HANSEN SOLUBILITY PARAMETERS IN CHROMATOGRAPHIC SCIENCES

ADAM VOELKEL, K. ADAMSKA

POZNAŃ UNIVERSITY OF TECHNOLOGY, POLAND

HSP 50 YORK 2017

• Energy of vaporization

• Cohesive energy density

SOLUBILITY PARAMETER THEORY

dVV

UUE

V

VparVT

g

l

V

Ec

V

RTH

V

Ec wcoh

Solubility parameter units : cal/cm3)1/2, (J/m3)1/2, (MPa)1/2

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HANSEN SOLUBILITY PARAMETERS (HSP)

hpd EEEE

V

E

V

E

V

E

V

E hpd

2222

hpdT

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HSP 50 YORK 20174

R.Tijssen H.A.H.Billet, P.J.Schoenmakers, Use of solubility parameters for predicting selectivity and retention

in Chromatography, J.Chromatogr., 122 (1976) 185-203

𝛿𝑇2 = 𝛿𝑑

2 + 𝛿𝑜2 + 𝛿𝑎𝛿𝑏

𝑙𝑛 𝛾𝑖ℎ =

𝑉𝑖

𝑅𝑇𝛿𝑑

𝑖 − 𝛿𝑑𝑗 2

+ 𝛿𝑜𝑖 − 𝛿𝑜

𝑗 2+ 2 𝛿𝑎

𝑖 − 𝛿𝑎𝑗

𝛿𝑏𝑖 − 𝛿𝑏

𝑗

ln𝐾𝑖 =𝑉𝑖

𝑅𝑇𝛿𝑇

𝑚2 − 𝛿𝑇𝑆2 + 2𝛿𝑑

𝑖 𝛿𝑑𝑆 − 𝛿𝑑

𝑚 + 2𝛿𝑜𝑖 𝛿𝑜

𝑆 − 𝛿𝑜𝑚 + 2𝛿𝑎

𝑖 𝛿𝑏𝑆 − 𝛿𝑏

𝑚 + 2𝛿𝑏𝑖 𝛿𝑎

𝑆 − 𝛿𝑎𝑚

HSP 50 YORK 20175

B.L.Karger, L.Snyder, C. Eon, Expanded Solubility Parameter Treatment for Classification and

Use of Chromatographic Solvents and Adsorbents, Analytical Chemistry, 50 (1978) 2126-2136

∆𝐸𝑙𝑠𝑐 = −𝑛 ∆𝐸𝐴

𝑗 𝑎𝑑 − ∆𝐸𝑠

𝑖 𝑗 + ∆𝐸𝐴

𝑖 𝑗 + ∆𝐸𝐴

𝑖 𝑎𝑑

j = solvent; ad – adsorbent; i = solute

∆𝐸𝑠 𝑖 𝑗 = 𝑉𝑖 𝛿𝑗

2− 2𝛿𝑑

𝑖 𝛿𝑑𝑗− 2𝛿𝑜

𝑖𝛿𝑜𝑗− 2𝛿𝑖𝑛

𝑖 𝛿𝑖𝑛𝑗

− 2𝛿𝑎𝑖 𝛿𝑏

𝑗− 2𝛿𝑎

𝑗𝛿𝑏

𝑖

∆𝐸𝐴 𝑖 𝑎𝑑 = 𝑉𝑖 𝛿𝑑

𝑖 𝛿𝑑𝑎𝑑 + 𝛿𝑜

𝑖𝛿𝑜𝑎𝑑 + 𝛿𝑖𝑛

𝑎𝑑𝛿𝑑𝑖 + 𝛿𝑖𝑛

𝑖 𝛿𝑑𝑎𝑑 + 𝛿𝑎

𝑖 𝛿𝑏𝑎𝑑 + 𝛿𝑎

𝑎𝑑𝛿𝑏𝑖

∆𝐸𝑙𝑠𝑐= ∆𝐸𝐴

𝑖 𝑎𝑑 −𝐴𝑖𝐴𝑗

∆𝐸𝐴 𝑗 𝑎𝑑

Ai, Aj – molecular area of “i” and “j”; 𝛿 – total solubility parameter; 𝛿𝑑 - dispersion solubility

parameter; 𝛿𝑜 - orientation solubility parameter; 𝛿𝑖𝑛 - induction solubility parameter;

𝛿𝑎 - proton donor solubility parameter; 𝛿𝑏 - proton akceptor solubility parameter

Liquid solid chromatography

HSP 50 YORK 20176

B.L.Karger, L.Snyder, C. Eon, Expanded Solubility Parameter Treatment for Classification and

Use of Chromatographic Solvents and Adsorbents, Analytical Chemistry, 50 (1978) 2126-2136

𝑖 𝑗 ↔ 𝑖 𝑘

Liquid liquid chromatography

j = solvent; k – liquid stationary phase; i = solute

∆𝐸𝑀 = 𝑉𝑖 𝛿𝑖2+ 𝛿𝑗

2− 2𝛿𝑑

𝑖 𝛿𝑑𝑗− 2𝛿𝑖𝑛

𝑖 𝛿𝑑𝑗− 2𝛿𝑖𝑛

𝑗𝛿𝑑

𝑖 − 2𝛿𝑎𝑖 𝛿𝑏

𝑗− 2𝛿𝑎

𝑗𝛿𝑏

𝑖

ibj

aj

bia

id

jin

jd

iin

jo

io

jd

id

jiS VE 2222222

jMkMllc EEE jSkS

llc EEE

∆𝐸𝑙𝑙𝑐

= 𝑉𝑖 𝛿𝑘2− 𝛿𝑗

2− 2𝛿𝑑

𝑖 𝛿𝑑𝑘 − 𝛿𝑑

𝑗− 2𝛿𝑖𝑛

𝑖 𝛿𝑑𝑘 − 𝛿𝑑

𝑗− 2𝛿𝑑

𝑖 𝛿𝑖𝑛𝑘 − 𝛿𝑖𝑛

𝑗− 2𝛿𝑜

𝑖 𝛿𝑜𝑘 − 𝛿𝑜

𝑗

HSP 50 YORK 20177

B.L.Karger, L.Snyder, C. Eon, Expanded Solubility Parameter Treatment for Classification and

Use of Chromatographic Solvents and Adsorbents, Analytical Chemistry, 50 (1978) 2126-2136

Retention in gas-liquid chromatography

𝛿𝐼 𝑖 𝑗 = 𝑅𝐼 𝑖 𝑗 − 𝑅𝐼 𝑎𝑙 𝑗

𝛿𝐼 𝑖 𝑗 =200 𝑉𝑖

∆𝐸𝑆 𝐶𝐻2 𝑗𝛿𝑎𝑙 − 𝛿𝑑

𝑖 𝛿𝑑𝑗+ 𝛿𝑖𝑛

𝑗− 𝛿𝑜

𝑖𝛿𝑜𝑗− 𝛿𝑖𝑛

𝑖 𝛿𝑑𝑗− 𝛿𝑎

𝑖 𝛿𝑏𝑗− 𝛿𝑏

𝑖𝛿𝑎𝑗

𝛿𝐼 𝑖 𝑗 retention index difference between a solute „i” and hypothetical n-alkane „al” ofthe same molar volume as „i” on stationary phase „j”

•Flory–Huggins interaction parameter

SOLUBILITY PARAMETER – IGC

o

oo

o

go V

V

ρ

ρVB

TR

p

MVp

Rχ

2

1

2

1111

1

11

12 1ln15.273

ln

1 and 2 denotes the solute and examined material, M1-the molecular weight

of the solute, p10-the saturated vapor pressure of the solute, B11-the second

virial coefficient of the solute,V10 -the molar volume, i-the density,

R -the gas constant.

115.273ln 111111

212

o

o

o

g

oVB

TR

p

VVp

Rχ

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GUILLET - DI PAOLA BARANYI APPROACH

s

RT

V

2

211

i

si

i

ii

VRTRTVRT 1

2

21

2

1

)12(2

1 2

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• Combination of the experimental data of Flory-Hugginsinteraction parameter with components of solubility

parameter for test solute and examined material

HSP THROUGH IGC PROCEDURES

2,2,12,2,12,2,1112 25,025,0 hhppddo

RT

V

where α, V , R, T are a corrective coefficient, molar volume of the test solute, gas constant and temperature

of measurement, respectively.

K. Adamska, R. Bellinghausen, A. Voelkel, New procedure of the determination

of Hansen Solubility Parameters by means of inverse gas chromatography,

J. Chromatogr. A, 1195 (2008) 146-149.

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BASIC RELATIONS

LSLSGLGLLLN AKAKKVV

Tm

FjtV

w

Rg

15.273

2

3'

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• Model of adsorption described by Snyder and Karger

SOLUBILITY PARAMETER FOR SOLIDS

constRTEV Ag ln

jhihjpipjdidiA VE

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HSP FOR SOLIDS

N

n

N

n

NhNNpNNdN

nhnnpnndn

hpd

N

n

...

...

...

...

*

VVV

.........

VVV

.........

VVV

E

...

E

...

E

111111111

XY

•Y - the column vector containing the N values of experimental measurements of the energy of

adsorption ( -EN) of N solutes,

•X - the experimental matrix, formed of elements (Xnk) , where , Vn is the molar volume of the nth

solute and is one of the Hansen Solubility Parameters of type k (k = d, p, or h) of the

respective test solute,

•Β - the vector which contains the real values of HSPs of the adsorbent,•ε – the vector which corresponds to the experimental errors, εn.

nk

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K. Bielicka-Daszkiewicza, A. Voelkel, M. Pietrzyńska, K. Heberger, J. Chromatogr. A, 1217 (2010) 5564–5570

Role of Hansen solubility parameters in solid phase extraction

HSPs and total solubility parameter for sorbents, eluents and analytes

HSP 50 YORK 201715

K. Bielicka-Daszkiewicza, A. Voelkel, M. Pietrzyńska, K. Heberger, J. Chromatogr. A, 1217 (2010) 5564–5570

:

left – indicated position of solvents right - indicated position of sorbents

Score plots for sorbent-analyte, solvent-analyte, sorbent-solvent systems

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I tutaj tabelki z posteru

Squares of differences fo sorbent-solvent (eluent) pairs

Squares of differences fo sorbent-analyte pairs

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Taking into account that the use of ethanol allowed to achieve better recovery, it can be

concluded that:

i) the sorbent for which the lowest (δP –δA)2 value is found should be selected as a material

of filling the needle device;

ii) the value of (δP-δS)2 does not have to be as small as possible,

iii) the interactions between the analyte and the solvent are more important for the

extraction process than the interactions between the polymer and solvent.

Therefore, for the selection of a suitable extraction system should start from finding lowest

value for (δP-δA)2.

THANK YOU FOR YOUR ATTENTION

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