Transport properties of fluorinated surfactants: viscosity and diffusion … · a maximum water content of 200 ppm (analysed by Karl-Fischer coulometry). The viscosity of 6:1 FTOH

Transport properties of fluorinated surfactants:viscosity and diffusion of mixtures involving

fluorinated alcohols

João de Oliveira Mateus Afonso

Instituto Superior Técnico, Lisboa, PortugalUniversity of Vanderbilt, Nashville, United States of America

November 2018

Abstract: This work will focus on studying thermodynamic properties of fluorotelomeralcohols, which are linear highly fluorinated molecules with a terminal OH group. Re-cently, experimental densities and viscosities of (CF3(CF2)3(CH2)OH + Butanol) and(CF3(CF2)5(CH2)OH + Hexanol) were reported and revealed large positive excessvolumes and large negative excess viscosities.This work consists on a computational methods namely, Molecular Dynamics simula-tions focused on studying the significant deviations to ideal behaviour of the transportproperties of this mixtures and the possible existence of nano structures. It was con-cluded that this behaviour results from the unfavourable dispersion forces between thehydrogenated and fluorinated chains.Molecular dynamics simulations were also used to calculate densities and excess vol-umes for three different systems, namely, (BuOH + HFB), (HexOH + UFH) and, (DOH+ PFO). Also, diffusion coefficients were calculated for the (BuOH + HFB) mixture andthe (HexOH + UFH) mixture.Experimental data for the viscosity of 2,2,3,3,4,4,5,5,6,6,7,7,7-tridecafluoroheptan-1-olas a function of temperature between 283.15 K and 353.15 K was also reported.Keywords: Viscosity, Molecular Dynamics, Fluorotelomer Alcohols, Segregation

1. Introduction

Fluorinated surfactants are fluorocar-bon based surfactants that match thetypical hydrophilic/hydrophobic surfactantbehaviour to lyophobic behaviour to-wards hydrogenated organic medium.Inside this class of surfactants, fluo-rotelomer alcohols, are linear highly flu-

orinated molecules with a terminal OHgroup, described by the general formula,CF3(CF2)n(CH2)mOH (n+1:m FTOH).

It is well known that mixtures of hy-drogenated and fluorinated chains displaysignificant non-ideal behaviour, reflectedon a tendency for phase separation, largepositive deviations from Raoult’s law, and,

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large positive excess properties, due toweak dispersion forces. However, the ad-dition of a polar alcoholic group to boththese mutually phobic segments providesthe existence of associative interactionsbetween these molecules. As a result,this mixtures have been reported to createan O · · ·HO network of hydrogen bondsand, simultaneously, segregate into hy-drogenated and fluorinated domains toachieve the best packing possible for thephobic segments.[8][9]

Mixtures of alcohols and fluorotelomeralcohols have also been shown to presentlarge non-ideal behaviour but the role pos-sible molecular structural arrangementsand molecular interactions has on the ther-modynamic properties of such mixtureshas not been thoroughly analysed. In ad-dition, experimental data of this mixturesis rather scarce.

Recently, experimental densitiesand viscosities of (2,2,3,3,4,4,4-heptafluorobutan-1-ol + Butanol) and(2,2,3,3,4,4,5,5,6,6,6-undecafluorohexan-1-ol + Hexanol) were reported which re-vealed large positive excess volumes andlarge negative excess viscosities[9][4]. Inthis work, molecular dynamics simulationswere performed, mainly, to understand thereason beyond the significant deviationsto ideal behaviour of the transport proper-ties of this mixtures. Nonetheless, otherproperties such as densities and excessvolumes were calculated and comparedwith literature data for three different sys-tems, namely, (BuOH + HFB), (HexOH +UFH) and, (DOH + PFO).

2. Computational Chemistry andMolecular Simulations

2.1. Molecular Dynamics Simulations

Molecular simulations provide a betterunderstanding experimental observationsand allow the identification of underlyingmechanisms by providing a insight of thesystem at a molecular level.

In Molecular Dynamics simulations, asimulation engine numerically integratesNewtons laws of motion to move particlesthrough time. This allows the observationof the system evolution during time andthe calculation of its transport properties.Therefore, MD simulations were the cho-sen method to conduct this computationalstudy over Monte Carlo simulations.

2.2. Force Field - OPLS

A force field is a mathematical expres-sion chosen to describe the intra- andinter-molecular potential energy of a col-lection of atoms, and the correspondingparameters that will determine the energyof a given ensemble.[2]

A force field requires the definition of in-termolecular interactions, non-bonded pa-rameters, and intra-molecular interactions,bonded parameters, existent in a system.

The intra-molecular or local contribu-tions to the total energy include bondstretching, angle bending and dihedral tor-sions.

U =∑bonds

1

2kb(r − r0)2 +

∑angles

1

2ka(θ − θ0)2

+∑

torsions

V n

2[1 + cos(nΦ− δ)]

(1)

2

where r0 and kb are stretching and bend-ing constants, respectively; ka is the equi-librium bond length and θ0 is the equilib-rium angle. Torsional energy is usuallyrepresented by a cosine function, whereΦ is the torsional angle, δ is the phase, ndefines the number of minima or maximabetween 0 and 2π (also called multiplicity)and, Vn determines the height of the po-tential barrier.

Regarding the non-bonded terms, Vander Waals interactions arise from the bal-ance between repulsive and attractiveforces. The 12-6 Lennard-Jones (LJ) po-tential is very often used to representthese interactions:

V (r) = 4�

[(σ

r

)12−

(σ

r

)6](2)

in which the first term represents the re-pulsive part of the potential while the sec-ond is the attractive term. The � is depthof the potential well, σ is the finite dis-tance at which the inter-particle potentialis zero and, r is the distance between par-ticles. The final term of the non-bondedparameters serves to describe the electro-static interactions. The electrostatic inter-action arises due to the unequal distribu-tion of charge in a molecule. This interac-tion between these point charges is gen-erally modelled by a Coulomb potential:

V (r) =∑i

∑j 6=i

qiqj4π�0rij

(3)

where �0 is the permittivity of free space, qare atomic charges and, rij is the distancebetween nuclei i and j.

3. Experimental Procedure

The 2,2,3,3,4,4,5,5,6,6,7,7,7-tridecafluoroheptan-1-ol (6:1 FTOH, CASnumber: 375-82-6) was purchased fromApollo Scientific, for which was claimeda 97% purity. Prior to experimental mea-surements, the 6:1 FTOH was dried withVWR Prolabo 4A molecular sieves toa maximum water content of 200 ppm(analysed by Karl-Fischer coulometry).

The viscosity of 6:1 FTOH was mea-sured in the temperature range of 283.15K and 253.15 K at atmospheric pres-sure using an automated SVM 3000 AntonPaar rotational Stabinger viscosimeter-densimeter. The temperature uncertaintyis ±0.02 K from 288.15 to 378.15 K. Theprecision of the dynamic viscosity mea-surements is ±0.5%.

4. Simulation procedure and details

Molecular dynamics simulations wereperformed by applying models based onthe atomistic optimized potential for liq-uid simulations all-atom (OPLS-AA) forcefield.[7] The necessary potential parame-ters for Butanol were published in the origi-nal OPLS-AA papers[7][13], while for Hex-anol and Decanol the parameters are pub-lished in the L-OPLS-AA papers, namelythe extension for alcohols.[11]

To describe the fluorinated alcohols, 3:1FTOH, 5:1 FTOH and 7:1 FTOH, themodel used in this work was built byusing the force-field parameters of the(−CF2 − CH2 − OH) segment from themodel of Trifluoroethanol developed byDuffy [3] and for the perfluoroalkyl “tail”(−CF3 − CF2−) from the OPLS-AA workon perfluoroalkanes.[13] The remaining di-

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hedral torsion parameters were taken fromthe work of Padua[10], and the partialcharge of the carbon atom in the first−CF2 group was adjusted to give themolecule a net zero.

According to the OPLS parametrization,the non-bonded Lennard-Jones interac-tions between different types of sites werecalculated using the geometrical meanrule for both size and energy. For thecross-interaction energy and the cross-interaction diameter between alkyl hy-drogen atoms and perfluoroalkyl fluorineatoms, in order to capture the weak unlikeinteractions between hydrogenated andfluorinated chains, it it was introduced cor-rections to the energy and size binary in-teraction parameters, ξ = 0.80 and υ =1.035, for (BuOH + HFB) as suggested byMorgado for the OPLS-AA force field [9]and ξ = 0.77 and υ = 1.035 for (HexOH +UFH) in the L-OPLS-AA force field.

All MD simulations were carried outwith the open-source package GROMACS(version 2018)[1][12], in cubic boxes withperiodic boundary conditions imposed inall directions and a time step of 2 fs.All bonds involving Hydrogen atoms wereconstrained to their equilibrium lengths,using the LINCS algorithm.[6] Simulationswere conducted for systems composed of300 molecules for (HexOH + UFH) and(DOH + PFO) and, 500 molecules for(BuOH + HFB) with the system size be-ing conserved as the molar ratio of alcoholto fluorinated alcohol was changed. Thegeneral simulation scheme was the follow-ing: Initially, the molecules were placedrandomly in the box and were allowed toequilibrate in the NPT ensemble for 2.5 ns,during this period, the density of the sys-

tem converged to mean values, then a 2.5ns long production run is performed. After-wards, 2 ns long equilibration runs wereperformed in the NVT emsemble at den-sities obtained from NPT simulations atatmospheric pressure which are followedwith NVT production runs from 5 to 50 nslong.

5. Densities and Excess Volumes

From the simulations performed, thesystems densities were collected directlyfrom the average values of the box vol-ume in the NPT production runs. Thedensities were calculated for (BuOH +HFB), (HexOH + UFH) and (DOH + PFO)at 298.15 K. The calculated densitiesshowed good agreement with experimen-tal data.

Figure 1: Densities of (BuOH + HFB) at 298.15 K

Figure 2: Densities of (HexOH + UFH)at 298.15 K

Figure 3: Densities of the mixture (PFO + Decanol) at 298.15K

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Subsequently, the related excess vol-umes were calculated and plotted in fig-ures 4 and 5. For the (BuOH + HFB)the values were compared with the ex-perimental data published by Morgado[9]while the (HexOH + UFH) system werecompared with experimental measure-ments performed by research collaboratorMariana Leitão.

V Em =x1M1 + x2M2

ρ12− x1M1

ρ1− x2M2

ρ2(4)

To model the unlike H − F interaction,the corrections on size and energy param-eters proposed by Morgado[9], ξ = 0.8 andυ = 1.035, were introduced in the forcefieldfor the (BuOH + HFB) mixture. The val-ues calculated for excess volume from MDsimulations for this system demonstratea good agreement with the experimentaldata.

Figure 4: Excess Volumes of (BuOH + HFB)

However, when the parameters mod-elled for (Hexane + Perfluorohexane) inthe L-OPLS force field, η = 1.035 andυ = 0.77, were applied to the mixture of(HexOH + UFH), the calculated excessvolumes are significantly lower than theones experimentally obtained. Accord-ingly, simulations were ran to parametrizethe best correction for the (HexOH + UFH)which is η = 0.77 and υ = 1.039.

Figure 5: Excess Volumes of (HexOH + UFH)

This correction was kept for the (DOH+ PFO) system. For this system, in-stead of comparing excess volumes, cal-culated and experimental molar volumeswere compared, figure 6.

Figure 6: Molar Volume of the mixture (PFO + Decanol) at298.15 K

6. Viscosities and Excess Viscosity

6.1. Pure compounds

The experimental measurements of theviscosity of 6:1 FTOH as function of tem-perature are plotted in the figure 7, along-side other different fluorotelomer alco-hols. As expected, the viscosities of flu-orotelomer alcohols increase with the in-crease in chain length. As far as known,this are the first reported viscosities for 6:1FTOH. Moreover, the viscosities of FTOHwere compared with the viscosity of differ-ent types of compounds.

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Figure 7: Experimental viscosities of fluorotelomer alcohols asa function of temperature

Figure 8: Experimental viscosities at 293.15 K

The measurements executed for 6:1FTOH show good agreement with pre-vious reported viscosities for other fluo-rotelomer alcohols. Also, FTOH have anhigher viscosity than the remaining typesof compounds due to the existence of hy-drogen bonds combined with the highermolecular weight of Fluorine.[5]

6.2. Mixtures

Due to its simplicity, the Green-Kubo re-lation based equilibrium molecular dynam-ics (MD) simulations is perhaps the mostwidely used method to calculate viscosi-ties. In this approach, the shear viscosityis calculated from the integral over time ofthe pressure tensor autocorrelation func-tion

η =V

kBT

∫ ∞0

〈Pαβ(t) · Pαβ(0)〉dt (5)

where V is the system volume, kB is theBoltzmann constant, T is temperature, Pαβdenotes the off-diagonal elements of the

pressure tensor, and the angle bracket in-dicates the average ensemble. To obtainthe viscosities from the MD simulations,the methodology proposed by Zhang wasused.[14]

The calculated viscosities for the (BuOH+ HFB) mixture , at 293.15 K were com-pared with viscosities experimentally mea-sured by Costa. [4].

Figure 9: Experimental and simulated viscosities of (BuOH +HFB) and simulated densities at 293.15 K

Figure 10: Experimental and simulated viscosities of (HexOH+ UFH) and simulated densities at 293.15 K

The simulations are capable of predict-ing the singular excess behaviour of vis-cosity in this mixtures, showing resultsclose to the experimental and revealinglarge negative deviations.

Figure 11: Experimental and simulated excess viscosities for(BuOH + HFB)

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Figure 12: Experimental and simulated excess viscosities for(HexOH + UFH)

7. Diffusion Coefficients and Hydrody-namic Radii

The diffusion coefficients of differentmixtures were calculated from the linearpart of the mean square displacement ofthe center of mass of the solute moleculesaccording to the Einstein equation:

D =1

6Nlimt→∞

d

dt

N∑i=1

< [ri(t)−ri(0)]2 > (6)

where [ri(t)− ri(0)]2 is the mean squaredisplacement of the solute and the brack-ets stand for average over time. The sum-mation extends to all solute molecules inthe simulation. The final value of diffusioncoefficient was obtained from the averageof 5 values obtained independently.

Figure 13: Diffusion coefficients at 293.15 K for (BuOH + HFB)and (UFH + Hexanol)

To further understand the molecules mo-tion in this mixtures the effective radiuswas calculated. By cancelling the ef-

fect different viscosities have on moleculesmovement, the effective radius allows abetter evaluation of the molecules motion.Therefore, a higher effective radius meansthe motion of the molecule in the mixtureis more difficult.

The translational motion of a solute in afluid solution at infinite dilution can be de-scribed by the Stokes-Einstein relation.

D =kBT

Cπηr(7)

where D is the diffusion coefficient, kB isthe Boltzmann constant, T is the abso-lute temperature, and C is equal to 6 forthe case of “stick” boundary conditions.Furthermore, because the calculated vis-cosities from MD simulations have an highof uncertainty, these hydrodynamic radiiwere calculated using experimental vis-cosities reported by Costa.[4]

Simulations of HexOH and UFH at infi-nite dilution in UFH and HexOH, respec-tively, were also performed and the corre-sponding diffusion coefficients and effec-tive radii calculated. These are included infigure 14. Figure ?? consisted of a singlemolecule of hexane and a single moleculeof perfluorohexane inserted in pure hex-anol, pure UFH and an equimolar mixture.This allows understanding the influenceof the weak interactions between hydro-genated and fluorinated chains have onthe flow in the absence of hydrogen bond-ing. This study was conducted at 343.15K to speed up the molecular dynamics ofthe (HexOH + UFH) system, making thesamplings faster.

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Figure 14: Hydrodynamic radius of HexOH and UFH at 343.15K with experimental viscosities

Figure 14 suggests that when diluted inHexanol, molecules of UFH tend to have ahigher motion than when pure as shownby the clear tendency of decreasing itshydrodynamic radii when the concentra-tion on Hexanol increases. RegardingHexanol, the change of effective radius ismuch smaller. Nevertheless, the resultsseem to indicate that there is an initialslight decrease of the effective radius ofHexanol in the mixtures, increasing after-wards.

Figure 15: Hydrodynamic radius at 343.15 K with experimentalviscosities

The Perfluorohexane molecule de-creases slightly its effective radius wheninfinitely diluted in Hexanol and evenmore significantly when in the equimolarmixture. This overall decrease could indi-cate that the weak dispersion interactionsbetween hydrogenated and fluorinatedchains can ”help” the movement of thefluorinated chain.

8. Liquid Structure

Intermolecular radial distribution func-tions (rdfs) provide a measure of the localstructure in liquids. They were calculatedfrom the simulation trajectories for the thefluorinated chain of UFH and PFO and, thehydrogenated chain of Hexanol and De-canol excluding the Hydrogens bonded toCarbon-1 and, the Oxygen and Hydroxylgroup, not only for pure like interactionsbut also for cross-interactions.

-Figure 16: Intermolecular rdfs between the Hydrogen and Flu-orine atoms (H or F) for (HexOH + UFH ) mixtures at differentcompositions, from molecular dynamics simulations.

-Figure 17: Intermolecular rdfs between the Hydrogen and Flu-orine atoms (H or F) for (DOH + PFO) mixtures at different com-positions, from molecular dynamics simulations.

Radial distribution functions generatedfor H − H and F − F group, increasenotably with the increase in concentra-tion of the second component. This astrong indication of segregation betweenhydrogenated and fluorinated segmentsand supports the conclusion of the pres-ence of different clusters of fluorinated and

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hydrogenated chains in the mixture.

(a) HexOH + UFH (b) DOH + PFOFigure 18: Snapshot of a MD simulation box consisting of anequimolar mixture. Alcohols (HexOH and DOH) are the bluechains and, fluorinated alcohols (UFH and PFO) are the greenchains

Intermolecular rdfs between the oxy-gen and hydroxyl hydrogen atoms for the(HexOH + UFH) system show that theaddition of the different alcohol also in-creases the variety of H-bonds formedupon mixing. Even so, the new es-tablished cross-interaction are strongerthan the intersections between identicalmolecules with the curve correspondingto hydrogen bonding between the Oxygenatom in HexOH, highest negative partialcharge, and the Hydrogen atom, highestpositive partial charge, in UFH being muchmore intense than the others, which fol-lows the difference of the partial chargesassigned to the interacting atoms.

Figure 19: Intermolecular rdfs between the oxygen and hy-droxyl hydrogen atoms for the (HexOH + UFH) at equimolarmixture.

The analysis of the rdfs indicate thatsimilar to what was previously seen byMorgado[9] for the (BuOH + HFB) sys-tem, mixtures of (HexOH + UFH) can be

regarded as nanostructured. This nanos-tructure consists of a O · · ·H network ofhydrogen bonds formed between the hy-droxyl headgroups, surrounded by the car-bon chain tails, which, in turn, segre-gate into hydrogenated and fluorinated do-mains. Figure 20, is a molecular dy-namics simulation snapshot obtained foran equimolar mixture of (HexOH + UFH)which illustrates such structure.

Figure 20: Snapshot of the O · · ·H network in a MD simulationbox consisting of an equimolar mixture of HexOH (blue chains)and UFH (green chains); coloured red are the Oxygen’s of bothmolecules and white are the Hydrogen’s

9. Conclusions and Future Work

The molecular dynamics simulationsperformed indicate that the large negativeexcess viscosities of mixtures of (BuOH +HFB) and (HexOH + UFH) results from anenhanced motion of fluorinated segmentswhen in contact with hydrogenated alco-hols due to the unfavourable dispersionforces.

The existence of mutual segregationbetween fluorinated and hydrogenatedchains was identified using radial distribu-tion functions. Also, the existence of anano structure composed by a O · · ·HOnetwork was identified for the (HexOH +UFH) mixture.

The comparison of the reported vis-cosities for 2,2,3,3,4,4,5,5,6,6,7,7,7-

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tridecafluoroheptan-1-ol with other fluo-rotelomer alcohols, present in literature,shows a good agreement with viscositiesreported for other fluorotelomer alcohols.

Acronyms

BuOH - ButanolHexOH - HexanolDOH - DecanolHFB - 2,2,3,3,4,4,4-heptafluorobutan-1-olUFH - 2,2,3,3,4,4,5,5,6,6,6-undecafluorohexan-

1-olPFO - 2,2,3,3,4,4,5,5,6,6,7,7,8,8,8-

pentadecafluorooctan-1-olFTOH - Fluorotelomer alcoholMD - Molecular DynamicsOPLS - Optimized Potential for Liquid SimulationAA - All AtomH-Bonds - Hydrogen Bondsrdf - Radial Distribution Function

References[1] M. Abraham, E. Lindahl, B. Hess, and GRO-

MACS Development Team. GROMACS UserManual version 2018, 2018.

[2] M. P. Allen and D. J. Tildesley. Computer Sim-ulation of Liquids. Oxford Science Press, sec-ond edi edition, 2017.

[3] R. Chitra and P. E. Smith. A comparison of theproperties of 2,2,2-trifluoroethanol and 2,2,2-trifluoroethanol/water mixtures using differentforce fields. Journal of Chemical Physics,115(12):5521–5530, 2001.

[4] M. A. Costa. Property Data and Phase Equi-libria for the Design of Chemical Processesinvolving Carbon Dioxide, 2017.

[5] M. G. Freire, A. G. Ferreira, I. M. Fonseca,I. M. Marrucho, and J. A. Coutinho. Viscosi-ties of liquid fluorocompounds. Journal ofChemical and Engineering Data, 53(2):538–542, 2008.

[6] B. Hess, H. Bekker, H. J. Berendsen, and J. G.Fraaije. LINCS: A Linear Constraint Solver formolecular simulations. Journal of Computa-tional Chemistry, 18(12):1463–1472, 1997.

[7] W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives. Development and testing of the OPLSall-atom force field on conformational en-ergetics and properties of organic liquids.Journal of the American Chemical Society,118(45):11225–11236, 1996.

[8] P. Morgado, J. Black, J. B. Lewis, C. R. Ia-covella, C. McCabe, L. F. Martins, and E. J.Filipe. Viscosity of liquid systems involv-ing hydrogenated and fluorinated substances:Liquid mixtures of (hexane+perfluorohexane).Fluid Phase Equilibria, 358:161–165, 2013.

[9] P. Morgado, A. R. Garcia, L. M. Ilharco, J. Mar-cos, M. Anastácio, L. F. G. Martins, andE. J. M. Filipe. Liquid Mixtures Involving Hy-drogenated and Fluorinated Alcohols: Ther-modynamics, Spectroscopy, and Simulation.The Journal of Physical Chemistry B, pageacs.jpcb.6b04297, 2016.

[10] A. A. Pádua. Torsion energy profiles and forcefields derived from Ab initio calculations forsimulations of hydrocarbon-fluorocarbon di-blocks and perfluoroalkylbromides. Journal ofPhysical Chemistry A, 106(43):10116–10123,2002.

[11] K. Pluhackova, H. Morhenn, L. Lautner,W. Lohstroh, K. S. Nemkovski, T. Unruh,and R. A. Böckmann. Extension of theLOPLS-AA Force Field for Alcohols, Esters,and Monoolein Bilayers and its Validation byNeutron Scattering Experiments. Journal ofPhysical Chemistry B, 119(49):15287–15299,2015.

[12] D. V. Spoel, E. Lindahl, B. Hess, andG. Groenhof. GROMACS: Fast, Flexible, andFree. Journal of Computational Chemistry,26(16):1701–18, 2005.

[13] E. K. Watkins and W. L. Jorgensen. Per-fluoroalkanes: Conformational Analysis andLiquid-State Properties from ab Initio andMonte Carlo Calculations. Journal of Physi-cal Chemistry A, 105(16):4118–4125, 2001.

[14] Y. Zhang, A. Otani, and E. J. Maginn. ReliableViscosity Calculation from Equilibrium Molec-ular Dynamics Simulations: A Time Decom-position Method. Journal of Chemical Theoryand Computation, 11(8):3537–3546, 2015.

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