggregation. The rapid instability at Crp (in contrast with suspension stability at saturated CMC adsorption) reveals that the reduced electrostatic repulsion plays leading role in the in the particle aggregation.
4.5. pH-dependence of the aggregation stability At absence of aggregation it is not possible to distinguish which CMC charge (the structural or net one) stabilize the suspension because the electrostatic repulsion is enough strong in the both CCMC ranges under and above Crp. A difference appears at approaching to Crp: the twofold higher structural charge at pH 6.0 should lead to twofold reduced CCMC where aggregation appears. But the I0(CCMC) shows out that particle mass begins to increase at CCMC equal at the two pH. This fact means that the colloid stability is determined by the net charges of the adsorbed CMC chains which are near at the two pH owing to the counterion condensation (section 3.2). In the range of instability some difference appears (Fig. 6, CCMC = 1 mg/dm3): the average mass is bigger at pH 6.0 (I0 = 1.6) than at pH 4.5 (I0 = 1.5). This fact is unexpected because the total (negative) charge of the recharged CMC-alumina particles is higher at pH 6.0 (Fig. 3, CCMC > 0.9 mg/dm3, 0). The finding can be explained with linking of the negative polyelectrolyte chains
18
to the positive bare surface when the total charge is enough small (at CCMC near to Crp); then the some higher net charge of CMC chains at pH 6.0 facilitates the aggregation when the particles collide. So, the aggregation instability confirms the inference done by the concentration dependences (CCMC) and (CCMC) that the condensed counterions are not released at adsorption of the polyelectrolyte chains. That is due to the rigidity of CMC chain, uneven particle surface and the big difference of their charge densities. The condensed counterions reduce the effective charge of CMC-alumina particles and by that diminish the aggregation stability.
5. Conclusions The polymer-concentration dependences of the light scattering intensity I0(CCMC), the electrophoretic mobility (CCMC) and the electric polarizability (CCMC) are measured at two pH where the net charge density of the polyelectrolyte chains (determined by the dissociation degree and the condensed counterion fraction ) is different: 1/2, = 0 at pH 4.5, and 1, = 1/3 at pH 6.0. The I0(CCMC) and the field-strength dependence of the relaxation time (E2) (determined by the particle mass and size, respectively) are used as criteria for particle aggregation. The I0(CCMC) and (E2) show out absence of particle aggregation in two CCMC ranges: under and above the recharging point Crp. The difference of (CCMC) at the two pH corresponds to the calculated fraction , so the condensed counterions are not released at CMC adsorption. The suspension stability under and above Crp does not depend on and due to enough strong electrostatic repulsion of positively or negatively charged CMC-alumina particles. Aggregates arise when CCMC approaches to Crp; the aggregation is maximal at 50:1 alumina/CMC mass ratio when the total charge is minimal. The I0(CCMC) begins to increase at almost equal CCMC at the two pH; the fact discloses that the particle aggregation corresponds to the net charge of CMC chains but not with the two times different structural charge. The particle aggregation is explained with polymer bridging of neighbour particles, considering the stability of bare alumina particles at absent of polyelectrolyte. The maximum of I0(CCMC) corresponds with the minimum of (CCMC) at the two pH; that reveals that the condensed ions behave as immobile at the interparticle interactions and chain bridging.
References [1] J. Goodwin, Colloids and interfaces with surfactants and polymers, 2nd ed., John Wiley, UK, 2009.
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[2] J. Gregory, S. Barany, Adsorption and flocculation by polymers and polymer mixtures, Advances Colloid. Interface Sci., 169 (2011) 1-12. DOI: 10.1016/j.cis.2011.06.004 [3] A.M. Zhivkov, Electric properties of carboxymethyl cellulose, in: T.G.M. van de Ven, (Ed.) Cellulose - Fundamental Aspects, InTech, Rijeka, 2013, Chapter 8 (pp. 1-31). [4] C.W. Hoogendam, A. de Keizer, M.A. Cohen Stuart, B.H. Bijsterbosch, J.A.M. Smit, J.A.P.P. van Dijk, P.M. van der Horst, J.G. Batellaan, Persistence length of carboxymethyl cellulose as evaluated from size exclusion chromatography and potentiometric titrations, Macromolecules 31 (1998) 6297-6309. DOI:10.1021/ma971032i [5] A.M. Zhivkov, R.P. Hristov, Polymer concentration dependence of kilohertz electric polarizability of alumina colloid particles with adsorbed carboxymethyl cellulose, J. Physics: Condensed Matter 22 (2010) 494112 (1-7 pp). [6] A.M. Zhivkov, R.P. Hristov, Electric polarizability dispersion of alumina particles with adsorbed carboxymethyl cellulose, RSC Advances, 4 (2014) 2715–2728. [7] A.M. Zhivkov, R.P. Hristov, Adsorption of carboxymethyl cellulose on alumina particles, J. Colloid Interface Sci., 447 (2015) 159-166. [8] F.Oosawa, Polyelectrolytes, Marcel Dekker, New York, 1971. [9] A.V. Dobrynin, Solutions of charged polymers, in: Matyjaszewski, K., Möller, M. (Eds.), Polymer Science: A Comprehensive Reference, 2012, Vol. 1, p. 81-132. [10] G.G. Gnesin (Ed.), Ceramic instrumental materials, Techniques, Kiev, 1984. [11] H. Li, Y. Li, J. Jiao, H.-M. Hu, Alpha-alumina nanoparticles induce efficient autophagydependent cross-presentation and potent antitumour response, Nature nanotechnology, 6 (2011) 645-650. [12] H. Lyklema, in: H. Lyclema (Ed.), Fundamentals of interface and colloid science, vol. IV, Elsevier, Amsterdam, 2005. [13] M. Kosmulski, Isoelectric points and points of zero charge of metal (hydr)oxides: 50 years after Parks’ review, Adv. Colloid Interface Sci. 238 (2016) 1-61. [14] M. Kosmulski, Compilation of PZC and IEP of sparingly soluble metal oxides and hydroxides from literature, Adv. Colloid Interface Sci. 152 (2009) 14-25. [15] S.S. Dukhin, B.V. Deryagin, Electrophoresis; Nauka: Moscow, 1976. [16] H.C.van de Hulst, Light Scattering by Small Particles; John Wiley: New York, 1957. [17] M. Kerker, The scattering of light and other electromagnetic radiation; Academic Press: London, 1969. [18] B.E. Eskin, Light Scattering by Polymer Solutions and Macromolecule Properties; Nauka: Leningrad, 1986.
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[19] A.M. Zhivkov, Geometry of purple membranes in aqueous medium, in: S.P. Stoylov, M.V. Stoimenova (Eds.), Molecular and Colloidal Electro-Optics, CRC: Taylor & Francis, New York, 2007, pp. 327-365. [20] C-P. Huang, W. Stumm, Specific adsorption of cations on hydrous γ-Al2O3, J. Colloid Interface Sci. 43 (1973) 409. DOI: 10.1016/0021-9797(73)90387-1. [21] G.S. Manning, Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties, J. Chem. Phys. 51 (1969) 924. DOI: 10.1063/1.1672157 [22] J.A. Davies, R.O. James, O.J. Leckie, Surface ionization and complication at the oxide/water interface, J. Colloid Interface Sci. 63 (1978) 480-499. [23] S.P. Stoylov, Relation between stability of oxide and clay disperse systems and the electric properties of their particles, Adv. Colloid Interface Sci., 50 (1994) 51-78. [24] U.G. Frolov, Surface adsorption layers and thermodynamic aggregative stability of disperse systems, Colloid J, (Russia) 57 (1995) 247-251. [25] N.V. Churaev, B.V. Derjaguin, Inclusion of structural forces in the theory of stability of colloids and films, J. Colloid Interface Sci. 103 (1985) 542-553. [26] B.V. Eremenko, M.L. Malysheva, I.I. Osipova, A.N. Savitskaya, T.N. Bezuglaya, Stability of aqueous suspension nanodimensional particles of aluminium oxide in aqueous solutions of electrolytes, Colloid J. (Russia), 58 (1996) 458-465.
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S0927-7757(17)30599-X http://dx.doi.org/doi:10.1016/j.colsurfa.2017.06.037 COLSUA 21724
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Revised date: Accepted date:
27-3-2017 12-6-2017 13-6-2017
Please cite this article as: Alexandar M.Zhivkov, Rosen P.Hristov, Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose, Colloids and Surfaces A: Physicochemical and Engineering Aspectshttp://dx.doi.org/10.1016/j.colsurfa.2017.06.037 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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>Crp = 0
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Highlights
Stability of alumina suspension with added (carboxymethyl)cellulose
Methods: electric light scattering and micro-electrophoreses
Electric polarizability, electrophoretic mobility and relaxation time
pH-dependent aggregation by polymer bridging at the recharging point
1
Stability of aqueous suspensions of alumina particles with adsorbed (carboxymethyl)cellulose
Alexandar M. Zhivkov and Rosen P. Hristov Institute of Physical Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 11, Sofia 1113, Bulgaria
Corresponding author; E-mail: [email protected]; Phone: +359 897 345 013
Abstract
The influence of the counterion condensation on the colloid stability of alumina suspension with added carboxymethylcellulose (CMC) is investigated by electric light scattering and microelectrophoresis. The electrophoretic mobility and the interface ion polarizability are used as criteria for the effective charge of CMC-alumina particles. The light scattering intensity I0 and the field-strength dependence (E2) of the relaxation time are used as criteria for aggregation. The polymer-concentration dependences (CCMC), (CCMC) and I0(CCMC) under and above the recharging point are measured at different degrees of proton dissociation and fraction of counterions condensed on the adsorbed polyelectrolyte chains: 1/2, = 0 at pH 4.5, and 1, 1/3 at pH 6.0. The results show out that the colloid stability is conditioned by the effective charge of CMC-alumina particles determined by the surface charge, the dissociated carboxylic groups of CMC chains and the condensed counterions. The particle aggregation about the recharging point (at 1:50 CMC/alumina) is explained with hetero-coagulation by polyelectrolyte chain bridging conditioned by the reduced total charge, surface charge-patches, low surface occupation and the high rigidity of CMC chains.
Key Words: Alumina particles; Carboxymethyl cellulose; Polyelectrolytes; Counterion condensation; Polymer adsorption; Polymer flocculants; Hetero-flocculation; Electric light scattering; Microelectrophoresis.
1. Introduction The electrostatic adsorption of polyelectrolytes on oppositely charged colloid particles is widely used for stabilization or flocculation of aqueous suspensions in biomedical, pharmaceutical
2
and industrial technologies. The interparticle interactions depend on the surface charge density and the quantity, net charge, flexibility and distribution of the adsorbed polyelectrolyte chains [1, 2]. We study the suspension stability of metal-oxide particles with adsorbed semiflexible polyelectrolytes; the rotational diffusion coefficient and the light scattering intensity are used as criteria for particle aggregation. In several consecutive works we investigate aqueous suspension of alumina (-Al2O3) particles with added (carboxymethyl)cellulose (CMC); the both substances are industrially produced and widely used in different technological processes. CMC is a weak polyelectrolyte with semiflexible chain [3]. It is chemical derivate of the cellulose (linear polymer composed of glucose rings) with covalently attached CH3COOH groups to the chain backbone which rigidity is determined by the impossibility of rotation between the neighbour glucose units; the measure for the chain rigidity is the high persistent length lp 17 nm [4]. The charge density of CMC is pH dependent due to dissociation of the carboxylic groups which dissociation degree [COO/COOH] increases from 0.2 at pH 3 to 1 at pH 6 in aqueous solution with low ionic strength; the apparent dissociation constant Ka() is function of : pKa = pH log[(1)]. At increasing polymer concentration the total particle charge decreases up to zero and then increases with opposite sign; i.e. overequivalent adsorption appears above the recharging point Crp. That is accompanied with change of the anion/cation ratio (counterions to the alumina surface and to the adsorbed CMC chains, respectively). As an indicator for this ratio we use the electrophoretic mobility and electric polarizability ; the employed methods are microelectrophoresis and electric light scattering. In the previous works [5, 6, 7] we have investigated the polymer-concentration dependences (CCMC) and (CCMC) at maximal charge of CMC chins when a fraction of Na+ counterions are electrostatically adsorbed (condensed) on the polyelectrolyte chins [8, 9]. The counterion condensation reduces the effective charge because of formation of [COONa] group-ion pairs; i.e. the net charge is determined by the difference of the structural charge (COO groups) and the condensed ion fraction [COONa][COO]. In this work we distinguish the contribution of the structural and the net charges to the colloid stability of CMC-alumina suspension. For that we investigate (CCMC) and (CCMC) at two (pH) where the different linear charge density determines presence or absence of counterion condensation. We designate the counterions to CMC-alumina as follows: condensed anions (immobile during the existence of the ion-group pairs), loosely bound anions (movable along the adsorbed polyelectrolyte chains) and diffuse cations (counterions to the particle surface); only the last two kinds of counterions contribute to the polarizability in kilohertz electric field [6]. The different
3
mobility and charge sign of the counterions allows distinguishing the structural and net charges by (CCMC) and (CCMC) and their influence on the colloid stability of CMC-alumina suspension. The results show out that the counterion condensation equalizes the total charge of the CMC-alumina particle in the range pH 4–6 where the charge of Al2O3 surface is maximal. Aqueous suspension with 50 g/m3 alumina is stable at high or low polymer concentration but rapid aggregation appears at 1 g/m3 CMC. The results should be useful to stabilize alumina suspensions by polyelectrolytes. In particular, such necessity appears when use dispersed aluminum oxides as activators at fritting of ceramics from high-melting compounds as nitrides and borides. In such cases the uniformly distribution of the alumina nanoparticles is very important for the mechanical properties of the products; that requires avoiding coagulation in the suspension used for slip forming [10]. The colloid stability is important when using alumina nanoparticles in medicine and pharmacy as adjuvant for vaccines, in particular as an antigen carrier for anticancer vaccine [11].
2. Materials and methods 2.1. Materials The used polyelectrolyte was sodium salt of carboxymethyl cellulose (NaCMC, Hercules) with degree of substitution DS = 1.2 (on average 80% of the glucose units have one, and 20% two CH2COONa+) and mean-weight molar mass Mw = 250 kg/mol. This mass corresponds to CMC chain with 952 monomer units and contour length Lc 490 nm [3=]. Alumina particles (γ -Al2O3, Degussa) with total surface 200 m2/g were used as adsorbent. The particles are stable aggregates of 20 nm spheroidal nanoparticles (irreversibly coalesced in the process of synthesis by pyrolysis) with irregular form and average size 0.3 m. As metal-oxide its surface charge is pH dependent [12]; the point of zero charge of Al2O3 surface is pH 7.59.5 [13, 14]. The suspension was prepared by dispergating alumina powder the particles in triple distilled water, 1 min ultrasound treatment (Techpan, Poland, 20 kHz) and mixing of equal volumes of the suspension and water solution of NaCMC, both with pH 4.5 or pH 6.0, followed by continuous stirring for 30 min; the final concentration was 0.05 g/dm3 -Al2O3. NaCl was added to the suspension at pH 6.0 to equalize the ionic strength Iion = 2.5104 mol/dm3 to that at pH 4.5. The pH was controlled before and after the electro-optical measurements; the difference did not exceed ±0.1 pH units. The electrooptical and electrophoretic measurements started about 1 hour after mixing of the alumina suspension and CMC solution; this time is enough for complete adsorption [7=].
2.2. Electrophoresis
4
According to Smoluchowski-Hückel-Henry’s equation [15] the electrophoretic mobility = (0/)f(a) is determined by the electrokinetic potential , bulk viscosity , dielectric permittivity 0. The function f(a) depends on the form, orientation and dimensionless size a of particles with long size a and thickness of the electric double layer (EDL); in case of spherical dielectric particles f(a) = 2/3 – 1 in the range a 1 – 100. Mark II apparatus (Rank Brothers, UK) with a flat quartz cell and dark field optical microscope was used. The time t for which chosen particles migrate on fixed distance lel was measured in a direct electric field with intensity E = 10 V/cm at alternately changing the polarity for a set of 20+20 particles in the two stationary planes where the electroosmotic flow is zero. The averaged value t and the standard deviation are calculated for each plain separately (the difference is about 1%) and the mean values are used to calculate the mobility = leltE. The practically does not depend on the non-adsorbed CMC because it’s inclement to the bulk viscosity is negligible.
2.3. Electric light scattering The intensity I0 of a light with wavelength 0 incoherently scattered by a suspension of particles with refractive index n1, mass M and size L, which are dispersed in a medium with refractive index n0, increases lineally with particle number concentration until they scatter as independent particles [16]. The intensity I at scattering angle depends on M, the relative refractive index n = n1n0 and also on the particle form and relative size L/ (where = 0n0 is the wavelength in the bulk) when L/ 1/20 [17]. In the Rayleigh–Debye–Gans theory the light scattering intensity I0 at random particle orientation is expressed by the function of internal interference P(θ) (called also form-factor): I0 = kcHMP(θ) ,
(1)
where k is the apparatus constant determined by the scattering volume and the solid angle of the photoreceiver; c is the weight concentration of the dispersed substance; and H is the optical constant of the suspension (defined by 0, n0 and n1) [18]. The electric field induced by metal electrodes causes electrooptical effect (EOE) because of orientation of the particles. The electric light scattering (ELS) is defined as ΔII0 = (IEI0 ) 1, where IE and I0 are intensities at presence and absence of electric field. The EOE is determined by the change of the internal light interference because of altered position of the particle’s optical electrons which oscillation is the primary cause of the light scattering. The EOE can be expressed by the functions P(θ, E) and P(θ) at presence and absence of electric field, respectively at certain
5
orientational degree at moment t after switching on/off the field and at random orientation of the particles of the ensemble [19]: It/I0 = [P(θ, E) P(θ )] − 1 = [A(KL) P(θ)] × (γ, E, T, t) ,
(2)
where A(KL) is optical function determined by the particle geometry (form and size); KL = 2π (L/λ) sin(θ2). At given A(KL) the EOE value It/I0 is determined by the orientational function
(γ, E, T, t) (increasing from 0 at random orientation to 1 at full orientation) which expresses the average orientation of the particles with electric polarizability γ in electric field with strength E at temperature T. At steady-state EOE Is the averaged degree of orientation depends only the ratio of the orientational energy γE2 to the energy of random motion kT; the γE2 = γEE in field E is determined by the induced dipole moment γE. At low degree of orientation (when γE2kT) the (γ, E, T) is a linear function of E2; then the initial slope [Is/I0E2]E0 (reduced EOE) is proportional to the polarizability : [IsI0]E0 = [A(KL) / P( (E2 15kT) .
(3)
In the process of particle orientation/disorientation the internal interference function P(,) alters its value with the time t. The transient EOE It at moment t after field switching off is: ItI0 = [A(KL) / P( (γ, E, , t= (IsI0) exp(t /) ,
(4)
where the relaxation time = 16Dr (the time for e-fold decreasing of It starting form the steadystate value Is) is defined by the rotational diffusion coefficient Dr kTL3 which is determined by the particle geometry (form and size L) and the medium viscosity 0 at temperature T. The EOE decay in the case of a monodisperse suspension is mono-exponential for particles with axial symmetry and polyexponential in case of polydisperse suspension. The I0 and I were measured at angle = 90 in electrooptical cell with interelectrode distance 2.6 mm by computerized home-made apparatus [7=] using sinusoidal voltage up to 140 V with frequency 1 Hz, generated by Wavetek-185 functional generator and amplified by Krohn-Hite7500 amplifier. The reproducibility (estimated as deviation from the averaged values) was better than ±5% for the steady-state EOE Is/I0 and ±7% for the relaxation time in the case of given suspension. The reproducibility of different series of suspensions prepared at the same conditions from the same stock (alumina suspension and CMC solution) was in the frame of ±10%.
3. Results The investigation is done in two stages. The aim of the first is to find two pH values where there are or not counterion condensation on the CMC chain but the charge density of the alumina
6
particles is the same. A concomitant purpose is to estimate the charge densities of the alumina surface and the adsorbed polyelectrolyte chains which determine the fractions of the diffuse, loosely bound and condensed counterions. The second part of the results presents the polymerconcentration dependences of the electrophoretic mobility (CCMC), electric polarizability (CCMC), and colloid stability at the two chosen pH values.
3.1. Surface charge density of bare alumina particles To condition electrostatic adsorption of the negatively charged CMC chains, pH must be in the acid range where the alumina surface is positively charged. The 0(pH) dependence (Fig. 1) allowed choosing pH 4.5 and pH 6.0 as the most appropriate; at these pH the mobility values are practically equal: 0 = 1.8 (m/s)/(V/cm) at ionic strength Iion = 1 mol/m3. The result is in agreement with the older data: 0(pH) has a plateau in the range pH 46 [20].
40
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0 . 10
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30
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-1
[m s V ]
1.5
10
0.5
1.6 0.0
0
C
1/2
1 NaCl
2
0
3
3 1/2
[mol/m ]
-0.5 4
5
6
7
8
9
pH
Fig. 1. pH-dependence of the electrophoretic mobility 0 (left ordinate) and the electrokinetic potential 0 (right ordinate) of bare -Al2O3 particles in aqueous suspension with ionic strength Iion = 1 mol/m3. The pH is adjusted by HCl or NaOH, the Iion = 0.25 mol/m3 is equalized by adding of NaCl. The 0 is calculated from 0 by Henry equation with correction factor f(a) = 0.72. Insert: Electrophoretic mobility 0 vs. square root of NaCl concentration at pH 5.25.
7
40
0 [mV]
2
4
36 6
2
32
0 [mC/m ]
8
1
4 28 2
3
24
0 0.0
0.5
1.0
1.5
C
1/2
2.0
2.5
3.0
1/2
NaCl
[mmol/L]
Fig. 2. The electrokinetic potential 0 (left ordinate, lines 1–3) and the surface charge density 0 (right ordinate, curve 4) of bare -Al2O3 particles in aqueous suspension vs. square root of NaCl concentration CNaCl = 0.25–10 mol/m3. The 0 is calculated from the 0 measured at pH 5.5 at Henry correction factor f(a) for dielectric spheres with radius a = 10 nm (line 1), 30 nm (line 2) and 150 nm (line 3). The surface charge density 0 (curve 4) is calculated for spherical particles with diameter 2a = 60 nm. The calculation of the electrokinetic potential of submicron particles with size 2a at thickness of the electric double layer (EDL) = 9.6 nm (Iion = 1 mol/m3) requires employing Henry equation 0 = (0/)f(a) instead Hückel (f(a) = 2/3) or Smoluchowski (f(a) = 1) ones; for dielectric spheres the value of f(a) increases from 0.67 to 0.98 in the range a = 1 – 100. Considering that the alumina particles are aggregates of 20 nm nanoparticles with irregular form and average size 300 nm, we have to approximate them to sphere and calculate f(a) with a in the range 10–150 nm. To choose the diameter 2a we use the dependence of 0 on the ionic strength Iion (Fig. 1, Insert) which shows false plateau at NaCl concentration CNaCl 1 mol/m3 because the f(a) diminishes with increasing of from 9.6 nm to 19.3 nm (Iion = 1–0.25 mol/m3). The calculated shows (Fig. 2) that the ion-concentration dependence (CNaCl)1/2 has nonlinear deviation at both 2a = 20 nm (line 1) and 300 nm (line 3), it is linear at 2a = 60 nm (line 2). That allows as to use a = 30 nm at which f(a) = 0.72 (a/ = 3.1 at Iion = 1 mol/m3). Then Henry’s equation gives = 35 mV at 0 = 1.80108 m2s1V1 in the range pH 4–6. The Gouy-Chapman theory (flat EDL) gives surface charge density 0 = 3.0103 Cm2 (1.9 elementary charges per 100 nm2 or 53 nm2 per charge) at Iion = 1 mol/m3. The average distance between two neighbour charged centers is equal to 7.8 nm, assuming that the surface charge is arranged as a hexagonal lattice [19]. At Iion = 10 mol/m3 the measured mobility is 0 = 1.59108
8
m2s1V1, accordingly f(a) = 0.84, = 27 mV, and 0 = 7.0103 Cm2 (4.3 charges per 100 nm2).
3.2. Linear charge density of free CMC chains At degree of substitution DS = 1.20 the average distance between the COOH groups is b0 = 0.43 nm [3=]. The degree of dissociation 0.5 and 0.95 determines the average distance between COO groups b1 = b0 0.86 nm and 0.45 nm, and the linear charge density (the ionized groups to the contour length) b11 = b0 1.17 nm1 and 2.21 nm1, respectively at pH 4.5 and pH 6.0. The dimensionless charge parameter lB/b1 (determined by the linear charge density and the Bjerrum length lB 0.712 nm at 20C) has values 0.83 and 1.58, respectively at pH 4.5 and pH 6.0. According to the Manning’s theory counterion condensation appears when >1 and the fraction of the condensed ions is = 11 [21]. So, at pH 4.5 there is not condensation but at pH 6.0 condensation of Na+ on COO groups appears and = 0.37. I.e. at pH 6.0 about 1/3 of the dissociated carboxylic groups are neutralized forming COONa+ group-ion pairs, and the effective linear charge density is equal to (1)b1 = b0 1.40 nm1; the 2/3 of COO groups have effective negative charge equal to that of the loosely bound Na+ counterions. The ratio of the net charges at pH 6.0 to pH 4.5 is equal to 1.40 1.17 = 1.20; i.e. the effective charge density at pH 6.0 is only 20% higher than at pH 4.5 although the fraction of dissociated carboxylic groups is almost two times higher.
3.3. Electrophoretic mobility of CMC-alumina particles The polymer-concentration dependence (CCMC) (Fig. 3) shows that the electrophoretic mobility of the alumina particles decreases with polymer concentration CCMC down to the recharging point Crp 0.9 mg/dm3 CMC and then its absolute value increases reaching plateau at CCMC > 30 mg/dm3. The change of sign shows out overequivalent adsorption of the negative CMC chains on the positive alumina particles. The linearity of (CCMC) in the region of Crp indicates that all added CMC chains are adsorbed on the particles at low CCMC [7].
9
. 10
8
2 1
1
[m s V ]
2
1
0
pH 4.5 -1
pH 6.0 -2 0.0
0.3
0.6
0.9
10
20
30
40
50
CCMC, mg/L
Fig. 3. Electrophoretic mobility of CMC-alumina particles vs. NaCMC concentration CCMC at pH 4.5 (▼) and pH 6.0 (▲) at ionic strength Iion = 0.25 mol/m3. The mobility reduction at CMC adsorption is caused by both chain charge and the hydrodynamic friction; the last is absent at = 0. That allows comparing the charge densities at the two pH using Crp values (CMC concentrations where the particle charge is equal to that of the adsorbed chains). Fig. 3 shows out that the ratio (Crp)pH4Crp)pH6 is about 1.1; this value corresponds approximately to the calculated 1.2 ratio of the net charge densities for free CMC chains at pH 6.0 and pH 4.5 (section 3.2). This result reveals that the [COONa+] group-ion pairs are not destroyed after adsorption of the polyelectrolyte chain on the particle surface; in case of full decondensation Crp at pH 6.0 ( 1) should be two times smaller than at pH 4.5 ( 1/2). So, the negative charge added to the positive particle surface by every adsorbed CMC chain is determined by the dissociation degree 0.5 at pH 4.5 or by the fraction of effectively charged carboxylic groups 1 0.6 at pH 6.0; that leads to near courses of (CCMC) curves at the two pH.
3.4. Kilohertz polarizability of CMC-alumina particles Inserts in Figs. 3, 4 show the field-strength dependences IsI0 = f(E2) at CCMC under and above the recharging point Crp. At these CCMC particle aggregation does nor appear (section 3.5); that means that the optical functions in Eqs. (2, 3) remain unchanged. The linearity of Is(E2) verify that the orientational energy is low compared to the thermal one (E2kT), so the line slope (reduced EOE) is proportional to the polarizability: (IsI0E2)E0 (const ). The bare particles (Fig. 4, lines 1) have equal values at the two pH; that is in agreement with the pH-independent surface charge in the range pH 46 (section 3.1).
10
pH 6.0
12
3 9
2
[(Is / I0) / E ] . 10
Is / I0 [%]
4
11
2
2
[m / V ]
pH 4.5 5
2 1
6
2
3 2
0
0 0.0
1
E . 10 0
10
0.2
-8
20
2
2
[V /m ] 30
0.4
0.6
0.8
1.0
CCMC [mg/L]
Fig. 4. Reduced EOE vs. NaCMC concentration CCMC under recharging point at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3 equalized by NaCl. Insert. Steady-state electrooptical effect IsI0 in sinusoidal electric field with frequency = 1 kHz vs. squared field strength E2 for bare -Al2O3 particles (lines 1) and at presence of NaCMC with concentration CCMC = 0.7 mg/dm3 (lines 2) at the same pH and Iion. Fig. 4 shows polymer-concentration dependence (CCMC) of the polarizability (in relative units) under Crp. The both (CCMC) curves have two regions: almost independent on CCMC and strongly decreasing. The linearity of the last shows out that the polarizability reducing (owing to the opposite charge and hydrodynamic friction added to the particle surface) is proportional to the quantity of the adsorbed CMC chains and that their charge do not depends on the degree of surface occupation in the range CCMC Crp. The difference between values at the two pH corresponds to the net charge density likewise that of the mobility . Above the recharging point (Fig. 5) the values also correspond approximately to the net charge density of the adsorbed CMC chains but in this CCMC range the difference at the two pH is smaller owing to higher adsorption at pH 4.5.
11
pH 6.0 pH 4.5
3
Is / I0 [%]
12 9
2
2
[(I / I0) / E ] .10
11
2
2
[m / V ]
4
6
1
3 2
0
0 0
10
E . 10
-8
2
2
[V /m ]
0
10
20
30
20
30
40
50
CCMC [mg/L]
Fig. 5. Reduced EOE vs. NaCMC concentration CCMC above the recharging point at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3. Insert. Field-strength dependence IsI0 = f(E2) at = 1 kHz for alumina particles at CCMC = 40 mg/dm3 at the same pH and Iion. The nearness of the (CCMC) curves values at the two pH (in the CMC range under and above Crp) reveals that the interface polarizability of CMC-alumina particles is due to the mobile counterions (diffuse Cl and loosely bound Na+) but the condensed Na+ do not participate remaining immobile in the applied kilohertz electric field with moderate strength.
3.5. Aggregation stability The increasing light scattering intensity I0 is indication for growing of the particle mass M (Eq. 1). The polymer-concentration dependences I0(CCMC) show out that particle aggregation appears in narrow CCMC range (Fig. 6, the I0 values are out of the scale at the recharging point Crp 0.9 mg/dm3). At Crp the suspension instability rapidly increases with the time up to visible turbidity followed by flocculation.
12
1.6
pH 6.0
1.5
pH 4.5
[rel. un.]
1.4 1.3
I0
1.2
2
1.1
1 1.0 0.0
0.3
0.6
0.9
10
20
30
40
50
CCMC [mg/L]
Fig. 6. Dependence of the light scattering intensity I0 (in relative units) on the polymer concentration CCMC at pH 4.5 (▼) and pH 6.0 (▲) under (line 1) and above (line 2) the recharging point at Iion = 0.25 mol/m3. The low I0 values are indication for absence of noticeable aggregation at CCMC Crp2 (line 1) and CCMC 5Crp (line 2). The suspension stability in the lower range can be explained with enough strong electrostatic repulsion between the positively charged particles (Fig. 3). But the absence of aggregation in the higher range is impressive because the total charge pass zero value in the process of recharging by adsorption of the negative CMC chains on the positive alumina surface. The fact can be explained with the faster polyelectrolyte adsorption compared to the relatively slow particle collision: the kinetics of the two processes is determined by the strongly different translational diffusion coefficients of the polymer random coil and the colloid particles. The slight increasing of I0 with CCMC could be ascribed to the adsorbed CMC but this is precarious inference because the increment M is too small compared to the large particle mass M. An alternative explanation is appearance of a small fraction of aggregates to which I0 cM is not enough sensitive. That is why we use the field-strength dependence (E2) of the relaxation time (Eq. 4) as a more sensitive criterion; at polydisperse suspension (E2) is curve and its curvature strongly increases at particle aggregation. Fig. 7 shows (E2) dependences for suspensions of bare alumina particles (curve 1) and with added CMC at saturated adsorption (curve 2). The (E2) reflects the degree of orientation (γ, E presented by the field dependence (IsI0)(E2) (curve 3). The near forms of the curves 1 and 2 show out absence of significant aggregate fraction which could be appear at passing over zero total charge at CMC adsorption; in the opposite case the curvature of the curve 2 should be significantly increased. The fact that the values practically coincide at the two pH confirms that the colloid
13
stability is pH-independent at high CCMC. The increment = 0 (lift of the curve 2 above the curve 1) is caused by the hydrodynamic friction of the adsorbed CMC chains, additional to that of the bare particle surface. The inference flows from the fact that the is almost the same at increasing degrees of particle orientation (E2) (curve 3); in the case of aggregation the should decrease with E2 (the curve 2 should approach the curve 1) owing to increasing contribution of the faster single particles.
5
[%]
20
4 15
2 3
Is / I0
[ms]
3
10
2
5
1
0 0
5
10
15 2
20 -8
E . 10
2
25
30
2
[V /m ]
Fig. 7. Relaxation time (left ordinate; curves 1, 2) and steady-state EOE IsI0 (right ordinate; curve 3) vs. squared field strength E2 in -Al2O3 suspension at absence of polymer (curves 1, 3) and at CMC concentration 30 mg/dm3 (curve 2) at pH 4.5 (▼) and pH 6.0 (▲) at Iion = 0.25 mol/m3. So, the (E2) dependence confirms the inference obtained by I0(CCMC) that addition of CMC to the alumina suspension does not lead to noticeable aggregation when CCMC is significantly above Crp. The coincidence of I0 and values at the two pH shows out that the colloid stability is pHindependent at enough high total charge: positive at low CCMC or negative at high CCMC. The aggregation near Crp is pH-dependent; the small difference at pH 4.5 and pH 6.0 is indirect indication that the total charge of CMC-alumina particles is determined by the net charge of adsorbed polyelectrolyte chins, not by their two times different structural charge.
4. Discussion 4.1. Static and electric light scattering To investigate the suspension stability we employ static light scattering and electrooptical criteria for particle aggregation. The using of I0(CCMC) is based on the dependence I0 NM2P() cMP() for light scattering of N particles (single or aggregates at chaotic orientation) with mass M in suspension with weight concentration c of the dispersed substance (Eq. 1). In the process of aggregation I0 increases because of the growing M (accompanied by reducing of N at constant c).
14
The aggregate size L (synchronously growing with M) has the opposite effect on I0 because P() P(, L/) has tendency to diminish its value with the relative size L/ but the dependence I0(L) is relatively weak (at = 90 when L is commeasurable with ) compared to that of I0(M). So, I0 is reliable criterion for aggregation of alumina particles with L 0.3 m suspended in aqueous medium in the visible range where = 0n0 0.30.6 m. An advantage of I0 is that it is applicable to particle with size and form (including spherical) which can not be oriented in electric field. On the other hand I0 cM is not sensitive to the small fraction of aggregates because it reflects the averaged mass M of all particles in the ensemble. To overcome this disadvantage of I0 we combining it with the relaxation time L3 which is very sensitive to the particle size L. However is not very sensitive to small fraction of aggregates as well; that is why we use its field-strength dependence (E2) as a criterion for polydispersity. The (E2) is based on the strong dependence L23 of the polarizability on the long particle size L; that leads to higher degree of orientation (γ, E2of the bigger particles in comparison to smaller ones. The relative contribution of the aggregates to I(E2) diminishes with E2 owing to increasing orientation of the small particles; accordingly decreases with E2. In the case of polydisperse suspension the form of (E2) is curve which curvature strongly increases at particle aggregation.
4.2. Alumina surface charge density The electric charge of oxide/water surfaces is caused by dissociation of amphoteric MOH groups, adsorption of the potential-determining H2O+ and OH ions, and physical adsorption of [Mz+(OH)z1]+ and [Mz+(OH)z+1] hydroxide complexes [22]. The electric properties of alumina particles are determined by ionization (AlOH2+ AlOH + H+ and AlOH AlO + H+) of the amphoteric AlOH groups. That allows describing the alumina surface as diprotic acid with intrinsic constants pK1 = 7.9 and pK2 = 9.1, respectively; the surface density of the exchange capacity (the sum [AlOH] + [AlOH2+] + [AlO]) is one functional group per 1.6 nm2 [20]. The strongly hydrated gelatinous surface layer causes shift of the shear plain (reducing of -potential), weak dependence of on the ‘surface’ charge density , and much less electrokinetic charge density ek as compared with pt obtained by potentiometric titration: ek pt5. The high potential in the boundary layer alters the local concentration of H2O+ and OH ions; therefore their replacement with Na+ and Cl (indifferent ions) increases pt and ek. The electric properties of metal oxides strongly depend on the method of synthesis, crystalline modification, impurities, and degree of hydratation. We have used -Al2O3 particles
15
(synthesized by the same method of flame pyrolysis of AlCl3) which have the same 0, pHiep 8.5 and plateau of 0(pH) at pH 4–6 (Fig. 1) as those in Ref. [20]. In electrooptical experiment the ionic strength Iion is kept constant by addition of NaCl (to avoid influence of Iion on ); that leads to different OHCl ratio of the counterions (CNaCl = 0 at pH 4.5 and 0.25 mol/m3 at pH 6.0). The plateau of 0(pH) dependence at pH-lowering (Fig. 1, curve 1) from pH 6 to pH 4 we explain with increasing difference in the local concentrations of H2O+ and OH (compared to the bulk) and exchange of Cl counterions with OH. The high charge density in the boundary layer leads to strong dependence of 0 on CNaCl (Fig. 2, curve 4): the electrokinetic charge increases from 0 = 1.6 to 13.3 mC/m2 in the range CNaCl = 0.25–50 mol/m3.
4.3. Chain/particle charge ratio The electrophoretically measured total charge of CMC-alumina particles allows estimating the average number of polyelectrolyte chains adsorbed on a colloid particle. That can be done correctly at absence of hydrodynamic friction: the zero electrokinetic charge at Crp ( = 0) reflects the charge equality of the positive alumina surface and the negative CMC chains. Assuming that alumina particles (aggregates of 20 nm nanoparticles) have form of oblong ellipsoid with long axis 300 nm and axes ratio 1.5, the envelope surface (hexagonally packed semispheres) of one particle has area S = 0.27 m2 and 2100 positive charges at pH 4–6 (section 3.1). The used CMC has chain contour length Lc = 490 nm (an average value owing the polymer polydispersity), linear charge density 1.17 nm1 or 1.40 nm1 (section 3.2), and 573 or 685 net charges at pH 4.5 and pH 6.0, respectively. Accordingly, at CCMC = Crp the particle charge is neutralized by 3.7 or 3.1 CMC chains; these values are minimal because the estimation takes into account only the envelope surface of a particle with regular form. According it the occupied surface is only 2 % (3 % at S = 0.17 m2 of the ellipsoid with smooth surface) assuming that one adsorbed CMC chain occupy area equal to the radius of gyration Rg = 44 nm of the random coil [3]. At the last assumption the average 2D net charge density of a dome (the projection of the negative polymer charges on the positive particle surface) is 37 negative charges per 100 nm2; i.e. 47 (pH 4.5) or 56 (pH 6.0) times higher than that of the bare alumina surface. The above estimations mean that the probability that a given particle can be rigorous neutral is vanishingly small: it is still positively or already negatively charged owing to the stepwise adsorption of large polyelectrolyte chains bearing about 6–7 hundred negative charges. It can be supposed that at Crp in the suspension there are CMC-alumina particles with both negative and positive charge, and that stimulates the aggregation, together with the reduced total charge. But the experiment does not confirm these suppositions: about Crp all CMC-alumina particles are either
16
positive or negative and the mobility of the single particles is not drastically different, although the dispersion of is in order of magnitude higher than for bare particles (Fig.3). So, the above estimated number of adsorbed CMC chains is actually much higher because the real surface area is several times larger owing to the irregular form of the alumina particles and the effective potential on the bare particle surface is induced not only by the outer charge centers but also by that ones lying under the envelope surface on a depth commensurable with the EDL thickness 20 nm. Nevertheless, it is obvious that the CMC-alumina surface is strongly unhomogeneous: a relatively small number of strongly charged negative domes are disposed on spacious positive area with low charge density. The seeming independence of the mobility and polarizability on the polymer concentration at low CCMC (Figs. 3 and 4 at CCMC 0.5 mg/dm3) is analogical to those of polyvalent inorganic or small organic ions. The reasons for this phenomenon could not be absence of CMC in the medium owing to its adsorption on the laboratory ware because the both polyelectrolyte chains and the glass surface are negatively charged and strongly hydrated. Another possibility is predominant CMC adsorption on the particle aggregates which are disregarded at the electrophoretic measurements and contribute relatively less to EOE owing to the small anisodiametricity. Additional investigations are required to explain the observed low-concentration plateaus of (CCMC) and (CCMC) dependences.
4.4. Polyelectrolyte induced aggregation The alumina suspension is stable at presence of CMC with low or high concentration; i.e. in the two CCMC ranges where the electrostatic repulsion is enough strong as it follows from the comparison of (CCMC) and I0(CCMC) (Figs. 2, 5). On the other hand at Crp rapid turbidity appears which is indication for fast coagulation; i.e. in the point of zero total charge the aggregation is rather diffusion limited. In contrast, at absence of polymer the alumina suspension is practically stable (during the measurements at the low particle concentration and the low ionic strength used in the experiment) even in the isoelectric point (Fig. 1, 0 = 0); the fact is in accordance with earlier observations [23]. The high colloid stability of aqueous suspension of oxides and hydroxides is determined by the strongly hydrated boundary layer which increases the thermodynamic stability by decreasing of the surface pressure [24] and determines the structural component in the extended DLVO theory [25]. In the case of bare alumina particles additional factor is their irregular form and uneven surface which do not allow forming of enough contact area at Brownian collisions. As result the threshold of coagulation strongly increases up to molar concentrations of indifferent electrolyte (1.8 mol/dm3 NaCl [26], which is 4 orders of magnitude higher than in our experiment).
17
The contrast of the suspension behaviour at presence or absence of CMC reveals that the particle aggregation is result of interparticle polymer bridging: a chain adsorbed on one particle contacts with a bare surface area of the approaching particle. This process is conditioned by: (a) the oppositely charged polyelectrolyte and particle surface; (b) strongly heterogeneous distribution of the surface charge of CMC-alumina particle (charge patches); (c) 3D-conformation of the adsorbed polymer chains which form domes because of the high rigidity of CMC chain; and (d) the small area occupied by the adsorbed CMC chins (owing to their small number and the random coil conformation before adsorption). Due to the chain semi-rigidity the CMC domes protrude above the particle surface and conditions by that the aggregation by chain bridging, in difference from the case of flexible polyelectrolytes where the charge-patch mechanism of the polymeric heteroflocculation of big colloid particles dominates [1]. The strong charge inhomogeneity of CMC-alumina particles raises a question: why the recharged particles do not aggregate at CCMC 5Crp (Figs. 5, 6) although on the surface there are enough bare areas which could connect a polyelectrolyte chains already adsorbed on an approaching particle? We explain that with two factors: (a) the low ionic strength Iion used in our experiments; and (b) the relatively fast rotational diffusion compared to the translational one. The second factor leads to averaging of the electrostatic potential for time at which two neighbour particles can approach on distance allowing polymer bridging. As combination of the two factors, the resulting electrostatic repulsion is enough strong (on distance relatively long in comparison with the prominent polymer domes) to prevent particle aggregation. The rapid instability at Crp (in contrast with suspension stability at saturated CMC adsorption) reveals that the reduced electrostatic repulsion plays leading role in the in the particle aggregation.
4.5. pH-dependence of the aggregation stability At absence of aggregation it is not possible to distinguish which CMC charge (the structural or net one) stabilize the suspension because the electrostatic repulsion is enough strong in the both CCMC ranges under and above Crp. A difference appears at approaching to Crp: the twofold higher structural charge at pH 6.0 should lead to twofold reduced CCMC where aggregation appears. But the I0(CCMC) shows out that particle mass begins to increase at CCMC equal at the two pH. This fact means that the colloid stability is determined by the net charges of the adsorbed CMC chains which are near at the two pH owing to the counterion condensation (section 3.2). In the range of instability some difference appears (Fig. 6, CCMC = 1 mg/dm3): the average mass is bigger at pH 6.0 (I0 = 1.6) than at pH 4.5 (I0 = 1.5). This fact is unexpected because the total (negative) charge of the recharged CMC-alumina particles is higher at pH 6.0 (Fig. 3, CCMC > 0.9 mg/dm3, 0). The finding can be explained with linking of the negative polyelectrolyte chains
18
to the positive bare surface when the total charge is enough small (at CCMC near to Crp); then the some higher net charge of CMC chains at pH 6.0 facilitates the aggregation when the particles collide. So, the aggregation instability confirms the inference done by the concentration dependences (CCMC) and (CCMC) that the condensed counterions are not released at adsorption of the polyelectrolyte chains. That is due to the rigidity of CMC chain, uneven particle surface and the big difference of their charge densities. The condensed counterions reduce the effective charge of CMC-alumina particles and by that diminish the aggregation stability.
5. Conclusions The polymer-concentration dependences of the light scattering intensity I0(CCMC), the electrophoretic mobility (CCMC) and the electric polarizability (CCMC) are measured at two pH where the net charge density of the polyelectrolyte chains (determined by the dissociation degree and the condensed counterion fraction ) is different: 1/2, = 0 at pH 4.5, and 1, = 1/3 at pH 6.0. The I0(CCMC) and the field-strength dependence of the relaxation time (E2) (determined by the particle mass and size, respectively) are used as criteria for particle aggregation. The I0(CCMC) and (E2) show out absence of particle aggregation in two CCMC ranges: under and above the recharging point Crp. The difference of (CCMC) at the two pH corresponds to the calculated fraction , so the condensed counterions are not released at CMC adsorption. The suspension stability under and above Crp does not depend on and due to enough strong electrostatic repulsion of positively or negatively charged CMC-alumina particles. Aggregates arise when CCMC approaches to Crp; the aggregation is maximal at 50:1 alumina/CMC mass ratio when the total charge is minimal. The I0(CCMC) begins to increase at almost equal CCMC at the two pH; the fact discloses that the particle aggregation corresponds to the net charge of CMC chains but not with the two times different structural charge. The particle aggregation is explained with polymer bridging of neighbour particles, considering the stability of bare alumina particles at absent of polyelectrolyte. The maximum of I0(CCMC) corresponds with the minimum of (CCMC) at the two pH; that reveals that the condensed ions behave as immobile at the interparticle interactions and chain bridging.
References [1] J. Goodwin, Colloids and interfaces with surfactants and polymers, 2nd ed., John Wiley, UK, 2009.
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