Physical Chemistry of Surfactant Solutions

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Physical Chemistry of Surfactant Solutions 2.1

Properties of Solutions of Surface Active Agents

The physical properties of surface active agents differ from those of smaller or nonamphipathic molecules in one major aspect, namely the abrupt changes in their properties above a critical concentration [1]. Figure 2.1 illustrates with plots of several physical properties (osmotic pressure, turbidity, solubilisation, magnetic resonance, surface tension, equivalent conductivity and self-diffusion) as a function of concentration for an ionic surfactant [1]. At low concentrations, most properties are similar to those of a simple electrolyte. One notable exception is the surface tension, which decreases rapidly with increasing surfactant concentration. However, all the properties (interfacial and bulk)

Fig. 2.1. Changes in the concentration dependence of a wide range of physico-chemical changes around the critical micelle concentration (c.m.c.) (after Lindman et al. [1]). Applied Surfactants: Principles and Applications. Tharwat F. Tadros Copyright 8 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30629-3

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2 Physical Chemistry of Surfactant Solutions

Fig. 2.2.

Illustration of a spherical micelle for dodecyl sulphate [2].

show an abrupt change at a particular concentration, which is consistent with the fact that at and above this concentration, surface active ions or molecules in solution associate to form larger units. These associated units are called micelles (selfassembled structures) and the first formed aggregates are generally approximately spherical. A schematic representation of a spherical micelle is given in Figure 2.2. The concentration at which this association phenomenon occurs is known as the critical micelle concentration (c.m.c.). Each surfactant molecules has a characteristic c.m.c. at a given temperature and electrolyte concentration. The most common technique for measuring the c.m.c. is by determining the surface tension, g, which shows break at the c.m.c., after which it remains virtually constant with further increases in concentration. However, other techniques such as self-diffusion measurements, NMR and fluorescence spectroscopy can be applied. Mukerjee and Mysels compiled various c.m.c.s in 1971 [3]; while clearly not up-to-date this is an extremely valuable reference. As an illustration, Table 2.1 gives the c.m.c. of several surface active agents to show some of the general trends [2]. Within any class of surface active agent, the c.m.c. decreases with increasing chain length of the hydrophobic portion (alkyl group). As a general rule, the c.m.c. decreases by a factor of 2 for ionics (without added salt) and by a factor of 3 for nonionics on adding one methylene group to the alkyl chain. With nonionic surfactants, increasing the length of the hydrophilic group, poly(ethylene oxide), causes an increase in c.m.c. In general, nonionic surfactants have lower c.m.c.s than their corresponding ionic surfactants of the same alkyl chain length. Incorporation of a phenyl group in the alkyl group increases its hydrophobicity to a much smaller extent than increasing its chain length with the same number of carbon atoms. The valency of the counter ion in ionic surfactants has a significant effect on the c.m.c. For example, increasing the valency of the counter ion from 1 to 2 reduces the c.m.c. by roughly a factor of 4.

2.1 Properties of Solutions of Surface Active Agents Tab. 2.1.

C.m.c. values of some surface active agents.

Surface active agent

C.m.c. (mol dmC3 )

(A) Anionic Sodium octyl-l-sulphate Sodium decyl-l-sulphate Sodium dodecyl-l-sulphate Sodium tetradecyl-l-sulphate

1:30 101 3:32 102 8:39 103 2:05 103

(B) Cationic Octyl trimethyl ammonium bromide Decetryl trimethyl ammonium bromide Dodecyl trimethyl ammonium bromide Hexacetyltrimethyl ammonium bromide

1:30 101 6:46 102 1:56 102 9:20 104

(C) Nonionic Octyl hexaoxyethylene glycol monoether C8 E6 Decyl hexaoxyethylene glycol monoether C10 E6 Decyl nonaoxyethylene glycol monoether C10 E9 Dodecyl hexaoxyethylene glycol monoether C12 E6 Octylphenyl hexaoxyethylene glycol monoether C8 E6

9:80 103 9:00 104 1:30 103 8:70 105 2:05 104

The c.m.c. is, to a first approximation, independent of temperature. This is illustrated in Figure 2.3, which shows that the c.m.c. of SDS varies (by ca. 10–20%) non-monotonically over a wide temperature range. The shallow minimum around 25 C can be compared with a similar minimum in the solubility of hydrocarbon in water [4]. However, nonionic surfactants of the ethoxylate type show a monotonic decrease [4] of c.m.c. with increasing temperature, as is illustrated in Figure 2.3 for C10 E5 .

Fig. 2.3.

Temperature dependence of the c.m.c. of SDS and C10 E5 [4].

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The effect of addition of cosolutes, e.g. electrolytes and non-electrolytes, on the c.m.c. can be very striking. For example, the addition of a 1:1 electrolyte to a solution of anionic surfactant dramatically lowers the c.m.c., by up to an order of magnitude. The effect is moderate for short-chain surfactants, but is much larger for long-chain ones. At high electrolyte concentrations, the reduction in c.m.c. with increasing number of carbon atoms in the alkyl chain is much stronger than without added electrolyte. This rate of decrease at high electrolyte concentrations is comparable to that of nonionics. The effect of added electrolyte also depends on the valency of the added counter ions. In contrast, for nonionics, addition of electrolytes causes only a small variation in the c.m.c. Non-electrolytes such as alcohols can also cause a decrease in the c.m.c. Figure 2.4 illustrates this for several alcohols [5], added to an anionic surfactant, namely potassium dodecanoate. The alcohols are less polar than water and are distributed between the bulk solution and the micelles. The more preference they have for the micelles, the more they stabilize them. A longer alkyl chain leads to a less favourable location in water and more favourable location in the micelles. The presence of micelles can account for many of the unusual properties of solutions of surface active agents. For example, it can account for the near constant surface tension above the c.m.c. (Figure 2.1). It also accounts for the reduction in molar conductance of the surface active agent solution above the c.m.c., which is consistent with the reduction in mobility of the micelles as a result of the counter ion association. The presence of micelles also accounts for the rapid rise in light scattering or turbidity above the c.m.c. The presence of micelles was originally proposed by McBain [6] who suggested that below the c.m.c. most of the surfactant molecules are unassociated, whereas in the isotropic solutions immediately above the c.m.c., micelles and surfactant ions (molecules) are thought to co-exist, the concentration of the latter changing very slightly as more surfactant is dissolved. However, the self-association of an amphiphile occurs in a stepwise manner with one monomer added to the aggregate at a time. For a long-chain amphiphile, the association is strongly cooperative up to a certain micelle size where counteracting factors became increasingly important. Typically, micelles are closely spherical over a rather wide concentration range above the c.m.c. Indeed, Adam [7] and Hartley [8] first suggested that micelles are spherical and have the following properties: (1) the association unit is spherical with a radius approximately equal to the length of the hydrocarbon chain; (2) the micelle contains about 50–100 monomeric units – the aggregation number generally increases with increasing alkyl chain length; (3) with ionic surfactants, most counter ions are bound to the micelle surface, thus significantly reducing the mobility from the value expected from a micelle with non-counterion bonding; (4) micellization occurs over a narrow concentration range due to the high association number of surfactant micelles; (5) the interior of the surfactant micelle has essentially the properties as a liquid hydrocarbon. This is confirmed by the high mobility of the alkyl chains and the ability of the micelles to solubilize many water-insoluble organic molecules, e.g. dyes and agrochemicals.

2.1 Properties of Solutions of Surface Active Agents

Fig. 2.4. Effect of alcohols on the c.m.c. of potassium dodecanoate [5] association. The presence of micelles also accounts for the rapid increase in light scattering or turbidity above the c.m.c.

To a first approximation, micelles can, over a wide concentration range above the c.m.c., be viewed as microscopic liquid hydrocarbon droplets covered with polar head groups, which interact strongly with water molecules. The radius of the micelle core constituted of the alkyl chains appears to be close to the extended length of the alkyl chain, i.e. in the range 1.5030 nm. As we will see later, the driving force for micelle formation is the elimination of the contact between the alkyl chains and water. The larger a spherical micelle, the more efficient this is, since the volumeto-area ratio increases. Notably, not all surfactant molecules in the micelles are extended. Only one molecule needs to be extended to satisfy the criterion that the radius of the micelle core is close to the extended length of the alkyl chain. Most surfactant molecules are in a disordered state. In other words, the interior of the

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micelle is close to that of the corresponding alkane in a neat liquid oil. This explains the large solubilization capacity of the micelle towards a broad range of non-polar and weakly polar substances. At the surface of the micelle, associated counter ions (in the region of 50–80% of the surfactant ions) are present. However, simple inorganic counter ions are very loosely associated with the micelle. The counter ions are very mobile (see below) and there is no specific complex formed with a definite counter-ion–head group distance. In other words, the counter ions are associated by long-range electrostatic interactions. A useful concept for characterizing micelle geometry is the critical packing parameter, CPP (discussed in Chapter 6). The aggregation number N is the ratio between the micellar core volume, Vmic , and the volume of one chain, v, N¼

Vmic ð4/3ÞpR 3mic ¼ v v

ð2:1Þ

where R mic is the radius of the micelle. The aggregation number, N, is also equal to the ratio of the area of a micelle, A mic , to the cross sectional area, a, of one surfactant molecule (Eq. 2.2). N¼

A mic 4pR 2mic ¼ a a

ð2:2Þ

Combining Eqs. (2.1) and (2.2), v 1 ¼ R mic a 3

ð2:3Þ

Since R mic cannot exceed the extended length of a surfactant alkyl chain, l max , l max ¼ 1:5 þ 1:265nc

ð2:4Þ

This means that, for a spherical micelle, v 1 l max a 3

ð2:5Þ

The ratio v/ðl max aÞ is denoted as the critical packing parameter (CPP). Although, the spherical micelle model accounts for many physical properties of solutions of surfactants, several phenomena remain unexplained, without considering other shapes. For example, McBain [9] suggested the presence of two types of micelles, spherical and lamellar, to account for the drop in molar conductance of surfactant solutions. The lamellar micelles are neutral and hence they account for

2.2 Solubility–Temperature Relationship for Surfactants

Fig. 2.5.

Various shapes of micelles (according to McBain [6, 9], Hartley [8] and Debye [11]).

the reduction in the conductance. Later, Harkins et al. [10] used McBain’s model of lamellar micelles to interpret their X-ray results in soap solutions. Moreover, many modern techniques such as light scattering and neutron scattering indicate that in many systems the micelles are not spherical. For example, Debye and Anacker [11] proposed a cylindrical micelle to explain light scattering results on (hexadecyltrimethyl)ammonium bromide in water. Evidence for disc-shaped micelles has also been obtained under certain conditions. A schematic representation of the spherical, lamellar and rod-shaped micelles, suggested by McBain, Hartley and Debye, is given in Figure 2.5.

2.2

Solubility–Temperature Relationship for Surfactants

This will be dealt with in detail in Chapter 3, and so only the main trends are summarized here. Many ionic surfactants show dramatic temperature-dependent solubility. The solubility may be very low at low temperatures and then increases by orders of magnitude in a relatively narrow temperature range. This phenomenon is generally denoted as the Krafft phenomenon, with the temperature for the onset of increasing solubility being known as the Krafft temperature. The latter may vary dramatically with subtle changes in the surfactant’s chemical structure. In general, the Krafft temperature increases rapidly as the alkyl chain length of the surfactant increases. It also depends on the head group and counter ion. Addition of electrolytes increases the Krafft temperature.

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2.3

Thermodynamics of Micellization

As mentioned above, the process of micellization is one of the most important characteristics of surfactant solution and hence it is essential to understand its mechanism (the driving force for micelle formation). This requires analysis of the dynamics of the process (i.e. the kinetic aspects) as well as the equilibrium aspects whereby the laws of thermodynamics may be applied to obtain the free energy, enthalpy and entropy of micellization. Below a brief description of both aspects will be given and this will be followed by a picture of the driving force for micelle formation. 2.3.1

Kinetic Aspects

Micellization is a dynamic phenomenon in which n monomeric surfactant molecules associate to form a micelle Sn , i.e., nS Ð Sn

ð2:6Þ

Hartley [8] envisaged a dynamic equilibrium whereby surface active agent molecules are constantly leaving and entering, from solution, the micelles. The same applies to the counter ions with ionic surfactants, which can exchange between the micelle surface and bulk solution. Experimental investigations using fast kinetic methods such as stopped-flow, temperature and pressure jumps, and ultrasonic relaxation measurements have shown that there are two relaxation processes for micellar equilibrium [12–18], characterized by relaxation times t1 and t2 . The first, t1 , is of the order of 107 s (108 to 103 s) and represents the life-time of a surface active molecule in a micelle, i.e. it represents the association and dissociation rate for a single molecule entering and leaving the micelle, which may be represented by Eq. (2.7). kþ

Sn S þ Sn1 Ð k

ð2:7Þ

where kþ and k represent the association and dissociation rate respectively for a single molecule entering or leaving the micelle. The slower relaxation time t2 corresponds to a relatively slow process, namely the micellization–dissolution, represented by Eq. (2.6); t2 is of the order of milliseconds (103 –1 s) and hence can be conveniently measured by stopped-flow methods. The fast relaxation time t1 can be measured using various techniques depending on its range. For example, t1 in the range of 108 –107 s is accessible to ultrasonic absorption methods, in the range of 105 –103 s it can be measured by pressure jump methods. t1 depends on surfactant concentration, chain length and temperature, and increases with increasing chain length of surfactants, i.e. the residence time increases with increasing chain length.

2.3 Thermodynamics of Micellization

The above discussion emphasizes the dynamic nature of micelles and it is important to realise that these molecules are in continuous motion and that there is a constant interchange between micelles and solution. The dynamic nature also applies to the counter ions which exchange rapidly with life times in the range 109 –108 s. Furthermore, the counter ions appear to be laterally mobile and not to be associated with (single) specific groups on the micelle surfaces [2]. 2.3.2

Equilibrium Aspects: Thermodynamics of Micellization

Two general approaches have been employed to tackle micelle formation. The first and simplest approach treats micelles as a single phase, and is referred to as the phase separation model. Here, micelle formation is considered as a phase separation phenomenon and the c.m.c. is then the saturation concentration of the amphiphile in the monomeric state whereas the micelles constitute the separated pseudophase. Above the c.m.c., a phase equilibrium exists with a constant activity of the surfactant in the micellar phase. The Krafft point is viewed as the temperature at which solid hydrated surfactant, micelles and a solution saturated with undissociated surfactant molecules are in equilibrium at a given pressure. In the second approach, micelles and single surfactant molecules or ions are considered to be in association–dissociation equilibrium. In its simplest form, a single equilibrium constant is used to treat the process represented by Eq. (2.1). The c.m.c. is merely a concentration range above which any added surfactant appears in solution in a micellar form. Since the solubility of the associated surfactant is much greater than that of the monomeric surfactant, the solubility of the surfactant as a whole will not increase markedly with temperature until it reaches the c.m.c. region. Thus, in the mass action approach, the Krafft point represents the temperature at which the surfactant solubility equals the c.m.c. 2.3.3

Phase Separation Model

Consider an anionic surfactant, in which n surfactant anions, S , and n counter ions Mþ associate to form a micelle, i.e., nS þ nMþ Ð Sn

ð2:8Þ

The micelle is simply a charged aggregate of surfactant ions plus an equivalent number of counter ions in the surrounding atmosphere and is treated as a separate phase. The chemical potential of the surfactant in the micellar state is assumed to be constant, at any given temperature, and this may be adopted as the standard chemical potential, mm , by analogy to a pure liquid or a pure solid. Considering the equilibrium between micelles and monomer, then, mm ¼ m1 þ RT ln a

ð2:9Þ

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where m1 is the standard chemical potential of the surfactant monomer and a1 is its activity, which is equal to f1 x1 , where f1 is the activity coefficient and x1 the mole fraction. Therefore, the standard free energy of micellization per mol of monomer, DGm , is given by, DGm ¼ mm m1 ¼ RT ln a1 F RT ln x1

ð2:10Þ

where f1 is taken as unity (a reasonable value in very dilute solution). The c.m.c. may be identified with x1 so that DGm ¼ RT ln½c:m:c:

ð2:11Þ

In Eq. (2.10), the c.m.c. is expressed as a mole fraction, which is equal to C/ð55:5 þ CÞ, where C is the concentration of surfactant in mole dm3 , i.e., DGm ¼ RT ln C RT lnð55:5 þ CÞ

ð2:12Þ

DG should be calculated using the c.m.c. expressed as a mole fraction as indicated by Eq. (2.12). However, most quoted c.m.c.s are given in mole dm3 and, in many cases, DGs have been quoted when the c.m.c. was simply expressed in mol dm3 . Strictly speaking, this is incorrect, since DG should be based on x1 rather than on C. DG obtained when the c.m.c. is expressed in mol dm3 is substantially different from that found with c.m.c. expressed in mole fraction. For example, for dodecyl hexaoxyethylene glycol the quoted c.m.c. is 8:7 105 mol dm3 at 25 C. Therefore, DG ¼ RT ln

8:7 105 ¼ 33:1 kJ mol1 55:5 þ 8:7 105

ð2:13Þ

when the mole fraction scale is used. However, DG ¼ RT ln 8:7 105 ¼ 23:2 kJ mol1

ð2:14Þ

when the molarity scale is used. The phase separation model has been questioned for two main reasons. Firstly, according to this model a clear discontinuity in the physical property of a surfactant solution, such as surface tension, turbidity, etc. should be observed at the c.m.c. This is not always found experimentally and the c.m.c. is not a sharp break point. Secondly, if two phases actually exist at the c.m.c., then equating the chemical potential of the surfactant molecule in the two phases would imply that the activity of the surfactant in the aqueous phase would be constant above the c.m.c. If this was the case, the surface tension of a surfactant solution should remain constant above the c.m.c. However, careful measurements have shown that the surface tension of a surfactant solution decreases slowly above the c.m.c., particularly when using purified surfactants.


2.3.4

Mass Action Model

This model assumes a dissociation–association equilibrium between surfactant monomers and micelles – thus an equilibrium constant can be calculated. For a nonionic surfactant, where charge effects are absent, this equilibrium is simply represented by Eq. (2.1), which assumes a single equilibrium. In this case, the equilibrium constant K m is given by Eq. (2.15). Km ¼

½Sn ½S n

ð2:15Þ

The standard free energy per monomer is then given by DGm ¼

DG RT RT ¼ ln K m ¼ ln½Sn RT ln½S n n n

ð2:16Þ

For many micellar systems, n > 50 and, therefore, the first term on the right-hand side of Eq. (2.16) may be neglected, resulting in Eq. (2.17) for DGm, DGm ¼ RT ln½S ¼ RT ln½c:m:c:

ð2:17Þ

which is identical to the equation derived using the phase-separation model. The mass action model allows a simple extension to be made to the case of ionic surfactants, in which micelles attract a substantial proportion of counter ions, into an attached layer. For a micelle made of n-surfactant ions, (where n p) charges are associated with counter ions, i.e. having a net charge of p units and degree of dissociation p/n, the following equilibrium may be established (for an anionic surfactant with Naþ counter ions), nS þ ðn pÞNaþ Ð Snp

ð2:18Þ

Km ¼

½Snp

½S ½Naþ ðnpÞ n

ð2:19Þ

Phillips has given a convenient solution for relating DGm to [c.m.c.] [17], arriving at Eq. (2.20), DGm ¼ ½2 ð p/nÞRT ln½c:m:c:

ð2:20Þ

For many ionic surfactants, the degree of dissociation ð p/nÞ is @0.2 so that, DGm ¼ 1:8RT ln½c:m:c:

ð2:21Þ

Comparison with Eq. (2.17) clearly shows that, for similar DGm, the [c.m.c.] is about two orders of magnitude higher for ionic surfactants than with nonionic surfactant of the same alkyl chain length (Table 2.1).

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In the presence of excess added electrolyte, with mole fraction x, the free energy of micellization is given by the expression, DGm ¼ RT ln½c:m:c: þ ½1 ð p/nÞ ln x

ð2:22Þ

Eq. (2.22) shows that as x increases the [c.m.c.] decreases. It is clear from Eq. (2.20) that as p ! 0, i.e. when most charges are associated with counter ions, DGm ¼ 2RT ln½c:m:c:

ð2:23Þ

whereas when p @ n, i.e. the counter ions are bound to micelles, DGm ¼ RT ln½c:m:c:

ð2:24Þ

which is the same equation as for nonionic surfactants. Although the mass action approach could account for a number of experimental results, such as the small change in properties around the c.m.c., it has not escaped criticism. For example, the assumption that surfactants exist in solution in only two forms, namely single ions and micelles of uniform size, is debatable. Analysis of various experimental results has shown that micelles have a size distribution that is narrow and concentration dependent. Thus, the assumption of a single aggregation number is an oversimplification and, in reality, there is a micellar size distribution. This can be analyzed using the multiple equilibrium model, which can be best formulated as a stepwise aggregation [2], S1 þ S1 Ð S2

ð2:25Þ

S2 þ S1 Ð S3

ð2:26Þ

Sn1 þ S1 Ð Sn

ð2:27Þ

As noted in particular in the analysis of kinetic data [10–15], there are aggregates over a wide range of aggregation numbers, from dimers and well beyond the most stable micelles. However, for surfactants with not too high a c.m.c., the size distribution curve has a very deep minimum, the least stable aggregates being present in concentrations many orders of magnitude below those of the most abundant micelles. For surfactants with predominantly spherical micelles, the polydispersity is low and there is then a particularly preferred micellar size. 2.3.5

Enthalpy and Entropy of Micellization

The enthalpy of micellization can be calculated from the variation of c.m.c. with temperature. This follows from


DH ¼ RT 2

d ln½c:m:c: dT

ð2:28Þ

The entropy of micellization can then be calculated from the relationship between DG and DH , i.e., DG ¼ DH TDS

ð2:29Þ

Therefore DH may be calculated from surface tension log C plots at various temperatures. Unfortunately, the errors in locating the c.m.c. (which in many cases is not a sharp point) lead to a large error in DH . A more accurate and direct method of obtaining DH is microcalorimetry. As an illustration, the thermodynamic parameters DG ; DH , and TDS for octylhexaoxyethylene glycol monoether (C8 E6 ) are given in Table 2.2. Table 2.2 shows that DG is large and negative. However, DH is positive, indicating that the process is endothermic. In addition, TDS is large and positive, implying that in the micellization process there is a net increase in entropy. As we will see in the next section, this positive enthalpy and entropy points to a different driving force for micellization from that encountered in many aggregation processes. The influence of alkyl chain length of the surfactant on the free energy, enthalpy and entropy of micellization has been demonstrated by Rosen [19] who listed these parameters as a function of alkyl chain length for sulphoxide surfactants. The results given in Table 2.3 show that the standard free energy of micellization

Tab. 2.2.

Thermodynamic quantities for micellization of octylhexaoxyethylene glycol monoether.

Temperature ( C)

DG (kJ molC1 )

DH (kJ molC1 ) ( from c.m.c.)

DH (kJ molC1 ) ( from calorimetry)

TDS (kJ molC1 )

25 40

21:3 þ 2:1 23:4 þ 2:1

8:0 þ 4:2

20:1 þ 0:8 14:6 þ 0:8

41:8 þ 1:0 38:0 þ 1:0

˚

˚

˚

˚

˚

Tab. 2.3. Change of thermodynamic parameters of micellization of alkyl sulphoxide with increasing chain length of the alkyl group.

Surfactant

DG (kJ molC1 )

DH (kJ molC1 )

TDS (kJ molC1 )

C6 H13 S(CH3 )O C7 H15 S(CH3 )O C8 H17 S(CH3 )O C9 H19 S(CH3 )O C10 H21 S(CH3 )O C11 H23 S(CH3 )O

12.0 15.9 18.8 22.0 25.5 28.7

10.6 9.2 7.8 7.1 5.4 3.0

22.6 25.1 26.4 29.1 30.9 31.7

˚

˚

˚

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becomes increasingly negative as the chain length increases. This is to be expected since the c.m.c. decreases with increasing alkyl chain length. However, DH becomes less positive and TDS becomes more positive with increasing surfactant chain length. Thus, the large negative free energy of micellization is made up of a small positive enthalpy (which decreases slightly with increasing chain surfactant length) and a large positive entropy term TDS , which becomes more positive as the chain is lengthened. The next section shows that these results can be accounted for in terms of the hydrophobic effect, which will be described in detail. 2.3.6

Driving Force for Micelle Formation

Until recently, the formation of micelles was regarded primarily as an interfacial energy process, analogous to the process of coalescence of oil droplets in an aqueous medium. If this was the case, micelle formation would be a highly exothermic process, as the interfacial free energy has a large enthalpy component. As mentioned above, experimental results have clearly shown that micelle formation involves only a small enthalpy change and, indeed, is often endothermic. The negative free energy of micellization is the result of a large, positive entropy. This led to the conclusion that micelle formation must be predominantly an entropy driven process. Two main sources of entropy have been suggested. The first is related to the so called ‘‘hydrophobic effect’’, which was first established from a consideration of the free energy, enthalpy and entropy of transfer of hydrocarbon from water to a liquid hydrocarbon. Table 2.4 lists some results, along with the heat ca; gas pacity change DCp on transfer from water to a hydrocarbon, as well as Cp , i.e. the heat capacity in the gas phase [2]. The table shows that the principal contribution to DG is the large positive DS , which increases with increasing hydrocarbon chain length, whereas DH is positive, or small and negative. To account for this large positive entropy of transfer several authors [19, 20] have suggested that the

Thermodynamic parameters for transfer of hydrocarbons from water to liquid hydrocarbon at 25 C.

Tab. 2.4.

Hydrocarbon

DG (kJ molC1 )

DH (kJ molC1 )

DS (kJ molC1 KC1 )

DC p (kJ molC1 KC1 )

DC p, gas (kJ molC1 KC1 )

C2 H6 C3 H8 C4 H10 C5 H12 C6 H14 C6 H6 C6 H5 CH3 C6 H5 C2 H5 C6 H5 C3 H8

16.4 20.4 24.8 28.8 32.5 19.3 22.7 26.0 29.0

10.5 7.1 3.4 2.1 0 2.1 1.7 2.0 2.3

88.2 92.4 96.6 105.0 109.2 58.8 71.4 79.8 88.2

– – 273 403 441 227 265 319 395

– – 143 172 197 134 155 185 –

˚

˚

˚

˚

˚


water molecules around a hydrocarbon chain are ordered, forming ‘‘clusters’’ or ‘‘icebergs’’. On transfer of an alkane from water to a liquid hydrocarbon, these clusters are broken, thus releasing water molecules that now have a higher entropy. This accounts for the large entropy of transfer of an alkane from water to a hydrocarbon medium. This effect is also reflected in the much higher heat capacity change on transfer, DCp , when compared with the heat capacity in the gas phase, Cp . The above effect is also operative on transfer of surfactant monomer to a micelle, during the micellization process. Surfactant monomers will also contain ‘‘structured’’ water around their hydrocarbon chain. On transfer of such monomers to a micelle, these water molecules are released and they have a higher entropy. The second source of entropy increase on micellization may arise from the increase in flexibility of the hydrocarbon chains on their transfer from an aqueous to a hydrocarbon medium [21, 22]. The orientations and bendings of an organic chain are probably more restricted in an aqueous phase than in an organic phase. Notably, with ionic and zwitterionic surfactants, an additional entropy contribution, associated with the ionic head groups, must be considered. Upon partial neutralization of the ionic charge by the counter ions when aggregation occurs, water molecules are released. This will be associated with an entropy increase that should be added to the entropy increase resulting from the above hydrophobic effect. However, the relative contribution of the two effects is difficult to assess quantitatively. 2.3.7

Micellization in Other Polar Solvents

In strongly polar solvents, such as formamide and ethylene glycol, micelles are formed with qualitatively the same features as in water. Figure 2.6 illustrates this, showing the surface tension results for cetylytrimethylammonium bromide (CTAB) in formamide and ethylene glycol [23]. The c.m.c. is higher in formamide than in water (100 mM compared with 1 mM in water). The micelles are also smaller and the aggregation number is lower. The results in polar solvents, other than water, indicate that self-assembly is much less cooperative. Consequently, the degree of counter-ion binding is also lower. 2.3.8

Micellization in Non-Polar Solvents

For simple amphiphilic compounds, the association is of low co-operativity in non-polar solvents and leads only to smaller and polydisperse aggregates. The aggregation number is in the range 1–5. However, introduction of even quite small amounts of water can induce a co-operative self-assembly, leading to inverse micelles.

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Fig. 2.6.

Surface tension log C results for (a) CTAB in formamide and (b) ethylene glycol [23].

2.4

Micellization in Surfactant Mixtures (Mixed Micelles)

Most industrial applications use more than one surfactant molecule in the formulation. It is, therefore, necessary to predict the type of possible interactions and whether this leads to synergistic effects. Two general cases may be considered: Surfactant molecules with no net interaction (with similar head groups) and systems with net interaction. These are discussed separately below [2]. 2.4.1

Surfactant Mixtures with no Net Interaction

This is the case when mixing two surfactants with the same head group but with different chain lengths. In analogy with the hydrophilic–lipophilic balance (HLB)

2.4 Micellization in Surfactant Mixtures (Mixed Micelles)

for surfactant mixtures (Chapter 6), one can also assume the c.m.c. of a surfactant mixture (with no net interaction) to be an average of the two c.m.c.s of the single components [2], c:m:c: ¼ x1 c:m:c:1 þ x2 c:m:c:2

ð2:30Þ

where x1 and x2 are the mole fractions of the respective surfactants in the system. However, the mole fractions should not be those in the whole system, but those inside the micelle. This means that Eq. (2.30) should be modified, c:m:c: ¼ x1m c:m:c:1 þ x2m c:m:c:2

ð2:31Þ

The superscript m indicates that the values are inside the micelle. If x1 and x2 are the solution composition, then, 1 x1 x2 þ ¼ c:m:c: c:m:c:1 c:m:c:2

ð2:32Þ

The molar composition of the mixed micelle is given by x1m ¼

x1 c:m:c:2 x1 c:m:c:2 þ x2 c:m:c:1

ð2:33Þ

Figure 2.7 shows the calculated c.m.c. and the micelle composition as a function of solution composition using Eqs. (2.32) and (2.33) for three cases where c:m:c:2 = c:m:c:1 ¼ 1; 0:1 and 0.01. As can be seen, the c.m.c. and micellar composition change dramatically with solution composition when the c.m.c.s of the two surfactants vary considerably, i.e. when the ratio of c.m.c.s is far from 1. This fact is used when preparing microemulsions (see Chapter 10) where the addition of a mediumchain alcohol (like pentanol or hexanol) changes the properties considerably. If component 2 is much more surface active, i.e. c.m.c.2 /c.m.c.1 S 1, and it is present in low concentrations (x2 is of the order of 0.01), then from Eq. (2.33) x1m @ x2m @ 0:5, i.e. at the c.m.c. of the systems the micelles are composed of up to 50% component 2. This illustrates the role of contaminants in surface activity, e.g. dodecyl alcohol in sodium dodecyl sulphate (SDS). Figure 2.8 shows the c.m.c. as a function of molar composition of the solution and in the micelles for a mixture of SDS and nonylphenol with 10 moles ethylene oxide (NP-E10 ). If the molar composition of the micelles is used as the x-axis, the c.m.c. is more or less the arithmetic mean of the c.m.c.s of the two surfactants. If, however, the molar composition in the solution is used as the x-axis (which at the c.m.c. is equal to the total molar concentration), then the c.m.c. of the mixture shows a dramatic decrease at low fractions of NP-E10 . This decrease is due to the preferential absorption of NP-E10 in the micelle. This higher absorption occurs because NP-E10 surfactant has a higher hydrophobicity than SDS.

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36


Calculated c.m.c. (a) and micellar composition (b) as a function of solution composition for three ratios of c.m.c.s.

Fig. 2.7.

2.4.2

Surfactant Mixtures with a Net Interaction

With many industrial formulations, surfactants of different kinds are mixed together, for example anionics and nonionics. Nonionic surfactant molecules shield the repulsion between the negative head groups in the micelle and hence there will be a net interaction between the two types of molecules. Another example is the case when anionic and cationic surfactants are mixed, whereby very strong interaction occurs between the oppositely charged surfactant molecules. To account for this interaction, Eq. (2.31) has to be modified by introducing activity coefficients of the surfactants, f1m and f2m in the micelle (Eq. 2.34).

2.4 Micellization in Surfactant Mixtures (Mixed Micelles)

Fig. 2.8. C.m.c. as a function of surfactant composition, x1 , or micellar surfactant composition, x1m for the system SDS þ NP-E10 .

c:m:c: ¼ x1m f1m c:m:c:1 þ x2m f2m c:m:c:2

ð2:34Þ

An expression for the activity coefficients can be obtained using the regular solutions theory, ln f1m ¼ ðx2m Þ 2 b

ð2:35Þ

ðx2m Þ 2 b

ð2:36Þ

ln

f2m

¼

where b is an interaction parameter between the surfactant molecules in the micelle. A positive b means that there is a net repulsion between the surfactant molecules in the micelle, whereas a negative b means a net attraction. The c.m.c. of the surfactant mixture and the composition x1 are given by Eqs. (2.37) and (2.38). 1 x1 x2 þ ¼ c:m:c: f1m c:m:c:1 f2m c:m:c:2 x1m ¼

x1 f2m c:m:c:2 m x1 f2 c:m:c:2 þ x2 f2m c:m:c:1

ð2:37Þ ð2:38Þ

Figure 2.9 shows the effect of increasing b on the c.m.c. and micellar composition for two surfactants with a c.m.c. ratio of 0.1. As b becomes more negative, the c.m.c. of the mixture decreases. Values of b in the region of 2 are typical for

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C.m.c. (a) and micellar composition (b) for various b for a system with a c.m.c.2 /c.m.c.1 ratio of 0.1.

Fig. 2.9.

anionic/nonionic mixtures, whereas values in the region of 10 to 20 are typical of anionic/cationic mixtures. With increasingly negative b, the mixed micelles tend towards a mixing ratio of 50:50, reflecting the mutual electrostatic attraction between the surfactant molecules. Both the predicted c.m.c. and micellar composition depend on the ratio of the c.m.c.s as well as on b. When the c.m.c.s of the single surfactants are similar, the predicted c.m.c. is very sensitive to small variations in b. Conversely, when the ratio of the c.m.c.s is large, the predicted value of the mixed c.m.c. and the micellar composition are insensitive to variations of b. For mixtures of nonionic and ionic surfactants, b decreases with increasing electrolyte concentration. This is due to the screening of the electrostatic repulsion on the addition of electrolyte. With

2.5 Surfactant–Polymer Interaction

some surfactant mixtures, b decreases with rising temperature, i.e. the net attraction decreases with increasing temperature.

2.5

Surfactant–Polymer Interaction

Mixtures of surfactants and polymers are very common in many industrial formulations. With many suspension and emulsion systems stabilized with surfactants, polymers are added for several reasons, e.g. as suspending agents (‘‘thickeners’’) to prevent sedimentation or creaming of these systems. In many other systems, such as in personal care and cosmetics, water-soluble polymers are added to enhance the function of the system, e.g. in shampoos, hair sprays, lotions and creams. The interaction between surfactants and water-soluble polymers furnishes synergistic effects, e.g. enhancing the surface activity, stabilizing foams and emulsions, etc. It is, therefore important to study systematically the interaction between surfactants and water-soluble polymers. One of the earliest studies of surfactant/polymer interaction came from surface tension measurements. Figure 2.10 shows some typical results for the effect of addition of poly(vinylpyrrolidone) (PVP) on the g log C curves of SDS [23]. In a system of fixed polymer concentration and varying surfactant concentrations, two critical concentrations appear, denoted T1 and T2 . T1 represents the concentration at which interaction between the surfactant and polymer first occurs. This is sometimes termed the critical aggregation concentration (CAC), i.e. the onset of association of surfactant to the polymer. Because of this there is no further

Fig. 2.10. g versus log C curves for SDS solutions in the presence of different concentrations of PVP.

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40


Fig. 2.11.

Binding isotherms of a surfactant to a water-soluble polymer.

increase in surface activity and thus no lowering of surface tension. T2 represents the concentration at which the polymer becomes saturated with surfactant. Since T1 is generally lower than the c.m.c. of the surfactant in the absence of polymer, ‘‘adsorption’’ or ‘‘aggregation of SDS on or with the polymer is more favourable than normal micellization. As the polymer is saturated with surfactant (i.e. beyond T2 ) the surfactant monomer concentration and the activity starts to increase again and there is a lowering of g until the monomer concentration reaches the c.m.c., after which g remains virtually constant and normal surfactant micelles begin to form. The above picture is confirmed if the association of surfactant is directly monitored (e.g. by using surfactant selective electrodes, by equilibrium dialysis or by some spectroscopic technique). Binding isotherms are illustrated in Figure 2.11. At low surfactant concentration there is no significant interaction (binding). At the CAC, a strongly co-operative binding is indicated and at higher concentrations a plateau is reached. Further increases in surfactant concentration produces ‘‘free’’ surfactant molecules until the surfactant activity or concentration joins the curve obtained in the absence of polymer. The binding isotherms of Figure 2.11 show a strong analogy with micelle formation and the interpretation of these isotherms in terms of a depression of the c.m.c. Several conclusions could be drawn from the experimental binding isotherms of mixed surfactant/polymer solutions: (1) The CAC/c.m.c. depends only weakly on polymer concentration over wide ranges. (2) CAC/c.m.c. is, to a good approxima-


Fig. 2.12. Association between surfactant and homopolymer in different concentration domains [24].

tion, independent of polymer molecular weight down to low values. For very low molecular weight the interaction is weakened. (3) The plateau binding increases linearly with polymer concentration. (4) Anionic surfactants show a marked interaction with most homopolymers (e.g. PEO and PVP) while cationic surfactants show a weaker but still significant interaction. Nonionic and zwitterionic surfactants only rarely show a distinct interaction with homopolymers. Figure 2.12 gives a schematic representation of the association between surfactants and polymers for a wide range of concentration of both components [24]. At low surfactant concentration (region I) there is no significant association at any polymer concentration. Above the CAC (region II), association increases up to a surfactant concentration, increasing linearly with increasing polymer concentration. In region III, association is saturated and the surfactant monomer concentration increases till region IV is reached, where there is co-existence of surfactant aggregates at the polymer chains and free micelles. 2.5.1

Factors Influencing the Association Between Surfactant and Polymer

Several factors influence the interaction between surfactant and polymer: (1) Temperature; increasing temperature generally increases the CAC, i.e. the interac-

41

42


tion becomes less favourable. (2) Addition of electrolyte; this generally decreases the CAC, i.e. it increases the binding. (3) Surfactant chain length; an increase in the alkyl chain length decreases the CAC, i.e. it increases association. A plot of log(CAC) versus the number of carbon atoms, n, is linear (similar to the log[c.m.c.] n relationship obtained for surfactants alone). (4) Surfactant structure; alkyl benzene sulphonates are similar to SDS, but introduction of EO groups in the chain weakens the interaction. (5) Surfactant classes; weaker interaction is generally observed with cationics than with anionics. However, the interaction can be promoted by using a strongly interacting counter ion for the cationic (e.g. CNS ). Interaction between ethoxylated surfactants and nonionic polymers is weak. The interaction is stronger with alkyl phenol ethoxylates. (6) Polymer molecular weight; a minimum molecular weight of @4000 for PEO and PVP is required for ‘‘complete’’ interaction. (7) Amount of polymer; the CAC seems to be insensitive to (or lowers slightly) with increasing polymer concentration. T2 increases linearly with increasing polymer concentration. (8) Polymer structure and hydrophobicity; several uncharged polymer, such as PEO, PVP and poly(vinyl alcohol) (PVOH), interact with charged surfactants. Many other uncharged polymers interact weakly with charged surfactants, e.g. hydroxyethyl cellulose (HEC), dextran and polyacrylamide (PAAm). The following orders of increased interaction have been listed for (1) anionic surfactants: PVOH < PEO < MEC (methyl cellulose) < PVAc [partially hydrolyzed poly(vinyl acetate)] < PPO @ PVP, and for (2) cationic surfactants: PVP < PEO < PVOH < MEC < PVAc < PPO. The position of PVP can be explained by the slight positive charge on the chain, which causes repulsion with cations and attraction with anionics. 2.5.2

Interaction Models

NMR data has shown that every ‘‘bound’’ surfactant molecule experiences the same environment, i.e. the surfactant molecules might be bound in micelle-like clusters, but with smaller size. Assuming that each polymer molecule consists of several ‘‘effective segments’’ of mass Ms (minimum molecular weight for interaction to occur), then each segment will bind a cluster of n surfactant anions, D , and the binding equilibrium may be represented by, P þ nD Ð PDnn

ð2:39Þ

and the equilibrium constant is given by, K¼

½PDnn ½P½D n

ð2:40Þ

K is obtained from the half-saturation condition, n K ¼ ½D 1/2

ð2:41Þ


By varying n and using the experimental binding isotherms one obtains Ms ¼ 1830 and n ¼ 15. The free energy of binding is given by, DG ¼ RT ln K 1/n

ð2:42Þ

DG was found to be 5.07 kcal mol1 , which is close to that for surfactants. Najaragan [25] has introduced a comprehensive thermodynamic treatment of surfactant/polymer interaction. The aqueous solution of surfactant and polymer was assumed to contain both free micelles and ‘‘micelles’’ bound to the polymer molecule. The total surfactant concentration, X t , is partitioned into single dispersed surfactant, X1 , surfactant in free micelles, Xf , and surfactant bound as aggregates, Xb , X t ¼ X1 þ g f ðK f X1 Þ g f þ g b nX p

ðKb X1 Þ g b 1 þ ðKb X1 Þ g b

ð2:43Þ

g f is the average aggregation number of free micelles, K f is the intrinsic equilibrium constant for formation of free micelles, n is the number of binding sites for surfactant aggregates of average size g b , Kb is the intrinsic equilibrium constant for binding surfactant on the polymer and X p is the total polymer concentration (mass concentration is nX p ). Polymer–micelle complexation may affect the conformation of the polymer, but is assumed not affect Kb and g b . The relative magnitudes of Kb ; K f and g b determine whether complexation with the polymer occurs as well as the critical surfactant concentration exhibited by the system. If k f > kb and g b ¼ g f then free micelles occur in preference to complexation. If K f < Kb and g b ¼ g f , then micelles bound to polymer occur first. If K f < Kb , but g b f g f , then the free micelles can occur prior to saturation of the polymer. A first critical surfactant concentration (CAC) occurs close to X1 ¼ Kb1 . A second critical concentration occurs near X1 ¼ K f1 . Depending on the magnitude of nX p , one may observe only one critical concentration over a finite range of surfactant concentrations. Figure 2.13 shows the relationship between X1 and X t for different polymer concentrations (SDS/PEO system), using Kb ¼ 319, K f ¼ 120, g b ¼ 51 and g f ¼ 54. In the region from 0 to A, the surfactant molecules remain singly dispersed. In the region from A to B, polymer-bound micelles occur; X1 increases very little in this region (large size of polymer bound micelles). If g b is small (say 10), then X1 should increase more significantly in this region. If nX p is small, the region AB is confined to a narrow surfactant concentration range. If nX p is very large, the saturation point B may not be reached. At B the polymer is saturated with surfactant. In the region AC, increases in X t are accompanied by an increase in X1 . At C the formation of free micelles becomes possible; CD denotes the surfactant concentration range over which any further addition of surfactant results in the formation of free micelles. The point C depends on the polymer mass concentration ðnX p Þ. The above theoretical predictions were verified by the results of Guilyani and Wolfram [26] using specific ion electrodes. This is illustrated in Figure 2.14.

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44


Fig. 2.13.

Variation of X1 with X t for the SDS/PEO system.

Fig. 2.14.

Experimentally measured values of X1 versus X t for SDS/PEO system.


2.5.3

Driving Force for Surfactant–Polymer Interaction

The driving force for polymer–surfactant interaction is the same as that for the process of micellization (see above). As with micelles the main driving force is the reduction of hydrocarbon/water contact area of the alkyl chain of the dissolved surfactant. A delicate balance between several forces is responsible for the surfactant/ polymer association. For example, aggregation is resisted by the crowding of the ionic head groups at the surface of the micelle. Packing constraints also resist association. Molecules that screen the repulsion between the head groups, e.g. electrolytes and alcohol, promote association. A polymer molecule with hydrophobic and hydrophilic segments (which is also flexible) can enhance association by ion– dipole association between the dipole of the hydrophilic groups and the ionic head groups of the surfactant. In addition, contact between the hydrophobic segments of the polymer and the exposed hydrocarbon areas of the micelles can enhance association. With SDS/PEO and SDS/PVP, the association complexes are approximately three monomer units per molecule of aggregated surfactant. 2.5.4

Structure of Surfactant–Polymer Complexes

Generally, there are two alternative pictures of mixed surfactant/polymer solutions, one describing the interaction in terms of a strongly co-operative association or binding of the surfactant to the polymer chain and one in terms of a micellization of surfactant on or in the vicinity of the polymer chain. For polymers with hydrophobic groups the binding approach is preferred, whereas for hydrophilic homopolymers the micelle formation picture is more likely. The latter picture has been suggested by Cabane [27], who proposed a structure in which the aggregated SDS is surrounded by macromolecules in a loopy configuration. A schematic picture of this structure, sometimes referred to as ‘‘pearl-necklace model’’, is given in Figure 2.15. The consequences of the above model are: (1) More favourable free energy of association (CAC < c.m.c.) and increased ionic dissociation of the aggregates. (2) An altered environment of the CH2 groups of the surfactant near the head group. The micelle sizes are similar with polymer present and without, and the aggregation numbers are typically similar or slightly lower than those of micelles forming in the absence of a polymer. In the presence of a polymer, the surfactant chemical potential is lowered with respect to the situation without polymer [28]. 2.5.5

Surfactant–Hydrophobically Modified Polymer Interaction

Water-soluble polymers are modified by grafting a low amount of hydrophobic groups (of the order of 1% of the monomers reacted in a typical molecule), result-

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46


Schematic representation of the topology of surfactant/polymer complexes (according to Cabane [27]).

Fig. 2.15.

ing in the formation of ‘‘associative structures’’. These molecules are referred to as associative thickeners and are used as rheology modifiers in many industrial applications, e.g. paints and personal care products. An added surfactant will interact strongly with the hydrophobic groups of the polymer, leading to a strengthened association between the surfactant molecules and the polymer chain. Figure 2.16 gives a schematic picture for the interaction between SDS and hydrophobically modified hydroxyethyl cellulose (HM-HEC), showing the interaction at various surfactant concentrations [1]. Initially the surfactant monomers interact with the hydrophobic groups of the HM polymer, and at some surfactant concentration (CAC) the micelles can crosslink the polymer chains. At higher surfactant concentrations, the micelles, which are now abundant, will no longer be shared between the polymer chains, i.e. the cross-links are broken. These effects are reflected in the variation of viscosity with surfactant concentration for HM polymer (Figure 2.17). The viscosity of the polymer rises with increasing surfactant concentration, reaching a maximum at an optimum concentration (maximum cross-links) and then decreases with further increase of surfactant concentration. For the unmodified polymer, the changes in viscosity are relatively small. 2.5.6

Interaction Between Surfactants and Polymers with Opposite Charge (Surfactant–Polyelectrolyte Interaction)

The case of surfactant polymer pairs in which the polymer is a polyion and the surfactant is also ionic, but of opposite charge, is of special importance in many


Fig. 2.16.

Schematic representation of the interaction between surfactant and HM polymer.

cosmetic formulations, e.g. as hair conditioners. This is illustrated by the interaction between SDS and cationically modified cellulosic polymer (Polymer JR, Union Carbide) (Figure 2.18) using surface tension (g) measurements [29]. The g log C curves for SDS in the presence and absence of the polyelectrolyte are shown in Figure 2.18, which also shows the appearance of the solutions. At low surfactant concentration, there is a synergistic lowering of surface tension, i.e. the surfactant–polyelectrolyte complex is more surface active. The low surface tension is also present in the precipitation zone. At high surfactant concentrations, g approaches that of the polymer-free surfactant in the micellar region. These trends are schematically illustrated in Figure 2.19.

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48


Viscosity–surfactant concentration relationship for HM-modified polymer solutions.

Fig. 2.17.

g log C curves of SDS with and without addition of polymer (0.1% JR 400) – c (clear), t (turbid), p (precipitate), sp (slight precipitate).

Fig. 2.18.


Fig. 2.19.

Schematic representation of surfactant–polyelectrolyte interaction.

The surfactant–polyelectrolyte interaction has several consequences on application in hair conditioners. The most important effect is the high foaming power of the complex. Maximum foaming occurs in the region of highest precipitation, i.e. maximum hydrophobization of the polymer. Probably, the precipitate can stabilize the foam. Direct determination of the amount of surfactant bound to the polyelectrolyte chains revealed several interesting features. Binding occurs at very low surfactant concentration (1/20th of the c.m.c.). The degree of binding b reached 0.5 (b ¼ 1 corresponds to a bound DS ion for each ammonium group). b versus SDS concentration curves were identical for polymeric homologues with a degree of cationic substitution (CS) > 0:23. Precipitation occurred when b ¼ 1. The binding of cationic surfactants to anionic polyelectrolytes also shows some interesting features. The binding affinity depends on the nature of the polyanion. Addition of electrolytes increases the steepness of binding, but the binding occurs at higher surfactant concentration as the electrolyte concentration is increased. Increasing the alkyl chain length of the surfactant increases binding, a process that is similar to micellization. Viscometric measurements have revealed a rapid increase in the relative viscosity at a critical surfactant concentration. However, the behaviour depends on the type of polyelectrolyte used. As an illustration, Figure 2.20 shows the viscosity–SDS concentration curves for two types of cationic polyelectrolyte: JR-400 (cationically modified cellulosic) and Reten (an acrylamide/(b-methylacryloxytrimethyl)ammonium chloride copolymer, ex Hercules).

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50


Fig. 2.20.

Relative viscosity of 1% JR-400 and 1% Reten as a function of SDS concentration.

The difference between the two polyelectrolytes is striking and suggests little change in the conformation of Reten on addition of SDS, but strong intermolecular association between polymer JR-400 and SDS.

References

(a) B. Lindman: Surfactants. T. F. Tadros (ed.): Academic Press, London, 2003, pp. 1984. (b) K. Holmberg, B. Jonsson, B. Kronberg, B. Lindman: Surfactants and Polymers in Aqueous Solution, 2nd edition, John Wiley & Sons, USA, 2003. 2 J. Istraelachvili: Intermolecular and Surface Forces, with Special Applications to Colloidal and Biological Systems, Academic Press, London, 1985, pp. 251. 3 P. Mukerjee, K. J. Mysels: Critical Micelle Concentrations of Aqueous Surfactant Systems, National Bureau of Standards Publication, Washington, 1971. 4 P. H. Elworthy, A. T. Florence, C. B. Macfarlane: Solubilization by 1

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Surface Active Agents, Chapman & Hall, London, 1968. K. Shinoda, T. Nagakawa, B. I. Tamamushi, T. Isemura: Colloidal Surfactants, Some Physicochemical Properties, Academic Press, London, 1963. J. W. McBain, Trans. Faraday Soc., 1913, 9, 99. N. K. Adam, J. Phys. Chem., 1925, 29, 87. G. S. Hartley : Aqueous Solutions of Paraffin Chain Salts, Hermann and Cie, Paris, 1936. J. W. McBain: Colloid Science, Heath, Boston, 1950. W. D. Harkins, W. D. Mattoon, M. L. Corrin, J. Am. Chem. Soc., 1946, 68, 220; J. Colloid Sci., 1946, 1, 105.

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