HLD-NAC

A guide to Optimal SurfactantsProfessor Steven Abbott

My thanks to, in alphabetical order:Professors Acosta, Aubry, Salager and Sabatini for their generous assistance in teaching me about HLD, and to Professor Acosta and his group for their continuing support and guidance in developing the software and database.

Images from their papers are used with grateful acknowledgement

This is my non-expert personal view of the fieldIt has been used as the basis for a number of tutorial talksIt is provided “as is” to stimulate discussion/debatePlease send feedback to steven@stevenabbott.co.uk The website for the HLD-NAC software package iswww.stevenabbott.co.uk/HLD-NAC.html

What I’m not talking about• My interest is in microemulsions for cosmetics,

oil-field recovery, nanoparticles etc.• I have no particular interest in or knowledge of

foams• I have no particular interest/knowledge in the

dynamics of classical micelles and their CMC behaviour

• I can’t talk about polymeric surfactants because they, too, are outside my knowledge base

• This talk is pseudo-ternary-phase-diagram free

Just an ordinary scientist

• I’m a formulator, not a surfactant scientist• I’ve read lots of surfactant theories• None of them provided a practical formulation tool • I want a rational choice of surfactants

– and I suspect that surfactant suppliers would love to reduce their inventories …

• I want to formulate efficiently, not trial-and-error– Surfactant formulation space is way too large

• I want to rationally swap to “green” surfactants

Microemulsion terminology

• Winsor Type I, o/w, lower (denser) phase• Winsor Type II, w/o, upper (lighter) phase• Winsor Type III, bicontinuous middle phase

In reality are bicontinuous

Generally a uniform size

Type I Type IIType III

I want to get this first time

Optimal Type III

EACN scan from Intelligent Formulation Green Surfactant project. Low EACN to left, high EACN to right

Water phase largerType I o/w

Oil phase largerType II w/o

I want:

• To be in the right phase, first time– Sometimes I want Type I, sometimes Type II,

sometimes Type III• To have a high solubility parameter (SP)

– ml water-in-oil/g surfactant– ml oil-in-water/g surfactant– Because surfactants are “bad” and “expensive”

• (To be free from liquid crystal phases)– I’ve no solutions to this issue but high SP means

low surfactant concentrations which will help

I want microemulsions because

• I can do clever cosmetic formulations with them

• But note that most published microemulsion cosmetic/pharma papers use them only because “nano is good”– These papers generally prove that if you shove a

lot of surfactant onto skin you can get things to go through. Nothing to do with microemulsions

Not HLB

• HLB really aren’t much use because they really only apply well to medium-sized, standard EO non-ionics– why should the % hydrophilic sorbitan be in any way

equivalent to % hydrophilic EO?

• With a choice of 2,000 surfactants, maybe 200 have your HLB, yet their properties are very different

• And they don’t predict much beyond basic o/w or w/o, and often not very well– Don’t predict effects of salinity, oil, temperature

Not CMC

• Critical Micelle Concentration• Tells you a lot about its desire to escape from

water and form micelles• But not a lot about making great w/o or o/w

emulsions• Generally lower is better because its not too

water soluble, and probably has long tails– the long tail is good for other reasons– CMC for extended surfactants are “meaningless”

Not CPPCPP=Vtail/(Ltail*Ahead)

Not CPP

• Critical Packing Parameter seemed to be a good idea for distinguishing between o/w and w/o surfactants based on whether head or tail is bulkier

• Theoretically bankrupt because microemulsion curvature is flat on the molecular scale …

• … and one can go seamlessly from o/w to w/o with surfactants of very different CPP values

• But they’re great for those interested in complex surfactant phases (hexagonal, laminar…)– And such phase behaviour in practice limits

microemulsion practicality

CPP=Vtail/(Ltail*Ahead)

CPP for phases in conc. surfactant

Any complete surfactant story would include HLD-NAC and the tendency to form liquid crystalline phases ...

But …

• Knowing the key parameters used in CPP is very important:– Head area, A– (Extended) Tail length, L

• And there may be some routes from CPP to Cc (see later)– But so far that’s speculative

HLD

• Hydrophilic Lipophilic Difference• Apparently simple, but a lot of work to get it

right from (in alphabetical order) Aubry, Sabatini and Salager

• You get the Optimal Surfactant when HLD=0– lowest interfacial energy– highest SP (Solubility Parameter – not HSP)

• ml/g i.e. ml of oil dissolved in water per g of surfactant– best cleaning, oil recovery and microemulsions

Same(ish) equation for i and non-i

• Ionics– HLD = ln(S)-K.EACN-αΔT+Cc

• Non-ionics– HLD=b.S-K.EACN+cΔT+Cc

S = Salt concentration, g/100mlK= Constant ~0.17EACN = Effective Alkane Carbon Numberα=temperature coefficient ~0.01. Note the - signΔT=temperature difference from 25°Cb = Salt dependency for non-ionics ~ 0.13c=temperature coefficient ~0.06. Bigger effect, opposite signCc=Characteristic Curvature, unique to each surfactant

EACNHexane = 6Decane = 10etc.ButBenzene = 0Limonene = 7IPM = 13Triolein = 16i.e. they behave like an alkane with those numbers of C

What does it mean? Ionics

• 0 HLD when ln(S)+ Cc = K.EACN + αΔT– as S goes up, Water solubility goes down– as Cc goes up, Water solubility goes down

– as EACN goes up, Oil solubility goes down– as T goes up, Oil solubility goes down

• because ionic is more soluble in water• The best surfactant for a hot cycle in a washing

machine is often bad for a cold cycle – and vice versa

What does it mean? Non-Ionics

• 0 HLD when b.S+cΔT+Cc = K.EACN– As S goes up, Water solubility goes down– As T goes up, Water solubility goes down

• EO is a strange beast so water solubility decreases with T

– As Cc goes up, Water solubility goes down

– As EACN goes up, oil solubility goes down

Why does it matter? - 1

• If you’ve got an easy oil (e.g. heptane) and just want a modest amount of o/w or w/o microemulsion (e.g. for nanoparticle manufacture), then trial and error will get reasonable results without any theory

• But …

Why does it matter? -2

• Difficult oils have large EACNs– No problem – balance with Salt or a large +ve Cc– But high Salt is often not practical + small Type III– And large +ve Cc usually means v. long tail which

generally means nasty liquid crystal phases and sticky messes

– AOT is an exception because its Cc=2.5 (SDS=-2.3) so can formulate with EACNs 25 higher than SDS

• Those two tails = lots of C but not too self-associative• The branches help bulk out and reduce self-association

Why does it matter? -3

• To get large amounts of o/w, w/o or to get a whole, stable Type III 50:50 emulsion is very hard without theory

• Especially if you want a high SP – best emulsion with least surfactant

• For cosmetics, surfactants are often “bad”, so less surfactant is desirable.

The parameters

• cΔT – No theoretical method to calculate c as EO

solubilities are hard to understand– But c seems to be a good solid number

• αΔT – No theoretical method to calculate α– No fundamental reason why different ionic

headgroups should have the same α– insufficent data to know either way

The parameters (cont)

• EACN– By definition OK for alkanes!– But where do EACNs for other oils come from?

• My view is that HSP can predict these• “Like dissolves like” so compatibility between

surfactant and oil will decrease EACN• But so far only found one good dataset (Aubry) to be

able to test

The parameters (cont)

• K– Known to be smaller (~0.1) for Extended

Surfactants than for “typical” surfactants (~0.17)– Why is K the value it is?

• Can it be calculated?• Is it truly a constant?

– Till there’s more data, assume that it is a constant

The parameters (cont)• Cc

– Characteristic curvature– A –ve value means that for “normal” conditions the

emulsion is curved around the oil, so it’s o/w Type I– A +ve value means curved around the water, so it’s

w/o, Type II– Sounds a bit like CPP, but is simply an observed

parameter, not something directly calculated (yet?) from shape/size

• Sodium Di-octyl sulfosuccinate is +2.5• Sodium Di-hexyl sulfosuccinate is -0.9• why do 2 Me groups (+ branching) give such a big change?

Scans, not phase diagrams

• A proper phase diagram varies– Oil, water, surfactant, brine, temperature– Need a 5D plot to visualise it– Life’s too short

• So take 10 test tubes, 50:50 o/w, modest amount of surfactant*

• And look for 2 (o+o/w) to 3(o+o~w+w) to 2 (w/o+w) phases as salt goes lowhigh

*Hope for SP of 10So 3% surfactant will dissolve 30g oil20:60:20 result

Scans not phase diagrams

More scans

Note the relatively large oil phase to the right of S*, showing a relatively large amount of water brought into the oil. I’m not clear why you don’t get the same phase volume to the left, though LC phases are part of the problem

The simple scan gives:

• S* - optimal salinity where HLD=0• You know EACN, you know ΔT=0 so you get Cc

– And you choose the oil so the data apply to you– You don’t care if things would be better with hexane!

• From the size of the middle phase you get SP• If you don’t get 2-3-2 phases then put all tubes in

a water bath and find T where you do– Especially good for non-ionics– That’s the theory – it’s never worked for me

Scans are:

• Tedious• Error prone• Limited by practical stock solutions

• Therefore

• High-throughput equipment is highly desirable!

High Throughput• Do in one day what a skilled technician can do

in a week• Much more versatile because can weigh any

amounts – no limits of stock solutions• Photo record/measure of phase volumes

A ChemSpeed Formax HT machine at VLCI

Measuring the parameters• Simple phase scans to find “optimal salinity”

S* followed by simple algebra give you: – EACNs (find S* for same surfactant in different

oils)– Ccs (find S* for same oil, different surfactant)– or extract more information from combined scans

Change proportion of unknown surfactant in known surfactant, and fit S* data to calculate Cc of unknown

DOE principles greatly reduce number of scans

Practical scans

• For experimental ease choose:– An EACN scan to get Cc of surfactant

• Fixed S, varying EACN e.g. TolHexadecane = 116 or Tol Squalane =124

– A surfactant scan using known Cc to get unknown Cc• Fixed S, Fixed EACN, vary known/unknown surfactant ratio

– Salt scans are harder to do• adding solid salt is hard without a robot• solid salt to EACN or surfactant scans can explore other

ranges if original scan fails to find HLD=0

Scanning for EACN

• Fix S and unknown oil, scan two known surfactants

• A key step in building up the utility of HLD-NAC as too few real-world oils are known

• Natural oils may show large variations due to differing levels of long chains and degrees of hydrolysis of glycerides– Customers might require EACN values from suppliers

so they can match with correct surfactant (blend)

Guesswork

• Impossible to scan full range with high accuracy

• So must guess Cc and plan scan around it• If guess is wrong then the scan helps narrow

the range for future scans• As we build up more Cc values, there will be

more prototypes for estimating Cc and more “right first time” scans

Planning• HLD-NAC software makes it easy to explore scan ranges

and scan issues• A complex 2-surfactant situation optimal at 6% salt

QC via HLD

• The “same” surfactant from different suppliers, and different batches from the same supplier might be different because of differing chain lengths, EO range, alcohol or acid levels

• The Cc will be an accurate QC tool to show functional equivalence of different batchs– Can use small EACN steps around the Cc to get

accurate values. Quick/simple test!

Calculating the parameters

• Cc can come from CxEOy correlations• Some evidence of link of Cc to CCP• EACNs some rules of thumb, group

contribution and, perhaps HSP• But till we have larger high quality databases,

it’s hard to know if predictions are of great value

The Exxon model

• H/L = VH/VL = (VoH+VW

H)/(VoL + VL

o)– Rather like CPP, but Vol_Head/Vol_Tail– Vols made up of intrinsic Vo

H ,VoL (calculable) and

associated VWH ,VL

o (unknowable?)• High H/L = Hydrophilic, Big Head = Head

outside = o/w• Low H/L = Lipophilic, Big Tail = Tail outside =

w/o• But H/L is NOT a constant for a surfactant

– Changes with salinity, T, oilRobbins M.L. et al, J. Coll. Int. Sci. 124, 462-485, 486-503, 1988 & 126, 114-132

Exxon continued• H/L changes with salinity

– “dehydration” of the associated water

• Curvatures & Volumes calculable• Many similarities with predictive capabilities of

HLD-NAC– Phase volumes etc.– But couldn’t compute τr/δr

– Little referenced since

Volume Fractions & Phase Volumes

A typical volume fraction scan Same thing but change cation!

A lovely bit of work from Exxon

Exxon nukes CPP

• Fig 3 of Paper II shows that small H/L ratio changes cause large S* shifts if L changes but small shifts if H changes

• Because S* depends on (Head+Water)/(Tail+Oil)• Fig 4 shows how the real sizes change

τr = τH/ τL δr =δH/δL

HLD-NAC

• We can do the HLD bit and get ourselves into the right formulation domain

• But we can’t predict phase volumes, fish diagrams, viscosities …

• Exxon were close to a predictive model, but they didn’t have the simple HLD and they couldn’t quite get the right parameters

• Hence we need HLD-NAC

What about NAC?

• First, the Net Curvature– Net Curvature=1/Roil-1/Rwater

– If you’ve got w/o then Rwater is meaningful, what of Roil?

– Give it a pseudo value = 3*Voil/As

• i.e. the ratio of volume to area of surfactant• As is calculated from number of molecules * surface

area per molecule

– So what? See next slide

Total amount of water

• Net curvature also = -HLD/L– L= extended length of surfactant tail

• So, 1/Rwater=HLD/L-1/Roil

• If Roil is very large then 1/Rwater=HLD/L or

• Rwater=L/HLD– So a long tail means large solubility– A small HLD also means large solubility– That’s why long tails and small HLD are so good!

Of course you can always increase total water by adding more surfactantor, for the same amount of water, more surfactant = smaller Rwater

Derived from scaling theory of the chemical potential (HLD) with the Kelvin equation

Taming infinity

• At HLD=0 the solubility would be infinite• That’s why we need NAC – Net Average Curvature• NAC=0.5*(1/Roil+1/Rwater)

– just the average of the two curvatures

• NAC turns out to be equal to 1/ξ– ξ (chi) is the De Gennes “coherence length”– The longest length for which the surfactant “pallisade”

can be considered to be a straight line– The longer it is, the larger the curvature– So Rwater is limited by the finite NAC

Everything now known

• The NAC limits the excesses of the NC• 1/Roil-1/Rwater=HLD/L• 1/Roil+1/Rwater=2/ξ• Calculations

– L from the structure– HLD from S, T, EACN and Cc– Vw/As requires known surfactant area– If we knew ξ we’d know everything

• But we don’t, however intuition isn’t bad

For large solubility:HLD = smallL = largeAs = largeξ = large

Chi

• Imagine the microsphere is made up of straight sections of length ξ

• The bigger ξ, the bigger the sphere so the greater the solubility

• ξ =a exp(2πk/kBT) – so stiff chains are good for a large ξ …– a=Tail+Boundary, k=stiffness, kBT - Boltzmann

• … but if the interface is too stiff then it loves to be ordered and we have liquid crystal phases

What happens at 50:50 Oil:Water?

• NC=0 (it’s neither o/w nor w/o)• NAC ≠0 (it’s limited by ξ)• So we have o/w curves and w/o curves

– in other words we have a sinuous interweaving of the two phases

– with straight lines of length ξ• typically 100Å

• And there’s more...

http://met.iisc.ernet.in/~lord/webfiles/s.jpg

More at 50:50

• If you have a small(ish) amount of surfactant you’ll have 3 phases

• If the SP of your surfactant is high (low HLD, large L, large As, large ξ) then the size of the middle, clear microemulsion phase is large– with essentially no surfactant in pure water or pure oil

• This is what we look for in phase scans– 1 That we actually have three phases– 2 That the middle phase is large

Optimal insolubility

• Any surfactant in the water or oil is doing nothing

• So an optimal surfactant has zero solubility in the water and in the oil

• And is therefore 100% at the interface• An impossible ideal, but a simple, clear goal

Proof of optimal insolubility

How much surfactant is needed to obtain 1 phase for 50:50 o:w

Surfactant solubility in oil phase

Other calculations

• Rd and Ld – radius & cylinder length• Vf - total dissolved volume fraction• Viscosity• Fish diagram

– Vary % surfactant, calculate o/w and w/o volumes via ξ and therefore HLD and therefore T* for each transition

– Can’t (yet) do the low % cutoff – needs surf. sol.

Calculating Shapes, Sizes, Viscosities

Simultaneous equations in Hn (NAC) and Ha (AC) give us true shape* of “drops” – cylinders of radius Rd and Length Ld

Correlates well with neutron scattering

Can calculate total Volume Fraction and Number Density from simple geometry

Viscosity can be predicted via “dilute rigid-rod theory”

N = Number Density of dropletsL = Length, d=Diameter of rodscg = rigid rod concentration, ρ=µE density

*As De Gennes points out, “whenever R> ξ, the shapes must be strongly non-spherical”

Formulation: failure is normal

• An average surfactant with an average “real world” oil will give no 3-phase at any sensible temperature or salinity– Cc is simply too far away– And high salinity tends to give narrow phases (Exxon)

• Even if there are 3 phases, the SP is small– L too small, As too small, ξ too small, HLD not zero

• So how do we choose the right surfactant(s)?

General Surfactant Design Rules

• Make the tail and head large– But without making liquid crystal phases - hard!

• Use mixtures– Long chains can be “balanced” by shorter chains– Impure is usually better than pure

• Use Linkers– Long-chain alcohols as hydrophobic linkers– Sodium Mono/Dimethyl Naphthalene Sulphonate as

hydrophlic linker– Works pretty well to increase L and As

– But only pretty well...

Linkers

No linkerLipophilic linker – e.g. Octanol

Di-block linker – e.g. PEP5-EO5 Lipophilic & Hydrophilic linkers

Extended surfactants• So put a linker in between a conventional

head and tail• PO chains are neutral compared to EO heads

and to HC tails• Typical example C14PO8EO2SO4Na

– C14 – a typical tail– PO8 – a long “neutral” linker section– EO2 – helps bulk up the head– SO4Na – typical anionic head

Problems

• Predicting ξ• Predicting Cc• Predicting EACNs• Predicting failure due to liquid-crystal phase

formation instead of expected microemulsion• Uniting terminology and similar approaches

(e.g. Exxon v HLD-NAC, %NaCl v g/100ml…)• Cranking out public-domain datasets

HLD-NAC software• It’s only as good as the theory and the data• The theory seems better than anything else out there• Acosta has worked hard to supply data• Sasol have published some on extendeds• Two ways forward?

– Groups take on measurement projects • See the Intelligent Formulation Green Surfactant Project

– Surfactant suppliers supply data for everyone’s good– One supplier gains competitive advantage …

Acknowledgements

• In alphabetical order, HLD-NAC is the fruit of work by Acosta, Aubry, Sabatini and Salager

• Each has been generous in their email discussions with me

• Edgar Acosta at U. Toronto is now the person taking forwad HLD-NAC and the current version of the software owes a lot to his help

• My colleagues at Syntopix, VLCI and Intelligent Formulation in the Green Surfactant project