Challenge to Reconcile Experimental Micellar Properties of the CnEm

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B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

The Challenge to Reconcile Experimental Micellar Properties of the CnEm Nonionic Surfactant Family William C. Swope, Michael Andrew Johnston, Andrew Ian Duff, James L. McDonagh, Richard L. Anderson, Gabriela Alva, Andy T. Tek, and Alexander P. Maschino J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11568 • Publication Date (Web): 18 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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The Journal of Physical Chemistry

The Challenge to Reconcile Experimental Micellar Properties of the CnEm Nonionic Surfactant Family William C. Swope,∗,† Michael A. Johnston,‡ Andrew Ian Duff,¶ James L. McDonagh,§ Richard L. Anderson,¶ Gabriela Alva,† Andy T. Tek,† and Alexander P. Maschinok †IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA ‡IBM Research Ireland, Dublin, Ireland ¶STFC Hartree Centre, SciTech Daresbury, Warrington, WA4 4AD, UK §IBM Research UK, SciTech Daresbury, Warrington, WA4 4AD, UK kDr. T.J. Owens Gilroy Early College Academy, 5055 Santa Teresa Blvd, Gilroy, CA 95020, USA E-mail: [email protected]

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Abstract We wished to compile a data set of results from the experimental literature to support the development and validation of accurate computational models (force fields) for an important class of micelle-forming nonionic surfactant compounds, the poly(ethylene oxide) alkyl ethers, usually denoted Cn Em . However, careful examination of the experimental literature exposed a striking degree of variation in values reported for critical micelle concentrations (CMC) and mean aggregation numbers (Nagg ). This variation was so large that it masked important trends known to exist within this family of molecules, thereby rendering most of the literature data to be of limited utility for force field development. In this work we describe some reasons for the wide variability in the experimental literature, and we present a set of CMC and aggregation number data for twelve Cn Em compounds that we feel is appropriate to use for the construction of and validation of computational models. The CMC values we selected are from the existing experimental literature and represent a carefully chosen and consistent subset that conveys important trends seen by many of the experimental studies. However, for a corresponding and consistent set of weight averaged aggregation numbers, we needed to perform new dynamic light scattering (DLS) experiments. The results of these experiments were carefully analyzed to obtain not just mean aggregation numbers, but also the underlying micelle size distribution functions. Several trends observed in the CMC and Nagg observables are highlighted and serve as challenges for developers of force field and simulation methodology. The analysis of the DLS experiments accounts for the fact that a broad distribution of micelle sizes exists for many of these compounds, and that one must be careful to use the appropriate weighted averages (e.g., mass weighted versus number weighted averages) in comparing results from different types of experiments and in comparing results from experiments with those from simulations.

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1. Introduction Surfactants are a class of amphiphilic molecules that play an important role in science and industry. Uses for surfactants vary widely and include key components for soap, detergent and toothpaste formulations, emulsifiers and stabilizers for food products, and even aircraft deicing agents. In cellular biology, surfactants can be used to break up cell membranes and in the pharmaceutical industry they are used to stabilize drug formulations and to facilitate drug delivery. Surfactant molecules have solvophobic and solvophilic components and a key feature is their ability to form aggregates in solution that are stabilized by solvophobic interactions: the aggregates are structured with the solvophobic components of the molecules clustered together to avoid solvent and the solvophilic components organized to be in contact with solvent. The smallest of these structures are the spherical micelles, which form under dilute conditions, but under various other thermodynamic conditions (e.g., solvent composition, higher surfactant concentration, temperature, salt content, pH) larger more complex structures can form such as micellar rods, long linear or branched wormlike micelles, vesicles, and even large, possibly transient, supra-micellar aggregates. At even higher concentrations many surfactants form interesting phases with long range lamellar or hexagonal order. As one of the simplest self-assembling structures, spherical micelles have received a large amount of scientific scrutiny. Studies have attempted to determine the structural features (size and shape) of micelles as well as the lowest concentration in solvent at which they begin to form, and the thermodynamic and molecular attributes that control these micellar characteristics. Since micelles are dynamic structures, the kinetics of micelle equilibration and the determination of time scales for structural reorganization are also of keen interest. Techniques for studying micelles have included static light scattering (SLS), measurement of the diffusion constant by dynamic light scattering (DLS) and nuclear magnetic resonance (NMR) methods, surface tension (ST) measurements, careful volumetric measurements, osmometry, titration calorimetry, small angle neutron scattering (SANS), measurements of 3



sedimentation rates, and fluorescence spectroscopy performed on dyes included with the solvent-surfactant mixture. The two most basic micellar properties are the surfactant concentration at which micelles first begin to form, known as the critical micelle concentration (CMC), and the average number of surfactant molecules in the micelles, known as the mean aggregation number (Nagg ). It is important to point out, however, that in spite of the long history of experimental measurements, for many surfactants there is often little consensus, and sometimes disturbing conflict, about even these two basic attributes. This situation is due to several factors. First, for many surfactants, properties can depend very sensitively on conditions such as temperature, compound purity, and the presence of additives such as salt in the solutions, potentially leading to difficulty to obtain reproducible measurements. Second, the various experimental methods employed to study micelles are actually measuring different observables and with different degrees of sensitivity. For example, one must exercise caution in comparing mean micelle sizes obtained from static and dynamic light scattering experiments, since the former measures an attribute related to the micelle spatial extent (usually expressed as radius of gyration, RG ), and the later measures a dynamical one related to the rate of diffusion (hydrodynamic radius, RH ). Even methods thought to be measuring the same type of property often give inconsistent results, such as diffusion measured by DLS versus NMR, or colligative properties measured by vapor pressure versus osmometry. Third, metrics of actual interest (e.g., CMC and Nagg ) have to be deduced indirectly with the use of numerous assumptions. One assumption often used, for example, in interpreting experimental results to obtain micelle sizes is that all the micelles in a sample are spherical and/or uniform in size. However, techniques such as DLS have shown that for many surfactants there may actually be a broad distribution of micelle sizes and shapes within each sample, suggesting that such assumptions are not supported and could lead to erroneous conclusions. Finally, due to the physics involved in the measurement techniques, different experimental methods necessarily produce different kinds of weighted averages over these size distributions (e.g., number aver-

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aged, mass averages, z-averaged). This creates difficulty, for example, preventing the direct comparison of average micelle sizes from light scattering (mass average), sedimentation experiments (z-average), and osmometry (number average). If the micelle sizes were uniform or very narrowly distributed, these measurements could in principle be numerically similar, but in fact such measurements should be expected to be different. Some of these complications were highlighted in a compilation 1 of aggregation numbers reported for the C12E6 surfactant compound. This a member of the class of alcohol terminated poly(ethylene oxide) alkyl ethers. The aggregation numbers reported at 25 ◦ C for this nonionic surfactant were 103 (vapor pressure), 555 (sedimentation), 400 (SLS), and 375 (membrane osmometry). In light of these issues, one would hope computer simulations could be effectively used to study micelle related phenomena and to aid in the interpretation of conflicting experimental results. Two issues conspire to make this approach difficult. The first issue is that these simulations are still computationally very demanding. This is because micelle formation and equilibration of the aggregation number distribution takes place on microsecond to millisecond time scales 2 , putting it well beyond the reach of brute force atomistic simulation methods. Also, micelles form under very dilute conditions, typically near 1% surfactant, by weight, so simulations at realistic micelle-forming concentrations must have hundreds of times more molecules of solvent than surfactant, and must include a prohibitively large number of particles if one hopes to observe and characterize even a small ensemble of micelles. Although attempts 3–11 have been made with varying degrees of success, all atom simulations are currently too expensive for a thorough investigation of micellar behavior. Some of the computational demand can be addressed by the use of coarse grained modeling approaches such as with united atom or beaded string models such as used with dissipative particle dynamics 12–22 (DPD). These approaches employ models with reduced complexity in the number of particles, and smoother interaction potentials, both of which allow larger dynamical time step sizes in the simulations. The reduced number of particles per molecule allows much

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larger simulations to be run. Therefore, although subject to the approximations introduced by the use of coarse grained models, simulations of micellar phenomena are becoming computationally tractable. Methods that are alternatives to brute force large scale simulations of surfactant and solvent mixtures have also been formulated for computing micellar properties. These allow the use of potentially smaller and shorter simulations, such as in the direct computation of micelle formation free energies 23 to obtain CMC estimates and micelle size distributions. These methods are very promising. The second issue that presents challenges to computer modeling of surfactants is the lack of accurate and validated force field parameters. Some efforts 24–26 have attempted to address this in the context of coarse-grained simulations, but a generally accepted set of parameters for molecules of interest is lacking. Such a set of parameters would have to depend on the nature of the molecule, the degree of coarse graining, and on the number of types of sites (number of bead types) used to represent the molecule. Furthermore, there are a number of functional forms available to describe interactions between coarse grained sites, each with its own set of parameters. At best, any such description might be limited to a small set of molecules, a specific range of thermodynamic conditions such as concentration, density, temperature and solvent, and it may provide an accurate description for only a limited set of properties and phenomena. In spite of all these caveats and potential limitations one would hope that a force field developed to accurately reproduce experimental observables for a range of related physical properties and for a suitably small set of closely related molecules should be useful for the prediction and study of these and similar properties for other similar molecules. Obviously, the first requirement for a force field development effort is a data set of relevant experimental data. The work described in this paper is meant to help address this issue. We chose a class of chemically simple, yet interesting and well-studied, surfactants that form micelles in aqueous solution. Surfactants to be used with water as the solvent are often classified as ionic (with either anionic or cationic hydrophilic “head” groups) or nonionic.

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One of the simplest and most studied class of nonionic surfactants are the poly(ethylene oxide) alkyl ethers. These molecules are simple linear diblock copolymers with an aliphatic carbon chain as the hydrophobic block joined to an alcohol terminated polyethylene oxide chain as the hydrophilic block, H(CH2 )n (OCH2 CH2 )m OH, often denoted Cn Em . The Cn Em family of compounds is a good choice for this effort for a number of reasons. In spite of their chemical simplicity this family exhibits a wide range of interesting micellar behaviors, and a large body of experimental results exists, going back almost 60 years. Depending on temperature and concentration and on the lengths of the alkane and ethylene oxide blocks, evidence has been reported for spherical micelles, rods, worm-like micelles, and the formation of very large supra-micellar aggregates. These molecules exhibit a lower critical solution temperature (LCST) above which the solution phase separates into waterrich and water-poor phases, in a liquid-liquid demixing phase transition. The solution goes from transparent to cloudy (cloud point). The mechanism for this transition is related to the thermally induced breakup of hydrogen bonding interactions between the hydrophilic groups and water, providing an entropic gain from increased flexibility, and a consequent decrease in the hydrophilicity (reduced solubility) of the ethylene oxide region. This transition is seen in many other polymer-solvent mixtures and has been a topic of intense study, with the Cn Em compounds serving as models materials. From the modeling and simulation perspective, this class of compounds has features that make them computationally tractable. Coarse grained simulations of these molecules usually represent them as a linear chain of interaction sites with only two types of sites (a hydrophilic type and a hydrophobic type). Finally, since the molecules are nonionic, the sites are usually treated in simulations as uncharged and the interactions are, therefore, very short ranged, allowing large and long simulations to be performed.

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Choice of molecules and literature CMC values For this study a set of molecules (Table 1) from the Cn Em family was selected that provides a range of hydrophobic and hydrophilic chain lengths and a consequent range of experimental CMC and aggregation number experimental observables for force field development and testing. The table conveys the wide range of CMC values (all measurements at a temperature of 25 ◦ C) reported in the experimental literature for each compound. The range reflects the effect of using different and evolving experimental methods, variation in practice among different research groups, different degrees of sample purity, and other variables. (See Supporting Information for sources and a discussion of methods.) However, general trends emerge when one considers subsets of the experimental data that use a common experimental approach. For example, the CMC decreases by about an order of magnitude with each addition of two carbon atoms to the hydrophobic chain. (The observation that the log of the CMC is linear in the hydrophobic chain length is also known as a Stauff-Klevens 27,28 relationship.) In contrast, extending the hydrophilic chain, with fixed hydrophobic chain length, results in a slight increase of the CMC. The amount of this increase is less with increasing hydrophobic chain length. One would hope that a force field could capture these general trends. Therefore, CMC values were selected from the experimental data set to be used as suggested target values for the purposes of force field optimization and validation, and these are reported in Table 1. In general this selection of target values favored experiments that measured surface tension. The rationale for the choices made in selecting the target CMC values is described in detail in Supporting Information. Two target CMC values (indicated by asterisks) each are proposed for C12E6 (0.072 mM, 0.082 mM) and C12E8 (0.084 mM, 0.109 mM), but only the larger ones are shown in the table. We note that surfactant concentrations reported in the literature are expressed in a variety of units such as molarity, weight percent, and mole fraction. In most cases these have been converted to molarity (millimole, mM) ignoring volume changes on mixing, assuming the experimental density of water (0.997040 g/mL at 25 ◦ C), and densities for pure surfactant 8


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Table 1: Properties of molecules used in this study Compound C6E3 29–33 C6E4 31,33–37 C6E5 30,32–35,37,38 C8E4 31,32,39,40 C8E5 31,40–42 C8E6 29,30,41,43 C10E5 35,36,41 C10E6 29,36,41,42,44–46 C10E8 41,42,44,45,47–50 C12E5 31,35,36,41,51–55 C12E6 29,31,36,41,42,53,55 C12E8 41,42,47–49,54–57

Literature Target CMC, mM mM 68-105 100. 72-106 106. 75-115 113. 6.5-11.7 8.0 6.0-11.0 9.0 7.6-10.8 9.9 0.68-1.00 0.86 0.46-0.95 0.90 0.28-1.15 1.00 0.035-0.071 0.064 0.060-0.087 0.082* 0.056-0.109 0.109*

CMC wt% 2.35 2.96 3.65 0.246 0.316 0.392 0.0327 0.0381 0.0512 0.00261 0.00371 0.00589

cc mM 624 592 230 270 310

37 55

Tc Tcloud ◦ ◦ C C 46.0 45 66.1 75 40.8 40 61.7 60.4 74.4 74 44 85 32.0 31.7 51.3 52 78

ρ g/mL 1.030 1.044 1.054 1.010 1.023 1.034 0.998 1.010 1.028 0.978 0.990 1.010

L nm 1.81 2.16 2.52 2.42 2.77 3.13 3.02 3.38 4.09 3.27 3.63 4.34

from a fit 58 to experimental density data at 25 ◦ C, ρn,m = (14n+44m+18)/(18.3n+39.13m) (g/mL). Table 1 shows the densities from this fit for the molecules used in this study. Table 1 also has critical concentrations and temperatures (for LCST behavior) from Schubert 31 and cloud temperatures corresponding to surfactant concentrations of 10 g/L taken from a compilation 58 of experimental results by Berthod. The cloud temperatures and the critical concentrations and temperatures are very sensitive to the hydrophilic chain length. These properties are relevant to the selection of an experimental data set for force field tuning and validation since it is known that these surfactant materials can exhibit unusual behavior even 20 ◦ C below their cloud temperature. Unless it is a design goal of the resulting force field to be accurate for the study of this sort of behavior, such data should probably not be used in the training set. We note that our DLS experiments performed on C12E5 at 25 ◦ C, only 7 ◦ C below the cloud temperature of this compound, showed evidence of large supra-micellar aggregates, suggesting the possible onset of phase separation. This affected the analysis of the DLS results for this compound and is discussed in detail in Supporting Information. The table also has approximate molecular lengths for extended (all trans) conformations of these molecules, approximated as L = 0.1258n+0.3552m−0.0111 (nanometer). Extended 9



molecular lengths are included in the table since they provide an approximate scale for the size of micelles, generally expected to have diameters in a range between this length and perhaps three times this length.

Literature Nagg values Unfortunately, after careful examination of the literature in search of consistent micelle size data for these molecules (Table 2), it was determined that new experiments were required to produce a data set appropriate for force field development. In fact, the results reported in the literature for Nagg showed much less consistency than the results reported for the CMC. Some of the challenges associated with generating this data have already been noted, and may account for the wide disparity of results seen in the literature. These include the thermal sensitivity 1 of size measurements even under conditions apparently far from cloud temperatures, sensitivity to impurities 31 , extended time to attain equilibrium after standard experimental procedures such as filtering, and the fact that different types of experiments produce averages over the cluster size distribution 1 with different types of weighting. For some of the compounds the micelle size distributions we produced show strong dependence on surfactant concentration, suggesting that rods, wormlike micelles, or other structures might be forming and becoming dominant over spherical micelles above some concentration range. Our results also suggest the possibility that there may be multiple sizes and shapes coexisting at equilibrium, resulting in multimodal particle size distributions, in which cases reporting a single aggregation number averaged over the entire distribution may not even be meaningful. Clearly, what is needed for force field development and validation is micelle size data produced consistently across all the compounds of interest, at sufficiently low concentrations that spherical micelles are expected to be the dominant species, and with an experimental technique capable of obtaining information about the micelle size distribution even if other types of aggregates might be present. 10


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Table 2: Aggregation numbers from the literature Compound C6E3 30,32,33,59 C6E4 33 C6E5 32,33,38,59,60 C8E4 32,61–63 C8E5 59,64–68 C8E6 43,69,70 C10E5 59,71 C10E6 67,69–71 C10E8 44,50,67,72 C12E5 1,66,73,74 C12E6 1,43,65,70,73,75–83 C12E8 1,57,61,65,74,83–88

Literature 24-57 28 21-55 23-147 17-90 30-41 17-172 66-105 46-70 112-4460 100-555 39-159

The experimental data set presented in this work consists of the CMC values obtained from the experimental literature (described above), but required new dynamic light scattering experiments to develop a consistent set of micelle aggregation number results against which force field optimization and validation could be performed. The structure of this paper is as follows. Section 2 describes the dynamic light scattering experiments that were performed and how the results were processed to produce mean aggregation data. Section 3 provides the aggregation number results, and section 4 provides concluding remarks, including an overview of important experimental trends a computational model should be able to reproduce.

2. Methods We chose to perform DLS experiments on our set of compounds to obtain a body of consistent information about the micelle sizes. DLS 89 is a light scattering technique capable of providing detailed information about micelle size distributions in a liquid sample and, therefore, should be quite useful to understanding micelle behavior. In DLS, also known as photon correlation spectroscopy (PCS), a high intensity laser light source is directed at a dilute solution of scattering objects, such as molecules or molecular aggregates, and the scattered light is detected with a sensitive (photomultiplier) light detector and its intensity recorded with high 11



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temporal resolution. The intensity-intensity time correlation function of the detected signal, called a correlogram, is computed, which exhibits a characteristic decay with increasing lag time. (See left graph in Figure 1.) The rate of decay of this correlation function can be related to the diffusion constant of the scattering objects, with larger, more slowly diffusing objects contributing more slowly decaying components to the correlation function. An ensemble of objects with identical diffusion constants would produce a simple exponentially decaying correlation function with a decay rate that is proportional to the diffusion constant. The analysis of DLS experimental correlation functions by a protocol endorsed by an international standards committee 90 produces a cumulant expansion that can give a mean size and a variance. However, this approach gives useful information only if the size distribution is unimodal and rather narrow. This is often not the case for surfactant solutions at micellar concentrations, since there can be micellar aggregates as well as larger objects such as vesicles present. Even if these larger objects are not present, there can be a range of micellar sized structures and shapes that preclude the cumulant approach. Alternatively, through a nonlinear fitting procedure, the correlation function can be resolved to obtain the fraction of the total correlation signal contributed from scatterers as a function of their diffusion constant. This procedure is equivalent to an inverse Laplace transform of a function exhibiting multiexponential decay and is implemented as part of the software associated with DLS instrumentation using an algorithm 91 known as CONTIN. (See solid curve in right graph in Figure 1.) The Stokes-Einstein formula provides a relationship between aggregate sizes and diffusion constants given by the following:

D=

kB T 6πηRH

(1)

where D is the diffusion constant, kB is the Boltzmann constant, T is the temperature, η is the solvent viscosity, and RH is the hydrodynamic radius of the diffusing particles. This

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Figure 1: Example correlogram (left) and micelle size distributions (right) produced from a DLS experiment on C12E6. The right graph shows a distribution indicating the fraction of the scattered light intensity from particles of different sizes (solid curve) and, from the same data, a distribution indicating the fraction of the total mass of micellar material from particles of different sizes (dotted curve). The difference in these curves reflects the fact that larger particles scatter much more light than smaller one. The mean particle diameter averaged over the solid curve (intensity-average diameter) is 10.7 nm, whereas averaged over the dotted curve (mass-average diameter), it is 7.3 nm. equation relates the radius of a spherical object to its diffusion constant in a solvent of known viscosity. However, if the diffusing object is nonspherical, the relationship serves as an operational definition of its hydrodynamic radius in terms of a measured diffusion constant. That is, the hydrodynamic radius is defined as the radius of an ideal sphere that diffuses with the same diffusion constant as the particle of interest, even if that particle itself has a complex nonspherical shape. With the use of the Stokes-Einstein relationship, the amount of the correlation function due to scattering from particles having a particular diffusion constant can be expressed as a scattering intensity-based size distribution, which provides the fraction of the total light intensity scattered from the ensemble of particles as a function of their hydrodynamic radius. (See solid curve in right graph of Figure 1.) From this intensity-based size distribution function, one may compute an intensity weighted mean size, hRH iI , and this is sometimes reported. However, scattering intensity increases as the sixth power of the characteristic size of the scattering object, so such an average weights the largest particles in the distribution much more than the more prevalent but smaller ones. To allow comparisons of light scat-

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tering results with other types of experiments and with simulation results, one is often more interested in a mean size that is mass-weighted or number-weighted over the distribution, rather than weighted by the intensity of the scattered light. If one has a measure of the refractive index of the scattering material, one can account for the strong dependence of the scattering on the particle size and transform an intensity based size distribution into a volume-based (or, equivalently, mass-based) size distribution. This gives the fraction of the total mass of the material that is visible to the instrument as a function of the hydrodynamic radius. (See dotted curve in right graph in Figure 1.) The vendor-supplied software associated with the instrument used to perform the DLS measurements reports this kind of information and it is the basis for computing mass averaged particle diameters and mass averaged mean aggregation numbers. Analysis of simulation data typically generates a tabulation of the number of aggregates observed in a simulation as a function of the number of molecules making up the aggregate. To make contact with simulation results, one might wish to process the experimental size distribution function to produce a mass based size distribution expressed as a function of aggregation number rather than as a function of hydrodynamic radius. With a few assumptions, this is easily done by deriving a relationship between the hydrodynamic radius of the aggregate and the aggregation number. To do this we assume the diffusing object consists of some number of surfactant molecules with some number of strongly associated water molecules that essentially diffuse together as a whole. Previous work 33 has shown that under this assumption the number of associated water molecules can be related to the number of ethylene oxide units in each molecule. We will assume in what follows that there are nW water molecules per ethylene oxide unit, so that for each Cn Em surfactant molecule, there are m nW water molecules. With this kind of assumption the relationship between the hydrodynamic radius and aggregation number is as follows: NS NS mnW 4 3 πRH = + 3 ρS ρW 14


(2)

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where ρS and ρW are the bulk number densities of pure surfactant and water, respectively, and NS is the surfactant aggregation number to be associated with molecular aggregates having a hydrodynamic radius of RH . The first term on the right gives the volume due to surfactant and the second gives the volume due to water. One might consider using partial molar volumes for the surfactant at micellar concentrations in this expression instead of the number density of pure surfactant. However, this is expected to make only a small difference, and the use of the pure surfactant density is consistent with ignoring the volume changes on mixing, as was assumed in converting weight percent to molarities, as mentioned above. One can rearrange this expression to produce the following:

NS

4 3 πR = 3 H

1 mnW + ρS ρW

−1 (3)

There has been much discussion in the literature about what value one should use for nW , and whether it should be the same for different molecules and constant with respect to temperature or other conditions. Early work 33 on the C6Em series suggested that nW ≈ 4, and we have used that value consistently for all the compounds and conditions in this study. Using the same data as in the previous figures, and employing this relationship, one may produce the result shown in Figure 2, which shows a mass-weighted particle size distribution as a function of the aggregation number. From this distribution, one may compute a massweighted mean aggregation number, hNagg iW , which works out to be 207 for this example. We emphasize that this procedure is different than computing an aggregation number from the mass weighted mean particle diameter of 7.3 nm. Use of Eqn. 3 with this value for the diameter produces a value of 137, which is not the correct mass weighted aggregation number. The difference in these two approaches reflects the fact that the C12E6 micelles are not uniform in size, but exist with a broad distribution of sizes. These two approaches to computing an aggregation number represent averages of different quantities over the micelle size distribution. One value (207) is computed from averaging the

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Figure 2: Example size distribution expressed as a function of the number of surfactant molecules in the aggregate. The curve gives the fraction of the total mass of micellar material from aggregates of various sizes. This graph is based on the same DLS experiment on C12E6 as was used to produce the previous figures. This function is normalized to integrate to unity. The mass weighted mean aggregation number is 207. cube of the diameter over the measured diameter-based size distribution, since the aggregation number is proportional to the cube of the diameter; the other (137) is based on the cube of the average of the diameter itself. One might ask if these two values have a statistically meaningful difference, since it could be that the distributions are sufficiently narrow and the uncertainties are so large that such a distinction does not matter from a practical perspective. After averaging data from 65 independent measurements of this type, one obtains the values in the second table of the Results section, which indicate that the mass weighted average hydrodynamic diameter is hDH iM = 7.08 ± 0.14 nm. The value of 0.14 nm is one standard error of the mean produced assuming the 65 measurements of the diameter are independent. Similarly, the mass weighted mean aggregation number is hNagg iM = 186 ± 11. However, if we use the mass weighted hydrodynamic diameter to compute an aggregation number we obtain 126 ± 7. This later value is smaller, and more precise than the other one, reflecting the fact that it was produced in a way that places greater weight on the more numerous but smaller micelles. However, it is not comparable to the type of micelle average aggregation number one usually computes from a simulation, where aggregation numbers are based on the number of surfactant molecules making up the micelle. Moreover, the two values differ by 60, which is statistically significant. Further discussion of this is provided in 16


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the Supporting Information.

3. Results For each of the twelve compounds of this study, DLS experiments were performed over a range of about 10 surfactant concentrations, typically from near to the target CMC up to about 50 times the target CMC. A single DLS experiment can be performed in a few minutes, but experiments were repeated every 10 minutes typically about 100 times and results were checked for drift, suggesting inadequate equilibration, and for fluctuations, suggesting dust, air bubbles or large aggregates. (Supporting Information includes a more detailed description of the sample preparation and other aspects of the experimental protocol and data analysis.) Resulting distribution functions were averaged and used to compute micelle size distributions, mass averaged mean micelle diameters, and mass averaged mean aggregation numbers. The long runs and averaging were particularly important for experiments on samples at very low concentrations, some of which were near the detection threshold of the instrument. For each compound the mass averaged particle diameters were plotted against the total surfactant concentration (see Supporting Information) and a range of concentrations was identified as producing what were hoped to be spherical micelles. We refer to these as the micellar concentrations. These were concentrations where the particle diameter was (1) relatively insensitive to the surfactant concentration, and (2) larger than the extended length of the molecule but smaller than three times this length. (See Table 1 for molecule lengths.) At concentrations higher than this, the aggregate size generally increased, suggesting the formation of larger micelles, possibly supra-micellar aggregates of micelles, rods, worms, or other nonspherical shapes. Tables 3 and 4 summarize the experimental micelle size results. These include the concentrations used and the mass averaged micelle diameters, hDH iM , and mass averaged aggregation numbers, hNagg iM . The concentrations are expressed in molarity and weight percent

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Table 3: Target size results for C6Em and C8Em Compound C6E3 C6E4 C6E5 C8E4 C8E5 C8E6

Conc, mM 128. 171. 270. 360. 266. 354. 18.2 24.2 33.0 55.0 29.7 49.5

Conc, wt% 3.01 4.01 7.51 10.01 8.56 11.4 0.558 0.744 1.16 1.93 1.17 1.96

Conc/CMC ncut 1.28 7 1.71 2.55 9 3.40 2.35 7 3.14 2.27 8 3.03 3.67 7 6.11 3.00 9 5.00

n99 303 471 242 242 130 130 353 852 191 461 256 256

hDH iM , nm 4.54(0.02) 4.65(0.03) 4.000(0.004) 4.02(0.01) 3.747(0.003) 3.719(0.008) 5.56(0.08) 5.94(0.04) 5.01(0.03) 5.10(0.08) 4.483(0.005) 4.64(0.02)

hNagg iM 81(1) 100(2) 46.3(0.1) 47.2(0.6) 31.8(0.1) 30.5(0.3) 110(4) 153(2) 65(1) 77(3) 44.7(0.4) 54(1)

Table 4: Target size results for C10Em and C12Em Compound C10E5

C10E6

C10E8

C12E5

C12E6

C12E8

Conc, mM 4.29 8.59 17.2 4.50 9.00 18.0 4.19 5.24 10.47 1.92 2.56 3.20 1.78 2.66 3.55 6.22 8.88 2.18 3.27 4.36 5.45

Conc, wt% 0.163 0.326 0.652 0.191 0.381 0.763 0.215 0.268 0.536 0.0784 0.105 0.131 0.0803 0.120 0.161 0.281 0.401 0.118 0.177 0.236 0.295

Conc/CMC ncut 4.99 9.99 10 20.0 5.00 10.0 9 20.0 4.19 5.24 7 10.47 30.0 40.0 10 50.0 21.7 32.4 43.3 8 75.9 108.3 20.0 30.0 11 40.0 50.0

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n99 681 1643 2552 245 245 592 302 195 302 418 418 418 1369 882 2127 1369 882 292 292 292 292

hDH iM , nm 6.62(0.1) 6.61(0.04) 7.28(0.08) 5.61(0.01) 5.52(0.01) 5.55(0.05) 5.52(0.05) 5.80(0.01) 5.21(0.03) 6.35 6.38 5.98 7.08(0.14) 6.41(0.05) 7.60(0.2) 6.53(0.2) 6.92(0.03) 6.20(0.01) 6.15(0.02) 6.14(0.01) 6.19(0.01)

hNagg iM 158(5) 198(7) 280(5) 74.4(0.4) 75.4(0.3) 90(3) 61(1) 66.8(0.4) 57(2) 143 143 99 186(11) 142(6) 257(20) 155(22) 158(3) 82.3(0.3) 81.0(0.4) 80.5(0.4) 81.3(0.3)

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as well as relative to the CMC from Table 1 that was selected as the target value. For the six smaller molecules the concentrations were generally in the range of 2 to 6 times the target CMC, concentrations hoped to be high enough that micelles were present in sufficient number for detection but not so high that rods, worms or other nonspherical shapes formed. For the three next larger (C10Em) molecules, with smaller CMC values, the concentrations chosen were relatively higher, in the range of 5 to 20 times the target CMC. And for the three largest (C12Em) molecules, with very small CMCs, the concentrations were in the range of 20 to 70 times the target CMC. These relatively higher concentrations needed to be used for the low CMC surfactants because going any lower would have placed the micelle concentrations close to or below the detection threshold of the instrument. However, it is possible that nonspherical micelles may have formed at some of the relatively higher concentrations used with the C10Em and C12Em molecules. With this possibility in mind, it is instructive to compare the mass weighted micelle diameters in Tables 3 and 4 with the extended molecule lengths in Table 1. The mass weighted mean micelle diameters range from about 1.3 to about 2.6 times the approximate extended length of the surfactant molecules, as one might expect for spherical micelles. The averaged micelle size distributions were also used to produce the mass weighted mean aggregation numbers. Statistical uncertainties (in parentheses in the tables) for the diameters and aggregation numbers represent one standard error (one standard deviation of the mean) computed assuming the results of the approximately 100 measurements made for each compound and concentration were uncorrelated. Supporting Information provides further details on the computation of the uncertainties. The graphs in Figure 3 show particle size distributions, P (n), for the compounds at the same micellar concentrations. These are expressed as probability densities as a function of aggregation number, so that P (n)dn is the fraction of the total mass of surfactant material that is in aggregates with between n and n + dn molecules. The mean aggregation number is the integral of n over this function. (Details of how these were produced from the experimental results are provided in the Supporting Information.) One can see that there is

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considerable variation among the molecules. The distributions become taller and narrower (more sharply peaked) and shift to smaller sizes with increasing numbers of ethylene oxide units, while holding the alkane chain length fixed. The distributions also become broader and shift to larger sizes with lengthening of the alkane chain, while holding the ethylene oxide block length fixed. For some compounds there is variation in the distributions with concentration (e.g., C10E8, C12E6), but for others very similar in structure (e.g., C12E8) there is not. The experimental micelle size distributions in Figure 3 exhibit a small size cutoff, corresponding to the smallest aggregates detectable by the instrument (also seen in Figures 1 and 2 ). We used these to produce an operational definition for the cutoff size suggested for use in simulations to classify aggregates as either submicellar (≤ ncut ) or micellar (> ncut ) based on the number of surfactant molecules in the aggregate. These are indicated in Tables 3 and 4. Details about how this was done are provided in Supporting Information. (Notice that in Figure 3 for C12E6 at some concentrations submicellar clusters were detected by the instrument, resulting in a small peak corresponding to sizes of less than about 10 molecules.) One can also see from Figure 3 that the experimental micelle size distributions are quite broad, with log-normal shapes that exhibit long tails that decay slowly and can extend to several times the mass weighted mean aggregation number. Tables 3 and 4 include columns labelled n99 , which is the aggregate size corresponding to where only one percent of the total mass of the surfactant is in aggregates larger than this. This information is included here to guide in the determination of a minimum system size for micelle simulations that will allow the formation of the largest aggregates seen in the experiments. The treatment of one compound, C12E5, deserves extra discussion. The appearance of large aggregates coexisting with smaller (micellar) ones was observed in the scattering data for C12E5, so the data for this compound was processed differently than the others. The results were consistent with the emergence of slowly decaying long wavelength density fluctuations in the vicinity of a liquid-liquid demixing transition, since the temperature of

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Figure 3: Averaged particle size distributions expressed as a function of aggregation number. The curves represent P (n), a probability density, such that P (n)dn represents the fraction of the total mass of micellar material with sizes in the range between n and n + dn molecules. The distributions have been normalized to integrate to unity. Some of the larger statistical uncertainties are shown (plus and minus one standard error), but most are comparable in size to the data symbols themselves and all are less than 0.001. Note that in these figures, the distributions have not been truncated and renormalized to remove the signal from submicellar (n ≤ ncut ) aggregates. The distributions shown for C12E5 reflect only the micellar size portion of the total distribution.

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the experiments (25 ◦ C) is close to the cloud temperature for this compound (31.7 ◦ C, Table 1). The contribution to the distribution function from the super-micellar aggregates was removed for this compound in Figure 3. See Supporting Information for further details.

4. Conclusion A set of compounds was selected for study that we hope can be used to aid in the development and validation of models for the simulation of micelles and related phenomena associated with the Cn Em nonionic surfactant family. This use necessitates a consistent set of experimental results on a diverse set of molecules that span an appropriate range of behaviors in the observables of interest. A consistent set of CMC data was selected from the literature, and new DLS experiments were performed to produce micelle size data for these compounds. The averaging method inherent in the experimental method for producing, for example, mean micelle sizes must be understood so that the same methodology can be applied to produce observables from simulation results. This is necessary so that direct comparisons can be made between experimental and simulated results, a prerequisite to supporting the tuning of force field parameters against experimental data for training and validation. An important goal for a useful force field is that it results in simulations that faithfully reproduce several important experimental trends in micellar behavior (CMC and Nagg ) as a function of hydrophobic and hydrophilic chain lengths and total surfactant concentration. First, we see that the CMC decreases by about an order of magnitude with each addition of two carbon atoms to the hydrophobic chain. Second, and in contrast, extending the hydrophilic chain, with fixed hydrophobic chain length, results in a slight increase of the CMC. The amount of this increase is less with increasing hydrophobic chain length. These trends make sense in that increasing the hydrophobic chain length makes the surfactant less soluble, thereby decreasing the CMC, and increasing the hydrophilic chain length makes it more soluble, thereby increasing the CMC.

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Experimental trends observed in micelle size data that should also be seen in simulations using a force field description include, first, that mass weighted mean aggregation numbers increase with increasing hydrophobic chain length (holding the hydrophilic chain length fixed), and, second, that they decrease with increasing hydrophilic chain length (holding the hydrophobic chain length fixed). Finally, there is a tendency for the aggregation number to increase with increasing surfactant concentration. These trends were exhibited by almost all of the data, except for C12E5 and in a few of the concentrations for some of the other molecules. We have taken advantage extensively of the capability of DLS experiments to produce particle size distributions. These distributions can be quite wide and have long tails. This may help to account for the wide range of aggregation numbers that have been reported in the literature, since different experimental techniques perform different weighted averages over these distributions. We note that the size distributions become narrower with increasing length of the ethylene oxide segment of these surfactants, and that there is somewhat better agreement among the various values reported in the literature for these compounds. We hope this data is of value in the formulation of more accurate force fields for the study of micellar phenomena.

Supporting Information Supporting information consists of extra discussion of (1) review of the literature for CMC values and criteria for selection of target CMC values, (2) review of the literature for aggregation number values, (3) experimental protocol and analysis of the DLS experimental data, including graphs of mass weighted micelle diameters as a function of surfactant concentration, (4) determination of ncut from experimental data, (5) special treatment of the DLS experimental data for C12E5, (6) tabulated particle size distributions for all compounds at micellar concentrations and a detailed description of the data analysis.

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Acknowledgement AID acknowledges support from the STFC Hartree Center program, Innovation: Return on Research, funded by the UK Department for Business, Energy & Industrial Strategy. We wish to thank Dr. Patrick Warren for carefully reading a late draft of the manuscript and for many insightful scientific comments and suggestions.

References (1) Herrington, T. M.; Sahi, S. Temperature dependence of the micellar aggregation number of n-dodecylpolyethyleneoxide surfactants. J. Colloid Interface Sci. 1988, 121, 107–120. (2) Aniansson, E. A. G.; Wall, S. N. Kinetics of step-wise micelle association. J. Phys. Chem. 1974, 78, 1024–1030. (3) Shelley, J. C.; Shelley, M. Y. Computer simulation of surfactant solutions. Curr. Opin. Colloid Interface Sci. 2000, 5, 101–110. (4) Tieleman, D. P.; van der Spoel, D.; Berendsen, H. J. C. Molecular dynamics simulations of dodecylphosphocholine micelles at three different aggregate sized: micellar structure and chain relaxation. J. Phys. Chem. B 2000, 104, 6380–6388. (5) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. Molecular dynamics simulation of sodium dodecyl sulfate micelle in water: micellar structural characteristics and counterion distribution. J. Phys. Chem. B 2002, 106, 3788–3793. (6) Garde, S.; Yang, L.; Dordick, J. S.; Paulaitis, M. E. Molecular dynamics simulation of C8E5 micelle in explicit water: structure and hydrophobic solvation thermodynamics. Mol. Phys. 2002, 100, 2299–2306. (7) Boek, E. S.; Padding, J. T.; den Otter, W. K.; Briels, W. J. Mechanical properties of

24


Page 24 of 35

Page 25 of 35 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


surfactant bilayer membranes from atomistic and coarse grained molecular dynamics simulations. J. Phys. Chem. B 2005, 109, 19851–19858. (8) Bandyopadhyay, S.; Tarek, M.; Lynch, M. L.; Klein, M. L. Molecular dynamics study of poly(oxyethylene) surfactant C12E2 and water. Langmuir 2000, 16, 942–946. (9) MacKerell, A. D. Molecular dynamics simulation analysis of a sodium dodecyl sulfate micelle in aqueous solution: decreased fluidity of the micelle hydrocarbon interior. J. Phys. Chem. 1995, 99, 1846–1855. (10) Bogusz, S.; Venable, R. M.; Pastor, R. W. Molecular dynamics simulations of octyl glucoside micelles: structural properties. J. Phys. Chem. B 2000, 104, 5462–5470. (11) Piotrovskaya, E. M.; Vanin, A. A.; Smirnova, N. A. Molecular dynamics simulation of micellar aggregates in aqueous solution of hexadecyl trimethylammonium chloride with different additives. Mol. Phys. 2006, 104, 3645–3651. (12) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 1992, 19, 155–160. (13) Groot, R.; Warren, P. Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 1997, 107 . (14) Moeendarbary, E.; Ng, T.; Zangeneh, M. Dissipative particle dynamics: Introduction, methodology, and complex fluid applications – A review. Int. J. Appl. Mechanics 2009, 01, 737–763. (15) Sanders, S. A.; Panagiotopoulos, A. Z. Micellization behavior of coarse grained surfactant models. J. Chem. Phys. 2010, 132, 114902. (16) Eggimann, B. L.; Sunnarborg, A. J.; Stern, H. D.; Bliss, A. P.; Siepmann, J. I. An online parameter and property database for the TraPPE force field. Molec. Simul. 2014, 40, 101–105. 25



(17) Maerzke, K. A.; Siepmann, J. I. Transferable potentials for phase equilibria-coarse-grain description for linear alkanes. J. Phys. Chem. B 2011, 115, 3452–3465. (18) Keasler, S. J.; Charan, S. M.; Wick, C. D.; Econonmou, I. G.; Siepmann, J. I. Transferable potentials for phase equilibria-united atom description of five- and six-membered cyclic alkanes and ethers. J. Phys. Chem. B 2012, 116, 11234–11246. (19) Minkara, M. S.; Lindsey, R. K.; Hembree, R. H.; Venteicher, C. L.; Jamadagni, S. N.; Eike, D. M.; Ghobadi, A. F.; Koenig, P. H.; Siepmann, J. I. Probing additive loading in the lamellar phase of a nonionic surfactant: Gibbs ensemble Monte Carlo simulations using the SDK force field. Langmuir 2018, 34, 8245–8254. (20) Mao, R.; Lee, M.-T.; Vishnyakov, A.; Neimark, A. V. Modeling aggregation of ionic surfactans using a smeared charge approximation in dissipative particle dynamics simulations. J. Phys. Chem. B 2015, 119, 11673–11683. (21) Vishnyakov, A.; Lee, M.-T.; Neimark, A. V. Prediction of the critical micelle concentration of nonionic surfactants by dissipative particle dynamics simulations. J. Phys. Chem. Lett. 2013, 4, 797–802. (22) Anderson, R. L.; Bray, D.; Del Regno, A.; Seaton, M. A.; Ferrante, A. S.; Warren, P. B. Micelle formation in alkyl sulfate surfactants using dissipative particle dynamics. J. Chem. Theory Comput. 2018, 14, 2633–2643. (23) Pool, R.; Bolhuis, P. G. Accurate free energies of micelle formation. J. Phys. Chem. B 2005, 109, 6650–6657. (24) Marrink, S. J.; de Vries, A. H.; Mark, A. E. Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 2004, 108, 750–760. (25) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The

26


Page 26 of 35

Page 27 of 35 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


MARTINI force field: coarse grained model for biomolecular simulations. J. Phys. Chem. B 2007, 111, 7812–7824. (26) Shinoda, W.; DeVane, R.; Klein, M. L. Coarse grained molecular modeling of nonionic surfactant self assembly. Soft Matter 2008, 4, 2454–2462. (27) Klevens, H. B. Critical micelle concentrations as determined by refraction. J. Phys. Colloid Chem. 1948, 52, 130–148. (28) Hatzopoulos, M. H.; Eastoe, J.; Dowding, P. J.; Rogers, S. E.; Heenan, R.; Dyer, R. Are hydrotropes distinct from surfactants. Langmuir 2018, 27, 12346–12353. (29) Corkill, J. M.; Goodman, J. F.; Harrold, S. P. Thermodynamics of micellization of non-ionic detergents. Trans. Faraday Soc. 1963, 202–207. (30) Borthakur, A.; Zana, R. Ultrasonic absorption studies of aqueous solutions of nonionic surfactants in relation with critical phenomena and micellar dynamics. J. Phys. Chem. 1987, 91, 5957–5960. (31) Schubert, K.-V.; Strey, R.; Kahlweit, M. A new purification technique for alkyl polyglycol ethers and miscibility gaps for water-CiEj. J. Colloid Interface Sci. 1991, 141, 21–29. (32) Frindi, M.; Michels, B.; Zana, R. Ultrasonic absorption studies of surfactant exchange between micelles and bulk phase in aqueous micellar solutions of nonionic surfactants with a short alkyl chain. 3. Surfactants with a sugar head group. J. Phys. Chem. 1992, 96, 8137–8141. (33) Ambrosone, L.; Costantino, L.; D’Errico, G.; Vitagliano, V. Thermodynamic and dynamic properties of micellar aggregates of nonionic surfactants with short hydrophobic tails. J. Colloid Interface Sci. 1997, 190, 286–293.

27



(34) Mulley, B. A.; Metcalf, A. D. Nonionic surface-active agents. Part IV. The critical micelle concentration of some polyoxyethylene glycol monohexyl ethers in binary and ternary systems. J. of Colloid Sci. 1962, 17, 523–530. (35) Donbrow, M.; Jan, Z. A. Refractometric determination of the critical micelle concentration of non-ionic surface-active agents. J. Pharm. Pharmacol. 1963, 15, 825–830. (36) Carless, J. E.; Challis, R. A.; Mulley, B. A. Nonionic surface-active agents. Part V. The effect of the alkyl and the polyglycol chain length on the critical micelle concentration of some monoalkyl polyethers. J. Colloid Sci. 1964, 19, 201–212. (37) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Standard Reference Data System: Washington, D.C., 1971; Vol. NSRDS-NBS 36. (38) Wieczorek, S. A. Thermodynamics of aqueous mixtures of polyoxyethene glycol monoethers VI. Excess molar volumes of (n-hexyl pentaoxyethene glycol monoether+ water) in the vicinity of the critical micelle composition. J. Chem. Thermodyn. 2000, 32, 529–537. (39) Stubenrauch, C.; Nydén, M.; Findenegg, G. H.; Lindman, B. NMR self-diffusion study of aqueous solutions of tetraoxyethylene n-octyl ether (C8E4). J. Phys. Chem. 1996, 100, 17028–17033. (40) Kato, S.; Harada, S.; Sahara, H. Ultrasonic relaxation and volumetric studies of the micelle/monomer exchange process in aqueous solutions of the nonionic surfactants C7E4, C8E4, and C8E5. J. Phys. Chem. 1995, 99, 12570–12575. ¨ (41) Van Ede, J.; Nijmeijer, J. R. J.; Welling-Wester, S.; Orvell, C.; Welling, G. W. Comparison of non-ionic detergents for extraction and ion-exchange high-performance liquid chromatography of Sendai virus integral membrane proteins. J. Chromatogr. A 1989, 476, 319–327. 28


Page 28 of 35

Page 29 of 35 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


(42) Casey, J. R.; Reithmeier, R. A. F. Detergent interaction with band 3, a model polytopic membrane protein. Biochemistry 1993, 32, 1172–1179. (43) Corkill, J. M.; Goodman, J. F.; Ottewill, R. H. Micellization of homogeneous non-ionic detergents. Trans. Faraday Soc. 1961, 57, 1627–1636. (44) Funasaki, N.; Hada, S.; Neya, S. Monomer concentrations of nonionic surfactants as deduced with gel filtration chromatography. J. Phys. Chem. 1988, 92, 7112–7116. (45) Funasaki, N.; Shim, H.-S.; Hada, S. Application of Tanford’s micellization theory to gel filtration chromatographic data for nonionic surfactants. J. Phys. Chem. 1992, 96, 1998–2006. (46) Wieczorek, S. A. Thermodynamics of aqueous mixtures of polyoxyethene glycol monoethers V. Excess molar volumes of (n-decyl hexaoxyethene glycol monoether+ water) in the vicinity of the critical micelle composition. J. Chem. Thermodyn. 1999, 31, 661–673. (47) Ueno, M.; Takasawa, Y.; Miyashige, H.; Tabata, Y.; Meguro, K. Effects of alkyl chain length on surface and micellar properties of octaethyleneglycol-n alkyl ethers. Colloid and Polym. Sci. 1981, 259, 761–766. (48) Meguro, K.; Takasawa, Y.; Kawahashi, N.; Tabata, Y.; Ueno, M. Micellar properties of a series of octaethyleneglycol-n-alkyl ethers with homogeneous ethylene oxide chain and their temperature dependence. J. Colloid Interface Sci. 1981, 83, 50–56. (49) Takasawa, Y.; Ueno, M.; Sawamura, T.; Meguro, K. Effect of alkyl chain length of octaethyleneglycol-n-alkyl ethers upon mixed surfactant solutions and upon the temperature dependence of surface tension. J. Colloid Interface Sci. 1981, 84, 196. (50) Ueno, M.; Kimoto, Y.; Ikeda, Y.; Momose, H.; Zana, R. Study on the aggregation

29



number of mixed micelles in aqueous binary mixtures of the bile salts and nonionic surfactant. J. Colloid Interface Sci. 1987, 117, 179–186. (51) Lange, H. Proceedings of the International Congress on Surface Activity. 1960; p 279. (52) Lange, H. Untersuchungen uber adsorbierte und gespreitete monomolekulare schichten von dodecylpolyglykolathern auf wasser. Kolloid Z. Z. Polym. 1965, 201, 131–136. (53) Nishikido, N.; Moroi, Y.; Matuura, R. The micelle formation of mixtures of polyoxyethylene type nonionic surfactants in aqueous solutions. Bull. Chem. Soc. Jpn. 1975, 48, 1387–1390. (54) Rosen, M. J.; Cohen, A. W.; Dahanayake, M.; Hua, X. Y. Relationship of structure to properties in surfactants. 10. Surface and thermodynamic properties of 2-dodecyloxypoly(ethenoxyethanol)s, C12H25(OC2H4)xOH, in aqueous solution. J. Phys. Chem. 1982, 86, 541–545. (55) Chen, L.-J.; Lin, S.-Y.; Huang, C.-C.; Chen, E.-M. Temperature dependence of critical micelle concentration of polyoxyethylenated non-ionic surfactants. Colloids Surf. A 1998, 135, 175–181. (56) Becher, P. Nonionic surface active compounds. I. Critical micelle concentrations of water-soluble ether alcohols. J. Phys. Chem. 1959, 63, 1675–1676. (57) Becher, P. Nonionic surface active compounds IV. Micelle formation by polyoxyethylene alkanols and alkyl phenol solution. J. Colloid Sci. 1961, 16, 49–56. (58) Berthod, A.; Tomer, S.; Dorsey, J. G. Polyoxyethylene alkyl ether nonionic surfactants: physicochemical properties and use for cholesterol determination in food. Talanta 2001, 55, 69–83. (59) Ortona, O.; Vitagliano, V.; Paduano, L. Microcalorimetric study of some short chain nonionic surfactants. J. Colloid Interface Sci. 1998, 203, 477–484. 30


Page 30 of 35

Page 31 of 35 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


(60) Paduano, L.; Sartorio, R.; Vitagliano, V.; Costantino, L. Equilibrium and transport properties of aqueous pentaethyleneglycol-1-hexyl ether and sodium hexanesulfonate at 25C. J. Colloid Interface Sci. 1997, 189, 189–198. (61) Corti, M.; Minero, C.; Degiorgio, V. Cloud point transition in nonionic micellar solutions. J. Phys. Chem. 1984, 88, 309–317. (62) Faucompre, B.; Lindman, B. Self-association of zwitterionic and nonionic surfactants. NMR self-diffusion studies. J. Phys. Chem. 1987, 91, 383. (63) Andersson, B.; Olofsson, G. Calorimetric study of nonionic surfactants. Enthalpies and heat capacity changes for micelle formation in water of C8E4 and Triton X-100 and micelle size of C8E4. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4087–4095. (64) Zulauf, M.; Rosenbusch, J. P. Micelle clusters of octylhydroxyollgo(oxyethylenes). J. Phys. Chem. 1983, 87, 856–862. (65) Zulauf, M.; Weckstrom, K.; Hayter, J. B.; Degiorgio, V.; Corti, M. Neutron scattering study of micelle structure in isotropic aqueous solutions of poly(oxyethylene) amphiphlles. J. Phys. Chem. 1985, 89, 3411–3417. (66) Binana-Limbelé, W.; Van Os, N. M.; Rupert, L. A. M.; Zana, R. Aggregation behavior and micellar dynamics in aqueous solutions of the nonionic surfactant pentaoxyethyleneglycol monooctyl ether: Effect of sodium halides. J. Colloid Interface Sci. 1991, 144, 458–467. (67) Alami, E.; Kamenka, N.; Raharimihamina, A.; Zana, R. Investigation on the microstructures in mixtures of water with the nonionic surfactants C8E5, C10E6, and C10E8 in the whole range of composition. J. Colloid Interface Sci. 1993, 158, 342–350. (68) Weckstrom, K.; Hann, K.; Rosenholm, J. B. Enthalpies of mixing a non-ionic surfactant

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with water at 303.15K studied by calorimetry. J. Chem. Soc., Faraday Trans. 1994, 90, 733–738. (69) Balmbra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Variations in the micelle size of non-ionic detergents. Trans. Faraday Soc. 1964, 60, 979–985. (70) Corkill, J. M.; Walker, T. Light scattering and diffusion studies in nonionic micellar systems. J. Colloid Interface Sci. 1972, 39, 621–631. (71) Imanishi, K.; Einaga, Y. Effects of hydrophilic chain length on the characteristics of the micelles of pentaoxyethylene n-decyl C10E5 and hexaoxyethylene n-decyl C10E6 ethers. J. Phys. Chem. B 2005, 109, 7574–7581. (72) Funasaki, N.; Shim, H.-S.; Hada, S. Micellar growth of octaethylene glycol decyl ether. J. Chem. Soc., Faraday Trans. 1991, 87, 957–961. (73) Okawauchi, M.; Shinozaki, M.; Ikawa, Y.; Tanaka, M. A light scattering study on micelle formation of nonionic surfactants as a function of concentration and pressure by applying small system thermodynamics. J. Phys. Chem. 1987, 91, 109–112. (74) Brown, W.; Pu, Z.; Rymden, R. Size and shape of nonionic amphiphile micelles: NMR self-diffusion and static and quasi-elastic light scattering measurements on C12E5, C12E7 and C12E8 in aqueous solution. J. Phys. Chem. 1988, 92, 6086–6094. (75) Attwood, D.; Elworthy, P. H.; Kayne, S. B. Membrane osmometry of aqueous solutions of pure nonionic and ionic surfactants. J. Phys. Chem. 1970, 74, 3529–3534. (76) Balmbra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Effect of temperature on the micelle size of a homogeneous non-ionic detergent. Trans. Faraday Soc. 1962, 58, 1661–1667. (77) Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. Size and shape of nonionic amphiphile (C12E6) micelles in dilute aqueous solutions as derived from quasielastic and intensity 32


Page 32 of 35

Page 33 of 35 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


light scattering, sedimentation, and pulsed field gradient nuclear magnetic resonance self diffusion data. J. Phys. Chem. 1983, 87, 4548. (78) Goto, A.; Sakura, R.; Endo, F. The solution state of nonionic surfactant micelles in aqueous solution. J. Colloid Interface Sci. 1978, 67, 491–497. (79) Ottewill, R. H.; Storer, C. C.; Walker, T. Ultracentrifugal study of a non-ionic surface active agent in D2O. Trans. Faraday Soc. 1967, 63, 2796–2802. (80) Paradies, H. H. Size and shape of nonionic micelles determined by X-ray scattering techniques. Colloids Surf. 1983, 6, 405–428. (81) Ravey, J.-C. Lower consolute curve related to micellar structure of nonionic surfactants. J. Colloid Interface Sci. 1983, 94, 289–291. (82) Triolo, L. J., R nad Magid; Johnson, J. S.; Child, H. R. Small angle neutron scattering from aqueous micellar solutions of a nonionic surfactant as a function of temperature. J. Phys. Chem. 1982, 86, 3689. (83) Zana, R.; Weill, C. Effect of temperature on the aggregation behaviour of nonionic surfactants in aqueous solutions. J. Phys., Lett. 1985, 46, 953–960. (84) Tanford, C.; Nozaki, Y.; Rohde, M. F. Size and shape of globular micelles formed in aqueous solution by n-alkyl polyoxyethylene ethers. J. Phys. Chem. 1977, 81, 1555. (85) Maezawa, S.; Hayashi, Y.; Nakae, T.; Ishii, J.; Kameyama, K.; Takagi, T. Determination of molecular weight of membrane proteins by the use of low angle laser light scattering combined with high performance gel chromatography in the presence of a non-ionic surfactant. Biochim. Biophys. Acta 1983, 747, 291–297. (86) Nilsson, P.-G.; Wennerstrm, H.; Lindman, B. Structure of micellar solutions of nonionic surfactants. Nuclear magnetic resonance self-diffusion and proton relaxation studies of poly(ethylene oxide) alkyl ethers. J. Phys. Chem. 1983, 87, 1377–1385. 33



(87) Magid, L. J.; Triolo, R.; Johnson, J. S. Small angle neutron scattering study of critical phenomena in aqueous solutions of C12E8, a nonionic amphiphile. J. Phys. Chem. 1984, 88, 5730. (88) Binana-Limbelé, W.; Zana, R. Effect of temperature on the aggregation behavior of the nonionic surfactant C12E8 in H2O and D2O solutions. J. Colloid Interface Sci. 1988, 121, 81–84. (89) Berne, B. J.; Pecora, R. Dynamic Light Scattering with Applications to Chemistry, Biology and Physics; Dover: Toronto, 2000. (90) ISO, Particle size analysis - Photon correlation spectroscopy ISO 13321:1996 ; 1996. (91) Provencher, S. W. Contin: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations. Comput. Phys. Commun. 1982, 27, 229–242.

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TOC Graphic

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Challenge to Reconcile Experimental Micellar Properties of the CnEm

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