Influence of Temperature and Concentration on the Self-Assembly of Nonionic CiEj Surfactants: A Light Scattering Study.

Nonionic poly(ethylene oxide) alkyl ether (CiEj) surfactants self-assemble into aggregates of various sizes and shapes above their critical micelle concentration (CMC). Knowledge on solution attributes such as CMC as well as aggregate characteristics is crucial to choose the appropriate surfactant for a given application, e.g., as a micellar solvent system. In this work, we used static and dynamic light scattering to measure the CMC, aggregation number (N agg), and hydrodynamic radius (R h) of four different CiEj surfactants (C8E5, C8E6, C10E6, and C10E8). We examined the influence of temperature, concentration, and molecular structure on the self-assembly in the vicinity of the CMC. A minimum in the CMC vs temperature curve was identified for all surfactants investigated. Further, extending the hydrophilic and hydrophobic chain lengths leads to an increase and decrease of the CMC, respectively. The size of the aggregates strongly depends on temperature. N agg and R h increase with increasing temperature for all surfactants investigated. Additionally, N agg and R h both increase with increasing surfactant concentration. The data obtained in this work further improve the understanding of the influence of temperature and molecular structure on the self-assembly of CiEj surfactants and will further foster their use in micellar solvent systems.

Introduction

Surfactants are amphiphilic molecules possessing a hydrophilic head and a hydrophobic tail group. Due to their amphiphilic nature, they self-assemble into aggregates (e.g., micelles, vesicles) in a given solvent above their critical micelle concentration (CMC). These aggregates can solubilize otherwise insoluble compounds, making them suitable for many industrial applications. Surfactant aggregates are used in pharmaceutical formulations to solubilize poorly water-soluble drugs and thus to enhance the bioavailability of these drugs.[1,2] In enhanced oil recovery, in food products, and in cosmetics, surfactants are used to produce (micro)emulsions by drastically reducing the interfacial tension between immiscible liquids.[3−5]

In recent years, so-called micellar solvent systems have gained increasing attention when used as “green” reaction media in the chemical and biochemical industry.[6−9] There, especially nonionic poly(ethylene oxide) alkyl ether surfactants are of interest.[10] These surfactants consist of an alkyl chain as hydrophobic tail and an ethylene oxide chain as hydrophilic head. They are thus denoted as CiEj, where i is the number of C atoms in the alkyl chain and j is the number of ethylene oxide units in the ethylene oxide chain.

Although CiEj surfactants were studied extensively in the last decades,[11] experimental data available in the open literature display a striking degree of variation as pointed out in a recent review by Swope et al.[12] Even for the most basic properties of surfactant solutions, such as the CMC and the aggregation number (Nagg), values reported in the literature differ significantly.[12,13] Possible reasons for this were elucidated extensively in the work of Swope et al.[12] One straightforward reason is the application of different measurement techniques with different sensitivities for the respective measures. For example, static light scattering (SLS) and dynamic light scattering (DLS) are often used to measure Nagg. However, only SLS gives a direct measurement of Nagg via the mass-averaged molecular weight (MW) of the aggregates. DLS measures the translational diffusion coefficient (Dt), which can be used to compute a hydrodynamic radius (Rh) of the aggregates. Assumptions about the shape and hydration of the aggregates are thus necessary to calculate Nagg from DLS measurements. Consequently, DLS-derived values of Nagg should be used with caution.

Additionally, both SLS and DLS measurements are sensitive toward attractive or repulsive forces between the aggregates.[14] These forces lead to either an increase (attractive forces) or decrease (repulsive forces) of the intensity of the scattered light, with surfactant/aggregate concentrations increasing beyond the CMC. Therefore, light scattering intensities measured at several concentrations are usually extrapolated to infinite dilution to obtain MW using Zimm’s procedure.[15] However, due to the concentration dependence of MW, an extrapolation to infinite dilution is not possible for surfactant aggregates.[16] Therefore, we studied concentrations in the vicinity of the CMC, where interactions between the aggregates are negligible and MW can be computed directly from the measured intensity of the scattered light. Moreover, light scattering intensity increases significantly near the binodal curve of a liquid–liquid equilibrium (LLE) due to concentration fluctuations.[17] CiEj surfactants exhibit an LLE in water at elevated temperatures. The onset of this LLE at a given concentration is often referred to as cloud point. Light scattering intensities of a surfactant solution measured near the binodal curve (that is the cloud point) of a CiEj solution have to be evaluated with caution due to contributions from fluctuations in the vicinity of the LLE to the overall light scattering intensity.

A further aspect is the general behavior of the CMC and Nagg of CiEj surfactants with increasing temperature, which is controversially disputed in the literature. While some authors report a monotonic decrease of the CMC with increasing temperature,[18,19] others found a minimum in the CMC vs temperature curve at elevated temperatures.[20] Studies that only reveal a monotonic decrease in the CMC often only considered temperatures up to 40 °C. It is thus fair to assume that 40 °C is too low to observe the minimum in the CMC. This is supported by the fact that for CiEj surfactants and for p,t-octylphenol poly(ethylene oxide) glycol monoether surfactants (a similar class of nonionic surfactants), the minimum in the CMC vs temperature curve is present at around 50 °C.[20−22]

The same controversial dispute applies to the behavior of Nagg for CiEj surfactants with increasing temperature.[23] As a matter of fact, the scattering intensity of aqueous CiEj solutions (constant surfactant concentration above CMC) increases with increasing temperature. Some authors solely attributed this increase to concentration fluctuations due to the existence of an LLE at elevated temperatures without considering any growth of the surfactant aggregates. However, other groups found that CiEj aggregates grow with increasing temperature and that these fluctuations only start to dominate the scattering intensity when closely approaching the LLE of the solution.[19,24] Thus, to minimize any contributions from fluctuations near the LLE to the measured light scattering intensity and thus to Nagg measurements, we only determined Nagg for temperatures 10 K below the respective cloud-point temperature (LLE phase boundary) of the solution.

In this work, we studied the influence of temperature, concentration, and molecular structure of the surfactant (hydrophilic and hydrophobic chain lengths) on the CMC, Nagg, and Rh values of four different nonionic CiEj surfactants, namely, pentaethylene glycol monooctyl ether (C8E5), hexaethylene glycol monooctyl ether (C8E6), hexaethylene glycol monodecyl ether (C10E6), and octaethylene glycol monodecyl ether (C10E8). We measured the CMC at different temperatures between 15 and 60 °C to identify the minimum in the CMC vs temperature curve using SLS. By varying both the hydrophilic and the hydrophobic chain lengths, the influence of the surfactant’s molecular structure on the minimum in the CMC vs temperature curve was elucidated. Further, the influences of temperature and molecular structure of the surfactant on the size (Nagg, Rh) of the aggregates were examined using SLS and DLS.

Additionally, growth of the surfactant aggregates with concentration was studied. We investigated concentrations in the vicinity of the CMC so that interactions between the surfactant aggregates were negligible and any increase in the scattered light could be related directly to the growth of the surfactant aggregates. The results presented in this work lead to a deeper understanding of the aggregation behavior of CiEj surfactants near the CMC. Detailed knowledge about the influences of temperature, concentration as well as molecular structure on the self-assembly of the investigated surfactants eases the choice of suitable surfactants for a given application and their application in micellar solvent systems.

Results

Critical Micelle Concentration

The CMCs were determined for four nonionic surfactants considered in this work (C8E5, C8E6, C10E6, and C10E8). CMCs were studied in the temperature range of 15–60 °C to determine the influence of increasing temperature on the CMC. For C8E5 and C8E6, the highest temperature measured was 55 °C due to a liquid–liquid phase separation in water at higher temperatures. Experiments were carried out using SLS analytics as described in Section . Measured SLS intensities for at least 10 surfactant concentrations below and above the CMC were extrapolated linearly, and the CMC was taken as the intersection point. CMCs are listed in Table . Measured raw SLS intensities (expressed as R(θ)) for all concentrations and temperatures studied can be found in Figures S1–S4 (Supporting Information).

Table 1

CMCs for All Investigated Surfactants of This Worka

	C8E5		C8E6		C10E6		C10E8
	CMC
T/°C	/g L–1	/103 mol L–1	/g L–1	/103 mol L–1	/g L–1	/103 mol L–1	/g L–1	/103 mol L–1
15	4.49	12.81	5.34	13.54	0.43	1.02	0.75	1.47
25	3.37 (0.01)	9.61 (0.03)	3.91 (0.07)	9.91 (0.18)	0.35 (0.00)	0.83 (0.01)	0.56 (0.01)	1.10 (0.02)
30	3.24	9.24	3.64	9.93	0.33	0.78	0.52	1.02
40	2.87	8.12	2.91	7.38	0.27	0.64	0.40	0.78
50	2.61	7.45	2.63	6.67	0.28	0.66	0.37	0.72
55	2.68	7.65			0.29	0.67
60			2.75	6.97			0.36	0.70

Temperatures between 15 and 60 °C were studied. For C8E5 and C10E6, the highest temperature investigated was 55 °C due to an LLE in water at around 60 °C. Values in parentheses (25 °C) give the standard deviations out of two measurements of independent samples.

For all surfactants investigated, CMCs are decreasing monotonically with increasing temperature in the considered temperature range (15–40 °C). The decrease in CMC is more intense at lower temperatures (around 15–25 °C) and levels off at higher temperatures (40–50 °C). However, further increasing the temperature to 50 °C or above does not lead to a decrease of the CMC (e.g., for C10E6) but to a slight increase from 0.27 to 0.28 g L–1. Increasing the temperature to 55 °C amplifies this increase of the CMC. This behavior was also found for C8E5, C8E6, and C10E8 in the temperature range of 50–60 °C. All investigated surfactants thus show a minimum in their CMC vs temperature curve at around 50 °C.

The results shown in Table further reveal the effect of the ethylene oxide chain length and carbon chain length on the CMC. Increasing the chain length of the hydrophilic ethylene oxide units from E6 to E8 at a fixed C10 leads to an increase by 74 and 32% in the CMC at 15 and 50 °C, respectively. In contrast, increasing the hydrophobic carbon chain length from C8 to C10 at fixed E6 leads to a decrease of the CMC by approximately 1 order of magnitude from 3.91 to 0.35 g L–1 at 25 °C.

Aggregation Number

Aggregation numbers were measured for the four nonionic surfactants (C8E5, C8E6, C10E6, and C10E8) in the temperature range of 15–50 °C to determine the influence of increasing temperature. Furthermore, for all temperature steps considered (15, 25, 30, 40, and 50 °C), Nagg’s were also determined at surfactant concentrations ranging from the CMC to approximately 2 times the CMC to elucidate the influence of increasing surfactant concentrations on Nagg at a constant temperature. Nagg’s were obtained from SLS measurements as described in Section . The refractive index increments dn/dc of the surfactant aggregates that are required to obtain Nagg from SLS measurements were measured for all surfactants considered at all temperatures investigated and can be found in Table S1 (Supporting Information). Figure shows the Nagg values at different temperatures and concentrations for all surfactants investigated. The raw data from Figure can be found in Tables S2–S5 in the Supporting Information.

Figure 1

Nagg for (a) C8E5, (b) C8E6, (c) C10E6, and (d) C10E8 at concentrations near the CMC and temperatures from 15 to 50 °C. Temperatures are indicated as follows: circles, 15 °C; squares, 25 °C; triangles, 30 °C; stars, 40 °C; diamonds, 50 °C. Error bars at 25 °C give the standard deviations out of two independent measurements.

For all surfactants investigated, Nagg increases with increasing temperature with the magnitude of the increase of Nagg differing significantly between the surfactants considered. While Nagg of C8E5 increases up to 3-fold upon increasing the temperature from 15 to 50 °C, the Nagg value of C8E6 only increases 1.3-fold within the same temperature interval. Further, the impact of temperature on Nagg is more profound at higher temperatures. However, Nagg also increases with increasing surfactant concentration. This is especially pronounced for C8E5 showing an increase in Nagg from 37 to 59 at 25 °C when increasing the surfactant concentration from 3.78 to 6.31 g L–1, respectively. The same behavior is true for Nagg of C8E6, C10E6, and C10E8 (increases with concentration near the CMC), although the growth for these surfactants is less pronounced compared to C8E5.

Besides temperature and concentration, also the molecular structure of the surfactant influences Nagg. An extension of the hydrophobic chain length from C8 to C10 at a fixed E6 leads to an increase in Nagg. For example, Nagg increases by about 30 and 70 molecules at temperatures of 15 and 50 °C, respectively. In contrast, extending the ethylene oxide chain from E5 to E6 and from E6 to E8 at fixed C8 and C10, respectively, leads to a decrease of Nagg.

Hydrodynamic Radius

Hydrodynamic radii of all surfactants investigated (C8E5, C8E6, C10E6, C10E8) were measured in the temperature range of 15–50 °C to elucidate the influence of temperature on Rh. Furthermore, surfactant concentrations ranging from the CMC to 2 times the CMC were investigated at a constant temperature to reveal the influence of increasing concentration on Rh near the CMC. Rh was computed from the translational diffusion coefficient Dt, which was measured via DLS, using the Stokes–Einstein equation as described in Section . Figure shows the results for all temperatures and concentrations investigated. The raw data from Figure can be found in Tables S2–S5 in the Supporting Information.

Figure 2

Hydrodynamic radius (Rh) of (a) C8E5, (b) C8E6, (c) C10E6, and (d) C10E8 at concentrations below and above the CMC. At concentrations below the CMC, no Rh was detectable. Temperatures are indicated as follows: circles, 15 °C; squares, 25 °C; triangles, 30 °C; stars, 40 °C; diamonds, 50 °C. Error bars at 25 °C give the standard deviations obtained from two independent measurements.

For concentrations below the CMC, no Rh was detectable due to the absence of surfactant aggregates at these concentrations. Exceeding the CMC leads to an abrupt increase in Rh. This increase flattens upon further increasing the surfactant concentration. This is especially pronounced for C8E6 but is also present for the other surfactants investigated. However, considering the effect of temperature on Rh, it can be seen that Rh is increasing with increasing temperature, e.g., for C8E5, Rh is increasing from 1.78 to 3.15 nm (an increase in Rh of almost 80%) at a fixed surfactant concentration of 6.3 g L–1 and temperatures ranging from 15 to 50 °C, respectively. For C8E6, this increase in Rh is less pronounced, with Rh increasing only by 30% (from 1.96 to 2.60 nm) at 7.8 g L–1 and 15 or 50 °C, respectively.

Discussion

Effect of Temperature and the Molecular Structure of Surfactant on the CMC

As presented in Section , the CMCs of all surfactants investigated in this work strongly depend on temperature. For C10E6, the CMC first decreases monotonically in the temperature range of 15–40 °C, before showing a minimum near 50 °C. Such a minimum in the CMC versus temperature curve was also found for C8E5, C8E6, and C10E8 in this work and is a well-known phenomenon for many ionic and nonionic surfactants.[21,26] As the temperature increases, hydrogen bonding between the ethylene oxide chain and the surrounding water molecules is weakened and dehydration of the ethylene oxide groups occurs.[22] Thus, the surfactant molecule becomes more hydrophobic shifting the onset of micelle formation toward lower concentrations. This effect is known to be stronger for longer ethylene oxide chains[22] and can be confirmed by our data comparing C8E5 with C8E6 and C10E6 with C10E8 (see Table ).

Simultaneously with the weakening of the hydrogen bonds for the ethylene oxide chain, the alkyl chain of the surfactant possesses a minimum solubility in water around room temperature.[27,28] Starting from there, the alkyl chain of the surfactant molecules starts to become more soluble with increasing temperature. Hence, the contribution of the hydrophobic alkyl chain is shifting the onset of micelle formation toward higher concentrations with increasing temperature.[29] Therefore, in the low-temperature region (15–40 °C), the contribution of the ethylene oxide chain dominates and the CMC decreases with increasing temperature. At the minimum in the CMC vs temperature curve, the contribution of the hydrophobic alkyl chain starts to predominate and the CMC increases upon further increasing the temperature.[20]

CMC data for the investigated surfactants in the literature comprise a rather broad concentration range as pointed out recently by Swope et al.[12] These authors evaluated CMC data at 25 °C for CiEj surfactants available in the literature and found that reliable CMC values for C8E5, C8E6, C10E6, and C10E8 are 3.15, 3.91, 0.38, and 0.51 g L–1, respectively. These values fit perfectly to the CMCs determined in this work. However, considerably less data are available regarding the influence of temperature on the CMC and thus the minimum in the CMC vs temperature curve is often unknown. Hence, we calculated the minimum in the CMC vs temperature curve from our experimental data using a second-order polynomial fit. We found the temperature of the minimum of the CMC of C8E5, C8E6, C10E6, and C10E8 to be at 50, 51, 47, and 55 °C, respectively. The minimum in the CMC for C10E8 was found by surface tension measurements at 61 °C,[21] while for C12Ej (j = 4, 6, 8), it was found to be around 50 °C.[20] These findings are in excellent agreement with our data. Extending the ethylene oxide chain is slightly shifting the minimum to higher temperatures. Contrarily, extending the alkyl chain is shifting the minimum to lower temperatures. The solubility of pure alkanes in water exhibits a minimum around room temperature. Therefore, a shift in the minimum temperature to lower temperatures is directly related to an increase in the hydrophobicity of the surfactant molecules. In line with this, extending the alkyl chain leads to a slight decrease of the minimum temperature. This was also found for other nonionic surfactants.[20−22,29]

Regarding the influence of the molecular structure of the surfactant (that is the hydrophilic ethylene oxide and the hydrophobic alkyl chain length) on the CMC, our results reveal two major findings: (1) Extending the alkyl chain by two carbon atoms leads to a decrease of the CMC by approximately 1 order of magnitude (see Table ). This decrease in the CMC is directly related to the increase in hydrophobicity with extending alkyl chain length and is well known for both nonionic and ionic surfactants.[30−33] (2) Extending the hydrophilic ethylene oxide chain leads to an increase in the CMC. However, the influence of the ethylene oxide chain on the CMC is less pronounced compared to the alkyl chain. An increase in CMC with increasing ethylene oxide chain length results from an enhanced hydrophilicity and was also found for other CiEj surfactants.[20,34]

The results shown in Table further reveal that extending the hydrophilic ethylene oxide chain increases the CMC more strongly at low temperatures (see C8E5 vs C8E6 and C10E6 vs C10E8). As mentioned above, at higher temperatures, the contribution of the alkyl chain to the CMC starts to predominate over the hydrophilic ethylene oxide chain. At 50 °C, the alkyl chain therefore mainly determines the CMC and the contribution of the ethylene oxide chain is of minor impact. Hence, the difference in the CMC with varying ethylene oxide and fixed alkyl chain length is higher at low temperatures and decreases with increasing temperature. Nonetheless, increasing the ethylene oxide chain leads to a slight increase in the CMC even at 50 °C.

Effect of Temperature, Concentration, and Molecular Structure of Surfactant on Nagg and Rh

As described in the previous section, the interactions of same-type surfactant molecules with each other and with the surrounding bulk water are altered significantly upon changes in temperature. All surfactants investigated in this work exhibit a strong increase in Nagg with increasing temperature as also found for other CiEj surfactants.[25,35−37] The growth of Nagg can be explained similar to the decrease of the CMC with increasing temperature (see Section ) by a decreasing intensity of the ethylene oxide chain interactions with the surrounding water molecules. At elevated temperatures, the effective head group area of the surfactant molecules is influenced by two major processes: a dehydration of the ethylene oxide chain and a decrease in the density of the ethylene oxide chain.[19,38−40] While the former leads to a decrease of the effective head group area, the latter leads to an increase of the effective head group area. However, Nagg is increasing with increasing temperature. Therefore, the dehydration of the ethylene oxide chains must overcompensate for the decrease in the density of the ethylene oxide chains. Thus, more surfactant molecules can be incorporated in an aggregate at elevated temperatures.

The increase of Nagg with increasing temperature is generally higher for C8E5 and C10E6 compared to C8E6 and C10E8. Growth of CiEj surfactants aggregates increases rapidly as the binodal curve (or the cloud point for a given concentration) is approached.[35,41] Cloud points for C8E5, C8E6, C10E6, and C10E8 in water (at 10 g L–1) are at 60, 74, 62, and 85 °C, respectively.[42,43] Thus, the rapid increase of Nagg with increasing temperature for C8E5 and C10E6 results from the proximity to their binodal curve in water, especially at 50 °C. Upon approaching the binodal curve, light scattering intensity is strongly influenced by concentration fluctuations.[17,44−46] For C12E6, it was found that these fluctuations start to dominate at approximately 10 K below the binodal curve, with this onset shifting toward the binodal curve at concentrations near the CMC.[24] However, we cannot exclude the contribution of these fluctuations to the overall light scattering intensity for C8E5 and C10E6 at 50 °C, and thus the Nagg’s at this temperature might be overestimated.

The molecular structure of the surfactant has a considerable influence on Nagg, as shown in Figure . Extending the hydrophilic ethylene oxide chain from E5 to E6 and from E6 to E8 leads to a decrease in Nagg due to an increasing effective head group area for a single surfactant molecule.[47] The decrease in Nagg for an extended ethylene oxide chain is stronger at elevated temperatures. While some authors attribute this to a transition temperature at which the aggregates start to grow from small monodisperse to large polydisperse aggregates,[48] others attribute this to a stronger contribution from the fluctuations near the binodal curve due to a shift of the binodal curve to higher temperatures upon extending the ethylene oxide chain.[44] On the other hand, extending the hydrophobic alkyl chain from C8 to C10 at a constant E6 increases the hydrophobic effect and thus the hydrophobic core volume.[30,49] Therefore, Nagg increases with increasing alkyl chain length for all temperatures investigated (see Figure ).

Besides temperature, also increasing surfactant concentration leads to an increase in Nagg near the CMC for all investigated surfactants (see Figure ). We studied Nagg in a concentration range starting from the CMC to approximately 2 times the CMC. Nagg values for the investigated surfactants available in the literature were all measured at considerably higher concentrations. Therefore, caution has to be taken when comparing Nagg values from this work and from the literature with respect to the measurement temperature and concentration. Table compares Nagg values from this work and from the literature considering both measurement temperature and concentration.

Table 2

Aggregation Numbers (Nagg) from This Work and the Literature for All Surfactants Investigated in This Worka,b

surfactant	T/°C	c/g L–1	c/CMC	Nagg	ref
C8E5	25	70	20.77	90	(50)
	25	11.6	3.44	65	(12)
	25	6.3	1.87	59	this work
	30	17	5.25	80	(51)
	30	6.3	1.94	68	this work
C8E6	r. t.	n. g.		32	(32)
	25	11.7	2.99	45	(12)
	25	7.83	2	44	this work
	30	n. g.		41	(52)
C10E6	25	n. g.		73	(52)
	25	50	142.86	105	(53)
	25	1.91	5.46	74	(12)
	25	0.76	2.17	78	this work
	30	9.22	27.94	66	(37)
C10E8	25	n. g.		66	(54)
	25	50	89.29	70	(53)
	25	2.15	3.84	61	(12)
	25	1	1.79	57	this work

r. t.: room temperature; n. g.: not given.

Nagg is given with respect to the temperature T and concentration c at which the measurements were conducted and c/CMC shows the factor by which the CMC is exceeded at the respective measurement concentration. CMCs from Table were used to calculate c/CMC.

For C8E5, our data show a strong increase of Nagg with concentration at all temperatures investigated (see Figure ). This can also be seen when evaluating the Nagg data from the literature with respect to concentration and temperature. The same applies to C10E6 and C10E8, although our data reveals that the increase of Nagg with concentration for these surfactants is lower compared to C8E5. However, the Nagg data in the literature for C8E6 shows no clear trend of Nagg with concentration. Possible reasons therefore are different measurement techniques that were used to obtain Nagg values. However, the Nagg values from this work show that Nagg is slightly increasing with concentration for C8E6. This emphasizes that a careful evaluation of the measurement concentration is necessary to obtain reliable Nagg values.

The Rh value of the aggregates is influenced by temperature and the molecular structure of the surfactant in the same way as Nagg. Increasing the temperature at a fixed concentration leads to an increase in Rh. Further, extending the ethylene oxide chain at a constant alkyl chain and extending the alkyl chain at a constant ethylene oxide chain leads to a decrease and an increase of Rh, respectively. The reasons for these are the same as for Nagg discussed above.

However, Figure shows an abrupt increase in Rh as the CMC of the surfactant is exceeded. This increase in Rh with concentration is far more profound than the increase of Nagg with concentration. This can be explained considering the different ways of data processing for SLS and DLS. While SLS measures the excess Rayleigh ratio and thus only the scattering of the aggregates, DLS measures the overall (dynamic) scattering and thus also the contribution from the surfactant monomers. Therefore, DLS measures the average intensity-weighted translational diffusion coefficient of the aggregates including the contributions of the surfactant monomers (as no bimodal size distribution is obtained).[55] Hence, due to the monomer contribution, using diffusion coefficients from DLS near the CMC for calculating Rh of the aggregates leads to an underestimation of the actual size. However, as the concentration increases, the aggregate contribution soon starts to dominate the measured diffusion coefficient.[55] This can be seen especially in Figure b for C8E6. For this surfactant, the obtained Rh values from the measured diffusion coefficients exhibit only a minor increase at higher concentrations. We measured an Rh value of 2.25 nm for C8E6 at 7.8 g L–1 and 25 °C, which is in perfect agreement with the Rh of 2.24 nm found at 11.7 g L–1 at the same temperature.[12] However, especially for C10E6 and C10E8, our data show that the diffusion coefficient and thus the obtained Rh values are still affected by the monomer contribution. Measurements at approximately 5 times the CMC resulted in Rh values of 2.80 nm and 2.90 nm for C10E6 and C10E8, respectively.[12] These values fit to the course of the Rh vs concentration curve measured in this work and emphasize that DLS data from surfactant solutions in the vicinity of the CMC must be evaluated carefully with respect to the contributions of surfactant monomers and aggregates.

Conclusions

In this work, the influence of temperature, concentration, and molecular structure (hydrophobic and hydrophilic chain lengths) on the self-assembly of four nonionic surfactants, C8E5, C8E6, C10E6, and C10E8, was investigated. Light scattering techniques (SLS and DLS) were used to determine the CMC as well as Nagg and Rh of the surfactant aggregates.

The CMCs of all investigated surfactants exhibit a minimum in their CMC vs temperature curve around 50 °C. This minimum results from a temperature-sensitive interplay of hydrophilic and hydrophobic interactions of the surfactant molecules among each other and with the surrounding water molecules. A significant growth of the surfactant aggregates with increasing temperature can be seen in both Nagg and Rh. Further, extending the hydrophobic alkyl chain by two carbon atoms leads to an increase of Nagg and Rh while simultaneously the CMC is reduced by approximately 1 order of magnitude. Contrarily, extending the ethylene oxide chain leads to a decrease of Nagg and Rh and a slight increase in the CMC.

The data shown in this paper further improve the understanding of the self-assembly of nonionic CiEj surfactants. The presented influence of temperature, concentration, and molecular structure on a microscopic scale facilitates the choice of a suitable surfactant for a given application, e.g., in a micellar solvent system, based on the surfactant aggregate structure.

Materials and Methods

Preparation of Surfactant Solutions

Surfactants and Millipore water (Milli-Q Synthesis, Merck, Darmstadt, Germany) were weighted gravimetrically using a BP 301S analytical balance (Sartorius, Göttingen, Germany) with an accuracy of ±0.1 mg into a 15 mL Falcon tube (Corning, New York). The surfactants used in this work are listed in Table . The total volume of each surfactant solution was set to 10 mL. All surfactant solutions were shaken thoroughly until the surfactant was fully dissolved. To remove emerging foam, the surfactant solution was subsequently centrifuged for 10 min at 3197g using an Eppendorf Centrifuge 5810 R (Hamburg, Germany). Afterward, the surfactant solution was filtered using a 0.1 μm hydrophilic poly(vinylidene fluoride) (PVDF) syringe filter (Berrytec, Harthausen, Germany). The filter was flushed with the surfactant solution before its use to ensure that the adsorption of surfactant molecules at the filter membrane was negligible.

Table 3

Surfactants Used in This Work with Molar Mass (M), Chemical Abstract Service (CAS) Number, Supplier, Mass Concentration as Given by the Supplier (w/v), and Purity

component	M/g mol–1	CAS-No.	supplier	w/v	purity (%)
C8E5	350.5	19327-40-3	Anatrace	50	≥99
C8E6	394.5	4440-54-4	Anatrace	50	≥99
C10E6	422.6	5168-89-8	Anatrace	25	≥99
C10E8	510.7	24233-81-6	Sigma-Aldrich		≥98

Composition Gradient Multiangle Light Scattering

Surfactant solutions were analyzed using composition gradient multiangle light scattering (CG-MALS) measurements. The CG-MALS setup consists of a pumping and dosing unit (Calypso II), an SLS detector (DAWN HELEOS 8+), and a refractive index (RI) detector (Optilab TrEX) from Wyatt Technology Corporation (Santa Barbara, CA). The DAWN HELEOS 8+ measures the scattered light at eight different angles between 20 and 150°. To measure the SLS and DLS signals simultaneously, the SLS detector at 106° was replaced with a DLS detector (DynaPro Nanostar, Wyatt Technology Corporation, Santa Barbara, CA) using a glass fiber.

The surfactant solutions were mixed in a specific ratio with Millipore water using a static mixer with the Calypso II unit. The mixed solution was subsequently pumped through an online 0.02 μm filter membrane (Anodisc 13, GE Healthcare, Germany) and was then injected into the HELEOS 8+ and Optilab TrEX. Afterward, the flow was stopped and the signals were measured for 5–10 min and light scattering intensities were averaged over the measurement time. The temperature of the DAWN HELEOS 8+ and the Optilab TrEX was kept constant within ±0.01 K. This procedure was repeated automatically for different mixing ratios.

Static Light Scattering

Surfactant monomers self-assemble into aggregates above their CMC in water. This self-assembly causes a sudden increase in the intensity of scattered light.[16] SLS measures the time-averaged intensity of the scattered light expressed as the excess Rayleigh ratio for a vertically polarized light source according to eq .Here, I(θ) and Isolvent(θ) are the total light scattering intensities of the solution and of the pure solvent both at a scattering angle θ, respectively. Intensities are normalized with respect to the intensity of the incident light I0. Further, V is the scattering volume and r is the distance of the detector from the scattering volume. The CMC for a given surfactant can thus be obtained by measuring R(θ) for different surfactant concentrations. Within this work, R(θ) was measured for at least 10 different surfactant concentrations from concentrations lower than the CMC to approximately 2 times the CMC. The CMC was then obtained as the inflexion point in the slope of the R(θ) vs concentration plot.

Further, the MW value of the surfactant aggregates was determined for different concentrations above the CMC using SLS. Since surfactant aggregates are growing with concentration, the classical double-extrapolation Zimm procedure cannot be applied to these systems.[25] To overcome this limitation, we studied dilute concentrations where interactions between the surfactant aggregates are negligible. The MW value of the aggregates was then obtained from SLS measurements using eq .Here, c is the total surfactant concentration, cCMC is the surfactant concentration at the CMC, R(θ) and RCMC(θ) are the total measured Rayleigh ratio and the Rayleigh ratio at the CMC, respectively, and P(θ) is the particle scattering function and gives the angular variation of the scattered light. However, for all systems investigated, no angular variation of the scattered light was observed and hence P(θ) was set to unity in this work. K* is an optical constant and is defined according to eq where n0 is the refractive index of the solvent at the incident wavelength, λ0 is the incident wavelength in vacuum, NA is Avogadro’s number, and dn/dc is the specific refractive index increment of the surfactant aggregates. We measured dn/dc for each surfactant at different temperatures using the RI detector. Only surfactant concentrations above the CMC were used to calculate dn/dc. Nagg was then obtained by dividing MW by the molecular weight of the respective surfactant monomer.

Dynamic Light Scattering

DLS detects the intensity fluctuations of scattered light due to Brownian motion. Time-dependent intensity fluctuations are used to compute an intensity autocorrelation function that contains information about the diffusion of the surfactant molecules in solution. For a surfactant solution, DLS can thus measure the intensity-weighted translational diffusion coefficient Dt of the surfactant aggregates in solution. We used the cumulants analysis in the commercial software package ASTRA (WYATT Technology) to obtain Dt from the intensity autocorrelation function. In a next step, Dt was then used to calculate the hydrodynamic radius Rh of the surfactant aggregates according to the Stokes–Einstein equation (eq ).For that purpose, the temperature T, Boltzmann constant kB, and dynamic viscosity η of the solution are required. Measurements of the solution viscosity showed no significant changes compared to the viscosity of water in the concentration range studied in this work (data not shown). Therefore, we used the viscosity of water at the respective temperature for η.