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Critical Micellar C oncentration? (C MC) of Binary and Ternary C ombinations at 300 K TABLE 1 @ Values in parentheses are obtained from Clint’s Eq. [15]. The average error in the CMC is +3%.

Table 1 Critical Micellar C oncentration? (C MC) of Binary and Ternary C ombinations at 300 K TABLE 1 @ Values in parentheses are obtained from Clint’s Eq. [15]. The average error in the CMC is +3%.

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The cationic surfactant CPC has two CMCs already reported (28, 29). The binary mixtures of CPC with other cationic sur- factants have shown two CMC values 48). But from Table 1, it has been observed that there is only one CMC for the binary mixtures of CPC with nonionic surfactants, Tw-40 and Bj-56. Except the CMC of the CPC/Tw-40 mix CMCs of the binaries lie between the i ture atacpc = 0.17, the ndividual values of the surfactants. The CMCs of the ternaries increased systematically with increasing proportion of CPC in the mixture. The CMC values of binary and ternary mixtures 0 f surfactants agree with literature values and are similar to the report on the binary and
The cationic surfactant CPC has two CMCs already reported (28, 29). The binary mixtures of CPC with other cationic sur- factants have shown two CMC values 48). But from Table 1, it has been observed that there is only one CMC for the binary mixtures of CPC with nonionic surfactants, Tw-40 and Bj-56. Except the CMC of the CPC/Tw-40 mix CMCs of the binaries lie between the i ture atacpc = 0.17, the ndividual values of the surfactants. The CMCs of the ternaries increased systematically with increasing proportion of CPC in the mixture. The CMC values of binary and ternary mixtures 0 f surfactants agree with literature values and are similar to the report on the binary and
Interfacial and Thermodynamic? Behaviors of Pure and Binary Mixtures at 300 K ' The average errors in AG 5, and AG $, are +4 and +3%, respectively. TABLE 2 where N is Avogadro’s number. Pmax and Amin Values have been evaluated from the least-square slopes of the z vs logC plot (figure not shown to save space). The zcmc, P2t,, and A®t val- ues for the binary and ternary combinations are presented in Tables 2 and 3, respectively. For the binaries, Cmax values in- crease with the mole fraction of CPC in the CPC/Tw-40 combi- nation, indicating the increase of synergistic interaction among the adsorbed CP* cations in the layers of the micelles, whereas Imax Values decrease in two other combinations. Obviously, the
Interfacial and Thermodynamic? Behaviors of Pure and Binary Mixtures at 300 K ' The average errors in AG 5, and AG $, are +4 and +3%, respectively. TABLE 2 where N is Avogadro’s number. Pmax and Amin Values have been evaluated from the least-square slopes of the z vs logC plot (figure not shown to save space). The zcmc, P2t,, and A®t val- ues for the binary and ternary combinations are presented in Tables 2 and 3, respectively. For the binaries, Cmax values in- crease with the mole fraction of CPC in the CPC/Tw-40 combi- nation, indicating the increase of synergistic interaction among the adsorbed CP* cations in the layers of the micelles, whereas Imax Values decrease in two other combinations. Obviously, the
FIG.2. Dependence of the CMC of the temary mixtures of CPC, Tw-40, anc Bj-56 on their compositions at 300 K. The base points are in terms of component mol% compositions. where I =[(2 —g)F'cp+ + Ttw—4ol, andr ®'=[(2 —g)Pcp+ + I'pj-5e], respectively. Deterrence mel De Peas AN «axel BS Er
FIG.2. Dependence of the CMC of the temary mixtures of CPC, Tw-40, anc Bj-56 on their compositions at 300 K. The base points are in terms of component mol% compositions. where I =[(2 —g)F'cp+ + Ttw—4ol, andr ®'=[(2 —g)Pcp+ + I'pj-5e], respectively. Deterrence mel De Peas AN «axel BS Er
FIG.3. Dependence of area!, of the ternary mixtures of CPC, Tw-40, and Bj-56 on their compositions at 300 K. The base points are in terms of component mol% compositions. Amin Values of the mixtures are in the reverse order. The in- terfacially adsorbed mixed surfactant monolayer of CPC/Tw- 40 is more compact compared to Tw-40/Bj-56 and CPC/Bj-56 monolayers. For CPC/Tw-40 and CPC/Bj-56, the observed max values are ~5-15% lower than the calculated values (except acpc = 0.17 in the CPC/Bj-56 mixture), whereas for Tw-40/Bj- 56, these cannot be predicted. For the temaries, both r2t, and A‘ are independent of the sample compositions. The observed riot values are ~5-20% higher (except the first composition) and the A®! values are ~5-20% lower than the calculated val- ues. The ternary mixtures are nonideal and complex, and ratio- nalization of the results may be a difficult task but qualifies for advanced investigation. The A®! composition profile in three- dimensional form is represented in Fig. 3. Like Fig. 2, this pattern is also folded. The r°t, values also show a similar trend (not shown to save space).
FIG.3. Dependence of area!, of the ternary mixtures of CPC, Tw-40, and Bj-56 on their compositions at 300 K. The base points are in terms of component mol% compositions. Amin Values of the mixtures are in the reverse order. The in- terfacially adsorbed mixed surfactant monolayer of CPC/Tw- 40 is more compact compared to Tw-40/Bj-56 and CPC/Bj-56 monolayers. For CPC/Tw-40 and CPC/Bj-56, the observed max values are ~5-15% lower than the calculated values (except acpc = 0.17 in the CPC/Bj-56 mixture), whereas for Tw-40/Bj- 56, these cannot be predicted. For the temaries, both r2t, and A‘ are independent of the sample compositions. The observed riot values are ~5-20% higher (except the first composition) and the A®! values are ~5-20% lower than the calculated val- ues. The ternary mixtures are nonideal and complex, and ratio- nalization of the results may be a difficult task but qualifies for advanced investigation. The A®! composition profile in three- dimensional form is represented in Fig. 3. Like Fig. 2, this pattern is also folded. The r°t, values also show a similar trend (not shown to save space).
Interfacial and Thermodynamic? Behaviors of Ternary Mixtures of CPC, Tw-40, and Bj-56 at 300 K ® The average errors in AG 5, and AGS, are +4, and +3%, respectively. TABLE 3
Interfacial and Thermodynamic? Behaviors of Ternary Mixtures of CPC, Tw-40, and Bj-56 at 300 K ® The average errors in AG 5, and AGS, are +4, and +3%, respectively. TABLE 3
@ Compositions and sequence as in Table 1A(1). > Pure micelles (n, ¢): CTAB (61, 51); SDS (50, 26); TX-100 (134, 5); Tw-20 (86, 12); Tw-40 (92, 12); Tw-60 (112, 5); Tw-80 (124, 5); Bj-35(40, 23); Bj-56 (141, 57). [The n and « values are taken from Refs. 48-50, 56, and 60.] “Kc was obtained using Eq. [13] with fluorescence data. Aggregation Number, Dielectric C onstant,> and Binding ,onstant (Kc)° for Binary Mixtures’ of Tw-40 and Bj-56 at 300 K
@ Compositions and sequence as in Table 1A(1). > Pure micelles (n, ¢): CTAB (61, 51); SDS (50, 26); TX-100 (134, 5); Tw-20 (86, 12); Tw-40 (92, 12); Tw-60 (112, 5); Tw-80 (124, 5); Bj-35(40, 23); Bj-56 (141, 57). [The n and « values are taken from Refs. 48-50, 56, and 60.] “Kc was obtained using Eq. [13] with fluorescence data. Aggregation Number, Dielectric C onstant,> and Binding ,onstant (Kc)° for Binary Mixtures’ of Tw-40 and Bj-56 at 300 K
FIG. 4. (1-Fr)~! vs [S]/FRr plots according to Eq. [13] for ST (10-5 mol dm~3) in a Tw-40/Bj-56 mixture at different mole ratios at 300 K:(a) 1:2; (b) 1:1; (c) 2:1; (d) 1:5; (e) 5: 1. Ordinate scales are indicated on the plots.
FIG. 4. (1-Fr)~! vs [S]/FRr plots according to Eq. [13] for ST (10-5 mol dm~3) in a Tw-40/Bj-56 mixture at different mole ratios at 300 K:(a) 1:2; (b) 1:1; (c) 2:1; (d) 1:5; (e) 5: 1. Ordinate scales are indicated on the plots.
FIG.5. The profile of dielectric constant (¢) and micellar aggregation num- ber (n) for pure and mixed surfactant systems (Tw-40/Bj-56 mixture according to Table 4). Open circle for pure micelles and closed circle for mixed micelles.
FIG.5. The profile of dielectric constant (¢) and micellar aggregation num- ber (n) for pure and mixed surfactant systems (Tw-40/Bj-56 mixture according to Table 4). Open circle for pure micelles and closed circle for mixed micelles.
FIG.6. Thedielectric constant («) and mole fraction of CPC (acpc) plot for CPC/Tw-40 (O), CPC/Bj-56 (C1), and CPC/Tw-40/Bj-56 (@) mixed surfactant systems.
FIG.6. Thedielectric constant («) and mole fraction of CPC (acpc) plot for CPC/Tw-40 (O), CPC/Bj-56 (C1), and CPC/Tw-40/Bj-56 (@) mixed surfactant systems.
TABLE 5 The values of Xp, 8, and activity coefficients (fg) are given in Table 5. The micellar composition (Xp) increases with in- creasing stoichiometric composition for different mixtures. For nonionic mixtures (Tw-40/Bj higher than the other two. T position and negative show s sults have been obtained witl 14-17, 49, 50). The activity 56 combinations according -56), Xp values are comparatively he amphiphilic mutual interaction parameter (fp) values are not constant with the mixture com- mall minor synergism. Similar re- h other surfactant mixtures (7, 12, coefficients of the amphiphiles in the mixed micelles of Tw-40/Bj-56, CPC/Tw-40, and CPC/Bj- to Rubingh’s treatment are lower for the former and nearly unity for the latter. In the mixed mi- celles containing CPC molecules, these have very low activities while nonionic amphiphilic molecules retain their normal activ- ity. This manifests molecular activity phenomenon of a pair of amphiphiles having similar tails but dissimilar headgroups. The where a is the mole fraction of a surfactant in the solution and x the mole fraction of that surfactant in the mixed micelle, is given by the relation
TABLE 5 The values of Xp, 8, and activity coefficients (fg) are given in Table 5. The micellar composition (Xp) increases with in- creasing stoichiometric composition for different mixtures. For nonionic mixtures (Tw-40/Bj higher than the other two. T position and negative show s sults have been obtained witl 14-17, 49, 50). The activity 56 combinations according -56), Xp values are comparatively he amphiphilic mutual interaction parameter (fp) values are not constant with the mixture com- mall minor synergism. Similar re- h other surfactant mixtures (7, 12, coefficients of the amphiphiles in the mixed micelles of Tw-40/Bj-56, CPC/Tw-40, and CPC/Bj- to Rubingh’s treatment are lower for the former and nearly unity for the latter. In the mixed mi- celles containing CPC molecules, these have very low activities while nonionic amphiphilic molecules retain their normal activ- ity. This manifests molecular activity phenomenon of a pair of amphiphiles having similar tails but dissimilar headgroups. The where a is the mole fraction of a surfactant in the solution and x the mole fraction of that surfactant in the mixed micelle, is given by the relation
Micellar C omposition (X#), Components Activity Coefficient (£8), and CMC gy in Ternary Mixtures of CPC /Tw-40/Bj-56 by the RH Method at 300 K at Different Stoichiometric C ompositions (a) lower than the experimental results and the difference is maxi- mum for composition 7. Both the calculated (RH method) and experimental CMC results are lower than the CMC cjint, indicat- ing the nonideal nature of a mixed mic ellar system. Thus, the RH model is applicable for multicomponent nonideal mixed micel- lar systems. For mixtures of ionic and nonionic surfactants, this model neglects effects due to binding of counterions, suggesting that deviations due to each effect eith er are small or can be em- pirically accounted for the net interac from a mixed micellar system. tion parameter determined low. The physicochemical properties of CPC in the mixed mi- celles have been influenced by the solvation (hydration) of the polyethylene oxide headgroups of Tw-40 and Bj-56 in which the environment of the headgroup (C5;H;N*H) of CPC resides. The g values in CTAB/TX -100/Tw-80 mixed micelles are high, whereas these values are significantly low in SDS/Tw-20/Bj-35 and CPC/Tw-40/Bj-56 mixtures. The max and Amin values for CPC/Tw-40/Bj-56 mixtures are comparable to those of SD S/Tw- 20/Bj-35. In these mixtures, CMCRy are comparable to CMC ops. But in the CTAB/TX-100/Tw-80 system (49), the RH theory has, however, ended up with unexpected results which fail to explain the experimental findings. The amphiphiles of the sys- tem are incompatible due to a difference in their nonpolar tails as well as their headgroup structures which add complications. The mixtures SD S/Tw-20/Bj-35 (50) and CPC/Tw-40/Bj-56 (herein studied) have heterogeneous character only with respect to the headgroups of the amphiphiles for each system and so compar- atively these systems are simple. This area thus needs further, detailed investigation.
Micellar C omposition (X#), Components Activity Coefficient (£8), and CMC gy in Ternary Mixtures of CPC /Tw-40/Bj-56 by the RH Method at 300 K at Different Stoichiometric C ompositions (a) lower than the experimental results and the difference is maxi- mum for composition 7. Both the calculated (RH method) and experimental CMC results are lower than the CMC cjint, indicat- ing the nonideal nature of a mixed mic ellar system. Thus, the RH model is applicable for multicomponent nonideal mixed micel- lar systems. For mixtures of ionic and nonionic surfactants, this model neglects effects due to binding of counterions, suggesting that deviations due to each effect eith er are small or can be em- pirically accounted for the net interac from a mixed micellar system. tion parameter determined low. The physicochemical properties of CPC in the mixed mi- celles have been influenced by the solvation (hydration) of the polyethylene oxide headgroups of Tw-40 and Bj-56 in which the environment of the headgroup (C5;H;N*H) of CPC resides. The g values in CTAB/TX -100/Tw-80 mixed micelles are high, whereas these values are significantly low in SDS/Tw-20/Bj-35 and CPC/Tw-40/Bj-56 mixtures. The max and Amin values for CPC/Tw-40/Bj-56 mixtures are comparable to those of SD S/Tw- 20/Bj-35. In these mixtures, CMCRy are comparable to CMC ops. But in the CTAB/TX-100/Tw-80 system (49), the RH theory has, however, ended up with unexpected results which fail to explain the experimental findings. The amphiphiles of the sys- tem are incompatible due to a difference in their nonpolar tails as well as their headgroup structures which add complications. The mixtures SD S/Tw-20/Bj-35 (50) and CPC/Tw-40/Bj-56 (herein studied) have heterogeneous character only with respect to the headgroups of the amphiphiles for each system and so compar- atively these systems are simple. This area thus needs further, detailed investigation.
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EngineeringThermodynamicsCritical micellar concentration
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