A new family of equations of state: COSMO-SAC-Phi · 2019. 3. 17. · COSMO method (solutes alone) vs COSMO-RS/SAC The COSMO method was originally developed for the computation of

A new family of equations of state: COSMO-SAC-Phi

Rafael de Pelegrini Soares

FED. UNIV. OF RIO GRANDE DO SULCHEMICAL ENGINEERING DEPARTMENTVirtual Laboratory for Properties Prediction

http://ufrgs.br/lvpp

October, 2018

COSMO method (solutes alone) vs COSMO-RS/SAC

The COSMO∗ method was originally developed for thecomputation of solvation effects

Belongs to the class of dielectric continuum models

,the cavities are discretized into segments or patches

Induced charges are computed by quantum chemistrypackages (time consuming) and then stored in adatabase (e.g. LVPP sigma-profile database†

http://github.com/lvpp/sigma)

∗A Klamt and G Schuurmann. In: J. Chem. Soc., Perkin Trans. 2 (1993),pp. 799–805†F. Ferrarini et al. In: AIChE Journal 64.9 (2018), pp. 3443–3455

http://github.com/lvpp/sigma



Belongs to the class of dielectric continuum models,the cavities are discretized into segments or patches







Belongs to the class of dielectric continuum models,the cavities are discretized into segments or patches





COSMO-RS – Surface contacting theory (mixtures)

In the COSMO-RS∗ methods werely on COSMO computations withthe molecules surrounded by aperfect conductor

Based on these pure substancecomputations, the mixture behavioris predicted (γi , µi )

The COSMO-SAC† formulationfollows the same idea

For every contact between segmentsm and n there is an energy change∆Wm,n

There are many possible contacts insolution

∗Andreas Klamt. In: The J. of Phys. Chem. 99.7 (1995), pp. 2224–2235†ST Lin and S.I. Sandler. In: Ind. Eng. Chem. Res. 41.5 (2002), pp. 899–913

COSMO-RS – Surface contacting theory (mixtures)

In the COSMO-RS∗ methods werely on COSMO computations withthe molecules surrounded by aperfect conductor

Based on these pure substancecomputations, the mixture behavioris predicted (γi , µi )

The COSMO-SAC† formulationfollows the same idea

For every contact between segmentsm and n there is an energy change∆Wm,n

There are many possible contacts insolution

∗Andreas Klamt. In: The J. of Phys. Chem. 99.7 (1995), pp. 2224–2235†ST Lin and S.I. Sandler. In: Ind. Eng. Chem. Res. 41.5 (2002), pp. 899–913

IntroductionCOSMO-SAC-Phi

Conclusions

COSMOCOSMO-RS or COSMO-SACSigma profile

Sigma profile – p(σ)

For a statisticalthermodynamics treatment(without using MD or MC),the 3D apparent surfacecharges are projected into asimple histogram

These pure compounddistributions, known as sigmaprofiles – p(σ), are the basisfor computing γi or µi inmixture

“It is always desirable to express the properties of a solution in terms that can becalculated completely from the properties of the pure components.” – J. M. Prausnitz.Molecular thermodynamics of fluid-phase equilibria. Third. Prentice-Hall, 1999.

Rafael de Pelegrini Soares COSMO-SAC-Phi - Equifase 2018 4 / 17


Conclusions

COSMOCOSMO-RS or COSMO-SACSigma profile

Sigma profile – p(σ)

For a statisticalthermodynamics treatment(without using MD or MC),the 3D apparent surfacecharges are projected into asimple histogram

These pure compounddistributions, known as sigmaprofiles – p(σ), are the basisfor computing γi or µi inmixture

“It is always desirable to express the properties of a solution in terms that can becalculated completely from the properties of the pure components.” – J. M. Prausnitz.Molecular thermodynamics of fluid-phase equilibria. Third. Prentice-Hall, 1999.



Conclusions

Model developmentInteraction EnergyResults

Model for liquid phases only?

The real solution should notcontain the perfect conductorsurrounding the molecules

For every contact betweenmolecules, the conductor ispartially excluded

Thus, all surface segmentsshould be in pairwise contact

Hence there is no free volumeand V = nibi



Conclusions


Model for liquid phases only?

The real solution should notcontain the perfect conductorsurrounding the molecules

For every contact betweenmolecules, the conductor ispartially excluded

Thus, all surface segmentsshould be in pairwise contact

Hence there is no free volumeand V = nibi


EOS combined with COSMO-RS/SAC

NRCOSMO∗: combination of COSMO with the so callednon-random hydrogen-bonding (NRHB) equation of state

σ-MTC†: an extension of the Mattedi-Tavares-Castier equationwhich combines the sigma-profile from COSMO computations withthe generalized van der Waals theory

Cubic EOS + MR + COSMO-SAC:

PR+WS+COSMO-SAC‡

PR+SCMR+COSMO-SAC§

PR+mSCMR+COSMO-SAC¶

. . .

All methods need some bridge to couple COSMO with the EOS

∗C. Panayiotou. In: Pure and Appl. Chem. 83.6 (Jan. 2011), pp. 1221–1242†C.T.O.G. Costa, F.W. Tavares, and A.R. Secchi. In: Fluid Phase Equilib. 409 (Feb.

2016), pp. 472–481‡MT Lee and ST Lin. In: Fluid Phase Equilib. 254.1-2 (June 2007), pp. 28–34§P.B. Staudt and R.P. Soares. In: Fluid Phase Equilib. 334 (Nov. 2012), pp. 76–88¶LH Wang, CM Hsieh, and ST Lin. In: Ind. Eng. Chem. Res. 57.31 (June 2018),

pp. 10628–10639


Conclusions


COSMO-SAC-Phi: seamless extension

By this pseudo-mixture, COSMO-RS, COSMO-SAC, or F-SAC can beused to compute µi and µh as long as we know the number ofmolecules and holes



Conclusions


COSMO-SAC-Phi: seamless extension



Conclusions


COSMO-SAC-Phi assumptions and equations

The real mixture is described byn = [n1, n2, . . . , ni , . . . , nN ]

The pseudo-mixture is describedby n = [n, nh]

No empty spaces (other thanholes) V =

∑i nibi + nhbh

For given (T ,V ,n):nh = 1

bh(V −

∑i nibi )

What should be the shape of a hole? Probably not a sphere,otherwise we will have empty spaces.



Conclusions






∑i nibi + nhbh


bh(V −

∑i nibi )




Conclusions






∑i nibi + nhbh


bh(V −

∑i nibi )




Conclusions



Attractive pressure

PA = −(∂Ar

A∂V

)T ,n

Dropping the A subscript(∂Ar

∂V

)T ,n

=(∂Ar

∂nh

)T ,n

(∂nh∂V

)T ,n(

∂V∂nh

)T ,n

= bh

µrh ≡(∂Ar

∂nh

)T ,nj 6=h

=(∂Ar

∂nh

)T ,n

PA = −(∂Ar

∂V

)T ,n

= − µrhbh

A missing step: how to computed µrh (residual) with COSMO-basedmodels, don’t they compute only µh (excess)?



Conclusions



Attractive pressure

PA = −(∂Ar

A∂V

)T ,n


∂V

)T ,n

=(∂Ar

∂nh

)T ,n

(∂nh∂V

)T ,n(

∂V∂nh

)T ,n

= bh

µrh ≡(∂Ar

∂nh

)T ,nj 6=h

=(∂Ar

∂nh

)T ,n

PA = −(∂Ar

∂V

)T ,n

= − µrhbh




Conclusions



Attractive pressure

PA = −(∂Ar

A∂V

)T ,n


∂V

)T ,n

=(∂Ar

∂nh

)T ,n

(∂nh∂V

)T ,n(

∂V∂nh

)T ,n

= bh

µrh ≡(∂Ar

∂nh

)T ,nj 6=h

=(∂Ar

∂nh

)T ,n

PA = −(∂Ar

∂V

)T ,n

= − µrhbh




Conclusions



Attractive pressure

PA = −(∂Ar

A∂V

)T ,n


∂V

)T ,n

=(∂Ar

∂nh

)T ,n

(∂nh∂V

)T ,n(

∂V∂nh

)T ,n

= bh

µrh ≡(∂Ar

∂nh

)T ,nj 6=h

=(∂Ar

∂nh

)T ,n

PA = −(∂Ar

∂V

)T ,n

= − µrhbh




Conclusions


COSMO-SAC-Phi: Ideal Gas reference

In order to replace the referenceto an Ideal Gas (IG), simplyapply the V →∞ limit

Alternatively put the compoundinfinitely diluted in holes

With the pseudo-mixture this is simple, just make:nIG = [n = 0, nh = 1] = [0, 0, . . . , 1]

With residual properties defined, we can compute not only pressure,but fugacity coefficients, etc.



Conclusions









Conclusions








Surface contacting theory – interaction energy

The COSMO-SAC∗ interaction energyis given by:

∆Wm,n =α′ (σm + σn)2

2︸︷︷︸electrostatic

−EHBm,n

2︸︷︷︸hydrogen bond

For strong HB, the distance of thebond is shorter than the sum of the vander Waals radii†

It is usually assumed that dispersionmostly cancels out for excess properties

∗ST Lin and S.I. Sandler. In: Ind. Eng. Chem. Res. 41.5 (2002), pp. 899–913†S. J. Grabowski. In: The J. of Phys. Chem. A 105.47 (2001), pp. 10739–10746





−EHBm,n









−EHBm,n





Surface contacting theory – dispersion

For an EOS we need a dispersioncontribution∗:



−EHBm,n

2 −EDispm,n

2

With per compound dispersion parameters:EDispm,n =

√δmδn

δm = δ0m

(1− exp(−δTm/T )

)

∗G.B. Flores, P.B. Staudt, and R.P. Soares. In: Fluid Phase Equilib. 426 (Oct.2016), pp. 56–64

Surface contacting theory – dispersion

For an EOS we need a dispersioncontribution∗:



−EHBm,n

2 −EDispm,n

2

With per compound dispersion parameters:EDispm,n =

√δmδn

δm = δ0m

(1− exp(−δTm/T )

)

∗G.B. Flores, P.B. Staudt, and R.P. Soares. In: Fluid Phase Equilib. 426 (Oct.2016), pp. 56–64


Conclusions


COSMO-SAC-Phi: first attempt

Repulsive pressure from a simplehard sphere model

COSMO σ-profiles from theopen source LVPP sigma-profiledatabase and COSMO-SACparametrization GMHB1808,both available athttp:

//github.com/lvpp/sigma




IDAC Results for 820 mixtures

Comparison for infinite dilution activity coefficient (IDAC) data

IDAC DeviationMixture Proposed Previous (σHB)water/hydrocarbon 0.84 2.18alcohol/water 0.20 0.41water/alcohol 0.57 0.62


Conclusions

ConclusionsLinks and more info

Conclusions

Potential inconsistencies for the hydrogen bond (HB) term arepresent in COSMO-SAC

The use of a constant area per HB site removes the parameter σHB

as well as improve the results

This method will be tested with more compounds and mixtures


Thank you!

The LVPP sigma-profile database is freely available athttps://github.com/lvpp/sigma

Our homepage: http://ufrgs.br/lvpp

Contact: [email protected]

Special thanks:

https://github.com/lvpp/sigma

http://ufrgs.br/lvpp

[email protected]

Documents

A new family of equations of state: COSMO-SAC-Phi · 2019. 3. 17. · COSMO method (solutes alone) vs COSMO-RS/SAC The COSMO method was originally developed for the computation of