University of Groningen Polymer-surfactant interactions … · Chapter 1 2 Figure 1.2 The soap...
Transcript of University of Groningen Polymer-surfactant interactions … · Chapter 1 2 Figure 1.2 The soap...
University of Groningen
Polymer-surfactant interactionsKevelam, Jan
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Citation for published version (APA):Kevelam, J. (1998). Polymer-surfactant interactions: Aqueous chemistry of laundry detergents [Groningen]:[S.n.]
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OO
OH
HO OH
O
O
O
OHHO
HOH3C
O
HOHO
O
O
O
COH
OHO
HOOH
HOHO
OH
OCH2O
O
C
O
O
OHHOHO
O
OH
O
HOHO OH
1
1
Figure 1.1 Chemical structure of a saponin from Acacia Auriculiformis.3
The use and science of laundry detergents
1.1 Detergents: from saponin to LAS
In ancient societies, and even today, people clean their clothes by beating the wet textiles on rocks near
a stream. This is good practice, because the mechanical agitation facilitates the removal of solid soil, andthe water dissolves the hydrophilic (‘water-loving’) stains composed of, for example, sugar, salt, and
certain dyes. However, oily soil is hard to remove in this way, since fatty substances do not dissolve in
pure water and remain attached to the fabric. Nature has allowed man to solve this problem by providing
saponins, soap-like substances which are found in chestnuts, in leaves and seeds of Saponaria Officinalis
(soapwort), in the bark of Quillaja saponaria Molina (South American soaptree), and in the fruits of
Acacia Auriculiformis (Figure 1.1.). These compounds produce a rich lather when dispersed in water.1, 2, 3
While these natural detergents were probably the first cleaning agents ever used in fabric
washing, the oldest substance manufactured for removal of oily stains is soap, the sodium salt of a long-chain carboxylic acid. A soap-like material found in clay cylinders during the excavation of ancient
Babylon provides evidence that soapmaking was known as early as 2800 B.C. Inscriptions on the4
cylinders state that fats were boiled with ashes. By the 15 century, soap was produced in Venice andth
Savone by treating animal or vegetable fats with aqueous
CH2
CH
CH2
OH
OH
OH
R1 C
O
O- Na+
R2 C
O
O- Na+
R3 C
O
O- Na+
closed soap
grained soap
repeatonce
lye
+
9% NaOH (emulsification)
18% NaOH (ester hydrolysis or saponification)
NaCl
H2O
H2O (grain ing)
NaOH
H2O and/o r NaCl
A triglyceride (fat)
lye (= aq. NaCl + glycerol)
+ residual fat
glycerol soap
1. 'Killing'(1 day)
2. Graining(1.5 days)
3. Washing(2 days)
4. Strenghtening(1 day)
5. Fitting(2.5 days)
neat soap lye+ +nigre
(liquid soap solution)
CH2
CH
CH2
O
O
O C
C
C
O
O
O
R1
R2
R3
Chapter 1
2
Figure 1.2 The soap boiling process. For beef tallow as a starting material, R , R and R = 6:5:851 2 3
mixture of C H , C H , C H (not necessarily n-alkyl chains).15 31 17 35 17 33
H+
++
H+-(Markovnikov regioselectivity)
2
+ SO3- Na+
ABS
1) H2SO4 / SO3
2) Neutr. with NaOH
The use and science of laundry detergents
3
Figure 1.3 Synthesis of ABS
sodium hydroxide. By the 18 century, soap manufacture was widespread throughout Europe and Northth
America, and by the 19 century ‘soap-boiling’ had become a major industry (Figure 1.2). As a matterth 5
of fact, soap became a detergent in the modern sense of the word when ‘Persil’ was launched on the
Western European market in 1907.6
From an ecological point of view, soaps stand up to modern demands: they are made fromrenewable sources and are readily biodegraded, not polluting rivers. One may ask why soap, having such
benefits, has been replaced synthetic detergents made from petrochemicals. Two main answers to this
question relate to performance and price:
1) Alkyl carboxylates are insoluble in ‘hard water’ due to strong complexation with Ca and Mg ions.2+ 2+
Hence, the wash performance is significantly decreased. Moreover, a curd-like precipitate forms and
settles on the fabric being washed. These residues gradually build up and cause both bad odour and
deterioration of the fabric. In contrast, synthetic detergents such as alkyl sulfonates are much more
calcium-tolerant, although some precipitation of these compounds in hard water occurs, leading toreduced detergency.7
2) The price argument is double edged. At the end of the 19 century, margarine had become a food-of-th
the-people. The technology of transforming animal and vegetable fats into edible alternatives to butter
opened the possibility of feeding the rapidly growing population using raw materials which are muchcheaper and available in much larger quantities than milk. The price of these fats increased with demand,
and the manufacture of soap, using the same raw materials, became less and less economical. At that8
time, the petroleum industry was growing and had a waste product, propylene, which was burnt off.
However, by acid-catalyzed oligomerization, this waste product could be converted into a branched, long-chain 2-alkene, which was subsequently reacted with benzene and sulfuric acid; the product from this
combined Friedel-Crafts alkylation/sulfonation was neutralized with NaOH to yield a mixture of long-9
chain branched sodium alkylbenzene sulfonates, abbreviated as ABS; the synthesis of one isomer
containing 4 propylene units is shown in Figure 1.3. By the 1960s the amount of ABS used for householdlaundry washing had grown to the point that significant buildup in the environment occurred and caused10
foam blankets on bodies of water. At the same time, commercialization of the Ziegler process for
ethylene oligomerization provided a relatively economic route to straight-chain hydrophobes that could
be converted into linear alkylbenzene sulfonates (LAS). Up to present, LAS (more specifically sodium11
dodecylbenzene sulfonate, NaDoBS, Figure 1.4) has been the ‘work horse’ of nearly all detergent
SO3- Na
+
H3C (CH2)n CH2OH +
O
H3C (CH2)n CH2O CH2 CH2OH
H3C (CH2)n CH2O (CH2 CH2O)<7>H
O
<6>
Chapter 1
4
Figure 1.4 Predominant isomer of NaDoBS.
Figure 1.5 Synthesis of Synperonic A7.
formulations.We note the striking similarity of the chemical structure of ABS and LAS to that of an ordinary
soap; in fact, all detergent molecules, or surfactants, are characterized by the presence of a water-loving
(hydrophilic) headgroup (sulfonate or carboxylate) and a water-hating (hydrophobic) alkyl chain. In the
following sections we will show that these properties are essential for the removal of fatty substancesfrom garments.
1.2 Modern household laundry detergent formulations
Since the introduction of synthetic surfactants, laundry detergent formulations have become more and
more complex. The first commercial detergent formulations already contained alkalies (sodiumcarbonate, sodium silicate) to enhance removal of acidic and fatty ester soils. Moreover, sodium sulfate
has been added in up to 50 wt% to add bulk to the formulation, and to form a free flowing powder. Soon,
nonionic surfactants were incorporated for enhanced oily soil removal. C EO is a common example5413-15 7
of such a surfactant, bearing the name of Synperonic A7: a long-chain alcohol coupled with on average7 ethylene oxide units (Figure 1.5). With time, additional functional additives have been introduced by
manufacturers of detergents with the purpose of improving the ‘cleaning action’.
1.2.1 Builders. Builders are substances that augment the detersive effects of surfactants. Most12
important is their ability to remove Ca and Mg ions from the wash liquor, thus preventing these ions2+ 2+
P O P O PO O O
Na+ -O
O-
Na+
O-
Na+
O-
Na+
O- Na
+Na
+ -O2C CH2 C
OH
CO2- Na+
CH2 CO2- Na
+
(STP) (NaCit)
The use and science of laundry detergents
5
Figure 1.6 Chemical structures of two important organic builders.
from interacting with the surfactant. Hardness ions can even ‘bind’ dirt onto (cotton) fabric by interactingwith the negative charges present on both soil and cloth.
Ions responsible for hardness can be sequestered by chelating agents, so that a strongly associated
but soluble complex is formed. Sodium triphosphate, STP, is particularly effective (pK = 6) and has55Ca
been the most widely used inorganic builder until its use became restricted after the 1960s in the US andlater in Europe. The presence of large amounts of phosphate in rivers, canals and lakes led to excessive
growth of algae due to eutrophication. The water became depleted with oxygen, causing starvation of
marine life. As an alternative to phosphate, trisodium nitrilotriacetate (NTA) has been recommended.13
However, NTA was withdrawn almost immediately in 1970 because adverse laboratory reports identifiedpossible teratogenic effects. Currently, trisodium citrate (NaCit) has found widespread use as a
biologically degradable sequestrant (Figure 1.6).
Zeolites constitute another class of builders. Type A zeolites are water-insoluble particles with
a size of ca. 10 µm. The empirical chemical composition is Na O.Al O .4.5H O. The mechanism of2 2 3 2
action involves ion exchange: sodium ions released from the zeolite crystals are replaced by calcium ions
in hard water.
1.2.2 Additives for secondary benefits. These compounds are usually costly and are added14
in low percentages. Sodium carboxymethyl cellulose (SCMC) is a cellulose derivative of which 0.4 - 1.5hydroxyl groups are linked to -CH CO Na moieties; its molecular weight ranges between 20,000 and2 2
500,000. This polymer prevents redeposition of soil on cotton.15
O
O
O
ON+ CH3SO4
-
OH
N+ Cl-
('traditional' di-n-alkyldimethylammonium chloride softener)
(example of an 'esterquat')
O
OH
HOO
O
CO2- Na+
O
OH
HOO
Na+ -O2C
O O
OHO
OH
OO
Na+ -O2C
Chapter 1
6
Figure 1.8 Chemical structures of fabric softeners.
Figure 1.7 Chemical structure of an anti-redeposition agent, sodiumcarboxymethyl cellulose.
This water-soluble cotton look-alike competes for soil particles in the wash liquor. Stilbene disulfonates
and coumarin derivatives are examples of fluorescent whiteners. These additives confer enhanced16
whiteness to the appearance of washed fabric. Whiteners deposit on the cloth, and when exposed to
ultraviolet light (present in sunlight), they emit some of the radiation energy in the blue part of the
spectrum. Enzymes are widely used in premium products, degrading proteinaceous stains (proteases),
starches (amylases) and fatty acids (lipases). Bleaches remove ‘chemical’ stains produced for exampleby fruit and wine. Sodium perborate, NaBO .3H O, is often used in combination with3 2
tetraacetylethylenediamine (TAED) as a bleach activator, which is necessary for effective bleaching at
low washing temperatures of 30 or 40 EC. Fragrances mask odors of other ingredients and provide brand
identity. Sodium silicate (Na O.xSiO ; x = 3-5) is a corrosion inhibitor, which protects metal parts of2 317
The use and science of laundry detergents
7
the washing machine. Ordinary soap is added in small quantities to suppress foaming, which isundesirable in washing machines.
Fabric softeners constitute another class of compounds for secondary washing benefits. Although
they may be present as a wash cycle additive (i.e., in the main detergent formulation), fabric softeners
are often added separately to the rinse water at the last rinse cycle after the main wash. The activeingredients are cationic surfactants, e.g. di-n-alkyldimethylammonium chloride (n-alkyl = n-C , n-C ,14 16
n-C ), or the more readily biodegradable esterquats. These compounds adsorb on cotton; the cationic18
headgroups couple to the carboxylate anions on the surface of the cloth, while the alkyl chains form a
fatty monolayer which lubricates the cotton fibers. The lubrication prevents friction damage to the fibers,leading to a more pleasant feel of the fabric. Moreover, reduced surface friction accounts for the ease of
fabric ironing and the reduced tendency for static electricity generation from the rubbing together of
dissimilar materials when fabrics are tumbled in an automatic dryer.18
Typical compositions of universal powdered detergent formulations are given in Table 1.1.‘Compact’ formulations are filler-free (see below).19
Table 1.1 Composition of powdered laundry detergent formulations in Western Europe (1997).
Ingredient weight % (traditional) weight % (compact)
Surfactants 10-15 10-25
Builders 28-55 28-48
Bleach 10-25 10-20
Bleach activator 1-3 3-8
Fillers 5-30 none
Corrosion inhibitors 2-6 2-6
Enzymes 0.3-0.8 0.5-2.0
Optical whitening agents 0.1-0.3 0.1-0.3
Anti-foaming agents 0.1-4.0 0.1-2.0
Water to 100% to 100%
1.3 The detergents market: Europe and the United States
The detergent ingredients market is huge. In 1996, US demand was 3 billion kg; sales were $7 billion.
Although large in volume - see Table 1.1 - the sales value of builders (22%) is dwarfed by surfactants
(45%) and additives for secondary benefits (33%). 1.3.1 Sales of powders and liquids. With reference to commercial formulations, two
developments can be discerned. In the US, liquid laundry detergent sales soared at the expense of
powders. Procter & Gamble liquid detergent sales grew 39% from 1993 to 1997, whereas powders
Chapter 1
8
increased only 4%. US-wide, the two product types have reached a 50/50 market split. Consumers findliquids more convenient to use, with a measuring cap as opposed to a cup which has to be dug out of a
box of dusty powder. Moreover, liquids dissolve more rapidly, especially in cold water, and this property
is becoming more and more important with the advent of high-efficiency, low temperature, low water
consumption washing machines. In Europe, however, liquids still have only 13% of the laundry14
detergent market, and powder formulations are expected to dominate the market for some years to come.
Better enzyme stability and/or building properties (especially in hard water areas) may account for this
pattern. In Europe, the trend is towards concentration of active ingredients, completely eliminating fillers
from formulations. These sodium sulfate-free powders are called ‘(super) compact’ laundry detergents.19
Compact powders have conquered mainly the Western European market, where they are responsible for
60% of total sales (1996). The Netherlands are the compact-champion: 90% of the laundry detergent
market is occupied by filler-free washing powders. Environmental advantages of compact formulations
accompany economic benefits when transportation and packaging costs are considered. For example, theamount of material required to package 1 kg of powder detergent has dropped from 90 to 60 g in the
years 1991-1995.
1.3.2 Developments in household laundry cleaning in Western Europe. The trend towards
compact detergent formulations is accompanied by a steady decrease per-head in the consumption ofwashing powder; for example, 8.7 kg/year in 1991 to 7.5 kg/year in 1996 (Germany). At the same time,
washing machines are becoming more and more efficient. Whereas in 1980, 120-140 l of water were used
per wash load, water consumption has been reduced to 50 l per 4.5 kg of dry fabric. Electric power
consumption has dropped by a factor of two over the same period, to 1.5 kWh per wash.19
1.4 Oily soil removal by detergents: how it works
Having summarized the (history of) consumer use and production of surfactants, we now consider the
reason why they are needed in laundry detergency. The special properties of water are at the heart of the
problem to remove oily soil from garments. In general, the apolar compounds present in the soil arevirtually insoluble in water due to their hydrophobicity. At sufficiently high concentrations, detergents
form micelles in aqueous solution due to the same hydrophobic effect; these dynamic entities solubilize
the fatty stains.
1.4.1 Hydrophobic hydration. Water can be regarded as a macroscopic network of moleculesconnected by hydrogen bonds. This description implies that the dissolution of an apolar molecule in20
water necessitates the formation of a cavity in the three-dimensional hydrogen bonded network. The
thermodynamics of such a process are quite characteristic. At room temperature, the Gibbs energy for
the transfer of n-butane molecules from the vapor phase at 0.101325 MPa to the hypothetical solutionphase of unit mole fraction is unfavorable by 25 kJ mol . The process is accompanied by a large entropy-1
decrease (- T)S = 50 kJ mol ), hence, the hydration of n-butane (and of other apolar gases) is-1 21
exothermic. It might be speculated that the orientation of the water molecules in the (first) hydration22, 23
layer gives rise to a bulk polarization phenomenon, leading to favorable London dispersion forcesbetween water and the hydrophobic solute. 35
The entropic penalty for the solvation of alkanes by water is an important fingerprint of
hydrophobic hydration. However, its molecular origin has been interpreted quite differently over the24, 25
past fifty years. In 1945, Frank and Evans published their classical study where the ‘iceberg model’26
The use and science of laundry detergents
9
was invoked to explain the negative entropy of hydration: the water molecules were proposed to be quasi-solidly structured around a nonpolar solute (increased hydrogen bonding in the hydration shell). Indeed,
the partial molar volumes at infinite dilution of nonpolar solutes in water (V ) are larger than theirj4
‘molecular’ volumes (V ) as calculated from Van der Waals radii. Although these observations arejM 27
consistent with the notion that the density of hypothetical ‘solid’ water of dense ice-III structure is lowerthan the density of bulk ‘normal’ water, one should take into account that the difference (V - V ) is anj j
4 M
average value, offering no direct information about the properties of water molecules in the vicinity of
individual solutes.
Theories on hydrophobic hydration have continued to change. Spectroscopic techniques havebeen refined and developed, allowing a structural interpretation at a molecular level. Good indications
for the absence of hydration cages was obtained by NMR relaxation measurements. Additional evidence28
for the absence of iceberg-like water structuring has been recently obtained from neutron scattering
studies and computer simulations. It was found that, at room temperature, the number and strength29a-d 29e,f
of the hydrogen bond interactions in the hydration shell are similar to those in bulk water. Thus,
(hydrogen bond) enthalpy losses are kept at a minimum. This condition is achieved by a certain21
preferred orientation of the water molecules. One OH-bond points to the bulk water, the other is oriented
tangentially with respect to the surface of the apolar solute. Of course, water molecules in the hydrationshell have less translational and rotational degrees of freedom as compared with their bulk counterparts,
and this accounts for the strongly negative entropy of solvation.30
Another characteristic of hydrophobic hydration is the temperature dependence of the enthalpy
of solvation. The partial molar isobaric heat capacity of the nonpolar solute in aqueous solution is largeand positive. In other words, the solvation process becomes less and less exothermic with increasing31
temperature. Interestingly, the Gibbs energy of transfer of a nonpolar molecule from the gas phase to
water only slightly increases. Hence, changes in enthalpic and entropic contributions to the hydration
process largely compensate each other! Fast and accurate computer simulation techniques have recently32
shed some light on this compensation phenomenon. Increased thermal motions hinder the tangential
orientations of water molecules in the first hydration shells surrounding the apolar solute. The number
of hydrogen bonds in bulk water also decreases with increasing temperature, but to a lesser extent.38
Hence, at higher temperatures, hydration of hydrophobic molecules is accompanied by a greater loss ofhydrogen-bond interactions, so that more enthalpy has to be paid. At the same time, the preferred
orientation of water molecules in the hydration shell is disturbed, so that the entropic penalty for
hydrophobic hydration becomes smaller.33
In conclusion, it is clear that the term ‘hydrophobic hydration’ is in fact misplaced. Alkanes donot hate water, but it is the water which is ‘alkanophobic’! Hydration effects result from a subtle balance8
of enthalpy and entropy. Both thermodynamic quantities are large, and oppose each other. Water is
special mainly because it is such a small molecule: each solute in solution is surrounded by a large
number of water molecules.34
1.4.2 Hydrophobic interactions. The tendency of nonpolar molecules to associate in aqueous
solutions is called the hydrophobic effect. What is so characteristic of hydrophobic interactions is the35
narrow concentration range over which aggregation of apolar molecules in water occurs. At present, there
is no satisfactory explanation for the occurrence of such a ‘critical aggregation concentration’ in termsof a physical mechanism.
Chapter 1
10
The state-of-the-art is based on the results of computer simulations, which are, however,contradictory. The idea is that aggregation of nonpolar molecules at low concentrations is hampered36
by the special orientation of water molecules in the first hydration shell. At a certain35, 37,33, 38
concentration of solute, the number of water molecules available to form a complete hydrophobic
hydration shell is insufficient, leading to interference and mutual obstruction of hydration shells and theinevitable sacrifice of hydrogen bonds. The result is demixing. This model accounts qualitatively for35
the sudden aggregation of hydrophobic solutes in water, at well-defined concentrations. However, the
model implies an extended hydrophobic hydration shell (as has been often assumed ). For example, the39
solubility of hexanol in water at room temperature is only 10 (expressed as a mole fraction), suggesting-3 40
that the hydration shell of one alcohol molecule is composed of, on average, 1000 water molecules. This
conclusion seems unacceptable. Indeed, neutron scattering studies indicate that hydrophobic hydration
shells are relatively small. A methane molecule is surrounded by a shell containing ‘only’ 19 ± 229
waters. Of course, the hydration characteristics of methane and hexanol are different - the latter29a
molecule having both a hydrophilic and a hydrophobic hydration sphere. Intuitively, however, the
experimentally determined hydration number for methane is much too small as compared with the
number of 1000 waters surrounding one hexanol molecule, as implied by the model.
From a thermodynamic point of view, bulk hydrophobic interactions and phase separation canbe in treated in terms of a solubility limit, which results from a balance between the positive mixing
entropy of the solute and the negative entropy of the water molecules entering the hydration shell from
the bulk (vide supra). Thus, as more and more nonpolar molecules are dissolved in water, their mixing
entropy degressively increases. The entropy of the water molecules decreases linearly with soluteconcentration. Therefore, the total entropy change of the system will become positive at a certain solute
concentration, and neglecting enthalpy, this will be the point where phase separation occurs. We contend,
however, that this thermodynamic view is just a description of trends in bulk properties of water; it does
not explain hydrophobic hydration in molecular terms. On the other hand, the model that appears to failquantitatively in predicting the number of water molecules present in the hydrophobic hydration shell
is in qualitative agreement with the thermodynamic description.
1.4.3 Formation of micelles. Amphiphiles are bifunctional molecules consisting of two
moieties: one polar, the other apolar. Soap and ABS are examples of amphiphilic compounds. In analogywith the solution behavior of alkanes in water, when dissolved in water at low concentrations, the entropy
of mixing causes the molecules to become individually dispersed in the solvent. When the amphiphile
concentration exceeds the critical micelle concentration, the mixing entropy term is overridden by the
entropy loss of solvating water molecules, and analogously to bulk hydrophobic interactions, phaseseparation occurs. The only difference is that pseudophase separation takes place instead of macroscopic
phase separation. This is due to the amphipolar binding properties of the bifunctional molecules: one end
strongly interacts with the solvent, whereas the apolar end prefers the vicinity of a nearby hydrophobic
moiety. Thus, amphiphiles cannot pack into large droplets. Instead they form a variety of structures suchas micelles (vide infra), where the size of the interfacial region between the dispersed amphiphile-rich
phase and bulk solvent-rich phase is considerably enhanced.41
In line with the above-mentioned model of bulk hydrophobic interactions, the notion of
micellization as pseudophase separation due to the presence of an ‘entropic’ solubility limit might besomewhat more realistic than the idea that micellization occurs as soon as complete hydrophobic
AN AN-1 + A(1)
The use and science of laundry detergents
11
hydration shells cannot be independently formed. The latter notion is hard to reconcile with the35
observation that the CMC does not decrease linearly with increasing alkyl chain length, but
exponentially. Thus, whereas the number of water molecules needed to form the hydrophobic hydration
shells around the surfactant monomers is expected to depend linearly on the alkyl chain length, in
practice, a tenfold reduction of the CMC upon chain elongation by two methylene units is observed.42,
Moreover, with regard to thermodynamics, the temperature dependence of micellization is akin to the50
dissolution/aggregation behavior of ordinary hydrocarbons in water, providing additional evidence that
micellization of amphiphiles is just an extension of phase separation of apolar solutes - in the colloidal
domain.25
1.4.4 Properties of spherical micelles. Laundry detergent formulations contain single-tailed
amphiphiles carrying anionic or nonionic headgroups, such as NaDoBS and C EO . Fabric softeners13-15 <7>
are composed of single-chain cationic amphiphiles; we mention n-dodecyl trimethylammonium bromide
(DTAB) as an example. As was recognized by McBain already in 1913, these compounds form micelles43
when dissolved in water at concentrations exceeding the CMC. According to the ‘standard’ model
proposed by Gruen, ‘decently behaving’ amphiphiles, such as NaDoBS and DTAB, form spherical44 45 46
micelles in aqueous solution. Almost all the methylene groups comprising the hydrocarbon chain of the
amphiphile are held within the micellar core. However, terminal methyl groups occasionally reach themicellar surface. Water molecules are almost completely excluded from the inner part of the micelle; only
two methylene groups (closest to the headgroup) are in contact with water. Finally, the alkyl tails fill the
core, which has the properties of a liquid n-alkane, the semi-flexible chains showing a high degree of
conformational disorder. Critical micelle concentrations for ionic amphiphiles are usually of the order47
10 to 10 M, and increase by a factor of 10 when the alkyl chain is extended by two methylene groups.-4 -2
Aggregation numbers are often between 40 and 100; the size of an ‘ordinary’ micelle is approximately42
5 nm so that a micellar solution is transparent to the eye. Micelles (A ) are in dynamic equilibrium with48N
their monomers (A): where N is the mean aggregation number. The association rate constant k is found to be between 2.1049 8
a
and 3.10 M s , close to diffusion controlled, and only slightly dependent on the nature of the surfactant.9 -1 -1
The residence time T of one amphiphile in the micellar assembly is related to the ‘exit’ rate constant kR e
by T = N/k . The residence time depends on the length of the alkyl chain. For example, T decreasesR e R
from 2.7×10 to 6.1×10 s on going from sodium n-octyl to n-dodecyl sulfate: the aggregation number-7 -6 50
increases from ca. 30 to ca. 60, while the exit rate constant decreases by a factor of 10.
1.4.5 The cleaning action of detergents. Oily soil, by its apolar nature, can be dissolved in the
hydrocarbon-like micellar interior. This is one of the mechanisms of detergency, called solubilization,51
and corresponds to the formation of ‘swollen’ micelles. Their size is somewhat larger than that of the52, 53
original micelles, but still far below the wavelength of visible light. Swollen-micelle systems can be
considered as oil-in-water microemulsions, since as opposed to grease droplets dispersed in water, the
swollen micelles are physically (and colloidally) stable.A major contribution to the cleaning power of detergents is provided not by their aggregation
cos 2 '(FW&(FS
(SW
Fabric
SoilWater
})a.cos2
(S/W
(F / S(F/W
Chapter 1
12
(2)
Figure 1.9 Contact angle in water/soil/fabric system.
in aqueous solution, but by their surface-active properties. Thus, amphiphiles are surfactants, which tendto concentrate at almost any water/liquid, water/gas or water/solid interface due to the tendency of the
apolar groups leave the aqueous phase while the headgroups tend to remain hydrated. Thus, when we add
a surfactant to a system comprising two immiscible phases (e.g., water and n-pentane), it will be adsorbed
at the interface between the two phases, and will orient with the hydrophilic group toward the aqueousphase and the hydrophobic group toward n-pentane. Where the surfactant molecules replace water and/or
pentane molecules of the original interface, the interaction across the interface is between the hydrophilic
group of the surfactant and water molecules on one side, and between the hydrophobic chains of the
surfactant and pentane molecules on the other side of the interface. Since these (‘like-like’) interactionsare much stronger than the original interactions between the highly dissimilar pentane and water
molecules, the tension across the interface (or the surface Gibbs energy per unit area, () is reduced. In54
other words: surfactants compatibilize aqueous solutions with their interface. When this theory is applied
to oily soil removal, the model only explains the emulsifying power of detergents: by the input ofmechanical energy, with the help of surfactants, layers of dirt can be dispersed as small droplets, and then
washed away. (Just as the oil droplets in mayonnaise are coated with a ‘protecting’ layer of lecithin, the
emulsified dirt is characterized by a surfactant-rich surface layer that acts as a potential energy barrier
against coalescence. More importantly, this layer prevents the dirt from coming into intimate contact withthe fabric, so that redeposition of the soil on the cloth is hampered. ) These droplets are much larger55
than swollen micelles, and hence the aqueous dispersion has a turbid appearance.
To understand the mechanism of oily stain removal, we have to take account not only of the soil
(S) and the water (W), but also the fabric (F). The equilibrium contact angle 2 between water and theother phases is related to the interfacial Gibbs energies per unit area of those phases (Figure 1.9). Imagine
that the interfacial areas fabric/water and fabric/soil are increased by a certain amount )a. The interfacial
area between the soil and the water is increased by )a.cos2. Thus, the resultant change of the interfacial
Gibbs energy is )G =w
-)a.( + )a.( + )a.cos2.( . Since as )a60, )G 60, we obtain cos2.( = ( - ( , orF/W F/S S/W w S/W F/W F/S
Equation 2 is Young’s equation. By adding a surfactant, the interfacial tensions between water and the54
The use and science of laundry detergents
13
Figure 1.10 Complete removal of oil droplets by hydraulic currents if 2 remains > 90E. Takenfrom [51].
Figure 1.11 Oil droplets cannot be removed completely if 2 remains < 90E. Taken from [51].
fabric, and between water and the soil, become exceptionally low: ( , ( 6 0. The interfacial tensionFW SW
between soil and the fabric does not change. Hence, in the presence of surfactant, ( > ( . Thus, cosFS FW
2 is negative, so that the contact angle is larger than 90E. As is shown in Figure 1.10, this means that the
area of contact between the soil and the fabric can be reduced to zero while maintaining the contact angle
at its equilibrium value. In other words: there are no thermodynamic restrictions on the removal of soilby hydraulic action, provided that surfactant is present. This mechanism of detergency is called roll-up.
In the absence of surfactant, part of the soil droplet can be withdrawn by mechanical action, but
as the area of contact is reduced, a neck is formed directly above the contact region (Figure 1.11). If the
contact angle is maintained, the drop must divide at this neck, leaving a small quantity of oil adhering56
to the substrate. This result confirms that detergents are required to remove all oily stains from the fabric
if water is the solvent.
1.5 Surfactant aggregate morphology and formation of liquid crystals
Apart from spherical micelles described above, surfactant molecules can aggregate into a variety of
colloidal structures, having different sizes and shapes. The morphology of these aggregates critically
p < 1/3cone
1/3 < p < 1/2truncated cone
1/2 < p < 1cylinder
sphericalmicelle
rodlikemicelle bilayer
Chapter 1
14
Figure 1.12 The packing parameter approach: the morphology of the surfactant aggregates isdetermined by the geometrical shape of the constituent monomers.
depends not only on the surfactant type, but also on temperature and the presence of salts. The aggregatesform liquid crystalline structures as the surfactant concentration increases. The formation of ordered
mesophases is driven by the relief of interaggregate repulsions. With respect to the ‘science of laundry
detergents’, detailed knowledge of liquid crystalline behavior is required for the formulation of liquid
detergents (characterized by high surfactant concentrations), whereas washing performance criticallydepends on the aggregate morphology in the wash liquor.
1.5.1 Micellar shape and geometric packing constraints. To a first approximation, the ability
of amphiphiles to form aggregates of a well-defined morphology depends on the molecular architecture
of the surfactant molecules. The packing properties of surfactants result from a balance between theoptimal cross-sectional surface area of the headgroups a , the volume v of the hydrocarbon chains, and57
0
the maximum length l that the chains can attain. The dimensionless packing parameter p = v/a lc 0 c
characterizes the surfactant’s ability to form spherical micelles (cone-shaped surfactant molecules,
H2O
H2O
The use and science of laundry detergents
15
Figure 1.13 Schematic view of a unilamellar vesicle.
p<1/3), worm-like micelles (truncated cone, 1/3<p<1/2) or bilayers (1/2<p<1). Figure 1.12 graphically58
illustrates the packing parameter approach.59
By input of mechanical energy, flat bilayers close to form spherical structures entrapping an
aqueous ‘pool’. These so-called vesicles may be uni- or multilamellar, depending on the number of60
concentric bilayers forming the structure. Moreover, depending on the size, one distinguishes between61
small unilamellar (Figure 1.13), large unilamellar and giant vesicles: SUVs (20-50 nm), LUVs (60-100062
nm) and GVs (> 1 µm). We stress, however, that vesicles formed from chemically pure amphiphiles are
metastable, and with time, they return to the flat bilayer state. This spontaneous change can be63
explained in terms of geometrical factors. A bilayer is composed of two monolayers (bilayer leaflets),
stuck together through hydrophobic interfaces. Each monolayer is characterized by an equilibriumspontaneous curvature which in general is non-zero. A bilayer composed of identical monolayers is
frustrated because the monolayer curvatures are equal in magnitude, but of opposite sign. In terms of
symmetry, the flat bilayer is least frustrated (i.e., has the lowest Gibbs energy) when its spontaneous
curvature is zero!64
Is the packing parameter explanation of surfactant aggregate morphologies satisfactory? In
general, the answer is ‘yes’. There are many (recent) examples of a wide variety of surfactant molecules
which obey these geometrical rules. For example, C EO forms vesicles, whereas C EO , having a12 3 12 7
larger headgroup, forms worm-like micelles. Even polystyrene-b-poly(acrylic acid) diblock copolymers65
form bilayer structures (PS-b-PAA = 400-b-16) or worm-like micelles (200-b-15) depending on the
‘hydrophobic chain length’ (ca. PS content) at constant ‘head group area’ (ca. PAA content). 66
In cases where the approach is unsatisfactory, it is still valid in reality, but the sensitivity of both
the geometry and packing of surfactant molecules to the experimental conditions may beunderestimated! Thus, micelles of NaDoBS in dilute aqueous solutions can be transformed into bilayer67
aggregates by addition of alkali metal chlorides. An increase in ionic strength leads to an increase in68
counterion binding to the micellar surface and a concomitant decrease of the hydration of the headgroups
(and Coulombic inter-headgroup repulsions). Consequently the effective optimal cross-sectional surfacearea of the headgroup decreases, the packing parameter increases and the morphology of the aggregate
is altered. The soap boilers used this principle. By adding large amounts of NaCl to a concentrated69
micellar solution of soap, the packing parameter of the surfactant molecules increases and large bilayer
structures are formed, which phase separate to form a solid-like material. For nonionic surfactants,temperature plays an important role. Headgroup hydration (and a ) decreases rapidly with increasing0
temperature. Consequently, the aggregate size increases. At even higher temperatures, the aggregates70
become so large that (at the cloud point) phase separation occurs. Finally, mixing of two different71, 72, 73
amphiphiles may result in aggregate properties that can only be understood on the basis of a larger-than-mean average packing parameter. For example, the electrostatic repulsions between ionic surfactants, and
Chapter 1
16
Figure 1.14 Schematic view of a continuouslamellar liquid crystalline phase. Taken fromref. [86].
the steric repulsions between nonionic surfactants are strongly diminished when these molecules are
mixed, because repulsive forces are completely different! Thus, admixing solutions containing nonionicand anionic surfactants, individually forming spherical micelles, produces a solution containing worm-
like micelles.74, 75
1.5.2 Formation of liquid crystals from surfactant aggregates. Upon gradually increasing the
concentration of ‘well-behaved’ surfactant above the CMC, more and more spherical micelles are formed.As a result, the mean distance between aggregates decreases. To accommodate the micelles, the system
undergoes a disorder/order transition. For example, micelles can pack in a cubic array, to form a76 77
lyotropic (solvent-dependent) liquid crystal. The molecular order is not perfectly long-range (as in a
crystal), nor isotropic (as in a liquid), but somewhere in between.78
For the purposes of this thesis, the lamellar liquid crystalline phase is most important. The
continuous lamellar phase is formed by a stack of ordered bilayer aggregates (Figure 1.14). The ‘neat
soap’ phase depicted in Figure 1.2 is an example of a continuous lamellar phase. Alternatively, separate
entities are formed upon closure of the bilayer sheets. Multilamellar vesicles appear when several bilayerspack around one another, rather like in an onion. Part of this thesis deals with multilamellar vesicles with
many layers, henceforth called lamellar droplets. The thickness of the water layers between the surfactant
lamellae (0.2-100 nm) may well exceed the bilayer thickness (2-3 nm), depending on, for example,
surfactant concentration.79
1.5.3 Phase behavior of liquid crystalline lamellar droplets in ‘structured’ liquiddetergents. ‘Concentrated’ liquid laundry detergent formulations may contain over 30 wt% of
surfactants. Hence, interaggregate interactions produce liquid crystalline phases. The resulting colloidal
dispersions are colloidally unstable: phase-separation will occur due to flocculation (vide infra). Twoapproaches are taken in practice to circumvent this problem. The lyotropic phase can be broken down
by addition of intercalating water-soluble compounds such as sodium p-xylenesulfonate. The presence80 81
of these so-called hydrotropes results in the formation of an isotropic liquid. Another possibility is to
induce the formation of liquid crystalline lamellar droplets, and to make the dispersion physically stable.In this way, an internally or surfactant-structured liquid detergent formulation is obtained. We focus82
attention on the latter approach.
The remainder of this chapter introduces the lamellar dispersions which have been studied in this
thesis, and previously by Van de Pas. These systems are models for commercial structured liquid82
laundry detergents. In studies of the microstructure, the physical stability and the rheology of such
The use and science of laundry detergents
17
detergent formulations, the number of components can be reduced to four: an anionic and a nonionicsurfactant, water, and electrolyte. Specifically, the model lamellar dispersion under study consists of83
28 parts (by weight) of NaDoBS, 12 parts of Synperonic A7, 60 parts of water and 20 parts of trisodium
citrate: the 40/60/20 system.
In the next stage we turn attention to the aggregation and phase behavior of the surfactant mixturein the aqueous salt solution. Sodium citrate breaks down the hydration layer of the poly(oxyethylene)
headgroup of the nonionic surfactants (‘salting-out’ or Hofmeister effect ). At the electrolyte84
concentrations employed, dehydration occurs to such an extent that the headgroups cannot be kept in
solution. Demixing occurs, according to the same mechanism as for temperature-induced ‘clouding’. .85
Moreover, the reduction of the optimal headgroup area results in an increase of the packing parameter,
which explains the transition to bilayer structures (arranged in a lamellar fashion) (Figure 1.15).86
Lamellar droplets are formed instead of a continuous lamellar liquid crystalline phase for two
reasons. We recall that formation of curved bilayer structures from a chemically pure surfactant isthermodynamically unfavorable. Indeed, one might argue that the lamellar droplets are metastable, their
formation being induced by the mechanical agitation involved in dissolving sodium citrate in a micellar
surfactant solution. However, the lamellar droplets are stable for more than 5 years, providing strong82, 86
indications that the droplets are thermodynamically stable. The reason is that a surfactant mixture is used,and if the compositions of the two monolayers are allowed to differ then, possibly, the spontaneous
Chapter 1
18
Figure 1.15 Schematic representation of a dispersion of lamellar droplets. Reproduced from ref.[82a].
curvature of the bilayer will be non-zero, thus favoring the formation of finite size vesicles. 87
E(inst) '& ",
b µ(a, inst)2
(4B,0)2 R 6
EVdW '& A
12 B D 2
Chapter 1
22
(3)
(4)
Spontaneous vesicle formation has been observed in dilute aqueous mixtures of (i) cationic and anionicsurfactants, and (ii) mixtures of ionic surfactants and alcohol cosurfactants with brine. This53, 88 89
enthalpic stabilization mechanism was originally proposed by Safran et al. who showed theoretically90
that the Gibbs energy of a two-component bilayer may sometimes be minimized in a state of nonzero
curvature, due to the spontaneous formation of different chemical compositions in the outer and innerleaflets.
Finally, we examine the reasons why these spontaneously formed multilamellar vesicles phase
separate. We have an indication of the factors that are at play on a colloidal level. Generally, in stable
dispersions, repulsive forces between particles are dominant. If attractive forces dominate, the particlesflocculate (reversibly) or coagulate (irreversibly). Van der Waals attraction is always experienced91, 92
between identical particulate matter. The attraction is due to ‘dispersion forces’ originating from electron
correlations. At any given instant, the electronic configuration of atom a corresponds to an instantaneous
dipole moment µ(a, inst). The electric field corresponding to µ(a, inst) polarizes atom b and induces adipole moment µ(b ,ind). The instantaneous energy of interaction E(inst) is then the dipole-dipole energy
corresponding to µ(a, inst) and µ(b ,ind):
where " ’ denotes the frequency-dependent polarizability with a frequency corresponding to the rate ofb
change of µ(a, inst). The Van der Waals attraction between two semi-infinite flat surfaces can be93
written in the form:
where D is the distance between the surfaces and A is the Hamaker constant, which is a measure of thestrength of the Van der Waals interaction. The Hamaker constant has a frequency-dependent and a zero-
frequency term. In the presence of 0.5 M of electrolyte, the zero-frequency term is almost completely
shielded at a separation of 1 nm. However, the frequency-dependent term hardly varies with salt94
concentration since the ions are too massive to follow redistributions of electrons. Overall, the Hamakerconstant is 4.5×10 J in pure water, and is reduced to 3.10 J in the 40/60/20 model system.-21 -21 82, 86, 95
The electrical double layer repulsion (E ) is the major long-range repulsion for charged particles.es
The electrical double layer comprises the charged bilayer and the (partially bound) counterions. For
entropic reasons not all counterions are tightly bound. Hence the charge density (exponentially) decaysfrom the surface. The ‘non-condensed’ counterions comprise the diffuse part of the double layer. Where
the diffuse parts of either double layers of adjacent surfactant bilayers overlap, the counterion
concentration starts to build up, and an osmotic flow of solvent into the overlap region keeps the surfaces
apart. When an electrolyte is added to the system, counterion binding increases, the surface charge92
density is reduced and the electrical double layer repulsion is diminished. This pattern is true for96
0 5 10 15 20 25 30-6
-4
-2
0
2
4
6
8
10
12
Secondary minimum
Primary minimum
Eto
t / a.
u.
Distance / nm
Etot ' EVdW % Ees % Evr % Eos
The use and science of laundry detergents
23
Figure 1.16 Total interaction energy as a function of distance between bilayers.
(5)
bilayer-bilayer interactions in lamellar droplets and for inter-droplet interactions.In the absence of salt, there is steric repulsion between the nonionic headgroups. The steric
interaction energy has several components: (i) a volume restriction term which is due to the loss of
configurational entropy of the PEO chains that occurs on head-to-head approach of the nonionic
surfactants (E ), and (ii) an osmotic interaction (E ), which results from an increase in the localvr os
concentration of PEO segments in the region where the headgroups overlap. (The osmotic term is97
generally most important.) However, in the presence of high electrolyte concentrations, water is a ‘bad
solvent’ for the poly(ethylene oxide) moieties; the PEO chains contract, the osmotic interaction may
become attractive, and the volume restriction term becomes insignificant at distance larger than 3 nm.Again, both intra- and inter-droplet repulsions are greatly reduced upon addition of salt.
The total interaction energy per unit area E when two bilayers approach each other may betot
approximated by:
Typically, the net interaction energy as a function of interparticle separation follows the profile outlined
in Figure 1.16. As follows from the discussion above, Van der Waals and osmotic attractions dominate
the repulsion in the presence of electrolyte. Hence, multilamellar stacks of bilayers are formed. The
location of the primary minimum, i.e. the interparticle separation where the energy is lowest, is of the
Chapter 1
24
order of several nm, according to X-ray diffraction measurements (Chapter 6). However, there are also(weaker) net attractive forces between the lamellar droplets, as indicated by the presence of the secondary
minimum. This secondary minimum appears to be quite deep (. several kT): it is usually observed that
the lamellar droplets are flocculated, and can hardly be redispersed upon shaking. The extent of
flocculation is determined by the same forces as those which act between bilayers. The interactionsbetween the lamellar layers and the lamellar droplets are of the same kind: the interaction forces are
coupled. The only difference is that the curvatures of two opposite layers within the droplet are of
opposite sign, whereas the curvatures of two layers in opposite layers have the same sign. As a
consequence, in the presence of electrolyte, the net attractive forces between lamellar droplets are smallerthan those between lamellae within droplets. Hence, the secondary minimum is more shallow than the
primary minimum.
1.5.4 Deflocculation of lamellar droplets by addition of decoupling polymers. The mutual
aggregation of lamellar droplets can be prevented by the addition of polymers which - due to the presenceof hydrophobic side-chains - adsorb onto the periphery of the multilamellar aggregates, while a water-
soluble backbone protrudes into the solution. Adsorption of these ‘hairy’ polymers prevents close91
approach of the droplets by a mechanism called steric stabilization. Provided that the aqueous98
electrolyte solution is a ‘good’ solvent for the polymer, i.e. the polymer coil is not collapsed, the sametype of steric/osmotic forces as described for PEO segments in salt-free aqueous solutions becomes
operative, and two repulsive (volume restriction and osmotic) interaction terms E and E are addedvr,pol os,pol
to the total interaction potential. However, provided that the polymers do not penetrate the droplets, only
the interaction potential between lamellar droplets changes, whereas the forces between lamellae withindroplets remain essentially unchanged. Thus, interlamellar forces are decoupled from intralamellar forces.
Hence these polymers are called decoupling polymers, see Figure 1.17.
The use and science of laundry detergents
25
Figure 1.17 Schematic representation of a lamellar dispersion in a good solvent (A), in a poorsolvent (B) and in a poor solvent with added decoupling polymer (C). (Solvency is notedwith respect to the surfactants.) The polymers are depicted in a thick line style. For alegend to surfactant structures, see Figure 1.15. Taken from ref. [82a].
Chapter 1
26
Van de Pas has developed a random copolymer of lauryl methacrylate and sodium acrylate of82
molecular weight 4000; the LMA/NaA monomer ratio is 1:25. This polymer, RAN4000, efficiently
stabilises lamellar droplets in a 40/60/20 system when added on top in concentrations of 0.5-2 wt.%.82,
In fact, this polymer is used in commercial concentrated structured liquid detergents.86 99
1.6 Polymer-surfactant interactions in (liquid) laundry detergent science.Outline of this thesis.
So far, we have explored the broad area of laundry detergent science with respect to the wash liquor and
the formulation of structured liquid laundry detergents. With regard to the wash liquor, we are concerned
with dilute surfactant solutions (concentration < 10 CMC). Hydrophobic interactions between surfactantmolecules and/or micelles and hydrophobic soil are involved in the actual detergency process. However,
a large number of components are present in detergent formulations. Therefore, we anticipate many
interactions between these additives, the surfactants, the soil and the fabric in the wash liquor. Thus, a
detailed understanding of detergency, taking into account all processes and interactions in the washliquor, presents an enormous challenge.
In a first attempt to gain some insight into the complicated interaction landscape, we studied the
interactions between surfactant monomers, micelles and vesicles, and hydrophobically-modified water-
soluble polymers (HMP) in dilute solutions. The decoupling polymers constitute one example of thisclass of polymers; they have an amphiphilic nature and are expected to interact with surfactant molecules
or aggregates through hydrophobic interactions. We will see that decoupling polymers can form micelle-
like structures which are called hydrophobic microdomains. Interactions with single-tailed micelles
critically depend on the presence of these domains, to which surfactant monomers may bind.Consequently, the concentration of free surfactant monomers in solution is reduced. Moreover, the
viscosity of the wash liquor may be influenced by the polymer, and the solution viscosity may be altered
by the polymers interacting with surfactants. A titration microcalorimetric / fluorescence spectroscopic
study on HMP-surfactant monomer and HMP-micelle interactions is reported in Chapter 2. Chapter 3 describes the interactions between surfactant bilayers and hydrophobically-modified
polymers in dilute solutions as studied by titration microcalorimetry and differential scanning
microcalorimetry. The aim of this research is to study the factors that determine the efficiency of
anchoring of hydrophobic side chains into (small unilamellar) vesicle bilayers. The underlying idea isthat the efficiency of anchoring of the polymer into the vesicle bilayer is of immediate relevance for steric
stabilization.
Chapters 4 and 5 are concerned with microstructural and rheological properties of concentrated
lamellar dispersions with added decoupling polymers. We have developed a decoupling polymer that isspecifically hydrophobically end-capped, in contrast to the commercial product RAN4000 which is less
well-defined because it contains, apart from ‘anchorless’ poly(sodium acrylate), fractions bearing more
than one anchor per polymer. Using this end-capped polymer, we have studied in detail the effects of
adsorbed polymer on the average lamellar droplet size, as a function of polymer concentration andmolecular weight. Moreover, the rheological properties of the model dispersions are interpreted in terms
of interparticle forces (Chapter 5). Finally, we show that by rational design of polymer structure, shear-
thinning properties of a lamellar dispersion can be amplified, so that solid particles can be suspended in
The use and science of laundry detergents
27
1. Budavari, S. (Ed.) The Merck Index, 11 ed., Merck&Co.: Rahway, 1989, p. 1328.th
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a liquid laundry detergent.Most of this work has been or will be published.100
AcknowledgementFruitful discussions with Sijbren Otto, Niek Buurma and Theo Rispens on the topic of hydrophobicinteractions are highly appreciated.
1.7 Notes and references
Chapter 1
28
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29
42. Van Os and Haak have compiled a large number of data regarding aggregation of many differentamphiphiles: Van Os, N.M.; Haak, J.R.; Rupert, L.A.M. Physico-Chemical Properties ofSelected Anionic, Cationic, and Nonionic Surfactants, Elsevier: Amsterdam, 1993.Paul Huibers’ homepage on the Internet provides access to interesting sites related toamphiphiles: http://web.mit.edu/huibers/www/surfsite.htm. At the time of writing, the site haslinks to 193 people in the field, 183 business sites, 98 sites on surfactant applications, 78publishers and publications, 40 conference sites, 19 professional societies and 81 universities andresearch centers.
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57. ‘Optimal’ refers to the condition where two opposing forces are in equilibrium. Hydrated and/orcharged headgroups repel each other, tending to increase the headgroup area. On the other hand,the hydrocarbon/water interface strives to be minimized.
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59. In Figures 1.12 and 1.13, the bilayers are shown composed of single-tailed surfactants, for easeof drawing. We stress that more generally, (vesicle) bilayers are composed of double-tailedamphiphiles.
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95. Compare: Marra, J. J. Colloid Interf. Sci. 1986, 109, 11.
96. For a full account of the theory, see (a) Overbeek, J.Th.G. In Colloid Science, Kruyt, H.R. (Ed.),Vol. 1, Elsevier: Amsterdam, 1952. (b) Lyklema, J. In Colloidal Dispersions, Goodwin, J.W.(Ed.), The Royal Society of Chemistry: London, 1982.
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