Handbook of Solvents - George Wypych - ChemTech - Ventech!

566 George Wypych
LW LW + − − +
( L
S L S L)
γ ( 1+ cos θ ) = 2 γ γ + γ γ + γ γ
L1 1 S 1 1 1
LW LW + − − +
( L
S L S L)
γ ( 1+ cos θ ) = 2 γ γ + γ γ + γ γ
L2 2 S 2 2 2
LW LW + − − +
( L
S L S L)
γ ( 1+ cos θ ) = 2 γ γ + γ γ + γ γ
L3 3 S 3 3 3
[10.1.3]
Solving this set of equations permits the calculation of solid parameters from equation
[10.1.1]. The work of adhesion, Wa, between a solid and a liquid can be calculated using the
Helmholtz free energy change per unit area:
LW LW + − − +
( L
S L S L)
− ΔG = Wa = γ + γ − γ = 2 γ γ + γ γ + γ γ [10.1.4]
SL SL S L SL S
Determination is simple. However, several measurements (usually 10) should be taken to
obtain a reliable averages (error is due mostly to surface inhomogeneity). There is a choice
between measuring the advancing or the receding contact angle. Advancing contact angles
are more representative of equilibrium contact angles. 3
Inverse gas chromatography data are interpreted based on Papirer’s equation: 4,5
D 12 / D 12 /
RT ln V = 2N(
γ ) a( γ ) + c
[10.1.5]
N S
L
where:
R gas constant
T temperature
VN net retention volume
N Avogadro’s number
γ D
dispersion component of surface energy
S, L indices for solid and liquid, respectively
a molecular area of adsorbed molecule
c integration constant relative to a given column.
D
Several probes are used to obtain the relationship between RTlnVN and aγL . From this
REF
relationship the reference retention volume, VN , is calculated and used to calculate the
acid-base interaction’s contribution to the free energy of desorption:
VN
ΔGAB = RTln
[10.1.6]
REF
V
N
If data from a suitable temperature range for ΔG AB can be obtained, the acid-base enthalpy,
ΔH AB can be calculated using the following equation:
where:
ΔHAB = KaDN + KbAN [10.1.7]
Ka acid interaction constant
Kb base interaction constant
DN donor number
AN acceptor number