Amphiphilic second-order phase transitions determined through NMR

Accepted Manuscript Amphiphilic second-order phase transitions determined through NMR

Teresa Reilly, Mohamed I.H. Mohamed, Teresa E. Lehmann, Vladimir Alvarado PII: DOI: Reference:

S0167-7322(18)30680-9 doi:10.1016/j.molliq.2018.07.066 MOLLIQ 9387

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

6 February 2018 24 June 2018 15 July 2018

Please cite this article as: Teresa Reilly, Mohamed I.H. Mohamed, Teresa E. Lehmann, Vladimir Alvarado , Amphiphilic second-order phase transitions determined through NMR. Molliq (2018), doi:10.1016/j.molliq.2018.07.066

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Amphiphilic second-order phase transitions determined through NMR

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1000 E. University Ave. Laramie, WY 82071, USA

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Teresa Reillya , Mohamed I. H. Mohamedb , Teresa E. Lehmannc , Vladimir Alvaradoa,∗

a Department

of Chemical Engineering, University of Wyoming, Laramie WY, 82071 USA of Petroleum Engineering, University of Wyoming, Laramie WY, 82071 USA c Department of Chemistry, University of Wyoming, Laramie WY, 82071

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b Department

Abstract

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In this work, nuclear magnetic resonance (NMR) spectroscopy is used to investigate surfactant phase behavior over a broad concentration region. This technique is an adaptation of a previously developed method applied to de-

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tect the critical micelle concentration (CMC) of surfactants. In this method, a surfactant concentration is correlated to the normalized intensity, or area,

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of the NMR signal for each surfactant. In this procedure a linear relationship develops on either side of the CMC, with a distinct change in slope where the

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primary phase change occurs. The research conducted herein investigates the NMR response at higher surfactant concentration, where the phase change consists of a change in micelle shape or other structural configurations. These

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secondary phase transitions can be expected from 10-90 wt.%, where the CMC measurements are conducted at concentrations <1 wt.%. The solutions were

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also analyzed with dynamic light scattering (DLS) and a cross-polarizer microscope to confirm suspected detected phase changes. Visible changes in the rheological response were observed and therefore carefully examined. In large part, the results seen with all methods corresponded with visible differences in the surfactant solutions and detected changes in the NMR protocol. ∗ Vladimir

Alvarado Email address: [email protected] (Vladimir Alvarado)

Preprint submitted to Journal of LATEX Templates

July 16, 2018

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Keywords: Surfactant, Phase Transitions, Nuclear Magnetic Resonance, Dynamic Light Scattering

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1. Introduction

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Surfactants are ubiquitous in today0 s world, including various types used in detergents, sticky notes, foams, and enhanced oil recovery techniques [1]. As

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such diverse agents, surfactants have various structures to suit these numerous needs. When assessing a surfactants suitability for a function it is important

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to keep in mind the assorted demands required on solubility. Changing the physico-chemical environment such as temperature, pH, concentration, and the species present can affect solubility. Oftentimes a surfactant will be insoluble in

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a particular solution until the incorporation of a co-solvent. In operations such as oil recovery, the surfactant charge is highly important. Carbonate surfaces are

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positively charged and anionic surfactants adsorb strongly on the surface. This can be diminished by addition of polymer or increased pH, for example through

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sodium carbonate [2, 3]. When creating a detergent, the type of surfactant selected is dictated by the type of dirt it will encounter, temperature, water hardness, and the average run time of a wash cycle; these variables are different

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around the world and as such different detergents are needed [1]. Surfactants are amphiphilic molecules possessing both hydrophilic and hy-

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drophobic portions. The hydrophobic end is typically comprised of a hydrocarbon tail(s) which is(are) soluble in nonpolar solvents. Alternately, the charged

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head group is preferentially soluble in polar solvents. The tail(s) has numerous carbons in the chain, but is(are) generally saturated, ending in a methyl group. The head-group can be classified as either anionic, cationic, zwitterionic, or nonionic, and this charge will have a strong influence on the applicability of the surfactant molecule. Above a certain concentration surfactants are known to aggregate into one phase micelles, i.e. the critical micelle concentration (CMC). A hydrocarbon chain is generally stiff and maintains angles of 109.5◦ , however micelles form above a critical temperature, the Krafft temperature, such that

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these hydrocarbon chains are fluid-like instead [1]. The number of surfactant molecules in a micelle depends on factors such as tail length and head group area, but there are generally 50-100 molecules [4, 5]. Equation 1 indicates the

3 3 4πRmic 4πRmic = 3vhc ahg

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N0 =

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relationship between surfactant structure and micelle size.

(1)

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where N0 is the aggregation number of the surfactant, which is largely dependent on the radius of the micelle (Rmic ) and the volume of the hydrocarbon tail (vhc ) or the area of the head group (ahg ) [1]. Salinity and temperature

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are relevant parameters as both can dehydrate the head group, which leads to decreased surface area and a change in the aggregation parameters. The CMC

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is dependent on species present, ionic strength, and surfactant nature. It is generally < 1wt.% and results in either spherical or ellipsoidal species. The CMC

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is fairly precise, as it occurs at a balance between two opposing interactions: hydrophobic interactions drive the tails together, but the charged headgroups

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push each other apart with electrostatic repulsion. The effect of surfactant structure and charge distribution on the value of the CMC was demonstrated by Comas et al. [6]. This work determined that polymers can affect the CMC

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through a weak electrolyte effect. Without the polymer in solution, the CMC was confirmed to relate directly to the structure. Surfactant solutions are sus-

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ceptible to external contamination such as salts or alcohols, which can either alter the head group area through dehydration or tangle with the tails to reduce the curvature of the system, respectively. The CMC can be determined

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through various techniques, such as ultraviolet-visible (UV-vis) spectroscopy, dynamic light scattering (DLS), fluorescence, and interfacial tension (IFT) reduction experiments [7, 8, 9]. Garcia-Olvera et al. developed a technique to measure surfactant concentration and detect the CMC through application of a high-field NMR technique [10]. Above the CMC, but still at low concentrations, spherical micelles are commonly reported. As the surfactant concentration increases, more micelles form

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rather than increasing the size of those already existing. Continuing to increase the concentration will lead to a second-order phase transition. Where first order transitions are surfactant-surfactant relationships and happens at an exact concentration, second order is aggregate-aggregate interactions and oc-

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curs over a more gradual concentration sweep. The first second order phase

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transition typically reported is when spherical micelles change to cylindrical mi-

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celles, accompanied by an increase in viscosity [11, 12]. The radii of cylindrical micelles are shown to relate to the length of the hydrocarbon tails. The length of cylindrical micelles is dictated by surfactant concentration and is compared

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to spaghetti; it can be very polydisperse. If concentration continues to increase, the shape can continue to change with increased packing parameters. Hexago-

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nal, cuboidal, lamellar, and finally crystalline shapes can be achieved in some surfactant systems [13]. Fontell applied deuterium NMR to detect phase tran-

side of a transition [14].

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sitions in surfactant species, noting a distinct change in peak shape on either

Different techniques have been proposed to identify the phase transition

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with respect to concentration of surfactant molecules. These techiniques include: differential scanning calorimetry (DSC) [15, 16, 17], Fourier-transform

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infrared (FTIR) [18, 19, 20], fluorescence polarization [21, 22, 23, 24], and NMR [25, 26, 27]. NMR, DLS, and microscopic techniques were applied in this work.

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To address the changes in viscosity observed and known to occur at phase transitions, viscosity was also measured. NMR is the most direct and non-destructive technique available for struc-

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ture determination, though it has also proven useful in its semi-quantitative applications. Garcia-Olvera et al., Lisitza et al. and Rane et al. have all applied this technique to not only measure the amount of species present, but also to determine the aggregation point, a primary phase transition, of surfactants and asphaltenes [10, 28, 29]. NMR offers an advantage over other techniques in that it can distinguish between different species present and can measure them simultaneously, provided each possesses a unique peak. This was demonstrated by Garcia-Olvera et al. in a work which measured the concentration 4

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of individual species from a mixture of three different species over the course of a coreflooding experiment [30]. The NMR technique has been exploited to measure concentration as well as CMC detection, and this work is an attempt to investigate NMR as a technique to detect phase transitions at higher surfactant

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concentration.

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In this study, the mean count rate (average number of photons detected per

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second) measured with a dynamic light scattering instrument is representative of an emerging macroscopic phenomenon, but is not directly size-dependent. In DLS measurements the fluctuation of scattered intensity at fixed angles is

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measured. Since this fluctuation results from the motion of particles, it is correlated with the particle diffusion coefficient. Changes in the calculated scattering

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intensity reflect changes in the optical properties of the material during concentration variations. Furthermore, surface modifications of aggregates are not always correlated with the diffusion coefficient that enters into the calculation

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of the hydrodynamic radius. The average count rate (average number of photons detected per second), on the other hand, seems to be much more reliable

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because of its raw sight, simplicity and reproducibility. Optical microscopy methods are useful to visualize large unilamellar vesicles

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or multilamellar vesicles (the dimensions of which can reach several microns), emulsion droplets, and other supramolecular assemblies like fibers and micro-

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tubules [31, 32]. To enhance the contrast between these aggregates and the medium in which they are suspended, the technique of differential interference contrast (DIC), which employs polarized light and two Nomarski prisms, can

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be used. A particularly important use of polarized light microscopy is the identification of liquid crystalline phases [33, 34, 35]. In this case, when polarized light propagates through liquid-crystalline structures with defects, placed between slide and coverslip, characteristic birefringent textures are formed that often allow for the phase assignment (e.g. lamellar and hexagonal phases). In this paper we show that the NMR technique developed by Garcia-Olvera et al. can be extended to high concentrations and used to detect phase transitions beyond the CMC [10]. Various measurements are taken on the high 5

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concentration range (5-60 wt.%) of S1 surfactant solutions in water. The CMC was determined with 1 H NMR to demonstrate competency with the NMR protocol applied. This experimental procedure was then followed for the higher concentration species. Apparent phase transitions were detected with this tech-

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nique. The diffusion coefficients were compared on a low-field or time-domain

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(TD) NMR device. The apparent secondary phase transitions detected with the

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high-field NMR instrument were also observed with the TD-NMR. Though compareable at high concentration, it was determined that this smaller instrument is not sensitive enough to detect the CMC. Furthermore, diffusion experiments

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were run on a high-field NMR to determine if the formation of microemulsions could be detected, as that is predicted to exist at concentrations <20wt.%. In-

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vestigations of the 5-60 wt.% concentration range were conducted to determine viscosity, DLS, and microscopes to confirm the existence of these transitions to validate the NMR results. NMR is capable of detecting these phase tran-

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sitions, although the actual changes to micelle shape are unknown with these

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techniques.

2. Materials and Methods

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2.1. Materials

The surfactant selected, called S1, is procured from Stepan (Northfield, IL),

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and has an activity of 86%. Salt in solution adds another layer of complexity to the mixture and was deemed unnecessary. The surfactant solution was mixed only in de-ionized water. When testing high-field 1 H NMR a deuterated solvent

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is required, and so D2 O was attained from Sigma Aldrich (St. Louis, MO). A second surfactant, S13B, was analyzed to confirm the changes seen in some instances, and has an activity of 82%. 2.2. Methods 2.2.1. Sample Preparation Samples were prepared at high concentration with the intent to dilute to low to minimize error. The surfactant was provided in a diluted form, therefore 6

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one needs to incorporate the activity coefficient when calculating the dilutions. Equation 2 shows this calculation and is provided below. [mL desired][Concentration desired] [Activity of surf actant]

(2)

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g surf actant =

Equation 2 provides the amount of surfactant required to dissolve into the de-

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sired volume (mL) of water. Phase transitions have been predicted up to 91

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wt.%, so high concentrations were desired. The original surfactant solution is fluid and spins under a stir bar, however an 80 wt.% solution is too viscous to spin and the stir bar only vibrates. The solution was diluted further to 60

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wt.% before it would allow the stir bar to spin at 25◦ C. This change in viscosity represents a phase transition between the initial solution and the 80 wt.%

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dilution, and another one between 80 and 60 wt.%. The 60 wt.% solution was considered the starting solution; 20 mL aliquots were extracted and preserved from the stock solution and more water was added to the stock to dilute to

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progressively lower concentrations. At 20 wt.% the stock solution was pulled from to dilute traditionally. A second solution was created at 25 wt.% to assess

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the error, which was determined to be minimal. It is important to note that the viscosity did not continue to decrease lin-

see Fig. 1

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early with concentration, but thickened substantially again from 45-40 wt.%,

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The differences in viscosity between the provided solution, the 80 wt.%, and the 60 wt.%, are a clear indications of phase transitions occurring. Changes this dramatic are very noticeable when handling the solutions for further testing.

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The solution again becomes too viscous to stir at 35 wt.%. A 30 wt.% sample will flow with gravity again, but will not spin easily. Solutions from here down visibly continue to decrease in viscosity. Further testing confirms the transitions observed and determines whether high field NMR can be trusted to detect the shape transitions.

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Figure 1: From right to left is 30%-35%-40%-45%, notice the difference in behavior among all. There are solutions which flow easily on either side of these concentrations.

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2.3. NMR 2.3.1. 300 MHz

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A 300 MHz Bruker Avance III (Billerica, MA) instrument has been used to successfully detect the CMC for surfactant solutions at low concentration

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(<1 wt.%) [10]. This experimental technique applies 1 H NMR to detect both the CMC and secondary phase transitions at higher concentrations. Samples

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are prepared at 90%/10% surfactant solution/D2 O ratios; the spectra are collected with 16 scans. They apply a spectral width of 12 ppm and an excitation sculpting solvent suppression incorporated into the pulse sequence. The NMR

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intensity is dependent on the receiver gain, which is adjusted according to the concentration of species in the solution. Surfactant structures are too complex

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to determine through simple 1D 1 H NMR techniques, so no reverse engineering is conducted through these experiments. In order to determine concentration instead of structure either the area under peaks or the intensity of the peaks are normalized over the receiver gain and plotted on a calibration curve. The salinity of the solution affects the NMR signal, another reason salt was omitted from these experiments [36]. This technique was applied to low concentrations to determine the CMC. The latter was to show competency before extending this technique to high

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concentrations of surfactant solution. These high concentrations were analyzed in an attempt to confirm the applicability of NMR for detecting secondary phase transitions. Some data points are missing, as the highly viscous solutions are too solid-like for the fluid state probe to shim.

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In addition to 1D 1 H NMR, diffusion NMR was conducted on the 5-20 wt.%

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solutions, as microemulsions are known to spontaneously form in this concen-

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tration range [1]. The average diffusion coefficient could change if the solution spontaneously forms more small structures. There was no change in slope in this concentration range with the original technique, but the transition could

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be too subtle to detect. These experiments were also conducted on the 300 MHz, but with a diffusion probe rather than a fluid state probe. A deuterated

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solvent is not required for these experiments, but the same samples were used for all measurements, and corrections were made for the diluted concentration values. Regarding diffusion NMR there are two common pulse sequences used,

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pulsed gradient spin-echo (PGSE), and pulsed gradient stimulated-echo (PGSTE). PGSTE is known for being less sensitive to J-coupling phase evolution

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effects than PGSE, so peaks basically remain in-phase [37]. Therefore, PGSTE measurements were conducted, and no solvent suppression was applied. The ex-

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periment was carried out for 128 scans with a gradient sweep from 6-200 Gauss. The water peak, and two strongest surfactant peaks were analyzed regarding

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area and intensity; area consistently gave the better fit. The initial intensity of magnetization and the diffusion coefficient, determined from the Stejskal-Tanner

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equation, were both recorded for all concentrations tested. 2.3.2. 20 MHz The TD-NMR diffusion experiments were applied to the whole concentration

range, the 0.1-1 wt.% to test for CMC determination, and the 5-60 wt.% to test for determination of secondary phase transitions. The instrument used was a Bruker minispec mq20 with temperature control and a gradient field. Before using relaxation time application, T2 , the instrument was tuned and the 90◦ and 180◦ pulse lengths were calibrated with the Bruker daily check sample. The

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diffusion values were calibrated using a CuSO4 sample at 25◦ C. A consistent amount of 1 cm of sample is injected into the sample tubes. A gradient of 30 gauss was selected to calculate the diffusion coefficient. Measurements were

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2.4. DLS Effective Diameter and Diffusion Coefficients

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repeated 5 times in order to average the values.

Dynamic light scattering was measured with a NanoBrook ZetaPALS Model

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173 plus. The position of the detector was at 90◦ relative to the laser source. This optics arrangement maximized the detection of scattered light while main-

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taining signal quality. Quartz cuvettes were filled with each sample. Temperature in the cell was monitored by an external probe. After stabilizing the

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temperature at 25◦ C the instrument measured the effective diameter in nm. Experiments were completed using the Particle Solution Software provided by

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Brookhaven Instruments Corporation (Holtsville, NY). 2.5. Polarized Optical Microscopy

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The microstructure of the samples was observed under polarized light. Photographs of samples were taken by a LEICA DM 2500P polarizing optical microscope from Leica Microsystems (Wetzlar, Germany). A CCD camera (LEICA

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DFC320) with a x200 magnification was used. Small volumes of surfactant were placed on thin glass micro slides that contained a spherical cutout/basin in the

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center where the material could rest.

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2.6. Mechanical Testing The extent of the materials linearity was determined through a strain sweep

of each concentration. This was completed on an AR-G2 rheometer from TA Instruments (New Castle, DE) with a 40-mm cone-and-plateat 1o -angle at 25◦ C.

The frequency was held constant at 1Hz and the strain was swept from 0.001% to 10%. A critical strain from about 0.01-0.5% will generally indicate electrostatically stabilized systems, where sterically stabilized systems will have a value around 1-5% [38]. Once this was determined, a frequency sweep was collected

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from 0.1-100 Hz below the critical strain to infer structural information from the tan(δ). A tan(δ) less than one indicates that the particles are highly associated due to colloidal forces. A high tan(δ) suggests the particles are highly

σo [cosδ + isinδ] γo

(3)

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G∗ = G0 + iG” =

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unassociated. The values are calculated through application of Eq. 3

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where σo represents the shear stress, γo is the amplitude of the strain, G’ is the elastic or real modulus which is in phase with the stress, and G” is the viscous or imaginary modulus which is 90◦ out of phase [39]. The tan(δ) is then the

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viscous over the elastic modulus, with the most stable systems giving values

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close to one.

3. Results and Discussion

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3.1. NMR

3.1.1. High Concentration (>5 wt.%)

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Most concentration values could be shimmed on the 300 MHz instrument, with a few exceptions. Some samples were unable to flow into the tube from the

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long-stemmed glass pipette, and some were too viscous to mix in the D2 O and allow the instrument to shim. Fig. 2 draws attention to the change in shape in the solution at differing concentrations. Fontell indicated that phase transitions

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should be accompanied by a distinct change in the NMR spectral shape [14]. In 1 H NMR the shape of a peak is typically indicative of the number of 2 J

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hydrogen neighbors it has. One neighbor will result in a doublet, while two equates a triplet pattern. Several differing 2 J values will lead to multiplets of multiplets which are all pieces to puzzling the structure together. In surfactant species the spectra are often not primary and would require more than just onedimensional 1 H NMR to deconvolute the myriad of overlapped peaks. The high degree of overlap simply indicates a large/complex structure, which will change if bonds are formed or broken, or if the overall structure were to change. This is possibly as seen in Fig. 2. 11

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S1_10wt%

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S1_20wt%

S1_50wt% 3.0

2.5

2.0

1.5

1.0

[ppm]

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3.5

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S1_30wt%

Figure 2: Comparative NMR of 10, 20, 30, 50 wt.% surfactant. Notice the dramatic difference

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in shape seen between 20-30 wt.% and again between 30-50 wt.%

At concentrations below 20 wt.%, the shape of the peaks observed shows

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no change other than in intensity/area. This seems to suggest that the micelle species existing at and below 20 wt.% are similar in structure. When

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concentration increases to 30 wt.% the shape changes from the previous lower concentration spectra, suggesting a change between 20-30 wt.%. Due to diffi-

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culties mentioned previously, no NMR data were collected for 35 and 40 wt.%. The solution changes viscosity at 45 wt.%, allowing measurements to continue. Application of the NMR technique in question is provided in Fig. 3. Once again

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at 60 wt.% the solution was too viscous to measure. This explains the missing points in the same location in Fig. 3.

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Analysis of the data presented in Fig. 2, following the deductions of Fontell, indicates a change between 20-30, 30-50, and the lack of data at 60 suggests a change between 50-60 wt.% as well. The NMR protocol demonstrated in Fig. 3 shows a decisive change in slope between 25-30 wt.%, but before that a more subtle change between 20-25 wt.%. The slight change in slope followed by the more dramatic shift seems indicative of a gradual transition beginning. This protocol goes on to suggest a phase transition between 30-45 wt.% as there are missing points which express a difference in behavior from the 30 wt.% to 12

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Figure 3: Normalized intensity curve, breaks in the curve should be indicative of phase transitions

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the increased concentration. The decrease in viscosity allows for NMR to be collected again at 45 wt.% and continues until 55 wt.%. The lack of data at 60 wt.% shows a transition again from 55-60 wt.%. This completely supports the

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data seen in Fig. 2, and supports what is seen in the viscosity differences. This shows that the NMR detects breaks where we have a known phase

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transition (30-45 wt.%), but also a dramatic change between 25-30 wt.%, which is in support of the difference noted in Fig. 2. Additionally, a subtle change is

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observed in the slope between 20-25 wt.%. This point does not correspond with a visible change in viscosity. The decrease in slope could still be related to a

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more subtle change in viscosity. We were unable to collect data on the 35-40 wt.% or 60 wt.% solutions due to sample thickness. The point at 45 wt.% is seemingly inconsistent with the last noted peak at 30 wt.%. This disparity in

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conjunction with the visible increase in viscosity and the lack of NMR data are all in support of a phase transition occurring between 30 and 45 wt.%. The points after 45 wt.% decrease in slope and there is a break between the three. This suggests a difference in behavior but also a transition on either side of 50 wt.%. The TD-NMR mq20 was applied to the same concentration sweep, with similar trend results in Fig. 4. Each measurement was repeated a minimum of five times to collect an average and provide information on standard deviation shown in the plot. The diffusion coefficient measured in the low-field technique 13

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Lowfield Phase Transitions?

Diffusion Coefficient (e-9)

2.5 2

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1.5

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1

0 10%

20%

30%

Concentration (wt%)

40%

50%

60%

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0%

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0.5

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Figure 4: mq20 concentration sweep comparing diffusion coefficients

is an average of the water and the surfactant in solution. Lindman et al. [40] saw that the diffusion coefficient of water will decrease with increasing surfactant

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concentration but stay in the same relative order of magnitude. They also saw that some surfactants could drop their diffusion coefficients by an order of

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magnitude as concentration increased, due in part to an increase in viscosity and droplet size. The diffusion coefficient of the surfactant is generally an order

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of magnitude lower than the water, and as it increases in concentration we see it drop the diffusion coefficient more and more but the relationship loses linearity

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between 20-25%, indicative of structuring. Diffusion data show a linear decrease in diffusion coefficient from 1-20 wt.%, with an increase from 25-35 wt.%. A change in the slope is generally correlated

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with a change in phase, as with the CMC detection using the high field NMR. The diffusion coefficient is known to correlate with the diameter of a particle, so this increase is likely related to a slight decrease in diameter as the solution becomes more concentrated and more closely packed. This change in diffusion coefficient is supported by the observed decrease in diameter seen in the DLS data to follow. As seen in the high-field measurements, there is a slight change in slope between 20-25 wt.%. In general, primary phase transition are known to

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be abrupt, occurring at an exact concentration consistently. Second-order phase transitions are known to be more subtle, and to occur over a larger concentration range. The NMR data shown in Fig. 2 shows a phase transition between 20 and 30 wt.%, which could progress after 20 wt.% until a full transition by 30

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wt.%. This could explain the consistently slight change in NMR data slope. The

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sudden drop between 35-45 wt.% supports figure 2 and the transition suggested.

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Concentrations 50 and 55 wt.% increase the diffusion coefficient slightly, but then 60 wt.% decreases it to its lowest value overall. These trends seem to indicate phase transitions between 20-25, 35-45, and 55-60 wt.%. Diffusion

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coefficient can be determined via the Stokes-Einstein equation. Equation 4 shows that the diffusion coefficient, D, is inversely related to both particle radius,

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r, and solution viscosity, η. These suspected transitions were investigated for confirmation with other techniques including DLS, viscosity, and microscopic analyzation.

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D=

kB T 6πηr

(4)

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3.1.2. Low-Concentration (<1wt.%)

Lower concentrations were analyzed with the high-field NMR instrument

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and the time-domain NMR system. The low concentration high field data were acquired to ensure competency with the reported technique. The TD-NMR diffusion was used to determine the diversity of the NMR technique developed

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by Garcia-Olvera et al. [10]. The mq20 instrument is much less expensive than the high-field instrument used previously, and as such CMC detection becomes

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more affordable if this instrument can be used instead. S1 diffusion NMR was examined from 0.1-1 wt.% on the mq20, and the corresponding measurements conducted at 300 MHz revealed a CMC value between 0.4-0.5 wt.%. The results are plotted in Fig. 5. The data collected in the low field experiment was not as clean and not as trustworthy as the data collected at high field. As a technique, this required further testing. Another surfactant, S13B, was mixed in the same 0.1-1 wt.% concentration range. 300 MHz and mq20 measurements were conducted in the

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S1 Low vs High Field Techniques

4000

2.26

3500

2.24

3000 2000

y = 5197.5x R² = 0.9987

2.2

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1500

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2.22

2500

Lowfield, Diffusion Coefficient (e-9)

2.28

y = 4064.3x + 372.71 R² = 0.9981

4500

1000

2.18

500 0

2.16

0

0.2

0.4

0.6

Concentration (wt%)

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High Field, normalized Intensity

5000

0.8

1

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Figure 5: Low concentration surfactant solutions. High field data (circles) indicates a CMC between 0.4-0.5 wt.% for S1. Low field data (diamonds) seems to suggest a similar break in

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slope, but is not as conclusive

same manner as for S1, and the results are in Fig. 6. The lack of clean data for the two low-field experiments leads to the conclusion that the mq20 does not

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have high enough resolution to detect the CMC with diffusion measurements. S13B Low vs High Field Techniques

16000 14000 12000

2.28 2.26

y = 13513x + 2.24 3009.5 R² = 0.9714 2.22

10000 8000

2.3

y = 18694x R² = 0.9985

6000

2.2

2.18

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4000

2.16

2000 0

2.14 0.2

0.4

0.6

0.8

1

Concentration (wt%)

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0

Lowfield, Diffusion Coefficient (e-9)

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18000

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High Field, normalized intensity

20000

Figure 6: S13B demonstrates a clear CMC at 0.7-0.8 wt.% from the 300 MHz (circles) data, but the TD-NMR data (diamonds) is inconclusive.

3.2. Microemulsion detection(5-20wt. %) The 300 MHz NMR instrument was also operated with the diffusion probe to analyze diffusion response in the concentration range 5-20 wt.%. This is above the CMC and below the first observed phase transition (approximately 16

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at 25 wt.%) where the literature predicts the formation of microemulsions. The surfactant S1 has two strong peaks; the diffusion procedure detects both and the water peak. The diffusion coefficients and the magnitude of current were recorded for these measurements, and detected an anomaly between 13-14 wt.%.

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Fig. 7 shows the abrupt discontinuity in diffusion coefficient for the water peak

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and a surfactants peaks. Similar behavior was observed for both surfactant

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peaks so, for brevity, only one is displayed here. This change is continuous for all values on either side, so the transition is considered reliable and not due to

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Diffusion Coefficients, 300 MHz

6.00E-08 5.00E-08 4.00E-08

2.00E-09 1.50E-09 1.00E-09 5.00E-10

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3.00E-08 2.00E-08 1.00E-08 0.00E+00

2.50E-09

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7.00E-08

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Diffusion Coefficient (water)

8.00E-08

0

5

10

15

20

-5.00E-10 water surfactant

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Concentration (wt%)

0.00E+00

Diffusion coefficient(S-2)

an artifact in measurements.

Figure 7: Diffusion coefficient is plotted over concentration. In the case of both water(circle)

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and surfactant(diamond) the diffusion coefficient undergoes a significant disruption between 13-14 wt.%

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We see this extra transition when measuring on the 300MHz for two reasons: the magnet is much more powerful and therefore sensitive, and we are able to separate the surfactant coefficient from the water, enabling visualization of more subtle species specific changes. This disruption is mirrored when analyzing the intensity of magnetization at a higher slice number, less dramatically for the surfactant peaks, but consistently for the water peak (see Fig. 8). The dramatic decrease in diffusion coefficient is likely due to some form of structuring in solution. As noted above, the diffusion coefficient is inversely related to

17

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Water, I(0) 1.8 1.6 1.4

1

T

I(0)

1.2

0.8

IP

0.6 0.4

0 0

2

4

6

8

10

12

14

16

18

20

US

Concentration (wt%)

CR

0.2

Figure 8: The initial intensity of magnetization- the I(0)- exhibits a change at 13-14 wt.% for

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the water peak, likely correlated with the same change in surfactant solution.

particle size. As such, the decrease could be related to an increase in micelle radius, or micelles existing in an aggregated state. There is no visible difference

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in the solutions at this concentration range, but further measurements were

phase transitions.

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conducted. DLS and microscopes can be applied to confirm or deny suspected

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3.3. Microscopic Characterization Results from optical microscopy can reflect the changes in the micelle struc-

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tures as the concentration increases. Using the Nomarski prisms slides the collected images were more descriptive for the structure as compared to those with and without the slide. The complete pink images represent samples that

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did not alter any of the polarized light passing through, which may be an indication that the sample did not form any structure besides micelles. As shown in Fig. 9, at low concentrations, from 5 to 10 wt.%, there were no structures detected, though these concentrations are above the CMC so the existing surfactants are micellar. The mainly pink slides continued to 20 wt.%, with the only anomaly existing in the form of sharp blue clusters. These shapes, which seem to affect the polarized light more than the lower concentrations, could be indicative of aggregated micelles in solution. Aggregates would coincide with 18

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the observed drop in diffusion coefficient between 10-15 wt.% seen in Fig. 7. At a concentration of 25 wt.%, the structures possessed texturing streaks and was very polarizing to the light. This change between concentration 20 wt.% and 25 wt.% is consistent with the 300 MHz observations were a phase transition

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between 20 and 30 wt.% was observed. The observed fine striation structur-

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ing continues to 30 wt.%. As the concentration increased to 35 wt.% the fine

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striations were replaced by pebbled structuring. These pebbles maintain, but get finer for 40 and 45 wt.%. At 50 wt.% a new checkered structure appears in several places throughout. These structures are observed also at 55 wt.%, and

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the rest of the solution appears almost porous. At 60 wt.% this new structuring

10 wt.%

25 wt.%

30 wt.%

15 wt.%

20 wt.%

35 wt.%

40 wt.%

55 wt.%

60 wt.%

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ED

M

5 wt.%

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disappears, and a more laminar/striated structure can be observed.

50 wt.%

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45 wt.%

Figure 9: Microscopic images of various surfactant concentrations

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Comparing the structures observed below 20 wt.% with those seen at 25

wt.%, a dramatic difference is apparent. The lower concentration structures are more sparsely distributed than those at higher concentration, any structures detected are smaller and dispersed. Between 30 and 45 wt.%, the appearance changes, but the transition is subtle compared to that seen between 20-25 wt.% and as such is regarded as a smooth second-order phase transition. Above 45 wt.%, the new structures appear, alongside a less cobbled, in-homogeneous solution. The highest concentration shows again a significant change between 19

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55-60 wt.%, which is seen in the physical appearance of the solutions. 3.4. DLS Effective Diameter and Diffusion Coefficients Light scattering is a technique sensitive to changes in size and concentration

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of the particles. Dynamic light scattering results reflecting these changes in

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particle size are shown in Fig. 10. The phase transitions detected from the

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NMR results are inserted to show the correlation. 5

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104 3

10

102

10

1 10

20

30

40

50

Surfactant Concentration (wt.%)

60

M

0

AN

Effective Diameter (nm)

10

ED

Figure 10: DLS diameter correlated with concentration. The apparent phase transitions observed throughout are shown on the plot as vertical lines.

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There is a consistent increase in the effective diameter with increasing concentration. The clear increase in the diameter between 10 wt.% and 15 wt.%

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correlates directly with high-field diffusion measurements. This transition seen with both high-field diffusion NMR and DLS is represented by a dotted line on Fig. 10. These related changes can be correlated with the change in the size of

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the particles and/or alteration of the structure. Kamranfar et al. reported that the micelles increased in diameter as the concentration was increased above the CMC, but before transitioning, which seems to be similar to our observations [12]. This in conjunction with the structures appearing in the microscope data supports the increasing micellar size Kamranfar et al. discussed, rather than the spontaneous formation of microemulsions. The change in the diameter between 20 wt.% and 25 wt.% is a large gap that correlates with the change in micrograph appearance observed at 25 wt.%. The 20

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data point at 35 wt.% is missing due again to solid-like behavior of the solution. At continuously increasing concentrations, the diameter increased significantly upto four times in magnitude. We argue that this change can be due to the formation of a lamellar phase where the diameter is increased and the rounded

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structure vanishes gradually. There is again another decrease in diameter be-

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measurements match well with data presented by DLS.

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tween 55-60 wt.%, and thus the drawn in transitions gleaned from the NMR

As observed qualitatively, the aggregates seem to increase in size significantly between 30-40 wt.%. This dataset serves to support and quantify that micro-

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scopic observation. Fig. 10 shows that above 40 wt.% the system diameter is relatively constant for a time, despite the visual differences noted in Fig. 1 and

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2. This calls to mind the “spaghetti” situation introduced earlier concerning cylindrical micelles, where the diameter can stay constant, but the length of the particles are allowed to grow and vary erratically. The diameter stays constant

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from 40-55 wt.% despite a change in viscosity physically observed in the solution. This change in viscosity could relate to the length of the micelles, while

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the diameter indicates that they are still present cylindrically. The difference between 55-60 wt.% with the increase in viscosity, the change in microscopic

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appearance, and the decrease in diameter are all in support of a phase change at this concentration. This is consistent with the NMR, which did not detect

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a change on the high field with the 5 wt.% concentration gap, but shows a decrease in diffusion coefficient on the low field with a 1 wt.% concentration

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gap.

3.5. Mechanical testing Rheology measurements were collected on the concentrations from 25-60

wt.% on the AR-G2 rheometer. A strain sweep was conducted to determine the critical strain and thus the linear region. Once the linear regime for strain was determined, frequency sweeps were collected under the critical strain. All of these plots can be found in the supplementary material, but are shown for 40 and 55wt.% in Fig. 11. As the concentration was swept the viscous and elastic 21

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55% G' 160

40% G"

40% G'

visco-elasticity (Pa)

140

55% G'

40% G"

40% G'

2500

visco-elasticity (Pa)

120 100 80 60 40

2000 1500 1000 500

20

0

0 0.1

55% G"

3000

1

10

0

100

200

300

400

frequency (rad/s)

500

600

700

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% strain

T

55% G"

CR

Figure 11: Strain (left) and frequency (right) sweeps for several surfactant concentrations

moduli would both change by several orders of magnitude but the dominant

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moduli would often change. This behavior is due to differences in structure. The raw elasticity values are compared for the concentration sweep as are the

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tan(δ) relationships in Fig. 12. Measurements were unsuccessful below 25 wt.%, likely because the systems are very thin and do not maintain good contact with the cone throughout the tests. Even the strain sweep at 25wt.% is not as linear

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as those at higher concentration with larger structures. Elasticity and tan(δ) values support a transition between 35wt.% and 40wt.%. 40 and 45wt.% are

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the only tan(δ) values above 1, and are considered to be less associated. Both concentrations render very good strain sweep tests, in which the G” is greater

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than the G’. 50wt.% is the only concentration to show a crossover in the frequency sweep examined, it switches from elastic dominant to viscous dominant

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at 10 Hz. Otherwise all other concentrations are elastic dominant in both the strain and frequency sweeps, though the values fluctuate considerably throughout. The lowest tan(δ) values correlate with the thickest most jelly-like solutions

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at 35 wt.% and 60wt.%. A strain sweep is applied to learn the linear regime for a system, which is below the critical strain. The critical strain and complex modulus were calculated from the strain sweep measurements and plotted against the concentration sweep. These specific values fluctuate inversely from each other, but the product of the two provides a good correlation with the yield stress, see Eq. 5 [38]. τy = G ∗ γy

22

(5)

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0.1Hz

10000

1Hz

10Hz

0.1Hz

10

1Hz

10Hz

1000 20

G"/G'

25

30

35

40

45

50

55

60

65

0.1

10

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G'

1 100

0.01

1 30

40

50

Surfactant Concentration

60

Surfactant Concentration

70

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20

CR

Figure 12: Elasticity (left) and tan(δ) (right) sweeps for several surfactant concentrations. These are provided for 0.1, 1, and 10 Hz

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Yield stress is the stress at which point the system loses ability to return to its original shape, as beyond it it becomes more plastic. It represents the force

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needed to start pumping the fluid. Both the complex modulus and the yield stress are plotted in Fig. 13. The yield stress calculations support the transition

6000

20000

4

18000

3

4000

2.5 2

2000 1000 0 20

30

40

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3000

50

60

1.5 1

Critical Strain (%)

M

3.5

5000

G*

4.5

Yield Stress (@1Hz)

7000

0.5

16000 14000 12000 10000 8000 6000 4000 2000

0

0

70

20

30

40

50

Surfactant Concentration

60

70

PT

Surfactant Concentration

Figure 13: Critical Strain and G* (left) and yield stress (right) sweeps for several surfactant

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concentrations. Provided for 1 Hz

between 25-30wt.%, 35-40wt.%, and 55-60wt.% seen throughout. All critical

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strain values are such that they suggest sterically stabilized systems.

4. Conclusions The experimental data are summarized in Table 1; the results indicate that NMR can be used to detect secondary phase transitions. The processed high-field NMR data show a slight deviation from linearity between 20-25 wt.%, but this change is not dramatic as it is between 25-30 wt.%.

23

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Table 1: Summary of Surfactant observations with various methods

60 MHz

Microscpe

concentration

Observation

5 wt.%

free flowing

+linear

-linear

–

10 wt.%

free flowing

+linear

-linear

–

15 wt.%

free flowing

+linear

-linear

20 wt.%

free flowing

+linear

-linear

25 wt.%

flows

slight slope

-slope

change

change

+linear

thicker

NOT linear

35 wt.%

thin jello-like

–

40 wt.%

does not

–

thick, jello-

highest peak

like,bubbles

so far

thin, flows

55 wt.%

thin, flows

60 wt.%

very thick

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50 wt.%

M

45 wt.%

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move

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30 wt.%

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300 MHz

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Visual

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Surfactant

– –

fine striation

striated

+linear

pebbled

–

pebbled

much lower

very fine pebbles

-nonlinear

+nonlinear

nonhomogeneous

-nonlinear

+nonlinear

nonhomogeneous

–

lowest

striated

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bubbles

NMR data from Fig. 2 predicts phase changes between 20-30 wt.%, supported by a difference in viscosity between the two solutions. It also predicts a difference

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between 30-45 wt.%, which is also observed in the difference in viscosity. The samples between were not collected due to the solid-like, highly viscous, behavior

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of those solutions. The signal for 45 wt.% spikes up, showing the highest peak on the calibration curve, and from there the last peaks collected continue to decrease with no linear trend. These responses in the 45-55 wt.% region show no conclusively linear slope, in contrast with the previous same phase systems display, as seen below 20 wt.% and either side of a CMC point. This is likely related to the gradual nature of secondary phase transitions. However, the fact that the NMR spectra cannot be collected at certain points seem indicative of its own transitions. These claims are also supported by the change in peak shape

24

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shown in Fig. 2, which Fontell indicated as related to phase change. It would be interesting to investigate the direction of the slopes elicited, as perhaps the changes are related to the transitions occurring. These points were collected at concentration gaps of 5 wt.% to assess as large a concentration gap as reasonably

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possible. These jumps, with the select missing points, leave questions about

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linearity. If there were more points assessed in between, it would provide more

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information about the curve, and when it changes direction. Given further experimentation, slope changes could be directly related to the shapes existing or the ionic charge of a surfactant. Testing this would require finer analysis,

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and a method to determine the shapes the surfactant is forming. The TD-NMR also shows linear behavior up to 20 wt.%, with a slight, but

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noticeable change between 20-25wt.%. After 25 wt.%, the diffusion coefficients almost plateau, but do increase slightly, showing a clear difference between 20-30 wt.% here as well. Above 35 wt.%, the diffusion coefficient drops dramatically,

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again related to the increase in viscosity shown after 35 wt.%. Samples at 50 and 55 wt.%. concentrations show a slight increase, which relates as they do flow

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more easily than do the samples both directly lower and higher concentrations. The lowest diffusion coefficient, which was somewhat unexpected, was measured

PT

at 60 wt.% concentration, as 35 wt.% is the most viscous. Phase transitions are depicted as any time the slopes change direction, which is seen in both NMR

CE

instruments between 25-30 wt.%, 30-45 wt.%, and 45 wt.% and everything above it. This all matches with the transitions observed in Fig. 2 and in the rheology results.

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Both NMR instruments note a slight change between 20-25 wt.%, also it is

noticed in the microscope data and DLS data and processed rheology data. This could be related to micellar packing, but the difference between the two may be more related to mobility of the solution. 25 wt.% could be the concentration for which micelles are touching each other rather than moving completely uninhindered in solution, or the concentration at the brink of the transition. This is not to say they lose mobility, but they are forced to interact with one another and put pressure on each other, a requirement to change shape. The difference 25

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between 25-30 wt.% on all measurements is more dramatic than that between 2025wt.%, in conclusion this difference is related to a phase transition. This change in shape could arise from a spherical → cylindrical or spherical → cuboidal phase transition. With the way that the diameter plateaus but the viscosity and NMR

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data continue to fluctuate from 40-55 wt.% it seems likely that cylindrical rod-

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like micelles are formed, and the difference in viscosity is related to the change

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in length. The decrease in diameter and diffusion coefficient and accompanied increase in yield stress indicate another phase change from 55-60 wt.%. Overall, the NMR data agree with the yield stress transitions at every turn,

US

and with the combined DLS and microscopic observations. It also completely agrees with the noted differences seen in NMR peak shape in Fig. 2. The only

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difference picked out by NMR that was not seen in sample preparation was the difference between 20-25 wt.%, but this was supported by both DLS, microscope, and mechanical measurements, and is thus believable, if a minor change in all

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cases. It could indicate the beginning of the transition which assuredly occurs between 20-30 wt.%. The location of the phase changes indicated by high-field

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NMR is supported by the changes observed in the microscope, known surfactant behavior, and the diameter behavior observed. The low-field NMR showed that

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it was not sensitive enough to detect the CMC, but that it correlates well with observed higher concentration transitions.

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Microemulsion detection was explored, with a clear change in diffusion coefficient existing between 13-14 wt.% in the high-field diffusion experiments. There was a difference noted between the diameter behavior in DLS and the

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microscopic images above and below these concentrations. There is no change here observed on the other NMR points acquired. This transition could relate to the spontaneous formation of microemulsions, however the presence of smaller molecules would likely lead to an increase in diffusion coefficient, where we see a decrease. This seems to relate more closely with an increase in micelle size, as predicted by Kamranfar et al. as concentration continues to increase beyond CMC but before a phase transition [12]. The microscope data seems to hint that instead of increasing individual micelle size, this concentration indicates 26

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formation of aggregated micelles in solution, which could also cause a decrease in diffusion coefficient. Regardless of the actual transition occurring, the data supports itself in that something is happening, but likely not yet a secondary phase transition or microemulsions.

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Further work could investigate measuring smaller changes in surfactant con-

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centration, instead of 5 wt.% jumps, in an attempt to fill in the gaps in the

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NMR data. This would fill in the curves and provide more indication as to the actual slope value, as there are places where there is minimal information about the NMR protocol slope. It would also be interesting to note if the slope

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changes differently depending on the shape transition occurring.

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5. Conflict of Interest

Authors declare there are no conflicts of interest to disclose regarding this

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publication. This research did not receive any specific grant from funding agen-

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cies in the public, commercial, or not-for-profit sectors.

6. Acknowledgements

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Authors would like to thank Dr. Alexander Goroncy for his assistance de-

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veloping the protocol for the high-field diffusion NMR probe.

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Highlights • NMR technique to detect second-order phase transitions at high surfactant concentration

T

• Transitions confirmed through alternative techniques including dynamic

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light scattering

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• Low-field NMR cannot detect first-order transitions, but can detect second-

AC

CE

PT

ED

M

AN

US

order ones

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Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13