Development of a method for measurement of relative solubility of nonionic surfactants

Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 Development of a method for measurement of relative solubility of nonionic surfactants Jiangying Wu, Yuming Xu, Tadeusz Dabros, Hassan Hamza CANMET Energy Technology Center-Devon, Natural Resources Canada, Suite A202, 1 Oil Patch Dr., Devon, Alta., Canada T9G 1A8 Received 9 June 2003; accepted 30 October 2003 Abstract Relative solubility number (RSN) provides a practical alternative to the HLB method of assessing hydrophilic lipophilic balance of surfactants. Traditionally, RSN has been determined by titration of a surfactant in benzene/dioxane solution with water. Owing to the toxicity of these solvents, a new procedure for determination of RSN, using less-toxic substances, toluene and ethylene glycol dimethyl ether (EGDE), was developed. The relationship between RSN and classic HLB values for some well-characterized classes of surfactants was investigated. Some factors that might affect RSN value were also studied. The results showed that RSN values determined using toluene/egde were linearly correlated with those determined using benzene/dioxane, indicating that toluene/egde solvent can be used to replace benzene/dioxane. It was found that, within the same surfactant family, RSN values determined at certain molar concentration showed a good linear relationship with classic HLB values. The surfactant concentration in RSN titration solvent affected the RSN values; the effect of salt concentration in the titration water was negligible. A generalized regression model was used to correlate RSN values with the structure parameters of surfactants such as carbon number in hydrophobic groups, C O number and free OH number. Crown Copyright 2003 Published by Elsevier B.V. All rights reserved. Keywords: Surfactant; Nonionic surfactant; Relative solubility number; HLB 1. Introduction RSN has been widely used in the surfactant chemical industry to assist formulation, quality control, and product selection. In emulsion research, RSN is useful in the selection of stabilizers and demulsifiers. For example, Márquez-Silva et al. used RSN as a demulsifier characteristic to study the dehydration of crude oil [1]. In their work they investigated the relationship between dehydration performance and the characteristics of oil, associated water, and demulsifier. As a result, they proposed an empirical equation correlating the acidity number of crude oil, water salinity, and the RSN of demulsifier. The standard RSN value is empirically defined as the volume in milliliters of distilled water necessary to produce persistent turbidity in a benzene/dioxane solvent system consisting of 1 g of surfactant sample and 30 ml solvent [2]. Corresponding author. E-mail address: yxu@nrcan.gc.ca (Y. Xu). It denotes the relative solubilities of a surfactant in water and in oil. Higher numbers indicate a more water-soluble product and lower numbers indicate a more oil-soluble product. Products with RSN < 13 are generally insoluble in water. Products with RSN values between 13 and 17 are dispersible in water at low concentrations and form gels at high concentrations. Products with RSN > 17 are considered soluble in water. Surfactant manufacturers have attached considerable importance to RSN because they think it can be used to reflect changes in the hydrophilic and lipophilic characteristics of nonionic surfactants. For example, Márquez-Silva et al. considered RSN as a measure of the combined affinity for the polar (hydrophilic) and nonpolar (lipophilic) components of the surfactant [1]. It is known that the relative affinities of surfactant for the oil and water phases play an important role in emulsion stability. Previous research demonstrates that when the ratio of interaction of the surfactant with water to its interactions with oil is near or equal to unity, Winsor type III systems are obtained [3], in which the rate of phase separation of emulsion is at a maximum [4,5]. Therefore, a 0927-7757/$ see front matter. Crown Copyright 2003 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2003.10.028

230 J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 comprehensive understanding of RSN is helpful in selecting the most effective demulsifier. Since the 1950s, hydrophile lipophile balance (HLB) value has been widely accepted as a unique parameter to represent the affinity balance between hydrophilic and hydrophobic groups of nonionic surfactants [6,7]. From the definitions of RSN and HLB, it can be seen that the two numbers measure similar properties. For instance, higher RSN or HLB values indicate higher solubilities of surfactant in water. HLB can be determined by experimentation and from a number of simple equations that permit calculations for certain types of nonionic surfactant [8]. However, the applicability of these equations is limited. Furthermore, in many industrial applications it is difficult to obtain sufficient structural information to enable the calculation using the equations. Experimental determination of the HLB value for a surfactant is complicated and subjective. Although dozens of experimental methods for determining HLB values have been tried, two have been commonly used: phase inversion temperature (PIT) [9,10] and emulsion inversion point (EIP) [11,12]. However, unlike the RSN procedure, these two methods are time-consuming and difficult to apply in day-to-day industrial operations. Therefore, the RSN measurement is often the method of choice for both research and industry. Although RSN values have been measured by many surfactant manufacturers and provided to customers as one of the parameters characterizing a surfactant, not much information on the procedure for determining RSN has been reported in the open literature. It is known that benzene/dioxane was the most commonly used RSN solvent, but the percentage of benzene in dioxane varied between companies, which ultimately resulted in discrepancies between reported RSN values. Furthermore, dioxane and benzene are extremely toxic chemicals. Therefore, it is desirable to develop a procedure that uses less-toxic compounds for RSN determination. An improved understanding of the fundamentals of RSN would also enable more effective use of this parameter. In this paper, we report our laboratory test results aimed at developing a procedure using two less-toxic compounds, toluene and ethylene glycol dimethyl ether (EGDE). We also attempted to establish a relationship between RSN and HLB and correlate RSN with the molecular structure of the surfactants investigated. 2. Experimental 2.1. Materials Five surfactants supplied by Champion Technology Ltd. (Houston, Texas) were used as our RSN standards. The RSN values for these five surfactants were provided by Champion Technology and were determined using traditional titration in benzene/dioxane solvent. The RSN values for the five standards covered the range from 5.7 to 19.6. Ethylene glycol dimethyl ether (analytical grade), toluene (analytical grade), and surfactants, listed in Table 1, were all purchased from Aldrich Chemicals and used as received. 2.2. Procedures for RSN measurement RSN was determined by titration of a surfactant in toluene/egde solution with deionized water. The titration was conducted using an auto titrator (Titrino, model 751 GPD) in a titration beaker furnished with a ground lid that has two holes for inserting a colorimeter probe and a solvent delivery tube. A colorimeter (Brinkman, model PC-920) was used to detect the end point. The titration procedure is as follows: (1) Premix toluene/egde at the desired volume ratio to obtain stock RSN titration solvent. (2) Weigh the desired amount of surfactant sample into the beaker. Add the desired amount of RSN titration solvent to the beaker and mix with a magnetic stirring bar until all surfactant is completely dissolved. (The amount of surfactant and solvent added will be discussed in detail in the following sections.) Table 1 Surfactants used in this study Surfactant Nominal structure HLB a MW a Surfactant Nominal structure HLB a MW a Brij30 PEO(4) lauryl ether 9.7 362 Igepal CO 890 PEO(40) nonylphenyl ether 17.50 1982 Brij35 PEO(23) lauryl ether 16.9 1198 Igepal CO 990 PEO(100) nonylphenyl ether 18.90 4626 Brij52 PEO(2) cetyl ether 5.3 331 Tween 20 PEO(20) sorbitan monolaurate 16.7 1228 Brij56 PEO(10) cetyl ether 12.9 683 Tween 40 PEO(20) sorbitan monopalmitate 15.6 1284 Brij72 PEO(2) stearyl ether 4.9 359 Tween 60 PEO(20) sorbitan monostearate 14.9 1312 Brij76 PEO(10) stearyl ether 12.4 711 Tween 80 PEO(20) sorbitan monooleate 15 1310 Brij78 PEO(20) stearyl ether 15.3 1152 Tween 85 PEO(20) sorbitan trioleate 11 1839 Brij98 PEO(20) oleyl ether 15.3 1150 Span 20 sorbitan monolaurate 8.6 346.5 Igepal CA 210 PEO(2) octylphenyl ether 4.80 294.4 Span 40 sorbitan monopalmitate 6.7 402.6 Igepal CA 520 PEO(5) octylphenyl ether 10.00 426.6 Span 60 sorbitan monostearate 4.7 430.6 Igepal CA 720 PEO(12) octylphenyl ether 14.60 735 Span 80 sorbitan monooleate 4.3 428.6 Igepal CO 210 PEO(2) nonylphenyl ether 4.6 308.5 Span 85 sorbitan trioleate 1.8 957.5 Igepal CO 720 PEO(12) nonylphenyl ether 14.20 749 a HLB value and average molecular weight are provided by Aldrich.

J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 231 (3) Titrate deionized water into the surfactant solution until the solution becomes persistently turbid. The end point is considered as the point at which the transmittance is reduced to 80% of original signal and remains at or below that value for 1 min or longer. (4) Record the volume (in ml) of deionized water titrated in at the end point. This volume is considered the RSN value for that surfactant. 3. Results and discussion 3.1. Toluene/EGDE solvent system In order to be suitable for RSN titration, the selected solvent system must produce titration values that reflect the change in its hydrophilic lipophilic property for various surfactants. To validate our new toluene/egde titration system, five surfactants with known RSN values were used for titration in each trial solvent. The titration values obtained from the new solvent system should not be expected to be the same as those obtained from standard solvent because of differences in solvent properties, however, the RSN values from the two solvent systems must be correlated. In the standard RSN titration procedure using benzene/dioxane solvent, 1 g surfactant was added to 30 ml solvent. To make our procedure as consistent as possible with the standard procedure, we adopted a similar concentration in our first series of experiments, i.e. 1 g surfactant in 30 ml solvent. For convenience, we use the term RSN(B/D) in this work to represent RSN values obtained from the dioxane/benzene system and RSN(T/E) for values obtained from our toluene/egde system. Since the toluene-to-egde ratio directly affects the RSN measurement results, several solvents with different toluene-to-egde ratios covering the range from 1 to 5% (v/v) were tested. To validate the new RSN procedure, RSN(T/E) values were plotted against RSN(B/D) values. Although we tested the solvents using eight different concentrations of toluene, for the sake of clarity, only three sets of data are shown in Fig. 1, i.e. 5.0, 2.6, and 1.0% (v/v). Fairly good linear relationships were obtained between the RSN(T/E) and RSN(B/D) values. Linear equations correlating the RSN val- Fig. 1. RSN values measured with toluene/egde at different compositions vs. RSN values measured with benzene/dioxane. ues for all eight solutions are listed in Table 2. It can be noted from Fig. 1 and Table 2 that the slope of the regression line decreases monotonically with increasing toluene concentration, indicating that the solvent system is more sensitive to RSN values at very low toluene concentrations. However, the RSN values obtained in these low-toluene solvents are very different from those obtained using the standard method. In order to make the RSN data from the new solvent system as comparable to the standard data as possible, a slope in Fig. 1 equal to or near unity would be ideal. Two criteria were used for selecting the best solvent composition: correlation coefficient (R 2 ) of the linear regression and the sum of the squares of the differences between the five measured RSN values and the standard RSN values, i.e. [RSN(T/E) RSN(B/D)] 2 or ( RSN) 2. The former measures how well the new RSN(T/E) values are correlated to the standard RSN values, while the latter measures how RSN(T/E) values differ from the standard values. The regression equations, correlation coefficients (R 2 ), and the sums of the RSN difference squares [ ( RSN) 2 ] for all eight solvent systems are listed in Table 2. Furthermore, we plotted the regression correlation coefficient and sum of the difference squares as functions of toluene percentage in the solvent, as shown in Fig. 2. As the graph shows, a transition point can be seen at a toluene concentration around 2.6% (v/v). The R 2 values increase almost linearly as the toluene concentration in the solvent decreases from 5 to 2.6% (v/v). Table 2 Fitting equations, R-squared values, and the sums of RSN difference squares Toluene in RSN solvent (%, v/v) Fitting equation Correlation coefficient (R 2 ) 5 RSN(T/E) = 0.5591RSN(B/D) + 2.5684 0.8729 49.4 4 RSN(T/E) = 0.693RSN(B/D) + 1.849 0.8935 27.2 3 RSN(T/E) = 0.9209RSN(B/D) + 0.3344 0.9354 6.2 2.7 RSN(T/E) = 1.0343RSN(B/D) 0.5099 0.9587 5.4 2.6 RSN(T/E) = 1.0895RSN(B/D) 1.0569 0.9718 4.8 2.5 RSN(T/E) = 1.1842RSN(B/D) 1.4359 0.9736 9.5 2.0 RSN(T/E) = 1.3997RSN(B/D) 3.1108 0.9881 27.1 1.0 RSN(T/E) = 2.343RSN(B/D) 10.6 0.9895 277 ( RSN) 2

232 J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 Fig. 2. Correlation coefficient and sum of RSN differences as a function of toluene concentration in the titration solvent. At concentrations below 2.6% (v/v), the R 2 values became almost constant. It is interesting to note that, at concentrations around 2.6% (v/v), the sum of the RSN difference squares shows a minimum. Both the transition point and minimum point occur at similar solvent compositions. This clearly demonstrates that there is an optimal solvent composition, which should be in the range between 2.6 and 2.7% (v/v) toluene. The reproducibility of this procedure was determined by repeating the RSN measurement for a selected surfactant, Tween 80 (PEO(20) sorbitan monooleate), at the same condition, i.e. solvent consisting of 2.6% (v/v) toluene and 97.4% (v/v) EGDE, 1 g surfactant in 30 ml solvent. A total of seven independent measurements were conducted on different dates giving an average of 13.28 and standard deviation of 0.059. As the data show, the reproducibility of the measurements was better than 1%. In order to test the applicability of the new RSN procedure, we measured the RSN values for a number of demulsifiers supplied by Akzo Nobel Surface Chemistry LLC. They also provided the RSN values for these demulsifiers. Their RSN values were measured using the benzene/dioxane solvent system, but the benzene concentration in their solvent was lower than that used by Champion Technology. Fig. 3 compares the RSN(T/E) values obtained using our new procedure and those provided by Akzo Nobel. The graphs indicate a reasonably good correlation between the two sets of RSN values, although RSN(T/E) values are consistently Fig. 3. RSN values for demulsifiers supplied by Akzo Nobel Surface Chemistry LLC. lower than RSN(B/D) provided by Akzo Nobel. It was also noted that the differences between the RSN(T/E) values measured in this work and those obtained from benzene/dioxane solvent for Akzo Nobel demulsifier are greater than those for the Champion standard surfactants. This discrepancy is, in our opinion, due to the difference in benzene concentrations in the titration solvents used by Akzo Nobel and Champion. Fig. 3 further shows that the RSN(T/E) determination procedure could be applied for industrial RSN measurements. Based on findings discussed above, we chose solvent comprising 2.6% (v/v) toluene and 97.4% (v/v) EGDE as the new standard solvent for all our RSN measurements. The RSN data reported below were all measured using this new standard solvent and from now on we will use RSN to denote RSN determined using the new solvent system. 3.2. Mechanism of RSN test procedure As mentioned earlier, RSN is a useful parameter related to the hydrophilic hydrophobic balance of nonionic surfactant. It is well known that the appearance of turbidity from a clear solution indicates a phase separation. In order to understand the phenomenon of the appearance of turbidity, a series of experiments were conducted to investigate the mechanism of the complex phase separation behind the RSN test procedure. In these experiments a small amount of oil-soluble dye powder was added to the system. After the turbid solution had been allowed to stand motionless for a few hours, it separated into two clear phases. On the top was a thin layer with darker color, containing an elevated concentration of the dye, and, therefore, more oil (toluene). This phenomenon was observed for all surfactants tested regardless of the RSN values. To gain a better understanding of phase separation behavior, we conducted five additional titration tests in which the compositions in the two phases were analyzed. At the end of titration the turbid system was allowed to separate into two phases, either by long-time settling or centrifugation, and samples from the top and bottom phases were collected using a micro-syringe. The organic composition was determined by gas chromatography and water content by Karl Fischer titration. Because the surfactant molecules did not elute from the GC column, the surfactant concentration could not be determined using GC. We also attempted other methods, however, no reliable data were obtained. Therefore, only the ratios of toluene/egde are reported. The results are listed in Table 3. Because the volume of the top phase is very small (0.1 0.6 ml) compared to the volume of the bottom phase (35 50 ml) the toluene-to-egde ratio in the bottom phase remained almost constant, which was also confirmed by GC analysis. As shown in Table 3, the toluene concentration in the top layer is always higher than that in the bottom phase, and depends upon the characteristics of the surfactant; more specifically, it increases with the RSN value of the surfactant. At the same time, the water content in the

J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 233 Table 3 Composition of two phases from RSN titration Surfactant H 2 O titrated (ml) or RSN Toluene-to-EGDE ratio Top phase Bottom phase Water content (wt.%) Top phase Bottom phase None 20.7 0.104 =0.026 7.3 44.5 Tween 20 16.3 0.080 =0.026 13.6 37.7 Tween 80 13.3 0.064 =0.026 13.4 33.6 Span 20 9.8 0.055 =0.026 6.8 27.2 Span 85 4.2 0.046 =0.026 4.3 14.6 top phase is much lower than that in the bottom phase. The water contents in both phases also increase with the RSN value of the surfactant. Bearing in mind the compositions of the two phases, we can speculate on the mechanism of the RSN titration. It is known that EGDE is miscible with both water and toluene, but water and toluene are immiscible. When a small amount of water is titrated into the RSN solvent (toluene and EGDE) without surfactant, EGDE dissolves both water and toluene. However, when the water addition exceeds a certain amount, the EGDE can no longer hold the toluene and water together, and new phase rich in toluene and low in water precipitates out. At this point the solution becomes turbid. When the turbid solution is allowed to stand, the precipitated low-water phase separates slowly from the bulk phase to the top due to the density difference. When the solvent contains surfactant, the hydrophobic group in the surfactant enhances the hydrophobicity of the system, while the hydrophilic groups are hydrated with water molecules. The ability of EGDE to dissolve water and toluene is altered by the presence of the surfactant. The amount of water that the solvent can tolerate depends on the hydrophobic hydrophilic characteristics of the surfactant. If the surfactant is more hydrophobic, the presence of surfactant increases the hydrophobicity of the solvent and, therefore, less water is needed to cause the phase separation, resulting in a smaller RSN value. For the hydrophilic surfactant, the surfactant molecules themselves bond to some water molecules because of hydration and increase the volume of water dissolved in EGDE. The more hydrophilic the surfactant, the more water is needed for hydration and, therefore, the higher the RSN value. From the explanation above, RSN can indeed be considered as a parameter that reflects the relative affinities of hydrophilic and hydrophobic groups in a nonionic surfactant. 3.3. Relationship between RSN and HLB Since the HLB is a well known and widely used property and relative solubility numbers are easily measured, it would be useful to find a relationship between them. Four families of surfactants with known HLB values and known chemical structures were selected to investigate the relationship between RSN and HLB. The surfactants included the Fig. 4. Relationship between HLB and RSN values determined in 1 g per 30 ml solution. Brij (PEO alkyl ether), Igepal (PEO alkylphenyl ether), Span (sorbitan ester), and Tween (PEO sorbitan ester) families. In the first series of RSN measurements we applied the procedure that uses 1 g surfactant in 30 ml solvent. The HLB and RSN values are shown in Fig. 4. It can be seen that there is no an overall correlation between RSN and HLB values. However, considerable correlations can be seen within individual surfactant families, especially for the Tween and Span families, in which very good linear relationships exist with R 2 values around 0.97. The correlations for the Igepal and Brij families are weaker. It is believed that the deviation from a linear relationship was caused by the large differences between the molecular weights of the surfactants. From the data in Table 1 we can see that the molecular weight for the Tween family varied from 1200 to 1800, and for the Span family, from 350 to 950. However, molecular weight changed from 330 to 1200 for the Brij family and from 300 to 4600 for the Igepal family. When the surfactant solutions contained the same mass (1 g) of surfactant, the large variations in molecular weight resulted in significant differences in the number of molecules in the solutions. Therefore, the use of molar concentration appears to be called for instead of mass concentration in the RSN determination. In the next series of measurements, RSN values were determined at surfactant concentrations of 0.02 and 0.05 mol/l in 30 ml RSN solvent. The titration results, shown in Figs. 5 and 6, confirm that when molar concentration of surfactant is used, the RSN values show very good linear relationships with HLB values. The R 2 values for linear regressions between HLB and RSN for all four families of surfactants are over 0.96, except for the Brij family at a concentration of 0.02 mol/l, where it is 0.896. These results indicate that RSN values determined at the same molar concentration represent the hydrophobic hydrophilic balance more accurately. An empirical relationship between RSN and HLB was established: HLB = A RSN + B (1) where A and B are empirical constants varying with surfactant family. Their values depend on characteristics of the

234 J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 Fig. 5. Relationship between HLB and RSN values determined in 0.05 mol/l solution. Fig. 6. Relationship between HLB and RSN values determined in 0.02 mol/l solution. hydrophobic and hydrophilic groups. The constants A and B for the four families of surfactants studied in this work are summarized in Table 4. By using Eq. (1) and the constants reported in Table 4, HLB values of nonionic surfactants of these families can be estimated from their measured RSN values using the procedures recommended in this paper. 3.4. Prediction of RSN values from molecular structure It is well known that surfactant properties such as critical micelle concentration (cmc), cloud point, HLB, etc., depend on molecular structure. In previous research several empirical relationships were developed to relate the surfactant properties to structure parameters such as ethylene oxide number and alkane carbon number for some homologous compounds [13 15]. Recently, Huibers et al. correlated cmc of nonionic surfactants with more general structure parameters [16]. The correlations were not limited to a homologous series but extended to a variety of nonionic surfactants. In their work they used topological descriptors that represent contributions from the size of the hydrophobic group, the size of the hydrophilic group, and the structural complexity of the hydrophobic group. A similar correlation was performed on cloud points of surfactants by Huibers et al. [17]. In this work we also attempted to correlate the RSN values to surfactant structure by adopting a scheme similar to that used by Becher [14] and Ravey et al. [18]. We had RSN values for 25 surfactants covering four surfactant families, i.e. PEO alkyl ether, PEO alkylphenyl ether, sorbitan ester, and PEO sorbitan ester. Unlike Becher and Ravey, we used the following three structure parameters: carbon number in hydrophobic group (C#), C O number (CO#), and free OH number (OH#). The C O number includes all ethylene oxide, C O in ether, and double bond C=O in ester. The reason for separating the free OH as an independent parameter is that we believe the contribution of the free OH group to the hydrophilic property is much greater than that of oxygen in ether or ethylene oxide. This is also true when using the group contribution method to calculate the HLB number, in which the assigned number for free OH group is much higher than that for the ethylene oxide group. The first parameter, C#, represents the hydrophobicity and the second two parameters, C O# and OH#, measure the hydrophilicity of the nonionic surfactants. The RSN values were correlated to the structure parameters by multiple parameter polynomial regression using STA- TISTICA 6.0. In the regression all possible combinations of the parameters were generated by the program and only the statistically significant terms were maintained to achieve the best regression. The following equation was obtained from the regression for RSN values (0.02 M surfactant solution in toluene/egde solvent): RSN = A + B CO# + C(CO#) 2 + D OH# + E(OH#) 2 + F C# (2) The regression coefficients and standard errors are listed in Table 5. The coefficient A, 20.7, represents the RSN number when the other parameters are all zero, which is the experimentally observed volume of water titrated to blank toluene/egde solvent. Positive numbers for coefficients B Table 4 Constants for empirical linear correlation between RSN and HLB (Eq. (1)) for four families of nonionic surfactants 0.05 mol/l 0.02 mol/l A B R 2 A B R 2 Brij (PEO alkyl ether) 0.568 2.0271 0.964 1.1019 11.357 0.896 Tween (PEO sorbitan ester) 0.6029 6.7624 0.971 0.6495 5.9761 0.961 Span (sorbitan ester) 1.0236 2.4167 0.967 0.8978 2.7488 0.965 Igpel (PEO alkylphenyl ether) 0.8596 9.3896 0.968 2.5189 43.11 0.964

J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 235 Table 5 Regression coefficients and S.E. for Eq. (2) Coefficient Value S.E. A 20.7 B 0.344 0.04 C 0.00287 0.0004 D 7.00 1.04 E 2.94 0.31 F 0.448 0.03 and D indicate that the RSN values increase with ethylene oxide group and free OH group. The negative numbers for coefficients C and E (second-order parameter) are corrections for the first-order parameters. Coefficient F is also negative, indicating the RSN value decreases with hydrophobic chain length. Eq. (2) was obtained from regression of all four families of surfactants. It is not limited to a specific family and, therefore, is a generalized model for at least these four families. Using Eq. (2) one can predict the RSN number of other surfactants in these families. Whether the equation is applicable to other families requires further investigation. Fig. 7 shows the scatter plot for the calculated RSN values versus the experimentally measured RSN values. As the plot shows, a reasonable prediction can be made using Eq. (2). 3.5. Effect of surfactant concentration It was noted earlier that the RSN changed when the surfactant concentrations in titration solution varied from 1 g per 30 ml to 0.05 mol/l as seen in Figs. 4 6. This indicates that the RSN values are also dependent on surfactant concentration in the titration solution. We investigated the effect of surfactant concentration in the titration solution on the RSN values for all four surfactant families; the titration results are presented in Figs. 8 11. The surfactant concentrations typically ranged from 0.01 to 0.1 mol/l. From the graphs in Figs. 8 11 it can be observed that the degree of the effect of surfactant concentration on RSN is dependent upon Fig. 8. RSN values as functions of concentration in titration solution for the Brij family. Fig. 9. RSN values as functions of concentration in titration solution for the Tween family. Fig. 10. RSN values as functions of concentration in titration solution for the Igepal family. Fig. 7. Scatter plot for predicted vs. measured RSN values obtained in 0.02 M surfactant in toluene/egde solution. Fig. 11. RSN values as functions of concentration in titration solution for the Span family.

236 J. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 232 (2004) 229 237 the RSN value of the surfactant. For surfactants with RSN greater than about 20, RSN increases with surfactant concentration. The greater the RSN value of the surfactant, the more rapidly RSN increases with concentration. For surfactants with RSN less than about 20, the RSN value decreases when the surfactant concentration increases. The smaller the RSN value of a surfactant, the more rapidly it decreases. The graphs also show that when the surfactant concentration approaches zero the RSN values approach about 21, as indicated before. The dependence of RSN on surfactant concentration can be explained by the surfactant properties. As mentioned earlier, the RSN value characterizes the hydrophobic and hydrophilic properties of the surfactant. The higher the RSN values, the more hydrophilic the surfactant. Therefore, more water is needed for the hydrophilic group to be hydrated. On the other hand, the low-rsn surfactants are more hydrophobic. The increase in the surfactant concentration increases the overall hydrophobicity of the system and, therefore, reduces the volume of water required to titrate to phase separation. This result provides a further confirmation of the mechanism of the RSN test procedure as described in the previous section. The results shown in Figs. 8 11 also explain why the correlations between HLB and RSN for the Igepal and Brij families are less satisfactory than those for the Tween and Span families when mass concentration is used in the titration, as shown in Fig. 4. In the first two families, some surfactants have high RSN values that are sensitive to the concentration. Different concentrations result in different RSN values. For example, in the Igepal series, there are two points (HLB 17.5 and 18.9) that are far from the regression line. These two points are actually for the two samples having much larger molecular weights than the rest samples. At the same mass concentration their molar concentrations would be much lower than those of the other points. These two points are also in the high-rsn range and are sensitive to concentration. Therefore, these two factors (lower concentration and higher sensitivity to concentration) resulted in lower RSN values and led to deviations from the regression line. If their concentrations were adjusted to molar concentrations similar to those of the other points the RSN values would be much higher and would therefore much closer to the regression line. For the Tween and Span families, the RSN values for all surfactants tested in this work are smaller than 20 and the concentrations used are in the range that is insensitive to small changes in concentration. Therefore, both mass concentration and molar concentration gave similar correlation results, as shown in Figs. 4 and 5. Figs. 8 11 also imply that it is important to choose an appropriate concentration for RSN measurement. If the concentration is too low, the RSN values measured are not sufficiently sensitive to the characteristics of the surfactant. Therefore, sufficiently high concentration of surfactant in RSN solvent is recommended. However, the solubility of surfactant in the solvent may limit the concentration. Table 6 Effect of salt concentration in water on RSN value DI water 0.05 M NaCl 0.1 M NaCl Brij30 19.30 18.50 18.19 Tween 20 16.85 16.40 16.34 Igepol CO210 18.71 18.07 17.73 3.6. Effect of salt concentration in titration water In the petroleum industry, the application of surfactant commonly involves salty water. Previous research has already demonstrated that the salt concentration in water phase has very little effect on the performance of nonionic surfactants [19]. In order to confirm that the RSN values measured using this new procedure can be also applied to salt water systems, we conducted several RSN measurements using two NaCl solutions, 0.05 and 0.1 M, as titration water. Three surfactants were chosen for the salty water titration at a surfactant concentration of 0.02 mol/l. The titration results, displayed in Table 6, show that salinity has a very small effect on measured RSN values. The RSN value decreases by about 1 ml when water salinity increases from 0 to 0.1 M. This result agrees with the previous findings that the performance of nonionic surfactant is hardly affected by the salt concentration in water. 4. Conclusions 1. The new RSN solvent system (EGDE and toluene) was developed to replace the standard solvent system (benzene and dioxane). The optimal toluene concentration in the solvent is 2.6% (v/v). The RSN values measured using the new solvent (2.6% (v/v) toluene and 97.4% (v/v) EGDE) system correlated very well with those measured using benzene/dioxane. 2. A generalized regression model was obtained for prediction of the RSN values for nonionic surfactants based on their structure parameters: carbon number in hydrophobic group, C O number, and OH number. 3. RSN values measured using molar concentration of surfactant show good linear correlation with HLB values. Although there is no universal correlation between RSN and HLB that covers all kinds of surfactants, good linear correlations exist within families of surfactants. 4. Surfactant concentration in the titration solution affects measured RSN values. However, the degree of the concentration dependence varies with the surfactant property. For high-rsn (>20) surfactants, RSN values increase with surfactant concentration. The higher the RSN value, the more rapidly the RSN changes with the concentration. For low-rsn (<20) surfactants, RSN values decrease sharply with increasing surfactant concentration in the initial low-concentration range, but the RSN values decrease only slightly with further increase in surfactant concentration.

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