Theory and experiment of reversing-pulse electric birefringence

Colloids and Surfaces A: Physicochemical and Engineering Aspects 148 (1999) 43–59

Theory and experiment of reversing-pulse electric birefringence The case of bentonite suspensions in the absence and presence of cetylpyridinium chloridek Kiwamu Yamaoka a,*, Viktor Peikov a,2, Ryo Sasai a,3, Stoyl P. Stoylov b a Department of Materials Science, Faculty of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 730, Japan b Bulgarian Academy of Sciences, Institute of Physical Chemistry, Acad. G. Bonchev St., 1113 Sofia, Bulgaria

Abstract Reversing-pulse electric birefringence (RPEB) of a fractionated bentonite sample (0.005–0.029 g/l ) was measured at 20°C and at a wavelength of 633 nm in aqueous media in the absence and in the presence of cetylpyridinium chloride (CPC ), a surfactant, at various concentrations (0.001–1.3 mM ). RPEB signals at weak electric fields showed either a hump each, or contrarily a dip each, in the build-up and reverse portions, depending on the concentrations of bentonite and CPC in suspension. The profile change of RPEB signals was interpreted as being due to the shift of the orientation axis from the symmetry axis to the plane of the disk-like particle. Observed RPEB signals were analyzed with the Y–S–K theory, which is based on an ion-fluctuation model and considers the contribution of three electric dipole moments to field orientation, and both electric and hydrodynamic parameters characteristic of RPEB profiles were evaluated by curve fitting with theoretical equations. The results are as follows: (1) the bentonite particle in the absence or in the presence of CPC possesses no permanent dipole moment; (2) it is oriented by applied field with the rootmean-square dipole moment due to ion-atmosphere fluctuation and the covalent dipole moment due to the polarizability anisotropy intrinsic to the particle; (3) the ratios of these two dipole moments either remain nearly constant or vary in a complex manner, depending on bentonite concentration, amount of added CPC, and field strength; and (4) the ratios of the relaxation time due to ion-fluctuation to the relaxation time due to overall particle rotation remain nearly constant for the bentonite suspension in the absence of CPC with increasing field strengths, though the system is polydisperse. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Bentonite; Cetylpyridinium chloride; Electric dipole moments; Ion-atmosphere fluctuation; Relaxation time; Reversing-pulse electric birefringence

* Corresponding author. Present address: 2-2-805, 5-Chome, Takaya Takamigaoka, Higashi-Hiroshima 739-21, Japan. k Combined excerpt from the lecture and poster presentation at the 8th Electro-Optic Symposium, St. Petersburg, 30 June–4 July 1997. Electro-optics in Dispersed Systems Series 8. Part 7 of this series is ref. [1]. 2 Present address: Bulgarian Academy of Sciences, Institute of Physical Chemistry, Acad. G. Bonchev St., 1113 Sofia, Bulgaria. 3 Present address: Department of Crystalline Materials Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan. 0927-7757/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0 9 2 7 -7 7 5 7 ( 9 8 ) 0 0 59 4 - 9

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1. Introduction Reversing-pulse electric birefringence (hereafter abbreviated as RPEB) is a specialized electro-optic method, which has long been applied to the diverse studies of polymers, polyelectrolytes, and colloids, in order to unravel the electric, optical, and hydrodynamic properties in solutions [2–5]. The observed RPEB results have often been interpreted only qualitatively, although they should contain rich and unique information, which is not easily extracted from other physico-chemical measurements. This is mostly because of the slow advance of RPEB theories. A widely used theory (hereafter abbreviated as the T–Y theory) was first reported by Tinoco and Yamaoka nearly 40 years ago [4] and has since been utilized extensively in the fields, for example, of polyelectrolytes [6 ], biopolymers [7], and clays [8]. These polymeric and colloidal materials are charged and almost always ionized in aqueous media, but their RPEB data have often been analyzed according to the classical T–Y theory [4], in which the particle orientation is considered to be due to the permanent dipole moment and the covalent (electronic and atomic) polarizability anisotropy. Some attempts were made to interpret RPEB signals of high molecular weight poly( p-styrenesulfonate), which is unlikely to possess any appreciable permanent dipole moment, in terms of slow-induced ionic dipole moments resulting from the translational motion of the counterion on the polymer surface [9]. However, the coupling of motions between the counterion and the overall rotation of a molecule or a particle was neglected in the T–Y theory, so that this theory is valid in the case where the rotational relaxation time is much larger than the ionic relaxation time. Recently, a new RPEB theory (abbreviated as the Y–T–S or Y–S–K theory) was developed by Yamaoka et al., by taking into account either two or three different electric dipole moments, which respond to a reversing-pulse field in the Kerr law region [10,11]. This theory is an extension of the previous one, which was derived by Szabo et al. [12] on the basis of the ion-atmosphere fluctuation concept of Oosawa [13]. These new theories consider the coupling of relaxation times arising from

ion-fluctuation and molecular rotation under applied electric field, so that the ionic relaxation time can be evaluated by knowing the rotational relaxation time. The Y–T–S [10] or Y–S–K [11] theory can be applied to RPEB signals resulting either from rod-like or disk-like molecules. The RPEB signals of disk-like montmorillonite [14] and ellipsoidal b-FeOOH (ferric hydroxide oxide) [15] particles were successfully analyzed by the Y–T–S theory. The field orientation mechanism of the disk-like montmorillonite particle dispersed in aqueous media was recently studied by RPEB techniques [14,16,17]. This study clearly showed that montmorillonite possesses no permanent electric dipole moment, contrary to a long-standing notion proposed by Shah [18], but that the particle is oriented by ion-fluctuating dipole moment and polarizability anisotropy [16,17]. In the present work, the RPEB method was applied to bentonite, another disk-like particle, in the absence and in the presence of cetylpyridinium chloride (CPC ), a cationic surfactant, with the following major objectives: (1) to ascertain if the bentonite and CPC-adsorbed bentonite possess the permanent dipole moment in aqueous media; (2) if not, to determine the type of electric dipole moment(s) responsible for field orientation; (3) to confirm if there exists sign-inversion and profile change in RPEB signals of bentonite in the absence and in the presence of CPC; (4) if any, to analyze the results observed with the increase in concentration of bentonite and CPC in terms of a sequential or a two-state model; and (5) to examine if the covalent polarizability anisotropy of the bentonite particle remains constant at applied weak fields. The analysis of experimental RPEB signals is made by duly considering the ionic dipole moment arising from ion-atmosphere fluctuation. For this purpose, simple mathematical expressions are presented for the RPEB signal of a multicomponent system.

2. Experimental 2.1. Materials The natural bentonite sample from a clay deposit near Varna, Bulgaria, was dispersed in 2 M NaCl,

K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

45

converted to the Na form, and fractionally centrifuged according to the procedure already described elsewhere in detail [19,20]. In the present study, the fraction sedimented by 20 min centrifugation at 4500 rpm was used (this sample was designated as fraction IV ). An average diameter of 296±48 nm was estimated from electron micrographs for the same fraction as this one in a previous work [19]. A 0.005 g/l suspension was sonicated at 0°C with a Tommy Seiko model UR-200P sonicator at a power level of 200 W (20 kHz) for 5 min for size reduction and deaggregation [16 ]. No salt was added, any excess ions being removed by dialysis [1]. The concentration of cationic surfactant CPC as monohydrate, supplied by Merck and Co., was varied from 0.001 to 1.3 mM. The CPC solution was added to bentonite suspension in small quantities. The critical micelle concentration of CPC is 0.9 mM [21].

system, an electric system, and a data accumulation and processing system [17]. The circuitry of a new reversing-pulse generator and a table of performance characteristics were also given [17]. Fig. 1 shows a photograph of the present apparatus. Electric birefringence signals were measured at 20°C and at a wavelength of 633 nm, and all other details were described elsewhere [1]. Electric birefringence Dn was usually expressed in terms of the experimentally observed optical phase retardation, d=(27pd/l)Dn, where d is the optical path of a Kerr cell and l is the wavelength of the incident light. No birefringence signal was observed for CPC solution in a 1 mM range.

2.2. Electric birefringence measurements

A schematic reversing-pulse electric field and typical RPEB signal patterns are shown in Fig. 2. The following theoretical expressions were derived to analyze quantitatively the characteristic beha-

Measurements were performed on a home-made RPEB apparatus, which consists of an optical

3. Theoretical

Fig. 1. Photograph of a home-made RPEB apparatus presently in use. O: optical system with a 5 mW He–Ne gas laser; WM: wave memory and computer for data accumulation and processing; P: high-speed and time-variable reversing-pulse generator.

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polarization of ion atmosphere is used in the present work. The theory assumes that a particle or macromolecule, either of cylindrical shape (or prolate ellipsoid of revolution) or of disk-like shape (or oblate ellipsoid of revolution), possesses three different electric moments, i.e. the permanent dipole moment m , the mean-square dipole 3 moment m2 1/2 due to the fluctuating ion atmo3 sphere at a single relaxation time t [12], and the I covalent (or electronic) dipole moment Da∞E resulting from the polarizability anisotropy Da∞ (=a∞ −a∞ ). The first two moments are assumed 33 11 to exist only along the axis of molecular symmetry (the 3 axis), to which the mutually orthogonal 1 and 2 (=1) axes are normal [10–12]. The normalized birefringence for the build-up process (cf. Fig. 2), D (t), defined as Dn (t)/Dn (2), is given B B B for the case 4Ht −1≠0 as [11]: I

A

p 3 D (t)=1− B 2 p+q+1

B

e−2Ht

A BA B C A B A BA BD

6Ht q I 4Ht −1 p+q+1 I p 3 − 1− 2 p+q+1 −

− Fig. 2. Schematic presentation of applied reversing-pulse electric field and RPEB signals (a–c). (a) Orientation due to electronically induced dipole moment Da∞E (no change in the reverse). (b) Orientation due to permanent dipole moment m or ion-fluctuating mean-square-average dipole moment m21/2 (dip in the reverse). (c) Orientation due to mixed dipole moments of Da∞E and m or m21/2 (either dips or humps in the build-up and reverse processes). The signals in build-up, reverse, and decay (D , D , and D ) are normalized. B R D

q

p+q+1

e−6Ht

(1)

and for the reverse process (cf. Fig. 2), D (t), R defined as Dn (t)/Dn (2), is given for the case R R 4Ht −1≠0 as: I

A A C A

3p D (t)=1− R p+q+1 −

vior of RPEB profiles with electric and hydrodynamic parameters.

+

3.1. Theoretical expressions for the single component system

×

Instead of the classical T–Y theory [4], a new Y–T–S (or Y–S–K ) theory [10,11] based on the

6Ht I 4Ht −1 I

e−(2H+t−I I )t

6Ht

I 4Ht −1 I 3p p+q+1 2q

p+q+1

B BA A BD

e−2Ht 2q

p+q+1

+

6Ht

B B

e−(2H+t−I I )t

I 4Ht −1 I

e−6Ht

(2)

(It should be noted here that the exponent of the second term on the right-hand side was inadver-

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K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

tently misprinted as exp(−6Ht) in the original paper [11].) Finally, the normalized birefringence for the field-off decay process (cf. Fig. 2), D (t), D defined as Dn (t)/Dn (0), is given as: D D

should be noted that hereafter the subscript 3 of m and m2  is omitted for brevity, unless other3 3 wise needed.

D (t)=e−6Ht D

3.2. Theoretical expressions for multicomponent system

(3)

where q is the ratio of ion-fluctuation polarizability s to the field-induced covalent (or electronic) 3 polarizability anisotropy Da∞, the sign of q can either be positive or negative, and so is the sign of p, depending on the sign of Da∞, which is generally positive for the prolate polarizability ellipsoid but negative for the oblate ellipsoid, and Dn(t) [=n (t)−n (t)] is the unnormalized birefringence d ) at time t either for build-up, reverse, or decay process. Other notations are defined as follows: p=b2/2c=m2 /kTDa∞, q=r2/2c= m2 / 3 3 kTDa∞=s /Da∞, b=m E/kT, r=(s /kT )1/2E, 3 3 3 c=Da∞E2/2kT and m2  (=n2e2 d2 ) is the mean3 3 square average electric dipole moment due to ionfluctuation along the symmetry axis, and H (= 1/6t) is the rotary diffusion coefficient of a particle. Thus, Eqs. (1)–(3) can be used for the quantitative analysis of diverse patterns of RPEB signals of rod-like and disk-like particles. If the particle possesses no permanent dipole moment (m =0), 3 then p=0 and Eqs. (1) and (2) reduce to the expressions derived in ref. [10]. In the Kerr law region, the steady-state birefringence Dn (t2) is given as: Dn(2)=n −n =2pC d ) v ×

A

A BA B B Dg

E2

n

15kT

m2  m2 3 + 3 +Da∞ kT kT

(4)

where n and n are the refractive indices of a d ) colloid suspension (or a solution) parallel and perpendicular to the direction of the electric field E, C is the volume fraction of the solute, and Dg v (=g −g ) is the optical anisotropy factor of the 3 1 solute, defined as the difference between the optical polarizabilities per solute volume along the 3 and 1 axes [5]. n is the refractive index of the suspension (or solution) in the absence of the electric field. It

Eqs. (1)–(4) may be extended to an RPEB signal of a multicomponent system consisting of m RPEB signals (or m components) as follows. (i) Build-up process m ∑ Dn (t) B j Dn (t) B D (t)= = j=1 B m Dn (2) B ∑ Dn (2) B j j=1 Dn (2) m m B j =∑ F D (t) (5) = ∑ D (t) j B j B j m j=1 j=1 ∑ Dn (2) B j j=1 where

A

B

p 3 j D (t) =1− e−2Hjt B j 2 p +q +1 j j 6H t q j Ij j − 4H t −1 p +q +1 j Ij j j p 3 j − 1− 2 p +q +1 j j 6H t q j Ij j − 4H t −1 p +q +1 j Ij j j

A BA B C A B A BA BD

)t Ij e−(2Hj+t−1

e−6Hjt

(6)

(ii) Reverse process m ∑ Dn (t) R j Dn (t) R D (t)= = j=1 R m Dn (2) R ∑ Dn (2) R j j=1 Dn (2) m m R j =∑ F D (t) = ∑ D (t) j R j R j m j=1 j=1 ∑ Dn (2) R j (7) j=1 where

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A A C A

B BA A BD

3p j D (t) =1− e−2Hjt R j p +q +1 j j 6H t 2q )t j Ij j Ij e−(2Hj+t−1 − 4H t −1 p +q +1 j Ij j j 3p 6H t j j Ij + + p +q +1 4H t −1 j j j Ij 2q j e−6Hjt × p +q +1 (8) j j (iii) Decay process

B B

m ∑ Dn (t) D j Dn (t) D (t)= D = j=1 D m Dn (0) D ∑ Dn (0) D j j=1 Dn (0) m m D j =∑ F D (t) = ∑ D (t) j D j D j m j=1 j=1 ∑ Dn (0) D j j=1 where

sum of the normalized m component signals, each of which is independent of the volume fraction (or concentration) C of the jth particle in a suspenvj sion, multiplied by the coefficient F ( j=1, m). j Since the total volume fraction C of m solute v species in the multicomponent system is given by the sum of the individual volume fractions, C of vj the jth component, the fraction f of these volume j fractions is related to F as: j f Dn(0, 2) · m m C j and ∑ f = ∑ vj =1 F= 1 j j m j=1 j=1 Cv ∑ f Dn(0, 2) · j j j=1 (12)

(9)

Dn (t) D (t) = D j =e−6Hjt (10) D j Dn (0) D j D (t) , D (t) , and D (t) are, respectively, the norB j R j D j malized birefringence signals of the build-up, reverse, and decay processes for the jth RPEB signal (originated from the jth component), while Dn (t) , Dn (t) , and Dn (t) are the observed B j R j D j RPEB signals of the same component. The coefficient F is given as the ratio of the j steady-state birefringence of the jth signal involved in the multicomponent system to the total steadystate birefringence of this system resulting from m signals: Dn (2) Dn (2) R j B j = F= j m m ∑ Dn (2) ∑ Dn (2) B j R j j=1 j=1 Dn (0) m D j and ∑ F =1 (11) = j m j=1 ∑ Dn (0) D j j=1 Thus, the normalized observed RPEB signal of a multicomponent system can be expressed by the

where Dn(0, 2) · denotes the steady-state birefrinj gence of the jth species in the pure state in which C =C . (Hereafter, subscripts B, R, and D in vj v Dn(0, 2) · are omitted, unless otherwise needed, j and 0 or 2 is referred to either the decay or the build-up and reverse processes). Thus, the normalized observed RPEB signal of the multicomponent system can also be expressed by the fraction f instead of F , and the steady-state signal j j Dn(0, 2) · in the jth pure state. The value of F j j may be either positive or negative, and either larger or smaller than unity, containing the observed steady-state signal Dn(0, 2) that j depends on C [cf. Eq. (4)]. vj 3.3. Sequential versus two-state transition In previous studies, some RPEB signal profiles of montmorillonite suspensions were found to change with applied electric fields in a seemingly unrelated manner [14,17]. Similarly, RPEB or conventional EB signals of bentonite [1] and saponite [22] show a series of profile changes in the presence of cationic surfactants. These changes may be interpreted either in terms of a sequential alteration of the electric and hydrodynamic properties of the clay particle with an increase in the surfactant concentration and/or the applied field strength or, alternatively, in terms of a chemical equilibrium between the initial state (or species) of clay particle and the final state (or species) of maximally adsorbed surfactant/clay particle.

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3.3.1. Sequential transition from the initial to the final state The normalized RPEB signal of the jth state resulting from a single species in a suspension with a particular set of parameters ( p , q , H , t ) may j j j I be reproduced from Eqs. (6), (8) and (10). jIn the following treatment, the term p in these equations is neglected, since the montmorillonite and bentonite particles possess no permanent dipole moment, i.e. m=0 and b=0 [1,14,16,17,23]. ( For the present CPC/bentonite system, see the succeeding section.) In the calculation of a sequential transition of RPEB signals of the single species, the hydrodynamic shape, e.g. H, may be assumed to be constant, whereas the electric moments should steadily vary with such external factors as applied electric field, ionic strength, and added surfactants. Fig. 3 shows such a hypothetical sequence of six transitions, to which RPEB curves 1 to 6 correspond, curves 1 and 6 being the initial and final states, respectively. The ratio q (=s /Da∞) of two 3 electric moments is varied sequentially from −0.5 (curve 1) to −3.0 (curve 6). These negative values indicate that the sign of the polarizability anisotropy Da∞ is negative. The ratio of two relaxation times t* (=t /t) is introduced for the sake of I brevity. Curve 1 shows a monotonic rise in the build-up process and a hump in the reverse. A distinct hump appears in each process, as values of q approach −1 (curves 2 and 3). It should be noted that d(2)=0 in the Kerr law region, if p= 0 and q=−1 [cf. Eq. (4)]. In such a case, therefore, the normalized signals, D (t), etc. in Eqs. (1)–(3) B should become indefinite. Curve 4 shows a dip in the build-up and another deeper one in the reverse. The dips become shallower with an increase in the absolute value of q (curves 5 and 6). These features are characteristic of the disk-shaped particle [10,11]. It should be noted that values of t* also affect the calculated signal profiles. The normalized RPEB curves generally exhibit a hump each in build-up and in reverse in the −1
49

Fig. 3. Theoretical RPEB curves for a sequential transition between the initial (1) and final (6) states. Values of the electric parameter q were varied between −0.5 (curve 1), −0.7 (curve 2), −0.8 (curve 3), −1.3 (curve 4), −1.8 (curve 5), and −3.0 (curve 6) at a constant parameter t* of 0.5 for solid line curves and another constant t* of 2 for dotted line curves. The ordinate is the normalized birefringence Dn(t)/Dn(2), while the abscissa is the reduced time 6Ht.

changes mostly in the electric and hydrodynamic parameters of a single species in suspension. 3.3.2. Two-component transition Now suppose that two different species (or components), denoted 1 and 6, are present in equilib-

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rium in a clay suspension and that the RPEB signals of these two species in the pure states, Dn(0, 2) · and Dn(0, 2) · , are denoted as curve 1 6 1 and curve 6, respectively. The clay suspension would give rise to an intermediary signal (2 to 5) if the equilibrium shifts with changes of the aforementioned external factors. In this case, the signal may be calculated from curves 1 and 6 with coefficients F and F (F +F =1) or with frac1 6 1 6 tions f and f ( f +f =1) with the aid of Eqs. (5), 1 6 1 6 (7), (9), (11) and (12) as follows: =F D(t) +F D(t) =F [D(t) obsd 1 1 6 6 1 1 −D(t) ]+D(t) 6 6 and D(t)

(13)

=f Dn(0, 2) · +f Dn(0, 2) · obsd 1 1 6 6 =f [Dn(0, 2) · −Dn(0, 2) · ]+Dn(0, 2) · 1 1 6 6 where D(t) is the normalized RPEB signal obsd observed for an intermediary state and Dn(2) is the corresponding observed steadyobsd state RPEB signal. Therefore, both f and F may be calculated, provided that the steady-state values are experimentally available: Dn(0, 2)

f d(2) · d(2) −d(2) · 1 obsd 6 and F = 1 (14) f = 1 1 d(2) · −d(2) · d(2) 1 6 obsd where the d(2) are the steady-state optical phase retardations corresponding to the quantities in Eqs. (11) and (13). Fig. 4 shows a series of intermediary RPEB signals (curves 2–5) calculated from two pure RPEB curve 1, for which q=−0.7, and curve 6, for which q=−1.8, and various values of F with 1 the aid of Eq. (13). The intermediary curves show complex profiles, none of which can be reproduced with a single set of parameters from Eqs. (6), (8) and (10). In the present calculation, the rotational diffusion coefficient in curve 1 is arbitrarily taken to be five-fold larger than that in curve 6, i.e. H =5H . Instead of a smooth 1 6 exponential decay predicted by Eq. (3), some of the intermediary curves either intersect the baseline or show a hump in the decay process. Such an anomalous effect has been taken as evidence of an equilibrium of two different (one positive

Fig. 4. Theoretical RPEB curves for a two-state transition model between the initial and final states, which are represented by curves 1 and 6, respectively. The intermediate states (2–5) are represented by the curves 1 and 6 multiplied by the coefficient F , values of which are 1.0 (curve 1), 3.0 (curve 2), −1.3 1 (curve 3), −0.33 (curve 4), −0.1 (curve 5), and 0 (curve 6). Values of the parameter q are −0.7 (curve 1) and −1.8 (curve 6). Values of t* are 2.5 (curve 1) and 0.5 (curve 6) and H =5H . 1 6

and the other negative) species or component RPEB signals in a suspension [24,25]. By analyzing a series of observed RPEB signals for a clay suspension with appropriate electric and hydrody-

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51

namic parameters, the mechanism of a multiple equilibrium involved in the suspension may be clarified.

4. Results and discussion 4.1. RPEB signals of bentonite in the absence and presence of CPC Fig. 5 shows a series of normalized RPEB signals observed for bentonite in the absence (signal a) and in the presence (signals b–g) of CPC in the very low electric field region. In the absence of CPC, the RPEB signal of bentonite exhibits a large hump each in build-up and reverse processes with positive sign [d(2)>0]. In comparison with the theoretical curves in Fig. 3, the profile immediately suggests that the parameter p+q lies in the range between −1 and 0 [11]. With increasing concentrations of CPC, however, the RPEB signals unexpectedly change the profile, which is associated with the reversal of sign to negative (signals c–g). At the highest CPC concentration of 1.3 mM, the signal shows a shallow dip in the build-up and a deep one in the reverse process. The sign reversal of the steady-state birefringence, d(2), from positive (signals a–b) to negative (signals c–g) probably results from the change in orientation of a disklike particle toward the direction of applied electric field from the plane to the symmetry axis (3 axis) with an increase in added CPC [17]. As indicated by Eq. (4), values of d(2) become either positive or negative, depending on the magnitude of p+q. If p+q>−1, d(2)>0, and if p+q<−1, d(2)<0, provided that the reduced optical anisotropy factor Dg/n is negative, just as observed for montmorillonite particles [16,17]. Values of d(2)

Fig. 5. Observed and calculated RPEB signals of bentonite and CPC/bentonite systems at weak electric fields. Each observed signal was normalized by the steady-state phase retardation d(t2). The sign and magnitude of d(t2), the latter being

abbreviated simply as d, the applied field strength E, and the time scale are indicated for each signal. Concentrations of CPC (mM ): 0 (a), 0.001 (b), 0.05 (c), 0.1 (d), 0.5 (e), 0.9 (f ) and 1.3 (g). Concentration of bentonite (g/l ): 0.005. Thin solid line curves (a–g) were simulated with the parameters q, t , and t I given in Table 1. Thick solid line curve c was simulated with an F value of −0.015, by assuming a two-state model (see text 1 for details). Both thin and thick lines are overlapped in this curve.

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were nearly zero at weak fields for a bentonite suspension containing 0.01 mM CPC, and the observed signals were too noisy to be drawn here. In such a case, the normalized signals become indefinite (vide ante). Signal a for bentonite particle without CPC can be reproduced quite well with a set of parameters q, H, and t by using Eqs. (1)–(3), as shown with I the solid line (curve a). Other RPEB signals (b–g) are also fitted satisfactorily, as indicated by the values of standard deviation (SD) in Table 1. It should be noted here that these fittings are obtained by setting the parameter p to zero. The fitting of the build-up process is slightly improved if a small negative p value is included (−0.06 to −0.08), whereas the fitting of the reverse process is bettered with a small positive p value (0.06 to 0.08). The overall fitting of any RPEB signal is not affected by including or excluding p (the standard deviations remain unaltered with and without p value), since these p values amount only to 3–4% of the large q value in each fitting. All the parameters evaluated from curve fitting are given in Table 1. Based on these results, therefore, it is safe to conclude that bentonite possesses no permanent dipole moment, just as montmorillonite [14]. This finding strongly indicates that the ionic dipole moment and the covalent polarizability contribute to the field orientation of bentonite particle in suspension. For curve g, which represents the highly adsorbed CPC/bentonite particle, the theoretical fitting is also good without the parameter p. Hence, CPC molecules at dilute con-

centrations are more or less randomly adsorbed on bentonite particle, not to add up to the net permanent dipole moment, even though each CPC molecule should possess the permanent dipole moment. At higher concentrations, however, CPC molecules may be intercalated between layers of a bentonite particle in an antiparallel, micelle-like bilayer fashion, or two or more particles may sandwich the CPC bilayers. If the CPC-adsorbed particles are aggregated, the field-off relaxation time would be much larger, but apparently this is not the case (cf. Table 1). The increase in absolute values of q with increasing CPC concentrations, being largest at 0.1 mM (signal d), indicates that the relative magnitude between two electric polarizabilities (s and Da∞) 3 is not constant but varies with added amounts of CPC (separation of these two quantities may be achieved only by fitting of the field strength dependence of steady-state birefringence observed over a wide field range to the theoretical SUSID orientation function [16,17]). The relaxation times (t I and t) of ion-fluctuation and rotational motion remain practically constant for signals c–g, indicating that the overall dimension of CPC-adsorbed bentonite is altered only slightly. Considering the parameters in Table 1 and also theoretical curves in Fig. 3, the change of RPEB profiles in Fig. 5 probably reflects a sequential transition of bentonite particle with addition of CPC (cf. Section 3.3.1); hence, the CPC molecules are adsorbed not disproportionately but evenly on each particle.

Table 1 Electric parameter, relaxation time, and steady-state birefringence of the bentonite/CPC system evaluated from RPEB signal Curves

[CPC ]a (mM )

E ( V/cm)

qb

tb (ms) I

tb (ms)

d(t2)b (deg)

Std. Dev.c

a b c d e f g

0 0.001 0.05 0.1 0.5 0.9 1.3

43 44 42 43 44 42 45

−0.913 −0.886 −2.063 −2.623 −2.058 −1.818 −1.824

3.52 4.46 5.20 6.60 5.40 4.67 3.78

20.90 17.73 7.61 6.49 7.72 11.06 9.55

0.013 0.013 −0.154 −0.190 −0.137 −0.057 −0.062

0.13732 0.09318 0.01297 0.01287 0.01131 0.03208 0.01836

a The concentration of bentonite=0.005 g/l. b Experimental errors: ±0.015 for q, ±0.10 ms for t and t, and ±0.001° for d(t2). I c The standard deviation between observed and calculated RPEB signals for each curve, defined as SD2=[ S(obsd i−calcd i)2]/(N−1), where the summation is over all experimental points and N is the number of data points.

K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

53

Attempts were made to explain the profile change of RPEB signals a–g in terms of the twostate model, by assuming an equilibrium between bentonite without CPC (signal a) and the fully adsorbed CPC/bentonite (signal g). By using Eq. (14) and the steady-state values of d(t2) in Table 1, values of f were evaluated for intermedi1 ary states as 1.0 (signals a and b), −1.227 (signal c), −1.707 (signal d), −1.00 (signal e), 0.889 (signal f ) and 0.0 (signal d). The assumption that signal g represents the fully CPC-adsorbed state is clearly wrong, because values of f should remain 1 equal to, or less than, unity. When signal d is instead taken as the fully CPC-adsorbed state, f 1 values are 1 for signals a and b, 0.1773 for signal c and 0 for signal d. In this case, only ca. 18% of bentonite particles remain totally unadsorbed and the rest in the suspension containing 0.05 mM CPC are fully adsorbed by CPC molecules. Considering these f values for intermediary states, 1 this all-or-none two-state equilibrium model is unrealistic and should be ruled out. 4.2. Field-strength dependence of steady-state birefringence Fig. 6 shows (a) the effect of the addition of CPC on the steady-state birefringence of CPCadsorbed bentonite at a constant particle concentration of 0.005 g/l and (b) the steady-state birefringence of bentonite without CPC at three different concentrations in the low electric field region. In this field strength range, bentonite itself at 0.005 g/l always gives rise to a positive birefringence. Interestingly, the addition of CPC to bentonite at concentrations higher than 0.05 mM changes the sign of birefringence to negative even at extremely low fields [Fig. 6(a)]. This negative birefringence, however, turns to positive at higher field strengths. The sign-inversion point E is s.i. defined as the field strength where the value of d(2) becomes apparently zero and thereafter its sign changes [17]. The bentonite suspension without CPC shows a positive birefringence at 0.005 g/l, values of d(2) being nearly proportional to the second power of field strength E2 up to 170 V/cm; thus, the Kerr law holds in this field range [dashed lines in Fig. 6(a,b)]. The magnitude

Fig. 6. Field-strength dependence of steady-state birefringence in terms of optical phase retardation d(t2) in the low field region. (a) The CPC/bentonite system at a bentonite concentration of 0.005 g/l. Concentrations of CPC (mM ): 0 (#), 0.001 ($), 0.01 ()), 0.05 (n), 0.1 (%), 0.5 (&), 0.9 (6), and 1.3 (+). (b) The bentonite system without CPC. Concentration of bentonite (g/l ): 0.005 (#), 0.01 (( ), and 0.029 (,). A 0.005 g/l sample sonicated for 5 min ($). Dashed lines indicate the E2 dependence of d(t2)

of d(2) of this 0.005 g/l sample is considerably lowered by sonication, probably because of the size reduction, but otherwise the sample behaves normally. As the bentonite concentration is increased to 0.01 g/l, values of d(2) are increased almost tangentially at the initial weak fields, but the sign remains positive. At the highest concentration of 0.029 g/l, however, values of d(2) are

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K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

surprisingly negative at weak fields and turn to positive at higher fields with a value of E at s.i. about 63 V/cm. This trend resembles the steadystate birefringence behavior of the CPC/bentonite system in Fig. 6(a) where E values mostly fall in s.i. the 240–250 V/cm range. 4.3. Effect of concentration of bentonite on RPEB signals Fig. 7 shows the effect of concentrations on the RPEB signal of bentonite without added CPC in the low field strength region. RPEB signals a and b at lower concentrations (0.005 and 0.01 g/l ) are positive in sign and associated with a double hump. However, this is not the case at 0.029 g/l, where RPEB signal c at 46 V/cm gives rise to a dip each in the build-up and reverse processes with a negative sign. Surprisingly, another signal d of the same sample at 89 V/cm, slightly above E , shows a s.i. double hump with positive sign, as observed for signals a and b. In comparison with theoretical RPEB curves in Fig. 3, this remarkable change in sign and profile may be attributed to the decrease in absolute value of the parameter |q| with increasing applied fields even in the low field region. It should be noted that similar behavior was observed for a montmorillonite suspension at nearly the same concentration [10,14,17]. Signals a–d simulated with Eqs. (1)–(3) are shown with solid lines in Fig. 7. The parameters obtained from curve fitting are all given in Table 2. Fittings are very good in all cases, even for signal d. As is seen from Table 2, values of q are in the −1
Fig. 7. Observed and calculated RPEB signals of bentonite without added CPC at different concentrations and at weak electric fields. Each signal was normalized by the steady-state phase retardation d(t2). Concentrations of bentonite (g/l ): 0.005 (a), 0.01 (b), and 0.029 (c) and (d). Thin solid line curves a, b, c, and d were calculated with parameters q, t , and t given in I Table 2. Thick solid line curve b was simulated with a coefficient f of 0.98, by assuming a two-state model (see text for details). 1

field with its symmetry axis at 46 V/cm (curve c) [because s >−Da∞ (=a∞ −a∞ )], whereas the par3 11 33 ticle tends to orient toward the field direction with its plane at 89 V/cm (curve d ) [because s <−Da∞ (=a∞ −a∞ )] [17]. 3 11 33 Interestingly, the rotational relaxation times for signals a, b, and d are comparable in magnitude; thus, the overall shape and dimension of bentonite possibly remain unaltered under the experimental

55

K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

Table 2 Electric parameter, relaxation time, and steady-state birefringence of the bentonite system at various concentrations and applied field strengths evaluated from RPEB signala Curves

[Bent]b (g/l )

E ( V/cm)

q

t (ms) I

t (ms)

d(t2) (deg)

Std. Dev.c

a b c d 1 2 3 4 5 6

0.005 0.01 0.029 0.029 0.005 0.005 0.005 0.005 0.005 0.005

43 45 46 89 43 66 88 110 130 152

−0.913 −0.912 −1.260 −0.935 −0.913 −0.840 −0.797 −0.790 −0.777 −0.772

3.52 5.50 130.00 1.34 3.52 3.27 3.87 2.54 1.88 1.52

20.90 15.00 4.28 13.42 20.90 14.50 10.00 9.68 8.72 8.53

0.013 0.012 −0.036 0.150 0.013 0.033 0.046 0.085 0.124 0.166

0.13732 0.16774 0.18046 0.06752 0.13732 0.03091 0.01978 0.00829 0.00617 0.01010

a All notations and experimental errors are the same as those given in Table 1. b The concentration of bentonite. c The standard deviation between observed and calculated RPEB signals, defined as in Table 1.

conditions. However, the relaxation times evaluated for curve c are extraordinary with a very large t value of 130 ms and a very small t value I of 4.3 ms, as compared with those of the others (cf. Table 2). A close resemblance of RPEB profiles and electric and hydrodynamic parameters for signals a, b, and d strongly indicates that the orientation mechanism and the gross shape and dimension of the bentonite particle in these suspensions are practically alike. The fact that signal c gives rise to an entirely different signal profile probably results from a unique shape of aggregated bentonite particles in suspension at a high concentration of 0.029 g/l and at a low field strength of 46 V/cm. Judged from the very small t value, the aggregated particle should be spheroidal with a small axial ratio and be oriented with its symmetry axis towards the field (vide post). Attempts were made to reproduce the observed RPEB signal by assuming that it results from the equilibrium between an unaggregated species (signal a) and a fully aggregated species (signal c) on the basis of the two-state model (cf. Section 4.1). With the data of d(2) in Table 2, the fraction f was calculated to be 0.980 [= 1 (0.012+0.036)/(0.013+0.036)] from Eq. (14). The curve calculated with f =0.98 was shown with a 1 thick solid line in the observed signal b. The profile of this simulated curve b (thick solid line) differs from both the observed signal and the other calcu-

lated one (thin solid line). The f value is close to 1 unity, indicating that only 2% of aggregated species, if any, make a contribution to signal b. Hence, the RPEB signal of the 0.01 g/l suspension may safely be attributed to the unaggregated bentonite particle with electric and hydrodynamic parameters different from those of species c. On the other hand, the profile of thin solid line curve b is very close to the observed signal b; therefore, the increase in bentonite concentration from 0.005 to 0.01 g/l does not result in two species in equilibrium, one unaggregated (signal a) and the other aggregated (signal c), to any appreciable degree. 4.4. Effect of applied field strength in the low field region Fig. 8 shows a series of RPEB signals of bentonite without CPC at the lowest concentration (0.005 g/l ), observed at various field strengths in the low field region, where the Kerr law holds [E<170 V/cm in Fig. 6(b)]. The profile of each signal is associated with a shallow hump in the build-up and another large one in the reverse process, immediately suggesting that the ratio q is larger than −1 but smaller than 0 (cf. Fig. 3). The analysis of each signal with Eqs. (1)–(3) reveals that: (1) the permanent dipole moment is essentially nil ( p=0); (2) the magnitude of q decreases by 21% between signals 1 and 6, indicating that

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K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

two electric polarizabilities s and Da∞ are affected 3 by applied fields; (3) the rotational relaxation time t is smaller at higher field strength in the 20.9–8.35 ms range, indicating that the bentonite sample is still polydisperse regarding the particle size in spite of fractionation [26 ]; and (4) the relaxation time of fluctuating ion atmosphere t I ranges between 3.87 and 1.52 ms, probably indicating that the ion-fluctuation is also size-dependent. The parameters characteristic of each RPEB signal are given in Table 2. The fact that the ratio of two relaxation times t* (=t /t) remains nearly constant I (on average 0.21±0.05, exclusive of the extraordinarily high value for signal 3) is in good accord with the ion-fluctuation theory, which assumes that the value of t is independent of applied fields I [10–13]. The results in Fig. 8 and Table 2 support the notion that bentonite particles are suspended in water in an unaggregated state at a dilute concentration of 0.005 g/l. Finally, it is worth mentioning the possibility that the magnitude of Da∞ is not constant but varies with applied electric field in the low field region [27]. The previous work on clay suspensions indicates that the electric parameters reach steady (or constant) values in the medium-to-high field strength region [1,16,17]. Whether values of Da∞ really remain constant or not, even at extremely high fields, where a complete orientation of disklike particles is experimentally attained (not by extrapolation to saturating fields with theoretical orientation function [16 ]), is open to future study with a reversing-pulse generator which can deliver much higher voltage electric pulses than those now in use in our laboratory. Indeed, a possibility of the sign reversal of polarizability anisotropy with field strength cannot be excluded for a flexible bentonite (we thank the referee who kindly suggested this possibility, pointing out the non-rigid nature of bentonite particle and the scattering effect of the large-size colloidal suspension on the sign reversal of birefringence with increasing field strengths [28]). Fig. 8. Effect of field strengths on observed and calculated RPEB signals of bentonite at the lowest (0.005 g/l ) concentration in the low field region. Field strength E, time scale, and steady-state phase retardation d(t2) are indicated for each signal. Solid line curves were calculated with a set of parameters (q, t , and t) given in Table 2. I

4.5. Possible models for field orientation of bentonite with and without CPC Based on the results given in the preceding sections, some oversimplified models may be pro-

K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

posed for the electric field orientation of bentonite at high and low concentrations and of sparsely and highly CPC-adsorbed bentonite. Fig. 9 shows such models, together with the roughly corresponding RPEB patterns. At a higher concentration (0.029 g/l ) and at a very weak field, the disk-like bentonite particle is aggregated in such a way that the whole shape is closer to a spheroid (card-house structure) with ample cavities for slower movement of counterions rather than a long stack of disks with compact inner space (book-house structure) [17]. This aggregated particle tends to orient toward the direction of applied field, with its symmetry axis (the 3 axis) exhibiting a negative RPEB signal with dips (top row, left). As the applied field strength is increased, the aggregated particle is partly dissociated to unaggregated, or at least less aggregated, particles, which tend to orient toward the field with their plane showing a positive RPEB signal with humps (top row, right). The bentonite particle at a dilute concentration (0.005 g/l ) is oriented toward the field direction with its plane, and a positive RPEB signal with humps is observed regardless of applied field in the Kerr law region (middle row, left and right). The bentonite particle sparsely adsorbed by CPC molecules is oriented toward the field direction with its plane, and a positive RPEB signal with humps is observed (bottom row, extreme left). Contrarily, the highly adsorbed CPC/bentonite particle is oriented toward the field direction with its symmetry axis, the adsorbed CPC possibly forming a micelle-like bilayer structure on the surfaces and/or between layers of the particle, and a negative RPEB signal with dips appears (bottom row, left). As the applied field strength is increased, both sparsely and highly adsorbed CPC/bentonite particles tend to orient in the same manner with the particle plane as the orientation direction, resulting in positive RPEB signals with humps (bottom row, rights). The regular arrays of CPC molecules highly adsorbed on bentonite (high [CPC ]) may collapse in part and the interlayer space may be contracted above the sign-inversion point, leading to the conversion of the orientation axis (bottom row, extreme right). Needless to say, the present models should be

57

considered only tentative, and hence they must be refined with the forthcoming experiments. It is an intriguing problem to be resolved experimentally in the future: how are the CPC molecules adsorbed on the surfaces and inserted between layers of a bentonite particle? If intercalated, a further question arises: do the CPC molecules stand upright between the layers to increase the interlayer space appreciably (as depicted in the present model ) or lie down to affect the space only slightly, in either case not yielding a net permanent dipole moment? Serious considerations are henceforth due with regard to the complementary effect of applied electric field on deforming or modifying not only the soft structures of aggregated particles and also highly adsorbed single particles, but also the layered and flexible structure of unaggregated bentonite particles [28].

5. Conclusion In the present work, we could amply demonstrate the importance of the RPEB method in the field of clay suspensions. Electro-optic techniques in general are quite useful, but the RPEB technique in particular is unique to display characteristic features in the reverse process and also, on some occasions, in the build-up process. Analysis of observed signals enables us to extract such vital information as the field orientation mechanism, the electric and hydrodynamic properties, unavailable with other physico-chemical methods, for colloidal systems. From the present experimental work, we can conclude that: (1) the disk-like bentonite particle suspended in aqueous media shows RPEB signals either with a double hump or with a double dip, depending on the concentration; (2) the RPEB signal of bentonite, highly adsorbed by CPC, undergoes a sign reversal with increasing applied electric fields. From the analysis with the Y–T–S and Y–S–K theories based on the fluctuation of ion atmosphere, we can conclude that: (1) the bentonite particle possesses no permanent dipole moment; (2) the field orientation results from two electric moments, i.e. the root-meansquare ionic moment originated from the ionfluctuation and the field-induced covalent dipole

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K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

Fig. 9. Possible field-orientation models of bentonite in suspension at a high concentration of 0.029 g/l (top row), CPC-adsorbed bentonite at a low concentration of 0.005 g/l (middle row), and unaggregated bentonite at 0.005 g/l at low and high CPC concentrations (bottom row) in the low field region. Only the cross-section of each disk-like particle is depicted. Adsorption modes of CPC on bentonite and self-assemblage of bentonite particles are presented only schematically here, adsorption on the edges of each particle being ignored.

K. Yamaoka et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 148 (1999) 43–59

moment arising from the polarizability anisotropy intrinsic to the structure and composition of the particle; (3) the ratio of these two moments varies sensitively with the concentration of bentonite particle in suspension or steadily with the amount of CPC adsorbed on the particle — thus, the change in RPEB profile is attributed to a sequential rather than a two-state transition; (4) the ratio of the relaxation time of the ion-fluctuation to the relaxation time of the overall Brownian rotation remains nearly constant in the low field region for bentonite particle in a dilute suspension, in accord with the ion-atmosphere polarization theory, though the individual relaxation time changes with applied electric field because of the size distribution of bentonite particles; and (5) the ratio of two electric moments ( m21/2 and Da∞E) of bentonite in a dilute suspension is affected slightly by applied electric fields even in the low field region.

Acknowledgments This work was supported in part by Grant-inAid for Developmental Scientific Research (B) 06554031 ( K.Y.) and Monbusho’s Grant-in-Aid for the Japan Society for the Promotion of Science 94062 ( V.P.) from the Ministry of Education, Science, and Culture, Japan, and by Sasakawa Scientific Grant 8-292 from the Japan Science Society (R.S.).

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