Fractional ionization and size of cetyltrialkyl ammonium bromide and hydroxide micelles as a function of head-group lipophilicity and temperature

Accepted Manuscript Fractional ionization and size of cetyltrialkyl ammonium bromide and hydroxide micelles as a function of head-group lipophilicity and temperature

V. Canale, R. Germani, G. Siani, A. Fontana, P. Di Profio PII: DOI: Reference:

S0167-7322(18)30279-4 doi:10.1016/j.molliq.2018.04.090 MOLLIQ 8993

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

30 January 2018 11 April 2018 17 April 2018

Please cite this article as: V. Canale, R. Germani, G. Siani, A. Fontana, P. Di Profio , Fractional ionization and size of cetyltrialkyl ammonium bromide and hydroxide micelles as a function of head-group lipophilicity and temperature. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Molliq(2017), doi:10.1016/j.molliq.2018.04.090

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ACCEPTED MANUSCRIPT Fractional Ionization and Size of Cetyltrialkyl Ammonium Bromide and Hydroxide Micelles as a Function of Head-Group Lipophilicity and Temperature V. Canale,a R. Germani,b,c G. Siani,a A. Fontana,a P. Di Profio*a,b a

Department of Pharmacy, University of Chieti-Pescara "G. d'Annunzio"

b

c

Department of Chemistry, Biology and Biotechnology, University of Perugia

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CEMIN - Center of Excellence on Nanostructured Innovative Materials, University of Perugia

*Corresponding Author: Pietro Di Profio, Department of Pharmacy, University of Chieti-Pescara "G. d'Annunzio", via

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dei Vestini 31, I-66100 Chieti (Italy); e-mail: [email protected]. Orcid ID: 0000-0002-8038-7940

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ABSTRACT

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We have measured the diffusion coefficients, D, of aqueous micelles formed by cetyltriethyl-, cetyltripropyl- and cetyltributyl-ammonium bromides (CTEABr, CTPABr and CTBABr,

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D

respectively) and cetyltriethyl- and cetyltripropyl-ammonium hydroxides (CTEAOH and CTPAOH, respectively) by dynamic light scattering (DLS) at several temperatures from 15 to 55°C and a range of surfactant (0.01 - 0.05 M) and salt (0.02 - 0.06 M NaBr; 0.05 - 0.3 M NaOH)

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concentrations. From values of D, we derived the respective fractional ionization values of micellar

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surfaces. For surfactants with bromide counterion we obtained fits of the diffusivity data using the linear interaction/DLVO approach, thus yielding estimates of the micellar hydrodynamic radius, Rh, and the micellar fractional ionization, , which ranged from 0.26 to 0.35. For CTEAOH and CTPAOH, the fits appeared to be poorly sensitive to changes in the London-Van der Waals interactions, as expressed by the Hamaker constant, and only a large fractional ionization could account for the observed diffusivities.

1

ACCEPTED MANUSCRIPT Keywords: Fractional Ionization; Surfactants; Micelles; Head-group Bulk; Dynamic light scattering; DLVO. Abbreviations: cetyltrimethyl ammonium bromide (CTABr); cetyltriethyl ammonium bromide (CTEABr); cetyltripropyl ammonium bromide (CTPABr); cetyltributyl ammonium bromide (CTBABr); cetyltrimethyl ammonium hydroxide (CTAOH); cetyltriethyl ammonium hydroxide

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(CTEAOH); cetyltripropyl ammonium hydroxide (CTPAOH); fractional ionization (); coefficient

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of variation (CV); critical micelle concentration (cmc); dynamic light scattering (DLS); Hamaker

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D

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constant (A); Derjaguin-Landau-Verwey-Overbeek theory (DLVO).

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ACCEPTED MANUSCRIPT 1. Introduction The aggregation behavior of ionic amphiphiles is an important process in several fields of science and technology.[1–8] In particular, several studies have recently focused on the interactions between charged surfaces as a means for controlling amphiphile aggregation,[9] tailoring pulmonary surfactants as drug carriers,[10] enhancing the encapsulation and targeting efficiency of

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liposomes,[11] tuning the wettability of rock beds in enhanced oil recovery,[12] and optimizing the

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interaction with graphene,[13] nucleic acids,[14] and clathrate hydrates.[7,15,16] It is known that

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the charge density[8,17] and the counter-ion specificity[18] on these polyelectrolytes are fundamental parameters affecting their interactions with other species. It is also known that, besides

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its charge, also the volume (bulk) of the counterion[19] and its valence[20] affect the size, shape and surface charge of micellar aggregates. The interaction between proteins and surfactants is

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another important process which is partly governed by the surfactant and/or protein charge,[21,22] as is the binding of cationic surfactants to nucleic acid molecules, which can be mainly ascribed to

D

electrostatic interactions.[14,23]

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An amphiphile basically has a long hydrocarbon chain and a charged or neutral head-group, and its aggregation into supramolecular structures is controlled, inter alia, by the concentration and kind of

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ionic species which may be present at the interface, either as counter-ions (in ionic micelles), or as externally added ions to zwitterionic species.[8] Light scattering techniques[24,25] have been

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extensively used as a non-invasive and accurate means for the determination of size, surface charge and potential of several colloidal systems, from aqueous micelles formed by a wide range of amphiphiles,[26,27] to reverse micelles in organic solvents.[28–30] The present work reports the surface fractional charge and size change of cationic micelles as a function of the head-group bulk, the nature of the counterion, and temperature. This was obtained by fitting diffusion coefficients vs. surfactant concentration data (as measured by DLS), to a linear interaction/DLVO model. The framework of the surfactants chosen for this study was the well known cetyltrimethylammonium ion, analogues of which were synthesized here by varying the 3

ACCEPTED MANUSCRIPT length of alkyl residues on the head-group from ethyl to n-butyl. Counter-ions tested were the bromide and hydroxide, as these represent low charge density, "hydrophobic" ions or high charge density, highly hydrated ions, respectively. Alkyltrimethylammonium bromides and hydroxides were already investigated in the past by DLS.[27,31,32] The results obtained in those works show that the fractional micelle ionization increases as the counterion is more hydrophilic and less prone

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to dispose of its hydration shell to become micellar bound. A similar picture was obtained when

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cetyltrialkylammonium (where alkyl = Me, Et, Pr, Bu) bromides and hydroxides were extensively

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investigated by using surface-associated kinetic probes[33] and electrical conductivity,[34] which also provided indirect evidence that an increasing head-group bulk further increases the micellar

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surface charge. Changes in the lipophilicity of the ammonium head-group also led to an activation of -chymotrypsin as a model enzyme in studies on the interaction between proteins and activating

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and/or stabilising amphiphiles.[21]

Here, we show the results of DLS studies in terms of the diffusion coefficients (D), and derived

D

surface fractional ionization (), of aqueous micelles formed by cetyltriethyl-, cetyltripropyl- and

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cetyltributylammonium bromides (CTEABr, CTPABr and CTBABr, respectively) and cetyltriethyland cetyltripropylammonium hydroxides (CTEAOH and CTPAOH, respectively) at several

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temperatures from 15 to 55°C and a range of surfactant (0.01 - 0.05 M) and salt (0.02 - 0.06 M

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NaBr; 0.05 - 0.3 M NaOH) concentrations.

2. Materials and methods 2.1. Chemicals CTEABr, CTPABr and CTBABr were synthesized by quaternization of the appropriate amine with hexadecyl bromide as described.[35] CTEAOH and CTPAOH were prepared from the respective sulfates by reaction with Ba(OH)2. (CTEA)2SO4 and (CTPA)2SO4 were synthesized starting from the respective bromides (CTEABr and CTPABr) by reaction with Ag2SO4 in methanol also as described.[36]

All

the

surfactants

were

pure

according

to

surface

tension

vs. 4

ACCEPTED MANUSCRIPT -log[surfactant] plots, showing no minima. Values of critical micelle concentrations (cmc's) for all tested surfactants are reported in Table 1, below.

Table 1 - Values of critical micelle concentrations (cmc's) for tested surfactants at 25°C CTEABr

CTPABr

CTBABr

CTEAOH

CTPAOH

cmc, 104 M

7.41

5.49

2.81

9.10

4.57

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Surfactant

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NaBr and NaOH added to the surfactant solutions to vary the ionic strength were reagent grade (purchased from Sigma-Aldrich, Italy). NaBr was dried in an oven and then kept under moisture-

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free conditions. Both salts were handled under nitrogen during the preparation of solutions.

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2.2. Dynamic Light Scattering

Sample solutions were prepared using bidistilled, deionized water filtered through 0.2 m

D

polycarbonate Millipore filters. Approximately 1 mL of sample was filled into a 6 mm diameter

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Pyrex glass tube, protected from dust by Parafilm caps, and centrifuged at 10000 rpm for 15 min to sediment dust particles. The cylindrical glass tube was fitted into a toluene-filled fluorimeter cuvette

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to provide refractive index matching against stray-light reflections. The cuvette was placed into a aluminum cell whose temperature was regulated by a Peltier element to ± 0.05°C. Laser light was

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from a Coherent Innova 70-3 argon-ion laser operating at 488.0 nm. Light scattered at 90° was collected from approximately one coherence area and focused onto the slit of a photomultiplier tube (Products for Research, Inc., USA). A 64-channel Nicomp Model 370 computing autocorrelator (PSS, Santa Barbara, USA) was used to calculate and display the diffusion coefficient, D, and associated derived parameters from cumulants analysis to the intensity autocorrelation function.[37] Generally, all measurements showed values of chi-squared close to 1, and a coefficient of variation (CV) below 20%, these values being an evidence of the monodispersity of micelle sizes. However, some DLS measurements for CTPAOH at [NaOH]>0.06M showed an increase of chi-squared and 5

ACCEPTED MANUSCRIPT variation coefficient values, together with non-linearly decreasing profiles of D, which possibly point to a real growth of micelles under those higher ionic strengths. Therefore, the latter were not considered in the following examination of intermicellar interactions, as also discussed below. Conversely, negative-slope profiles for CTBABr were considered in our analysis, because D values were still monodisperse (i.e., chi-squared close to unity and CVs <20%).

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The theory of linear interaction has been quite extensively described earlier,[31,32,38,39] therefore

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just an outline thereof is reported hereinbelow. The micellar diffusivity, D, in dilute surfactant

(1)

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D = D0 [1 + (Kt + Kh)]

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aqueous solutions varies linearly as a function of the micellar volume fraction, :

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In eq. (1), D0 represents the diffusivity at infinite dilution (critical micelle concentration, cmc), where intermicellar interactions are negligible. Kt and Kh are thermodynamic and hydrodynamic

D

correction coefficients,[24] where Kt is proportional to the second virial coefficient, and can be

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written as:[40]



2 W ( x) / kT ] Kt  8  240 dx(1 x) [1 e

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(2)

where x is the intermicellar separation parameter (x = (r - 2a)/2a, where a = particle radius, r =

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separation between particles). The numerical term (i.e., 8) in eq. (2) is the value for the hard-sphere interaction. Hydrodynamic perturbations can be written in a similar form:[41] 

W ( x) / kT ] K h  6.44  0 dxF(x)[1 e

(3)

where: F(x) = 12(1+x) - (15/8)(1+x)- 2 + (27/64)(1+x)- 4 + (75/64)(1+x)- 5

(4)

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ACCEPTED MANUSCRIPT Also in eq. (4), the numerical term (-6.44) is the contribution for hard-sphere interactions. The negative sign refers to the hydrodynamic correction being opposed to the thermodynamic one, thus "slowing down" the particle diffusivity. When applying this approach to ionic, non-rigid species (e.g., micellar aggregates), Kh and Kt also contain contributions from micellar surface charge repulsions WR (x), and an attractive, van der Waals potential WA (x). The complete derivation of

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those potentials are fully described in the literature.[31,32,35,41,42] WR (x) is dependent on the

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micellar surface charge, Q, and the strength of the attractive interaction, as given by WA (x), is quantified by the Hamaker coefficient, A. The micellar charge is one of the unknown adjustable

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parameters in the fitting iteration. We express Q as the product N, where  is the fractional

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ionization, and N is the micellar aggregation number. By fixing N, we let  be the variable parameter to determine from best fits. As relates to N, it is reasonable to fix it to a constant value for

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each surfactant where the diffusivity profiles show a convergence of quasi-linear fans of D vs. [surfactant] as the latter tends to the cmc. This behavior is usually interpreted in terms of the

D

presence of minimum-size micelles throughout the concentration range explored, thus justifying the

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choice of keeping a constant N value for each of the surfactants (see Table 3).[35] Furthermore, it is known that, for low ionic strengths, N varies little with changing salt concentrations,[42,43] and the

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fits show a relative insensitivity to the micelle aggregation number, N, which may be ascribed to the

on 1/N.[31]

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approximately linear dependence of Kt + Kh in N which approximately cancels the dependence of 

The importance of the Hamaker coefficient, A,[44] is usually smaller for salt/surfactant systems, as compared to the repulsive term, under low ionic strength conditions (i.e., almost all cases studied here, except two slightly negative-slope profiles for CTBABr at higher T, see Fig. 3, 40 and 55°C). On the other hand, the contribution of A dominates when increasing the ionic strength of the solution. Finally, the parameter a, i.e., the micellar radius, is known for each surfactant and is approximated to the hydrodynamic radius, Rh, which can be estimated by applying the Stokes-

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ACCEPTED MANUSCRIPT Einstein relation to the common intercept D0 of the diffusivity profiles in the limit of vanishing surfactant concentration:

Rh = kT/6D0

(5)

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where  is the shear viscosity of the solution (H2O + NaBr or NaOH), k is the Boltzmann constant,

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and T is the temperature (K). While the application of the linear interaction - DLVO approach has

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been recently questioned and revisited in its applications to solid and other nanoparticles,[39] we believe this simple, general purpose approach remains valid as relates to the determination of

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fractional ionization of spherical surfactant micelles in water.

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3. Results and discussion 3.1. Bromide Surfactants

D

Plots of diffusion coefficients (D) vs. [surfactant] are reported in Figures 1-3. Behaviors of D vs.

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[surfactant] vary as a function of added NaBr concentration; higher positive slopes are observed as the ionic strength is reduced for all surfactants (CTEABr, CTPABr and CTBABr) at all investigated

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temperatures, whereas profile slopes decrease and eventually turn slightly negative for CTBABr at 40 and 55°C in 0.06 M NaBr. Even in the latter case, however, experimental curves show a

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common intercept at infinite dilution, D0, which is obtained by extrapolating the fitting lines down to the cmc. This feature is consistent with the existence of "minimum-sphere" micelles under the experimental conditions investigated. In other words, the variations of profile slopes as the ionic strength varies are to be mainly ascribed to intermicellar interactions, rather than a real size variation of the micelles, in agreement with previous evidence.[31]

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ACCEPTED MANUSCRIPT (a) 15°C 14 12

107 D (cm2/s)

10 8 6 4

0.01

0.02

0.03

0.04

0.05

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[CTEABr], M

(b) 25°C 18

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16 14 12 10

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107 D (cm2/s)

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2

8 6

2

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D

4

0.03

0.01

0.03

0.01

0.02

0.04

0.05

0.04

0.05

(c) 40°C 26 24 22

107 D (cm2/s)

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20

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[CTEABr], M

18 16 14 12 10

8 6 4 2 0.02

[CTEABr], M

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ACCEPTED MANUSCRIPT (d) 55°C 40 35

107 D (cm2/s)

30 25 20 15 10

0.01

0.02

0.03

0.04

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5

0.05

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[CTEABr], M

Figure 1(a)-(d) - Diffusivity vs. [CTEABr] at 15, 25, 40 and 55°C in aqueous NaBr at the following

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concentrations: 0.02 M (), 0.04 M (), 0.06 M ().

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(a) 15°C 14

8

6

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4

D

10

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107 D (cm2/s)

12

2

0.02

0.03

0.04

0.05

[CTPABr], M

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0.01

10

ACCEPTED MANUSCRIPT (b) 25°C 18 16

107 D (cm2/s)

14 12 10 8

4 2 0.02

0.03

0.04

(c) 40°C 26

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24 22

18

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107 D (cm2/s)

20

16 14 12 10

D

8

2

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6 4

0.05

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[CTPABr], M

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0.01

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6

0.01

0.02

0.03

0.04

0.05

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[CTPABr], M

(d) 55°C

40

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36 32

107 D (cm2/s)

28 24 20 16 12

8 4 0.01

0.02

0.03

0.04

0.05

[CTPABr], M

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ACCEPTED MANUSCRIPT Figure 2(a)-(d) - Diffusivity vs. [CTPABr] at 15, 25, 40 and 55°C in aqueous NaBr; symbols as in Figure 1.

(a) 15°C 14

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12

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8

6

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107 D (cm2/s)

10

4

2 0.02

0.03

0.04

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0.01

0.05

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[CTBABr], M

(b) 25°C

D

20

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107 D (cm2/s)

15

10

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5

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0.01

0.02

0.03

0.04

0.05

[CTBABr], M

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ACCEPTED MANUSCRIPT (c) 40°C 24

20

107 D (cm2/s)

16

12

8

0.01

0.02

0.03

0.04

0.05

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[CTBABr], M

(d) 55°C 35

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30 25 20

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107 D (cm2/s)

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4

15 10

0.02

0.03

0.04

0.05

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0.01

D

5

[CTBABr], M

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Figure 1.

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Figure 3(a)-(d) - Diffusivity vs. [CTBABr] at 15, 25, 40 and 55°C in aqueous NaBr; symbols as in

By examining diffusivity profiles obtained at four temperatures (15, 25, 40 and 55°C), two main features are to be noted (Table 2). First, hydrodynamic radii of "minimum-sphere" micelles, for a given surfactant, decrease slightly as the temperature increases. This feature has been already observed for CTABr micelles,[31] which shows a monotonic increase of hydrodynamic radii as the temperature decreases from 55 to 15°C. From this finding, we may infer that there is some micellar growth as temperature decreases, independently of ionic strength. This might imply a parallel

13

ACCEPTED MANUSCRIPT increase of N; however, as detailed above, the fits to experimental data are relatively insensitive to N because the dependence of K on N nearly cancels out with the dependence of  on 1/N. Second, values of Rh appear to be directly proportional to the head-group bulk, increasing slightly from approximately 2.8 nm for CTEABr to approximately 3.0 nm for CTBABr at 25°C. This slight increase of micellar hydrodynamic radius with the size of alkyl residues on the head-group

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(approximately 7-10% from CTEABr to CTBABr within experimental error) may seem at odds

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with the reported parallel decrease of micellar aggregation numbers, N (Table 3). However, this

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apparent contradiction can be (and has been) justified by considering that N can decrease due to a looser micellar structure due to an increased steric and ionic repulsion among bulkier head-

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groups.[31] On the other hand, values of Rh appear to be essentially dependent on the effective size of the surfactant molecules.

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Under the lowest ionic strength (0.02 M NaBr), the repulsive contribution to W(x) is predominant due to the low screening to the micellar repulsions. Thus, following the fitting strategy described

D

above, fractional micelle ionization obtained by fitting the model to the experimental data under

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low ionic strength should allow to obtain reliable values for . In this way, we obtain, e.g., for CTEABr at 15°C,  = 0.26 (Table 3). On the other hand, at higher ionic strengths, micellar charge

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screening is sufficiently large that the contribution of the attractive term to W(x) becomes predominant, so that Kt + Kh is less sensitive to , but highly dependent on A. Best fits were

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obtained by iteratively repeating this procedure, and values of  and A could be determined in a relatively unambiguous way. Once best fit values for  and A are obtained for a given temperature, their reliability was then tested by using the same values in the fitting to diffusivity profiles at different temperatures. Therefore, the only variable is the micellar hydrodynamic radius, Rh, as obtained by applying the Stokes-Einstein relation (eq. (5)) to the extrapolated diffusivity at the cmc. It is shown that values of Rh decrease monotonically as T increases (see Table 2). As can be seen from Figures 1-3, fits are

14

ACCEPTED MANUSCRIPT equally good at all four temperatures. A first result from those fits is that  increases as the head group becomes bulkier, going from  = 0.26 for CTEABr to 0.35 for CTBABr. These values are markedly lower than values obtained from ratios of conductivity plots, while they are closer to those obtained by fitting kinetic data from reactions of micellar-bound organic probes.[35] This increase in fractional ionization with the head-group bulk can be explained as the result of unfavourable

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interactions of the hydrated halide ions with bulkier alkyl groups. Steric repulsions also lead to a

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lower positive-charge density on the micellar surface as the alkyl residues become larger. The same

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interpretation has been given in the literature,[31,32] where regardless of the method used to estimate micellar binding of the halide ion, it decreases with increasing bulk of the N-alkyl

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headgroups. This conclusions is consistent with extensive evidence for specific, non-Coulombic, micelle-counterion interactions.[35] Fractional surface ionization values are also insensitive to

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temperature and, as a first approximation, to the overall ionic strength of the solution. The latter statement, however, is likely correct only for salt (i.e., NaBr in this case) concentrations below 0.1-

D

0.2 M, above which extensive micellar growth is known to take place, thus invalidating the choice

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of keeping N constant. Furthermore, when increasing salt concentrations well above that of surfactant in solution, an entropically-driven invasion of anions into the interfacial micellar region

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has been described,[45] which leads to a massive change of micellar surface charges. As relates to the evaluation of the attractive interactions, we adopted values of the Hamaker

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parameter from A = 11 to 20 kT with increasing the head group bulk, over the range of NaBr concentrations of 0.02 to 0.06 M, and temperatures from 15 to 55°C (Table 3). This range of A values is roughly in agreement with a range of published values for similar colloid systems.[31,41] Observed increases in A could be explained with an higher contribution of the bulkier alkyl residues on the head group to the van der Waals attractions. A similar approach has been followed when dealing with micelles made by cationic surfactants having hydrocarbon tails with different lengths.[32]

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ACCEPTED MANUSCRIPT From the obtained trends for  and A as a function of head group bulk (see Table 3), it is apparent that both electrostatic repulsions and van der Waals attractions increase going from CTEABr to

Surfactant

T = 15 °C

T = 25 °C

T = 40 °C

CTEABr

28.5

28.0

26.6

CTPABr

29.4

29.1

28.5

27.7

CTBABr

30.7

29.7

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Table 2 - Values of Rh for bromide surfactants. Rh, Å

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CTBABr, thus balancing, to a certain extent, their effects on the overall micellar diffusivity D.

28.1

T = 55 °C

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25.6

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28.3

Hamaker parameter (kT)

CTPABr



A

N

80

0.26

11

70

0.30

A

N



A

16

50

0.35

20

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3.2. Hydroxide Surfactants



CTBABr

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N

D

CTEABr

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Table 3 - Fitting parameters: N = micelle aggregation number;  = fractional ionization; A =

Figures 4-5 show the diffusivity profiles of CTEAOH and CTPAOH at 15, 25 and 40°C under

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different NaOH concentrations.

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ACCEPTED MANUSCRIPT (a) 15°C 14

10 7 D ( cm 2 / s )

12

10

8

6

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4

2 0.01

0.02

0.03

0.04

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(b) 25°C 20

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18

14

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107 D(cm2 / s)

16

12 10

D

8

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6 4

0.01

0.02

0.03

0.04

0.05

0.06

[CTEAOH], M

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(c) 40°C

0.05

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[ CTEAOH ], M

30

10 7 D ( cm 2 / s )

AC

25

20

15

10

5

0.01

0.02

0.03

0.04

0.05

[ CTEAOH ], M

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ACCEPTED MANUSCRIPT Figure 4(a)-(c) - Diffusivity vs. [CTEAOH] at 15, 25 and 40°C in aqueous NaOH at the following concentrations: 0.08 M (), 0.2 M (), 0.3 M ().

(a) 15°C 18

PT

16

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12 10 8

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107 D (cm2 / s)

14

6 4

0.01

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2 0.02

0.03

0.04

0.05

0.06

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[CTPAOH], M

(b) 25°C 25

10

CE

5

D

15

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107 D (cm2 / s)

20

AC

0.01

0.02

0.03

0.04

0.05

0.06

[CTPAOH], M

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ACCEPTED MANUSCRIPT (c) 40°C 30

107 D (cm2/s)

25

20

10 0.01

0.02

0.03

0.04

0.05

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[CTPAOH], M

RI

PT

15

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Figure 5(a)-(c) - Diffusivity vs. [CTPAOH] at 15, 25 and 40°C in aqueous NaOH at the following

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concentrations: 0.05 M (), 0.06 M ().

It is known that hydroxide ions are much more hydrated than bromide ions, and estimates of

D

hydration numbers of 6 vs. 1.5, respectively, have been reported.[46,47] Given the very high

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diffusion coefficients observed at low [NaOH], our study was limited to high ionic strengths to obtain reliable data. Even with such a limit, experiments at 55°C were not easy to perform due to

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excessively fast diffusions. Moreover, for CTPAOH, trends of D vs [surfactant] were remarkably non-linear at NaOH concentrations higher than 0.06M, and values of variation coefficients were

AC

higher than 20%; therefore we did not consider those data for inclusion in the fitting procedure. This phenomenon may be explained as a true micellar growth for CTPAOH above a threshold ionic strength, though we prefer not to speculate further on such an ambiguous evidence (see section 2.2, above). It was also observed that the extrapolated hydrodynamic radii were smaller than with the corresponding bromide surfactants, and Rh appeared to decrease slightly as the temperature increased (Table 4). A comparison with CTEABr and CTPABr profiles shows that higher ionic strengths in solution should be used to effectively screen intermicellar repulsions for CTEAOH and

19

ACCEPTED MANUSCRIPT CTPAOH, which is straightforward to explain considering the higher surface charge of the latter two surfactants. An attempt to fit the model to the experimental data showed an intrinsic indetermination: given the high surface charges of these aggregates, the fitting procedure were quite insensitive to the value of A, as already reported for CTAOH,[27] and values of  were 0.58 and 0.65 (±25%) for CTEAOH

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and CTPAOH, respectively. These values are slightly higher than the surface fractional ionization

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found for CTAOH at 25°C (approximately 0.5). Similarly to the case of bromide micelles under low

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ionic strength (see above), the insensitivity of hydroxide micelles to A may be also related to the fact that, with highly charged micelles, intermicellar repulsions are so high that it is statistically

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unlikely that two or more micelles can approach each other close enough to overcome the electrostatic repulsion barrier, which would permit the shorter-range van der Waals attractions to

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take place. However, this phenomenon might be apparently reverted if a combination of high added salt and high micellar ionization lead to a certain ionic strength which effectively starts to screen

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intermicellar repulsions, as may be the case for CTPAOH at [NaOH] >0.06M.

Table 4 - Values of Rh for hydroxide surfactants.

CTEAOH

AC

CTPAOH

Rh, Å

T = 15 °C

T = 25 °C

T = 40 °C

26.5

26.3

26.0

23.1

23.4

18.4

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Surfactant

It should be emphasized again that, for both bromide and hydroxide surfactants, theoretical fits were limited to data taken within range of conditions in which no micellar growth occurred, as evidenced by an absence of steep negative-slope diffusivity profiles, which do not converge at the cmc.

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ACCEPTED MANUSCRIPT 4. Conclusions The present study shows that the diffusion behavior of cetyltrialkylammonium bromide surfactants, as measured by dynamic light scattering under various ionic strengths and temperatures, can be fitted to a model based on the linear interaction/DLVO approach, provided that (i) extensive micellar growth is excluded, as indicated by a common intercept of D profiles at the cmc; and (ii)

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micelles remain spherical and monodisperse, as can be inferred from low CV and chi-squared

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values. Estimates of the micellar hydrodynamic radius, Rh, and the micellar fractional ionization, ,

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for these systems show a consistent pattern of increasing size as a function of the head-group bulk, which is reasonable for straightforward steric reasons. Moreover, for any given surfactant, Rh

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decreases as temperature increases from 15 to 55°C. The fractional surface micellar charge was estimated by fitting diffusivity profiles under low ionic strength, where fits were most sensitive to

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slight changes in . Values of  increase going from CTEABr to CTBABr ( = 0.26 to 0.35), thus confirming a pattern known from the literature, which is based on chemical reactivities of

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associated probes.

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For CTEAOH and CTPAOH, values of Rh were smaller than for the corresponding bromides, but the fits appeared to be poorly sensitive to changes in the Hamaker parameter, A, and only a very

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large fractional ionization ( = approximately 0.6) could account for the observed diffusivities. As anticipated above, the presence of a relatively large surface charge on cetyl trialkyl ammonium

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micelles with hydroxide counterions should reasonably make the intermicellar repulsions predominant with respect to the attractive (i.e., van der Waals) counterpart, which is quantified by the Hamaker parameter. As a result, the dependence of fits on A is looser than with bromide counterions. CTPAOH also showed a remarkable departure from the spherical, monodisperse micelle range at higher ionic strengths (i.e. > 0.06M NaOH; data not shown), as demonstrated by high coefficients of variation of light scattering measurements, and non-monotonically decreasing D vs [CTPAOH] profiles which did not converge at the cmc. As an explanation for this, one may argue that, given 21

ACCEPTED MANUSCRIPT the high surface ionization of CTPAOH micelles (specifically, higher than that for CTEAOH), hydroxide ions from added NaOH and those dissociated from the micellar surface add up, and a threshold ionic strength in solution is trepassed to overcome intermicellar repulsions, thus leading

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to predominant micellar attractions and growth.

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Graphical abstract

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ACCEPTED MANUSCRIPT

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Highlights for manuscript:  Cetyltrialkylammonium bromide and hydroxide micelles were investigated by dynamic light scattering.  Linear inteaction-DLVO theory was adopted as a simple approach to evaluate interaction behavior of micelles.  Micelles remained essentially spherical throughout the temperature and ionic strength ranges.  Fractional ionization, , for bromide micelles ranged from 0.26 to 0.35, with Hamaker parameters increasing with the head group bulk  Fractional ionization for hydroxide micelles is much higher (0.58 to 0.65); fits are rather insensitive to the Hamaker parameter.

28