Inverted Polarity Micelle Enhanced Ultrafiltration

A critical review, by Federico Talens-Alesson, © 2008

Background (I)

• The basis of the paper is a study of the binding of inorganic cations onto micelles of anionic surfactants, a type of colloidal particles.

• By means of a membrane separation, it is possible to split a micellar solution in two:

– a rejected solution containing the micelles and any cations bound to it, plus the proportional part of bulk phase with monomer surfactant and unbound cations

– a permeated solution containing the rest of the bulk phase, with monomer surfactant and unbound cations

Background (II)

Air Pressure

Line

Membrane

Porous Membrane Support

Outlet

A dead-end Ultrafiltration cell

Reject Solution

Colloidal aggregates are rejected by suitable membranes (2,000 to

50,000 Da)

Permeate

Background (III)A typical way to perform the experiment is:

• To cause the filtration of half of the volume of a sample

• To analyze the content in surfactant and cations on both half-volumes.

• To substract the values for the permeated (lower) from the reject (higher): the difference is the concentration of micellar surfactant and micelle-bound cations

• To calculate the binding ratio cation to surfactant in the micelles.

Background (IV)Micelles are electrically charged colloidal particles. As such,

their environment consists of the following three parts:

• the surface of the charged colloid

• a charged region (usually considered divided in two parts, known as the Stern and the diffuse layer) containing a net amount of opposite charge that cancels out the surface charge of the colloid.

• the remainder of the solution, which is electrically neutral

Background (V)

Cationic electrolytes

Stern Diffuse Bulk

-

-

-

-

-

-

-

Anionic electrolytes

Ani

onic

Mic

elle

Sur

face

Charge concentration profiles

Schematic view of the charge distribution around a charged colloid: the example refers to an anionic micelle

Background (VI)In the case investigated here, the authors rely on an earlier observation (by myself, now that I think about it) about the fact that under some conditions the charges of mixtures of Al3+ and Zn2+ ions bound to DS- micelles appear to exceed the charge of the micelles.

Background (VII)

The explanation given, by reference to other researchers (No, not me. Somebody else.) is that a layer of liquid, made stagnant by the proximity of the surface of the colloid (known as a boundary layer) somehow captures and drags along some ions from the solution.

Background (VIII)Under the specific conditions of some experiments, this seems to happen to both cations and anions farther away from the colloid surface, and creates the impression of a charge inversion, due to the exclusion from the charge inventory of the same-charge ions included through this mechanical capture effect.

Cation charge concentration

Background (IX)

Anion charge concentration

Diffuse layer

Boundary layer

Case I: Part of the diffuse layer is beyond the mechanical barrier and is not dragged along: the charge binding ratio appears to be less than 1

Cation charge concentration

Background (X)

Anion charge concentration

Diffuse layer

Boundary layer

Case II: Part of the diffuse layer is contained within the boundary layer: a partial charge balance for cations and micellar surfactant would indicate an apparent excess of positive charge

Background (XI)

Changing conditions may compress the diffuse layer and expand the boundary layer.

This has been reported in the work extensively plagiarized by the authors to result in “apparent charge inversions” of up to 40%.

For a 60 monomer micelle, this would mean that up to 8 Al3+ or 12 Zn2+ ions have become included together with their counter-ions within the boundary layer.

Background (XII)

Some facts:

•a solution 0.1M in a given ion contains 1 ion per 16.6 nm3

•the surface of a sphere 5 nm in diameter is 78.5 nm2

•a cube containing a single ion, with 7.85 nm2 of side area would have a volume of 22 nm3 (equivalent to a concentration 0.075M)

•the distance of the center of the cube to the surface of the sphere would be 1.4 nm

2.8 nm

Background (XIII)

If the sphere containing a micelle and its diffuse layer has a diameter of 5 nm, it would only take the total diameter of

the micelle and its boundary layer to be 8 nm to hold enough cations for an apparent charge ratio of 1.4.

Physically, this could be possible and hence the fact that it is observed does make sense.

Discussion (I)

The results reported by the “authors” of the paper indicate binding ratios Zn2+/SDS over 2.

There are a number of problems here, because these values involve the binding of 2 or more Zn2+ cations per surfactant molecule in the micelle (the surfactant has a charge of -1). The claim therefore is that under some conditions there is a

charge inversion of 300% or higher.

Discussion (II)That requires the following:

1- there will be an accumulation of charge around the micelle (involving the contents of the Stern and diffuse

layer) to compensate the charge of the colloid

2- beyond that, the concentration in the solution will be that of the bulk phase

3-enough of the bulk phase will be incorporated into the boundary layer to ensure that the binding ratio be what is

reported.

Discussion (III)1- there will be an accumulation of charge around the micelle to cause electro-neutrality (involving the contents of the Stern and diffuse layer).

That requires that the Stern and diffuse layers contain enough charge to neutralize the charge of the micelle. In their experiment 14 (Table 10, page 198) they show an example of binding ratio (attributable to Zn only) of 2.399.

The experimental conditions are: 0.05M SDS, 0.075M Zn2+. The concentration of Al3+ is given as 0.04M (should be as 0.04M Al2(SO4)3, double of what they indicate (see slide XX), but in their article they they indicate (section 2.2.3, page 190) that they failed to obtain any reliable data for Al3+.

Discussion (IV)For a binding ratio 2.399 over a solution containing roughly

0.05M of micellar surfactant (the monomer surfactant concentration for a solution with such concentrations of

polyvalent cations will be less than 10-3M) would require 0.025M of Zn2+ bound or within the diffuse layer:

0.05M DS- x (-q) + 0.025M Zn2+ x (2q) = 0

That means that the bulk of the solution will contain:

0.075M Zn2+(initial) - 0.025M Zn2+(“spent”) = 0.05M Zn2+

Discussion (V)With 0.025M Zn2+ bound to 0.05M DS-, the binding ratio

will be:

0.025M Zn2+/0.05M DS- = 0.5

Therefore, it is required that the hydrodynamic binding has a value of 2.399 - 0.5 = 1.899

That means that the volume of solution in a liter of solution 0.05M DS- should be:

1.899 x 0.05 mole DS- = VS x 0.05 mole liter-1 Zn2+(bulk solution concentration)

Discussion (VI)

That is, the volume should be 1.899 liters, TWICE THE VOLUME OF THE SOLUTION. This is absurd.

Of course, the result should be expected considering that initial Zn2+ concentration is 0.075M and the initial SDS

micellar concentration is about 0.05M.

There is no way that the solution may contain enough ZN2+ for a binding ratio higher than 1.5, assuming that the

equilibrium was totally displaced to bound form (which is never the case with cation to anionic micelle systems).

Discussion (VII)

What went wrong?

Essentially, the work had been lifted fromthe M.Sc. Thesis of a student who, in practice, was being supervised by me. The authors of the paper had no idea about the basic principles of

colloid science (or apparently, basic common sense) and in the process of lifting the results and passing them as their own only saw the spectacular figures and could not fathom that

they were physically impossible

Discussion (VIII)SDS - Sodium

Dodecyl Sulphate

Al2(SO4)3 - Aluminium Sulphate

ZnSO4 - Zinc Sulphate (ml) [SDS]R - [SDS]P

[Al2(SO4)3]R -

[Al2(SO4)3]P

[ZnSO4]R -

[ZnSO4]P11 0.05M 0.04M 0M 0.002715 012 " " 0.0312M 0.01303 0.0087 0.6676913 " " 0.0625M 0.01207 0.03 2.48550114 " " 0.075M 0.01959 0.047 2.39918315 " " 0.096M 0.04275 0.013 0.304094

SDS concentration in

Permeate

SDS concentration in Retentate

Zinc concentration in

Permeate

Zinc concentration in Retentate

Aluminium ion concentration in Permeate

Aluminium ion concentration in Retentate

11 0.000355 0.00307 0 012 0.00027 0.0133 0.0173 0.02613 0.00023 0.0123 0.03 0.0614 0.00021 0.0198 0.035 0.08215 0.00025 0.043 0.064 0.077

These are spreadsheet results. Highlighted in yellow the binding ratios Zn/SDS

obtained by ratio of the differences in concentration between retentate and permeate.

Discussion (IX)

4 ml of permeate were diluted to 100 ml, and the remainder 6 ml were also diluted

to the same volume as retentate.

Samples titrated were 25 ml, except SDS for the retentate, which was 10 ml.

Hyamine 0.0041M was used for the analysis of SDS, and EDTA 0.02M, with

Hexamine as buffer agent and methylthymol blue as indicator.

Both reactions have 1 to 1 stoichiometries.

Discusion (X)retentate vol reagent conc reagent vol sample conc sample dilution from originalSDS 2.9 0.0041 10 0.001189 16.6666667 0.019816667Zn 4.1 0.02 25 0.00328 16.6666667 0.054666667permeate vol reagent conc reagent vol sample conc sample dilution from originalSDS 0.05 0.0041 25 0.0000082 25 0.000205Zn 2.6 0.02 25 0.00208 25 0.052

Comparing Discussion (VIII) and the above table, calculated from the data on the figure in Discussion (IX), we can see that the values for SDS concentration are correct, but those

for Zn are not.

If the binding ratio Zn/SDS in micelles is calculated from [Zn]ret - [Zn]per/([SDS]ret -

[SDS]per) the value is 0.1360 +/- 0.0378*

This is a far cry from 2.399

* assuming an error of +/-0.05ml for all the volumes of reagent titrated on 25 ml burette, except SDS in permeate (+/-0.01ml on a 5 ml burette), and an error of 0.01ml on volume of samples taken on 10 or 25 ml pipette.

Discusion (XI)Another interesting example can be found in their sample 22 (page 198,

Table 10). There we can see a binding ratio Zn2+/SDS of 2.11

The data from the original notebook are to the right. Permeate volume

was 2.2 ml diluted to 100, and retentate volume was 7.8 ml diluted

to 100.

Sample volumes are the same. In this case, the value found from the

calculation with the actual results is 2.03, close to the value given by the

authors.

Discussion (XI)What went wrong this time is that they did not take into

account error propagation in the various calculation leading to the binding ratio values.

For a magnitude of the form:

A = (B-C)/(D-E)

the expression for the error propagation incurred in the calculation of A, depends on the errors of B,C,D and E, which

we will designate as eB, eC, eD and eE.

Discussion (XII)

The expression would be:

eA/A = e(B-C)/(B-C) +/- e(D-E)/(D-E)

withe(B-C) = eB +/- eC

ande(D-E) = eD +/- eE

Discussion (XIII)retentate vol reagent conc reagent vol sample conc sample dilution from original concentration rel error absol errorSDS 1.1 0.0041 10 0.000451 12.82051282 0.00578205 0.00244184 1.4119E-05Zn 2.3 0.02 25 0.00184 12.82051282 0.02358974 0.02239911 0.00052839permeate vol reagent conc reagent vol sample conc sample dilution from original concentration rel error absol errorSDS 0.06 0.0041 25 0.00000984 45.45454545 0.00044727 0.15537758 6.9496E-05Zn 0.35 0.02 25 0.00028 45.45454545 0.01272727 0.51984416 0.0066162

On the basis of the above tabulated calculations, the binding ratio Zn/SDS is 2.03. If we assume an error of 0.2ml on a 25 ml burette (cumulative error

between initial and final readings, including human error and not only precision) and we calculate the error as per the previous slides, we find that

the result has to be given as:

2.03 +/- 1.35

That is, there are no significant digits because all are affected by error.

Discussion (XIV)

The details of the error calculation can

be followed in this spreadsheet

error 25 ml burette 0.2error 5 ml burette 0.02

error coeficiente 1.35209006Retentate conc (M) rel error abs error de asociacion zn-SDSSDS 0.00578205 0.00100828 5.8299E-06Zn 0.02358974 0.02239911 0.00052839 value error del calculoPermeateSDS 0.00044727 0.06219576 2.7818E-05 2.03616153 0.6640387Zn 0.01272727 0.51984416 0.0066162

Discussion (XV)The final question is about the whole point of the work. It is presented as a

way to obtain enhanced removal of metallic pollutants, but on the other hand it requires the addition of very high concentrations of whichever is to be

considered the reagent (is it Al3+ or Zn2+) being used to enhance (?) the removal of the other.

If we go back to Discussion (VIII), it is hard to see what is the benefit of removing Al3+ by leaving behind the amounts of Zn2+ shown there, when precipitation of Al(OH)3 can be achieved with final concentrations in the

order of ppb.

On the other hand, the data (particularly permeability data) where used (not by the authors) to produce a publication on fouling during MEUF and

colloidal stability of micelles.