Combining Freezing Point Depression and Self-Diffusion Data for

Subscriber access provided by UNIV OF DURHAM

B: Liquids; Chemical and Dynamical Processes in Solution

Combining Freezing Point Depression and SelfDiffusion Data for Characterizing Aggregation Markus M. Hoffmann, Sarah Bothe, Torsten Gutmann, and Gerd Buntkowsky J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03456 • Publication Date (Web): 18 Apr 2018 Downloaded from http://pubs.acs.org on April 19, 2018

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

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

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

The Journal of Physical Chemistry

Combining Freezing Point Depression and Self-Diffusion Data for Characterizing Aggregation Markus M. Hoffmann,*1 Sarah Bothe,2 Torsten Gutmann,2 Gerd Buntkowsky2 1

Department of Chemistry and Biochemistry, The College at Brockport, State University of New York, Brockport, NY, 14420, U.S.A.

2

Institute of Physical Chemistry, Technical University Darmstadt, Alarich-Weiss-Straße 8, D-64287 Darmstadt, Germany

1 ACS Paragon Plus Environment

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

Page 2 of 33

ABSTRACT: The colligative property freezing point depression is evaluated as a means for estimating the extent of aggregation for solutions of poly(ethylene oxide) alcohol (C10E6) nonionic surfactant in cyclohexane. Combined with additional measurements of self-diffusion coefficients, it is shown that both un-aggregated C10E6 as well as reverse micelles are significantly present for the entire range of measured C10E6 concentration (0.048 molkg-1 - 2.35 molkg-1). A change in speciation near 0.2 molkg-1 is indicated by both the results from freezing point depression and self-diffusion coefficients measurements. It is shown that average reverse micelle radii and aggregation numbers obtained from the ratio of solvent and C10E6 self-diffusion coefficients are consistent with prior reported results. However, unreasonably small radii for the reverse micelles as well as for the cyclohexane were obtained from analysis of the results by the Stokes-Einstein equation using additional measured solution viscosities. The concentration of reverse micelles and un-aggregated C10E6 was calculated from the freezing point depression results using the aggregation numbers obtained from ratio of self-diffusion coefficients. These concentrations indicate that the reverse micelles become smaller in average size and increase in number with increasing temperature without an increase in un-aggregated C10E6.


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


INTRODUCTION Surface activating agents (surfactants) are molecules possessing both hydrophilic and hydrophobic structural components. These types of molecules form the basis of surface and colloid sciences.1 Surfactants tend to aggregate when dissolved in both, polar and nonpolar solvents.2 In polar solvents such as water, these aggregates are referred to as micelles. Micelles are of near spherical geometry with the nonpolar structural component of the surfactant forming the core and the polar structural component forming a surrounding shell that can favorably interact with the polar solvent. Micelles can solubilize nonpolar solutes in water by confining them into their nonpolar core. Conversely, reverse micelles can solubilize polar solutes into nonpolar solvents by forming a reversed architecture of the aggregate structure where the shell consists of the nonpolar component of the surfactant that can interact favorably with the nonpolar solvent while the polar component forms the core.2 Reverse micelle formation is particularly promoted by water as a co-solute, which is readily present as an impurity in the hygroscopic surfactant3 and acts as a nucleation site.2 The water confined within the polar reversed micellar core is often referred to as water pool.4 Although somewhat less common than micelles, reverse micelles are immensely important in a variety of sciences and technologies, most prominently recognized in the fields of biotechnology (extraction of biomolecules, drug delivery, models for biological systems etc.)2,

5-8

and

nanotechnology,2, 5-6 where through the confinement of reverse micelles controlled nanostructures can be synthesized with narrow distribution of size.5 It has been pointed out that for these applications, it is important to know the concentration of un-aggregated, “free” surfactant besides structural parameters such as the revers micelle size and aggregation number.5 Within this context, it is important to point out some additional principle differences between micellar aqueous solutions and reverse micellar solutions in organic media of low polarity. The onset of micelle formation at the critical micelle concentration (cmc) is typically a sharp transition. Further addition of surfactants 3 ACS Paragon Plus Environment


Page 4 of 33

causes more micelles to be formed while the concentration of single surfactant molecules remains that of the cmc, which is usually neglected for concentrations exceeding the cmc. In contrast, the formation of reverse micelles may in cases be gradual, and the concentration of single surfactant molecules may not be negligible at concentrations where reverse micelles are present.4-5,

9

For

example, while there was evidence from Small-Angle Neutron Scattering (SANS) measurements for a cmc, i.e., a sharp transition of reverse micelle formation, in the case of the ionic surfactant sodium bis(2-ethylhexyl) sulfo-succinate (AOT) in several alkane solvents, a nonionic surfactant of the type poly(ethylene oxide) alcohol (Scheme 1) showed a gradual transition of reverse micelle formation.10 It may be possible to gain access to the information on “free” surfactant concentration from measurement of colligative properties because they readily lead to an estimate of the actual total solute species concentration. Colligative properties of solutions, such as osmotic pressure, boiling point elevation and freezing point depression, are properties that only depend on the number of dissolved solutes but not their identity. Common, longstanding chemistry laboratory curriculum experiments involve the determination of the molecular weight of non-dissociable organic solutes by means of the boiling point elevation or freezing point depression,11-14 recognizing that absolute change in phase transition temperature relative to the pure solvent, ∆T, is proportional to the solute molality, m, according to eq 1 with K being either the molal freezing point depression or boiling point elevation constant. ∆ =

(1)

An underlying assumption in eq 1 is that the solute does not aggregate, which is the case for many organic solutes in organic solvents. Conversely, solute aggregation is in principle detectable by a lesser ∆T than expected from solution molality. Therefore, the motivation of this study is to test if freezing point depression may lead to a useful estimate on the extent of reverse micelle formation. In this model study, cyclohexane was chosen as nonpolar solvent for the nonionic surfactant solute 4 ACS Paragon Plus Environment

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


C10E6 because of its rather high freezing point depression constant15 of 20.8 Kmol-1kg making it particularly sensitive to aggregation phenomena. The freezing point depression results are correlated with self-diffusion coefficients obtained from diffusion ordered spectroscopy (DOSY) NMR experiments. Although not an initial motivation of this study, the obtained self-diffusion data are interesting in their own right as they illustrate shortcomings of the Stokes Einstein equation, which is widely used to obtain access to aggregate size information.16-17 Therefore, a critical discussion of radii evaluation from the self-diffusion coefficients and experimental viscosity data is presented as well. To the best of our knowledge, this is the first report utilizing freezing point depression in combination with other property measurements to obtain structural and concentration information about reverse micelle formation for nonionic surfactants. We are only aware of work using freezing point depression for finding aggregation numbers for micelles of ionic surfactants in aqueous solutions via calculation of osmotic coefficients.18

O HO n

CmH2m+1

Scheme 1: poly(ethylene oxide) alcohol, with m representing the number of carbon atoms in the alkyl chain and n the number of ethylene oxide repeat units.



Page 6 of 33

EXPERIMENTAL Chemicals and Sample Preparation. The cyclohexane was purchased for the differential scanning calorimeter (DSC) experiments from Sigma Aldrich with a mass purity of 99.5% and for all other experiments from Pharmco-Aaper (reagent grade, purity checked by 1H-NMR spectroscopy). The surfactant C10E6 was generously donated by Rochester Midland Corporation, who purchased it in large quantities from Air Products. The water content of 8.8 × 10-3 mass fraction in the surfactant was measured with a Mettler Toledo C20 Coulometric Karl Fischer Titrator in five replicates. The polydispersity of the surfactant was analyzed in prior work,19 and its average composition is summarized in Table S1. Solutions were prepared in sample vials by mass using an electronic balance having a precision of 1 × 10-4 g. The estimated standard uncertainty in solution concentration is generally 0.001 molkg-1, except for the small (~10µL) samples for DSC measurements that were filled and sealed as quickly as possible in an aluminum crucible to minimize loss of cyclohexane solvent by evaporation. For NMR sample preparation, each sample was filled in PYREX® glass capillaries and sealed. These were then placed in standard 5 mm NMR tubes filled with D2O as the lock solvent. DSC Experiments. Freezing points of the samples contained in alumina crucibles were determined by DSC measurements with a DSC 214 Polyma® calorimeter from Netzsch. Each sample was cooled with liquid nitrogen from 25 °C to -35 °C at a rate of 5 °C min−1. NMR Measurements, The DOSY experiments were carried out on an Avance 300 instrument from Bruker-Biospin with a variable temperature broadband probe. The probe temperature sensor had a precision of 0.1 K and was calibrated against the known temperature dependencies of methanol and glycol chemical shifts.20 The NMR tubes were not spun during measurements. At least 15 minutes were allowed for the sample to equilibrate with respect to


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


temperature. A stimulated echo based pulse program, which has been shown to reduce systematic errors from eddy currents and thermal gradients, was used.21-22 The gradient strength was calibrated against the known self-diffusion coefficient of water.23-24 The stimulated echo intensities, I(g), were obtained as a function of magnetic field gradient strength, g, of the sine shaped gradient pulses and fitted according to eq 2

=

∆ /

(2)

where I0 is the stimulated echo intensity in absence of any gradient, γ is the gyromagnetic ratio for 1

H, and ∆ the diffusion time, which was set to 0.1 ms. A total of 16 scans were acquired for each of

16 varied field gradient strengths. The length of the gradient pulse, δ, was adjusted to each sample and temperature condition, while delays for eddy currents and gradient recovery were set at 5 ms and 0.1 ms, respectively. The fits to eq 1 were carried out in two ways, using the signal height or the signal area. The reported self-diffusion coefficients and uncertainties are the average and standard deviations from each analysis as well as in the case of C10E6,which displays several spectral 1H NMR features, from the results of each separately analyzed spectral feature. Viscosity and Density Measurements. The viscosity and density of each sample were measured in parallel using an AMVn rolling ball viscometer and a DMA 4100 vibrating tube density meter. Both instruments are manufactured by Anton Paar and control the temperature within 0.02 K by Peltier systems. The viscosity measurements of all solutions required the use of a 1.6 mm capillary. Boiled ultra-pure water (Anton Paar lot 1012) was used to calibrate the 1.6 mm capillary as well as the density meter.15 The 1.6 mm capillary calibration was verified against neat hexadecane.15 Viscosity and density measurements are the average of at least twelve repetitions, and the reported



Page 8 of 33

values represent the average and the standard deviations to these. For each sample, results agreed within the reported uncertainties for the first and last measurements of a temperature series obtained at 293.15 K.

RESULTS AND DISCUSSION DSC Studies. Figure 1 illustrates the effect of reverse micelle formation on the freezing point depression of cyclohexane as measured by DSC. In DSC, the instrument is measuring the heat flow required to cool (or warm) a sample at a constant cooling (heating) rate. During the phase transition of freezing, the sample liberates heat on its own, thus causing the negative peaks observed in Figure 1. In the case of neat cyclohexane, the liberation of heat was too fast for the instrument’s cooling control to keep a constant cooling rate, and the sample temperature actually increased slightly for a short period of time resulting in a crossover line shape for the negative cyclohexane freezing peak in Figure 1. However, this instrumental artifact does not impact the accuracy of the onset temperature at which the freezing phase transition begins, which for pure cyclohexane compares well with prior reported ones.14,

25

The onset temperature in Figure 1 is reduced for a

solution of 0.46 mol·kg-1 biphenyl in cyclohexane by the expected amount of about 10 K based on the freezing point depression constant for cyclohexane of 20.8 K·mol-1·kg.15 In contrast, a solution of 0.42 molkg-1 C10E6 reduces the onset temperature in Figure 1 much less than expected by eq 1 because of the formation of reverse micelles, which reduces the effective number of C10E6 solutes. The actual solution molality, msolute, consisting of freely dissolved C10E6 plus the present reversed micelles is readily evaluated from eq 1 and the observed freezing point depression. The results and their uncertainties are summarized as Table S2 in the supplementary material.


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


Figure 1. DSC cooling curves of neat cyclohexane, 0.42 molkg-1 C10E6 in cyclohexane and 0.46 molkg-1 in cyclohexane. The asterisks indicate the onset temperatures for the freezing.

Figure 2 shows a graph of msolute against the molality of C10E6, m. Several observations can be made from Table S2 and Figure 2. Reverse micelle formation is indicated for all investigated C10E6 concentrations. Figure 2 further indicates that msolute is linearly dependent on m, with an abrupt change in slope near m = 0.2 molkg-1. The solid line in Figure 2 was obtained from respective linear fits, which resulted in eq 3.

= 0.6664 " 0.0043 for 0 molkg-1 < m < 0.2 molkg-1 = 0.2402 " 0.0759 for 0.2 molkg-1 < m < 2.5 molkg-1

(3)

To better understand the meaning of the observed linear dependence in Fig. 2, it is instructive to discuss the significance of the slope values in eq 3. If all added C10E6 would remain individually dissolved, then the slope would exactly be of value 1. Aggregation causes the slope to be lower than 1. The fact that msolute increases linearly with m means that a fixed fraction of added C10E6 is forming micelles.This observation could be explained by the presence of stepwise equilibria for the formation of reverse micelles Sn from surfactant S, i.e., S+ S ⇌ S2, S+ S2 ⇌ S3, S+ S3 ⇌ S4, etc. 9 ACS Paragon Plus Environment


Page 10 of 33

each with its respective corresponding equilibrium constant.26-27 A stepwise growth model is also supported by the observed absence of a sharp aggregation transition at a critical micelle concentration.10 Apparently, not the majority of surfactant molecules but only a fraction of added surfactant is involved in the micelle formation equilibria, while the remaining fraction remains unaggregated. Observed sharp slope decrease in Figure 2 is indicative of some change in dominant equilibrium reverse micelle speciation that requires a larger fraction of added C10E6 molecules. Independent measurements from which size information can be obtained are needed to shed further light in this matter. Therefore, we measured self-diffusion coefficients and solution viscosity for C10E6 solutions in cyclohexane to obtain average solute radii. Before presenting these results in the next section, a few more comments are in order. Firstly, we ignored so far that the studied C10E6 contained water in a mass fraction of 8.8 × 10-3. This should be of insignificance in the freezing point data treatment in this section because it can be assumed that the water will be essentially exclusively solubilized within the reverse micelles.8 Secondly, it is important to note that given the nature of the freezing point depression measurements, any temperature dependence on the reverse micelle equilibria cannot be accounted for. Nevertheless, it is remarkable that linearity in Figure 2 is evident even up to a C10E6 concentration of m = 2.5 molkg-1, which expressed in C10E6 mole fractions amounts to about xC10E6 = 0.2. Overall, the results from the freezing point depression show that not only reverse micelles but also un-aggregated C10E6 is significantly present over the entire measured range of compositions.


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


Figure 2. The molality of all solutes present (free surfactant and reverse micelles), msolute, as a function of C10E6 molality, m, in cyclohexane obtained from freezing point depression. Self-Diffusion and Viscosity. This subsection presents experimental data for the selfdiffusion coefficient, D, and viscosity, η. As it is well known,16 these data should provide access to the average C10E6 speciation radii, r, via the Stokes-Einstein equation shown in eq 4.

* ,

+ ) = -.

(4)

In eq 4, kB is the Boltzmann constant, T the temperature in Kelvin, and c is a constant, discussed in more detail in the next subsection. Inspecting the self-diffusion coefficients obtained from the C10E6 spectral lines, DC10E6, listed in Table S3, they follow a linear dependence when plotted as the natural log of the molality, as illustrated in Figure 3.



Page 12 of 33

Figure 3. The self-diffusion coefficients obtained from C10E6 spectral lines DC10E6 at 15 °C (), 30 °C (), and 40 °C() as function of the natural log to the solution molality. The lines are leastsquare linear fits. For comparison, the self-diffusion coefficients of the cyclohexane solvent, DC6H12, at 15 °C (×) are also shown. The experimental standard deviations of DC10E6 are summarized in Table S4, and the coefficients of the linear fits of DC10E6 versus ln(m) are listed in Table S5. The self-diffusion coefficients of the cyclohexane solvent have also been measured and are summarized in Table S6 with their standard deviations listed in Table S7. The value of DC10E6 = (14.9 ± 0.4) × 10-10 m2s-1 at 25 °C is slightly higher than (14.57 ± 0.06) × 10-10 m2s-1 reported by Kato et al.,24 but still agrees within measurement uncertainty. From Table S6, the addition of 0.048 molkg-1 C10E6 does not change the cyclohexane selfdiffusion coefficients within measurement uncertainty. Only higher C10E6 concentrations lead to a measurable decrease of DC6H12. This decrease in DC6H12 with increasing C10E6 concentration does not follow the natural log of m as illustrated for the 15°C data in Figure 3. Thus, the linear decrease of 12 ACS Paragon Plus Environment

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


self-diffusion coefficient to ln(m) only applies to DC10E6. This linear decrease to ln(m) seems to suggest a continuous growth of the average C10E6 speciation radii. Additional insights can be derived from the ratio of self-diffusion coefficients of solvent to solute, DC6H12/DC10E6, as a function of m, which is shown in Figure 4 for three exemplary temperatures. The graphs in Figure 4 are reminiscent to the graph in Figure 2. Thus, linear line fits are added for the low and high concentration regions in Figure 4 to accentuate the resemblance. The intersections of the low and high concentration linear fits are between 0.20 and 0.25 molkg-1 in close agreement to Figure 2. Therefore, the self-diffusion data are confirming a likely change in the dominant equilibrium reverse micelle speciation near 0.20 molkg-1. Figure 4 also illustrates the earlier mentioned shortcoming that the DSC data cannot track temperature dependencies of the present speciation. Figure 4 clearly shows that DC6H12/DC10E6 decreases with increasing temperature, which is consistent with the notion that higher temperature reduces the reverse micelle concentration and/or size. Presuming that chemical equilibrium in the C10E6 solutions in cyclohexane establish faster than the DSC cooling rate of 5 min°C-1, the obtained values for msolute represent lower bound estimates since the number of present species can only be expected to be larger at elevated temperatures.



Page 14 of 33

Figure 4. Ratio of self-diffusion coefficients of cyclohexane solvent and C10E6 solute, DC6H12/DC10E6 at 15 °C (), 30 °C (), and 40 °C() as a function of C10E6 molality. The solid lines are linear fits to the low and high concentration regions. The viscosity data are summarized in Table S9 with standard deviations listed in Table S10. Agreement with literature data for pure cyclohexane is within 3.5%.28 The temperature dependence of the viscosity for each composition in Table S9 follows Arrhenius-type behaviour according to 12

/ = 0 34

(5)

for the investigated range of temperatures, which can be seen in the linearity of ln(η) as a function of 1/T in the graphs shown in Figure 5. In eq 5, Ea is the activation energy associated with flow resistance, A the pre-exponential factor, and R is the gas constant. The viscosity data for 0.046 molkg-1 and 0.095 molkg-1 were omitted in Figure 5 to avoid clutter. The obtained slopes (=Ea/R) and intercepts (=lnA) from the least square linear line fits to the Arrhenius plots were fit as shown in Figure S1 to second order polynomials, which are 14 ACS Paragon Plus Environment

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


summarized in Table 1. Therefore, a universal fit for the solution viscosity that is valid for the investigated ranges of molality and temperature has been obtained:

ln/ = 7∑=:> 9:,

Combining Freezing Point Depression and Self-Diffusion Data for

Recommend Documents