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Theory and Mechanism of Thin-Layer Chromatography
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Theory and Mechanism of Thin-Layer Chromatography
Teresa Kowalska, Krzysztof Kaczmarski, Wojciech Prus
Table of contents
I. INTRODUCTION
II. BASIC PHYSICAL PHENOMENA
A. Capillary Flow
B. Broadening of Chromatographic Spots
C. Volatility of Solvents
III. MEASURES OF CHROMATOGRAPHIC SYSTEM EFFICIENCY
A. Model of Theoretical Plates
B. Van Deemter Equation
C. Separation and Resolution
D. Selectivity of Separation
IV. SEMIEMPIRICAL MODELS OF PARTITION AND ADSORPTION
CHROMATOGRAPHY
A. Martin-Synge Model of Partition Chromatography
B. Snyder-Soczewiński Model of Adsorption Chromatography
C. Snyder Concept of Solvent Polarity and Selectivity
D. Scott-Kucera Model of Adsorption Chromatography
E. Kowalska Model of Adsorption and Partition Chromatography
F. Kowalska Model of Retention with Use of Multicomponent Mobile Phase
V. PRACTICAL CONSEQUENCES OF ESTABLISHED MODELS
A. Quantification of Sorbent Activity
B. Quantification of Solvent Elution Strength
C. Quantification of Solvent Polarity and Selectivity
D. Optimization of Mobile Phases
1. Snyder's Approach (Solvent Elution Strength)
2. Snyder's Approach (Solvent Polarity and Selectivity)
3. Soczewiński's Approach
4. The Adsorption-Partition Model
5. Other Approaches
E. Considerations on the Molecular Level
1. Role of Intermolecular Interactions Based of Chemical Potential Concept
2. Role of Intermolecular Interactions - Multilayer Adsorption
VI. ATTEMPTS TO ENHANCE THIN-LAYER PERFORMANCE
A. High-Performance Thin-Layer Chromatography
B. Overpressured Thin-Layer Chromatography
C. Centrifugal-Layer Chromatography
REFERENCES
1
Theory and Mechanism of
Thin-Layer Chromatography
Teresa Kowalska1, Krzysztof Kaczmarski2, Wojciech Prus3
1
2
3
Silesian University, Katowice, Poland
Rzeszów Universiy of Technology, Poland
University of Technology and the Arts in Bielsko-Biała, Poland
I. INTRODUCTION
Chromatographic theory describes the physicochemical relationships governing separations.
Usually, semiempirical models of the chromatographic process that have a relatively simple
thermodynamic background and give a bulk picture of the physical or chemical phenomena are
involved. Macroscopic models of the chromatographic process cannot mirror the respective
separation mechanisms in any other way. Exceptions to this rule, if any exist, are rather negligible.
It is important to keep in mind two facts. First, one always has to be aware of the
complexity of chromatographic processes, and consequently of limitations of the existing
semiempirical models. Second, one cannot forget that the study of chromatography theory has only
begun relatively recently and that there is much additional work to be done before it reaches its full
potential.
In this chapter, basic knowledge about important physical phenomena in the
chromatography will be introduced (Section II), as well as the main concepts regarding efficiency
of separation (Section III). Further, the six overall semiempirical models of partition and adsorption
chromatography will be reviewed (Section IV), and their usefulness in everyday laboratory practice
will be discussed (Section V). Finally, the reader's attention will be drawn to attempts that have
been made to enhance performance of thin-layer chromatography (TLC) (Section VI).
2
II. BASIC PHYSICAL PHENOMENA
A. Capillary Flow
Transfer of a mobile phase through the thin layer is induced by capillary forces. Stationary phases
(in adsorption, size-exclusion, and ion-exchange chromatography) and supports (in partition
chromatography) are all microporous solids showing high specific surfaces (ranging from ca.
50 m2/g with celluloses to ca. 500 m2/g with silica), and for this reason they can be regarded as
capillary agglomerations.
Solvents or solvent mixtures contained in the chromatographic chamber enter capillaries of
a solid bed, attempting to lower both their free surface area and their free energy. The free-energy
gain ∆Em of a solvent entering a capillary is given by the following relationship:
∆E m = −
2γV n
r
(1)
where γ is the free surface tension, Vn denotes the molar volume of the solvent, and r is the
capillary radius.
From Eq. l it follows that the capillary radius r is very important for capillary flow, and a
smaller radius leads to more efficient flow. Preparation of the commercial stationary phases and
supports cannot provide all pores of ideally equal diameter, which results in certain side effects that
contribute to broadening of the chromatographic spots. This problem will be discussed in the next
subsection.
B. Broadening of Chromatographic Spots
The most characteristic feature of chromatographic spots is that the longer the developing time and
the greater the distance from the start, the greater their surface areas become. This phenomenon is
not restricted to planar chromatographic methods only, but occurs in each chromatographic
technique. Spot broadening is due to eddy and molecular diffusion, to the effects of mass transfer,
and to the given mechanism of solute retention.
Eddy diffusion of solute molecules is induced by an uneven diameter of the stationary phase
or support capillaries, which automatically results in an uneven flow rate of the mobile phase
through the solid bed. In this way some solute molecules displace faster, while others are retarded,
compared with the average displacement rate of the major portion of solute.
3
Molecular diffusion has nothing to do with the presence of a solid bed in the
chromatographic system. It is the regular diffusion in the mobile phase, the driving force of each
dissolving process, and for this reason it needs no further explanation.
The effects of mass transfer take place separately in the stationary and mobile phases. First
let us describe the effect in the stationary phase. It can occur that for some energetic reason a
fraction of solute molecules is "captured" by the stationary phase a little while longer than the
major portion of solute. Such retardation results in broadening of a chromatographic spot.
Two different effects of mass transfer are observed in the stagnant and flowing mobile
phase. Certain amounts of mobile phase can be trapped within the partially closed pores, and only
gradually and slowly are replaced by a fresh portion of eluent. This is what we call the stagnant
mobile phase. If the solute molecules occasionally "dive" into such a blind pore, they will miss the
main stream of the flowing mobile phase that carries the major portion of solute.
With the flowing mobile phase another phenomenon is observed. Those molecules that are
in touch with the solid material move more slowly, while the others, passing through the center of
the pores, displace more quickly. This friction-induced inequality of the flow rates additionally
contributes to broadening of a chromatographic spot.
Mechanisms of solute retention, which are also responsible for spot broadening, differ from
one chromatographic technique to another, and their role in this process is far less simple than that
of diffusion and mass transfer.
All the aforementioned phenomena, which jointly contribute to spot broadening, used to be
described as an effective diffusion. This is a convenient term, which apart from being concise and
informative, also underlines the fact that these phenomena occur simultaneously.
Spot broadening results in mass distribution of solute in a given chromatographic spot. This
distribution is presented by a respective concentration profile, which in practice can be established
densitometrically. In Fig. l two examples of such concentration profiles are shown.
Numerous efforts have been undertaken aiming to establish relevant theoretical models that
4
conc.
2
[g/cm ]
a
b
Figure 1 Two examples of concentration profiles: (a) symmetrical without tailing, and (b) skewed with tailing.
could describe broadening of chromatographic spots and formation of the concentration profiles.
The most interesting models are those that regard spot broadening as a two-dimensional process.
Two models of two-dimensional broadening of chromatographic spots were established by
Belenky et al. (1,2) and by Mierzejewski (3). The common basic concept that enabled elaboration
of these two models in Fick's second law, which describes the velocity of the concentration changes
with a substance at a given point of a system:
δc
= − divJ
δt
(2)
where c and t are concentration and time, respectively, and J denotes the mass flux of the
investigated substance.
Upon the further assumptions of Belenky's dynamic model (1,2), the following dependence
was established, defining concentration of solute at time t and at the given point of sorbent layer,
described by the coordinates x and y (see Fig. 2):
5
x
direction
of
development
y
start
Figure 2 The diffused chromatographic spot. Illustration of
Belenky's and Mierzejewski's models of spot broadening.






2
 1
q
y 2 
(
x − vt )
+
c ( x, y , t ) =
× exp− 
  (3)
2DL R f t 
1− R f 2 

1− R f 2 
 2  
⋅ v ⋅τ  R f t
2 D +
4πR f t D L  D L +
⋅ v ⋅τ 

  L




R
R
f

f
 




where q is the total amount of solute in a chromatographic spot; Rf is the basic TLC parameter
introduced in Section III.C of this chapter; DL denotes the effective diffusion coefficient that
characterizes broadening of a chromatographic spot; v is the migration velocity of the
chromatographic spot center; and τ is the parameter representing a time lag in establishing
equilibrium between the mobile and stationary phases (τ is also a function of the particle size of a
solid bed).
From the main dependence of Belenky's model it follows that the concentration of solute in
the chromatographic spot is described by a two-dimensional Gaussian distribution function, which
can be rewritten in a simpler form:
 1  ( x − vt ) 2 y 2  
+ 2 
c( x, y, t ) = c max exp− 
2
σ x  
 2  σ x
where
6
(4)
c max =
q

1− R f 2 
4πR f t D L  D L +
⋅ v ⋅τ 


R
f



1− R f
σ x2 = 2 D L +
Rf


⋅ v 2 ⋅τ  R f t


σ y2 = 2 D L R f t
(5)
(6)
(7)
Mierzejewski's approach (3) to the problem was different. That author introduced four
vectors, denoting speed of the two-dimensional effective diffusion of solute: two of them parallel to
ρ
σ
the migration direction x but showing the opposite turns ( H x ,1 and H x , 2 ), and the analogous two
ρ
σ
vectors perpendicular to this direction ( H y ,1 and H y , 2 ). His relationship for solute concentration at
time t, and at the point described by the coordinates x and y, is given below:
 (K + 1) 2 ( x − l s ) 2 y 2 
q
− 
c ( x, y , t ) =
exp− 
2
2 ( j −1)
4 g 
4πgw
 16 gw K
where
(8)
ρ
σ
H x,2
(H x,1 + H x,2 )
; l s = v ⋅ t . Additionally, if
g = H y2 t H y = H y ,1 = H y , 2 ; w =
; K=
2H y
H x ,1
(
)
x ≥ ls, j = 1, and if x < ls, j = 2.
As can be deduced from Eq. 8, Mierzejewski's model also describes the concentration of
solute in the chromatographic spot by a two-dimensional Gaussian distribution that can be
presented in a simpler form:

 (K + 1) 2 ( x − l s ) 2
 1
c( x, y, t ) = c max exp− 
σ x2
 2 
y 2  
+ 2 
σ y  
(9)
where
c max =
q
4πgw
σ x2 = 8 gw 2 K 2( j −1)
σ y2 = 2 g
(10)
(11)
(12)
As can be seen by observation of actual thin-layer chromatograms, many experimental
concentration profiles can in fact be described by the Gaussian distribution curves.
7
C. Volatility of Solvents
Unlike the situation in column chromatography, the thin-layer microporous solid bed stays in
unhindered contact with a usually voluminous space of the chromatographic chamber. The
so-called sandwich chamber is an exception in this respect. Therefore, in thin-layer
chromatography some special measures need to be undertaken to facilitate achievement of
thermodynamic equilibria between the mobile-phase components in the gaseous and liquid forms.
To make this point clear, let us imagine that to an empty chromatographic chamber we
simultaneously introduce mobile phase and the chromatographic plate, automatically initiating the
chromatographic process. What happens then in the "free" room over the mobile-phase surface?
First it was occupied by air components and water vapors only, but after adding solvent, or solvent
mixture, it starts filling with the mobile phase molecules. This process will last until saturation of
the "free" room with the gaseous mobile-phase components is completed. Where do these gaseous
mobile-phase components come from? Partially from the bulk liquid, and partially from the
chromatographic plate surface. In this way we obtain an unwanted change of the mobile-phase
composition directly within the solid bed pores. One can imagine how much this phenomenon
affects separation, and how damaging it proves to be for reproducibility of the retention data.
The mental experiment presented above was aimed at explaining the necessity of saturation
of the chromatographic chamber with the gaseous mobile-phase components prior to initiation of
the chromatographic process proper. In other words, it was meant to demonstrate indispensability
in this process of thermodynamic equilibrium between the gaseous and liquid mobile-phase
components. Due to them, evaporation cannot affect the mobile-phase composition in either the
bulk form or in the capillaries of the solid bed. Equation 13 gives the thermodynamic condition of
these equilibria:
µ i ( g ) = µ i (l )
i = 1,2,..., n
(13)
where µi(g) and µi(l) are the chemical potentials of the ith mobile-phase component in the gaseous
and liquid form, respectively, and n denotes the number of components.
In Fig. 3 a scheme of the chromatographic system with the achieved thermodynamic
equilibria between the gaseous and liquid mobile-phase components is presented.
8
Figure 3 Scheme of thermodynamic equilibria between
the gaseous and liquid mobile-phase components
in a presaturated chromatographic chamber.
III. MEASURES OF CHROMATOGRAPHIC SYSTEM EFFICIENCY
A. Model of Theoretical Plates
The model of theoretical plates originates from the theory of distillation. It was adapted to
chromatography in the pioneer work on the physicochemical foundations of this method
accomplished by Martin and Synge (4,5). The utility of this model in the highly sophisticated
column techniques, e.g., gas or high-performance liquid chromatography, is long and indisputably
recognized. The demand for the concept of theoretical plates in thin-layer chromatography seemed
lesser in proportion to the comparatively lower separation efficiency of this method. In view of the
recent and successful attempts to enhance efficiency in this field also (see Section VI), the idea of
theoretical plates applied to thin-layer chromatography for the first time became really and fully
relevant.
Broadening of a chromatographic spot can be simply expressed in terms of the theoretical
plate number N of the given chromatographic system:
N=
16 ⋅ l ⋅ z
w2
9
(14)
where l and z are the migration lengths of the mobile phase and solute, respectively, and w is the
chromatographic spot width in the direction of the mobile-phase migration (see Fig. 4).
Although the numerical values of N attained for different solutes on the same
chromatographic plate proved to coincide fairly well, they usually differ significantly from the
analogous values characteristic of another plate type. For this reason, the quantity N can be
regarded as an approximate measure of the separating efficiency of chromatographic plates. It is
proportional to the migration length of the mobile phase l, so that, the z/w ratio being constant, an
increase in l results in an increase of N and better separation. This proportionality of N and l is
given by the following relationship:
N=
l
H
(15)
where H is the so-called HETP value (i.e., height equivalent of a theoretical plate). The quantity H,
or simply the plate height, measures the efficiency of a given chromatographic system per unit
length of the migration distance, l, of the mobile phase. Small H values mean more efficient
chromatographic systems and larger N values. The main goal of efforts to enhance performance of
thin layers is the attainment of small H values and maximum N values. As in other
chromatographic techniques, the efficiency of a given TLC system is better (i.e., H is smaller) for:
Smaller particles of stationary phases or supports
Lower mobile-phase flow rates
Less viscous mobile phases
Smaller solute molecules
B. Van Deemter Equation
In the preceding subsection the simplest measure of spot broadening was introduced in the form of
the quantity H, or the plate height. One of the most important chromatographic relationships, the
Van Deemter equation, attempts to estimate the relative contributions of eddy and molecular
diffusion, and of the effects of mass transfer, on H. It is an empirical equation, originally
established for the column chromatographic techniques, but valid also for thin-layer
chromatography.
The Van Deemter relationship can be written in the complete version.
H = A ⋅ u 0.33 +
B
+ C ⋅u + D ⋅u
u
10
(16)
or simplified,
H = A ⋅ u 0.33 +
B
+ C ⋅u
u
for D ≈ 0
(16a)
where u is the flow rate of the mobile phase, and A, B, C, and D are the equation constants,
measuring contributions of the different spot-broadening processes to the quantity H. The effects of
eddy diffusion and mass transfer on the flowing mobile phase are described jointly by A. The
molecular diffusion is reflected in B, while C and D correspond to the effects of mass transfer in the
stagnant mobile and stationary phases, respectively. The constants A, B, C, and D depend mostly on
the parameters of the microporous solid, but they are also influenced by the nature of the solute and
mobile phase, and by the working temperature of the chromatographic system.
Each constant of Eq. 16 can be defined as a function of certain properties of the
chromatographic system. Let us briefly review the appropriate empirical relationships.
Giddings (6) proposed the following expression for A:
A = 2λd p
(17)
where dp is the diameter of a solid particle and λ depends on the microscopic arrangement of solid
bed.
B is given as:
B = 2γD m
(18)
where Dm is the diffusion coefficient of the solute in the mobile phase, while γ is a correction factor
mirroring the nonlinearity of diffusion due to the labyrinth arrangement of micropores.
C is described by the following equation:
C=
ω ⋅ d p2
Dm
(19)
where ω is a proportionality factor. Similar to γ in Eq. 18, it also depends on the labyrinthine
arrangement of micropores.
D is described by the relationship
D=
σ ⋅ d 2f
Ds
(20)
where df is the thickness of the stationary-phase layer, Ds is the diffusion coefficient of the solute in
the stationary phase, and σ is a proportionality factor.
11
C. Separation and Resolution
The Rf coefficient is the basic quantity used to express the position of solute on the developed
chromatogram. It is calculated as the ratio:
Rf =
distance of chromatographic spot center from start
distance of solvent from start
(21)
Using symbols from Fig. 4, Rf can be given as
Rf =
z
l
(21a)
Rf values are between 0 (solute remains on start) and 1.0 (solute migrates with front of
mobile phase).
front
w
l
z
start
Figure 4 The thin-layer chromatographic parameters used
in calculation of the theoretical plate number N.
The traditional (and so far the only) method of determination of the numerical values of
analyte Rf coefficients quasi-automatically assumes the following preconditions:
(a) Circular (or ellipsoidal) chromatographic band shape; and
(b) Gaussian distribution of the mass of the analyte in this band.
On the basis of these assumptions, the position of a band on the chromatogram is defined
12
by measuring the distance between the origin and the geometrical center of the band. Despite
the considerable imprecision of this definition for asymmetric (i.e., tailing) and non-Gaussian
bands, two features of the definition are very important:
(i) The traditional definition regards the center of a chromatographic band as the point at
which the local concentration of the analyte is the highest.
(ii) The traditional definition also regards the center of the chromatographic band as the center
of gravity of the mass distribution of the analyte in the band.
For the ideal, circular bands with Gaussian analyte concentration profiles, the band centers
described by assumptions (i) and (ii) are, in fact, identical.
For densitograms obtained from non-circular (i.e. tailing) bands with non-Gaussian
concentration profiles, it can be stated that:
•
The numerical value of the Rf coefficient for a given chromatographic band can be
determined for the maximum value of the concentration profile of the band (which is the
point at which the local concentration of the analyte is the highest). The Rf coefficient
determined according to this definition can be denoted as Rf(max).
•
Alternatively, the numerical value of the Rf coefficient can be determined from the center
of gravity of the distribution of analyte mass in the band. With the non-symmetrical
chromatographic bands, this value cannot be identical with that obtained from the
maximum of the analyte concentration profile. The Rf coefficient determined in this second
manner can denoted Rf(int).
To determine the center of gravity of the analyte mass distribution in the chromatographic
band one has to establish the baseline, remove the noise from the densitogram, subtract the
baseline signal, define the beginning (i = 0) and end (i = k) of the chromatographic band, and,
finally, calculate the position of its center of gravity by use of the relationship:
k
 d + d i −1  d i + d i −1
I i
⋅ (d i − d i −1 ) =
⋅
⋅
∑
k
2
2
 d i + d i −1 

i =1 
I
 ⋅ (d i − d i −1 )
∑
2

i =1 
k
1
 d + d i −1  d i + d i −1
⋅ (d i − d i −1 )
⋅ ∑ I i
⋅
2
2
S i =1 

d sr . =
1
(22)
where S denotes the chromatographic band surface, and I(di) is the detector signal at a distance di.
With an increasing implementation of the thin-layer chromatographic laboratories with
scanners, it seems quite important to reconsider definition of the Rf coefficient and the ways of its
practical determination.
13
The main goal of chromatography is separation of a given solute mixture. However, it can
happen that the chromatographic spots of two adjacent solutes overlap to a smaller or greater
degree. Therefore, a demand arises for a measure of their separation. This demand is fulfilled by
introduction of the quantity Rs, called resolution. The resolution Rs of two adjacent
chromatographic spots l and 2 is defined as being equal to the distance between the two spot
centers, divided by the mean spot width (Fig. 5);
z1
z2
front
start
w1
w2
a
b
Figure 5 Illustration of resolution in thin-layer chromatography: (a) chromatogram; (b) corresponding concentration
profiles of chromatographic spots.
Rs =
z 2 − z1
0.5(w1 + w2 )
(23)
The quantity Rs, serves to define separation. When Rs = l, the two spots are reasonably well
separated. Rs values larger than l mean better separation, and smaller than l poorer separation. In
Fig. 6 an example is given of separation as a function of resolution (Rs) and the relative spot
concentration (understood as the ratio of the concentration profile maximum heights). From the
example it becomes evident that spot overlap becomes more disturbing when concentration of
solute in one spot is much greater than in the other.
Utilizing the quantity Rf, Eq. 23 can be rewritten in the following way:
14
Rs =
[
l ⋅ R f ( 2) − R f (1)
0.5(w1 + w2 )
]
(23a)
where Rf(1) and Rf(2) are the Rf values of the chromatographic spots l and 2, respectively.
Assuming Gaussian concentration profiles of two closely spaced (i.e., overlapping)
chromatographic spots, and mean Rf value for both of them (Rf(1) ≈ Rf(2) ≡ Rf), Snyder (7) managed
to transform Eq. 23 to the following form:
(I)
 K
R s = 0.25 ⋅  2
 K 1
1/1
(II)
 
 − 1 ⋅ R f N ⋅ (1 − R f
 
1/12
R S = 0.7
1/1
1/12
R S = 0.9
1/1
(III)
1/12
R S = 1.1
Figure 6 Separation as a function of Rs and the relative spot concentration
(the ratio of the concentration profile maximum heights).
15
)
(24)
where K1 and K2 are distribution coefficients of solutes l and 2 between the stationary and mobile
phases ("distribution" is used in a general sense and means partition, adsorption, or any other
phenomenon, depending on the retention mechanism of a particular chromatographic technique).
Eq. 24 is the thin-layer chromatographic version of a fundamental chromatographic
relationship that allows discussion of spot resolution in terms of the influence of K2/K1, N, and R f .
Each of these three quantities is sensitive to changes in the different factors, and Eq. 24 makes
discussion of their relative importance for retention possible. Thus K2/K1 can monitor
interdependence between the stationary and mobile phases, R f can monitor elution strength of the
mobile phase, and N depends on the length of the mobile-phase migration and on the plate height
(i.e., l and H, respectively).
D. Selectivity of Separation
Selectivity of separation is seldom referred to in the case of thin-layer chromatography, although no
serious reason can be given for avoiding this term. To the contrary, selectivity of separation is a
useful chromatographic notion, no matter which particular technique, column or planar, is being
considered. In the case of thin-layer chromatography, the separation factor α can be defined as:
α=
K2
K1
(25)
which remains in full conformity with the definition used for the column techniques. In fact, the
quantity α makes use of part of term I in Eq. 24, describing resolution Rs of two overlapping
chromatographic spots. It can be stated that with greater difference between distribution
coefficients of solutes l and 2 (K1 and K2), greater selectivity of separation (α) and better resolution
(Rs) are observed. With K1 = K2 the two chromatographic spots entirely overlap (α = l) and the
respective spot resolution Rs is nil. According to Snyder and Kirkland (8), several options for
increasing α are available, and can be ranked in order of decreasing promise:
Change of mobile-phase composition
Change of mobile-phase pH
Change of stationary phase
Change of temperature
Special chemical effects
16
IV. SEMIEMPIRICAL MODELS OF PARTITION AND ADSORPTION
CHROMATOGRAPHY
Partition and adsorption mechanisms of solute retention are the two most universal mechanisms of
chromatographic separation, both operating on a physical principle. In fact, practically all solutes
can adsorb on a microporous solid surface or be partitioned between two immiscible liquids. It is
the main aim of the semiempirical chromatographic models to couple the empirical parameters of
retention with the established thermodynamic quantities generally used in physical chemistry. The
validity of these models for chromatographic practice can hardly be overestimated, because they
often and successfully help to overcome the old trial-and-error (or, elegantly said, empirical)
approach to running the analyses.
A. Martin-Synge Model of Partition Chromatography
The basic principle of solute retention in partition chromatography is its distribution between the
two immiscible liquids. Therefore, partition chromatography often used to be called liquid-liquid
chromatography, even if the liquid stationary phase was substituted by a chemically bonded one.
Partition chromatography was first among the chromatographic techniques to gain
thermodynamic foundations, owing to the pioneering work of Martin and Synge (4,5), the 1952
Nobel Prize winners in chemistry. It was their simple and simultaneously fruit-bearing idea to
ascribe thermodynamic meaning to the so-called retardation parameter of the solute (i.e., Rf' or the
thermodynamic Rf coefficient in thin-layer chromatography). The quantity Rf' is the idealized Rf
value, undisturbed by the disadvantageous side effects accompanying the real chromatographic
process. Rf' is related to Rf through the following empirical dependence:
R /f = ξR f
(26)
where ξ is the disturbance factor [l ≤ ξ ≤ 1.6 (9)].
According to Martin and Synge, R'f can be viewed as
R /f =
tm
nm
mm
≡
=
t m + t s nm + ns mm + m s
(I)
(II)
17
(III)
(27)
where tm and ts denote time spent by a solute molecule in the mobile and stationary phases,
respectively, nm and ns, are numbers of solute molecules equilibrially contained in the mobile and
stationary phases, and mm and ms are the respective mole numbers.
Term I of Eq. 27 can be understood as the relative time spent by solute molecules in the
mobile phase, while terms II and III denote the molar fraction of solute in that phase. All the
dependences are based on the assumption as to partition equilibrium gained by the system.
Equation 27 can further be transformed in the following way:
R /f =
mm
c mV m
=
=
m m + m s c mV m + c s V s
1
c V
1+ s ⋅ s
c m Vm
(27a)
where cm and cs are molar concentrations of solute in the mobile and stationary phases,
respectively, while Vm and Vs are volumes of these phases.
The cs/cm ratio from Eq. 27a can be expressed as
K=
cs
cm
(28)
where K is the equilibrium constant of partition, or simply the partition coefficient. Combining
Eqs. 27a and 28, we obtain the final form of the Martin-Synge dependence:
R /f =
1
V
1 + K  s
 Vm



(27b)
This equation unites the retention parameter of solute, Rf', with the established physicochemical
quantity K, its thermodynamic meaning being
ln K =
∆µ p
RT
(29)
where ∆µp is the chemical potential of partition.
The physical meaning of the partition coefficient K is fully analogous to that from the
Nernst partition law, and consequently the numerical values of K obtained in the static experiment
correspond well with those established chromatographically (10). This fact can be regarded as a
favorable premise of the approaches aimed at prediction of the retention parameter Rf on the basis
of the known thermodynamic characteristics of partition.
18
B. Snyder-Soczewiński Model of Adsorption Chromatography
The basic principle of solute retention in adsorption chromatography is its distribution between the
sorbent and the mobile phase. For this reason adsorption chromatography is often called
liquid-solid chromatography.
The semiempirical model of adsorption chromatography, analogous to that in Section IV.A,
was established only in the late 1960s independently by Snyder (7,11) and Soczewiński (12). The
authors assumed that some part of the mobile phase rests adsorbed and stagnant on a sorbent
surface. This adsorbed mobile phase formally resembles the liquid stationary phase in partition
chromatography. Thus, instead of an inconvenient necessity of discussing solute concentration on a
solid surface, one can introduce a quantity expressing its concentration in the adsorbed mobile
phase. Otherwise the Snyder-Soczewiński model benefits from the partition chromatographic
concept of viewing the quantities Rf' and Kth (where Kth is the adsorption equilibrium constant, or
simply
the
thermodynamic
adsorption
coefficient).
The
main
relationship
of
the
Snyder-Soczewiński model of adsorption chromatography is
R /f ≡
tm
nm
mm
c m (V m − V aWa )
=
=
=
t m + t a n m + n a m m + m a c m (V m − V aW a ) + c aV aWa
(30)
where Va is the volume of the adsorbed mobile phase per mass unit of sorbent and Wa is the
considered mass of sorbent.
The final form of Eq. 30 is
R /f =
1
VaWa
1 + K th ⋅
Vm − VaWa
(30a)
where Kth = ca/cm.
In chromatographic practice, usually VaWa << Vm and Kth[VaWa/(Vm-VaWa)] >> 1, and
therefore Eq. 30a can be rewritten in a simplified version:
R /f ≈
1
VW
K th ⋅ a a
Vm
(30b)
In most cases Eq. 30b describes the experimental results well enough, and there is no urgent
demand for its complete form (i.e., for Eq. 30a). The approach to adsorption chromatography
proposed by Snyder and Soczewiński proved effective in many respects and enabled quantification
19
of the important chromatographic parameters such as sorbent activity and the elution strength of
solvents. These problems will be discussed more extensively in Section V.
C. Snyder Concept of Solvent Polarity and Selectivity
The original Snyder-Soczewiński model assumes competition between the solute and the solvent
molecules to the active sites on the solid surface of stationary phase, its outcome quantitatively
related to the net energy of adsorption (i.e. to the difference between the adsorption energies of the
solvent and the solute; for more details see Sections V.A and V.B). However, the net energy
concept encompasses a more detailed nature of these forces which are responsible for the process
of adsorption. This deficiency is a particular shortcoming with the solvents which to a large extent
govern solute retention, due to their overwhelming excess over the solute molecules in the
chromatographic systems.
In order to develop a quantitative measure of the solvent's relative ability to
intermolecularly interact with the solutes as proton acceptors, proton donors, and strong dipoles
Snyder established a new semiempirical model (13,14) coupling the solvent's polarity index (P')
with the so-called corrected gas-liquid partition coefficients or solubility constants (Kg") of the
selected test solutes: ethanol (a model proton donor), dioxane (a model proton acceptor), and
nitromethane (a model strong dipole). The main relationship of this approach is
( )
P ' = log K g//
ethanol
( )
+ log K g//
dioxane
( )
+ log K g//
nitromethane
(31)
where Kg" is a measure of the excess retention of the given solute (i.e. ethanol, dioxane, and
nitromethane) relative to an n-alkane of equivalent molar volume.
The individual terms of the trinomial given by Eq. 31 divided by the polarity index (P') are
the selectivity parameters, xe, xd, and xn:
xe =
xd =
xn =
( )
log K g//
ethanol
(32a)
P'
( )
log K g//
dioxane
(32b)
P'
( )
log K g//
nitromethane
(32c)
P'
The magnitudes xe, xd, and xn represent the fraction of P' contributed by interactions
associated with ethanol, dioxane and nitromethane, respectively.
20
Although the introduced concept of solvent polarity and selectivity cannot be regarded as a
semiempirical model of the adsorption or partition chromatography in its own rights, it certainly
remains in the mainstream of Snyder's viewing the role of the solvents in the process of retention as
a valuable supplement to the approach presented in the preceding subsection.
D. Scott-Kucera Model of Adsorption Chromatography
The approach of Scott and Kucera (15,16) aimed to define the equilibrium constant of solute
distribution, K, for example, Kth from Eq. 30a, between the stationary and mobile phases in terms of
the balance of forces between the molecules of the solute and the molecules of each phase. They
defined the distribution coefficient K of a solute between the two phases in the following way:
total forces acting on the solute in the stationary phase
=
total forces acting on the solute in the mobile phase
forces between solute and stationary phase × probability of interactions
=
forces between solute and mobile phase × probability of interactions
K=
(33)
Considering the situation with respect to adsorption chromatography, Eq. 33 can be
rewritten as
K th =
( ) ( )
(P ) + F (P )
F p/ Pp/ + Fd/ Pd/
Fp
p
d
(33a)
d
where Fp' and Fd' are the polar and dispersive forces, respectively, between the solute molecules
and the stationary phase; Fp and Fd are the polar and dispersive forces, respectively, between the
solute molecules and the mobile phase; and Pp', Pd', and Pp, Pd are the probabilities of the solute
molecule interacting with the polar and dispersive moieties of the stationary and mobile phases,
respectively.
The probability of interaction of a solute with one of the phases is some function of the
absolute temperature, proportional to the concentration of the interacting moieties in each of the
respective phases:
K th =
F p/ f 1 (T )c /p + Fd/ f 2 (T )c d/
F p f 3 (T )c p + Fd f 4 (T )c d
(33b)
where cp', cd' and cp, cd are the concentrations of polar moieties and dispersive moieties in the
stationary and mobile phases, respectively, and T is the absolute temperature.
21
If the hypothesis is made that the dispersive forces result from mass interaction, then cd is
proportional to the density of the dispersing medium, which can be expressed as a concentration in
terms of the mass per unit volume. Thus,
c d = Ad
(34)
where A is a constant and d is the density of the low-polar solvent. Inserting Eq. 34 in 33b, we
obtain:
K th =
F p/ f 1 (T )c /p + Fd/ f 2 (T )c d/
F p f 3 (T )c p + Fd f 4 (T ) Ad
(33c)
The authors further assumed that the dispersive forces on highly active sorbents, if present at all, do
not have a significant effect on solute retention, which in the case of, e.g., silica, allows
simplification of Eq. 33c:
K th =
F p/ f 1 (T )c /p
F p f 3 (T )c p + Fd f 4 (T ) Ad
(33d)
Correlations of the quantity Kth, as defined by Scott and Kucera with the basic retention
parameter of solute, i.e., the Rf coefficient, can be done with the help of Eq. 30a or 30b.
E. Kowalska Model of Adsorption and Partition Chromatography
In Kowalska's approach (17,18) to adsorption and partition chromatography, the basic
consequences were drawn from the effect of spot broadening. The author pointed to the fact that
broadening of a chromatographic spot occurred due to the effective diffusion, and in this respect it
resembled dissolving. Therefore the change of the chemical potential accompanying the transfer of
solute from the start to the chromatographic system, ∆µi, could be given by the following
relationship:
ln x i f i =
∆µ i
RT
(35)
where xi and fi are the molar fraction and the activity coefficient of solute, respectively, in the
chromatographic "binary solution".
The "binary solution" concept assumes two components of a system, i.e., "solute" and
"solvent". "Solute" is understood in a traditional way as a chromatographed substance, while
stationary phase is meant as "solvent". The effects of the mobile phase (and in partition
chromatography of the support) are expressed in an indirect way through the activity coefficient.
22
The molar fraction of solute, xi, is defined as
xi =
ci
c i + c ch
(36)
where ci, and cch are molar concentrations of the chromatographed substance and the stationary
phase (i.e., of the "solute" and "solvent"), respectively, in the chromatographic spot; ci, and cch, can
further be defined as
ci =
ni
n
and c ch = ch
vi
vi
(37)
where ni and nch are the molar aliquots of "solute" and "solvent", respectively, contained in the
chromatographic spot, and vi is the spot volume (see Fig. 7).
Assuming thermodynamic equilibria within the thin-layer chromatographic system and the
nonsymmetrical way of expressing the chemical potential of the "solute", its activity coefficient fi
was derived as equal to
f = 1+
ci
c ch
(38)
Figure 7 The chromatographic spot as a three-dimensional structure (with volume vi)
in chromatographic "binary solution" model.
The approach proposed by Kowalska can be regarded as the only semiempirical model of
the chromatographic process based on the effect of spot broadening, and its practical usefulness
will be discussed in Section V.
F. Kowalska Model of Retention with Use of Multicomponent Mobile Phases
23
The Kowalska model of adsorption and partition chromatography presented in the preceding
subsection was not a proper retention model simply because it did not couple any recognized
retention parameter of the solute with the thermodynamic magnitude of the chemical potential.
However, it positively emphasized the very specific role played by the mobile phase in transfer of
the solute molecules through the chromatographic system. The molecular-level conclusions drawn
with aid of that earlier approach (see Section V.E) plus the systematically growing importance of
the chemically bonded stationary phases (applied in what is formally considered as partition, or
synonymously liquid-liquid chromatography, but what in fact is the liquid-solid or adsorption
mode) gave rise to the unified (adsorption/partition) retention model focused on the
chromatographic systems which employ multicomponent mobile phases.
The new model was first introduced in (19) and aimed at a new physicochemical interpretation to
the Rf coefficient. Accepting the indisputable value of the Rf coefficient for the theory and practice
of chromatography, it must in this place be underlined that the physicochemical contents of this
factor have not as yet been sufficiently studied and utilized. In (20) a new general definition of the
Rf coefficient was given in the following form:
R f = ∑ χ i ⋅β i ⋅ ∆µ i / stph ⋅ q i
(39)
i
where i denotes the mixed mobile phase moieties, χ is the volume fraction of a given moiety, β
denotes the degree of dissociation of the respective H-bonded moiety, ∆µ is the respective standard
chemical potential of the solute partitioning between the ith liquid moiety and stationary phase, and
q is the respective proportionality coefficient. When mentioning the mobile phase moieties it needs
explanation that in the discussed model the recognized thermodynamic concept was introduced of
mentally dividing the multicomponent mobile phases into the individual liquid moieties. For
example, in the methanol-water mixture the three following moieties may be distinguished:
Pure methanol (l);
Pure water (2);
The mixed H-bonded methanol-water moiety (3).
Then the general definition of the Rf coefficient was elaborated into a number of the
particular relationships referring to the common binary (and ternary) mobile phases, employed in
the adsorption and partition chromatography. The most important relationships are listed below:
Mobile phases: Methanol-water and methanol-buffer (21,22):
R f = x1 ⋅ A + x 2 ⋅ B + C
24
(40)
where x1 and x2 are the volume fractions of methanol and water (or buffer), respectively, and A, B,
and C are the equation constants with the profound thermodynamic meaning.
Mobile phases: Acetonitrile-water and acetonitrile-buffer (23,24):
R f = x1 ⋅ A + x 2 ⋅ B + 2.92 ⋅ x 2 ⋅ n"+ x 2 ⋅ C + D
(41)
where x1 and x2 are the volume fractions of acetonitrile and water (or buffer), respectively, A, B, C,
and D are the thermodynamically relevant equation constants, and n" refers to the average
self-associated water cluster.
Mobile phases: Tetrahydrofuran-water and tetrahydrofuran-buffer (25,26):
R f = x1 ⋅ A + x 2 ⋅ B + 4.51 ⋅ x 2 ⋅ n"+ x 2 ⋅ C + D
(42)
where x1 and x2 are the volume fractions of tetrahydrofuran and water (or buffer), respectively, A,
B, C, and D are the thermodynamically relevant equation constants, and n" refers to the average
self-associated water cluster.
Mobile phases: Aliphatic alcohol-n-paraffin hydrocarbon (27):
R f = x1 ⋅ A + x 2 ⋅ B + C
(43)
where x1 and x2 are the volume fractions of alcohol and hydrocarbon, respectively, and A, B, and C
are the thermodynamically relevant equation constants.
V. PRACTICAL CONSEQUENCES OF ESTABLISHED MODELS
Consequences of the established models are manifold, and their importance is both theoretical and
practical. In the following subsections we focus attention on the main practical aspects of the
approaches that have been introduced.
A. Quantification of Sorbent Activity
Sorbent activity depends on the following three parameters:
Specific surface area
Density of the free (i.e., unoccupied) active centers per unit of sorbent surface area
Energy of intermolecular interactions between a solute molecule and a given type of sorbent active
centers
25
Specific surface area depends on the chemical structure of the sorbent (silica, alumina,
cellulose, etc.) and on the technology of its manufacturing. It can be measured and expressed
numerically.
The density of the free active centers per unit of the sorbent surface area also depends on the
chemical structure of the sorbent, and additionally on the number of molecules other than those of
the solute or mobile phase occupying sorbent active centers. These are mostly water molecules,
which block (deactivate) active centers on a sorbent surface, and the degree of deactivation usually
depends on the storage conditions of the precoated chromatographic plates. The density of the free
active centers can also be measured and expressed numerically.
The energy of intermolecular interactions between a solute molecule and a given type of
sorbent active centers depends as much on the chemical nature of the sorbent as on the nature of the
solute itself. Therefore, with a given sorbent the energy of intermolecular interactions differs from
one solute to another.
As can be easily deduced, quantification of sorbent activity cannot be done in the absolute,
but in relative values only. The most complete approach to this problem was derived from the
Snyder-Soczewiński model of adsorption chromatography, and it will be briefly discussed here.
The thermodynamic adsorption coefficient Kth (see Eq. 30a) can be defined in the following
way:
log K th =
∆µ a
2.303RT
(44)
where ∆µa is the chemical potential of adsorption.
Simplifying Eq. 44, we can write:
log K th = ∆E
(44a)
where ∆E (that is, ∆µa/2.303 · RT) is the dimensionless energy of adsorption. It equals the
difference between the energies of adsorption of the solute (EXa) and the solvent (ESa; a
monocomponent mobile phase is assumed). The quantity EXa is a function of the sorbent surface
energy Ai and the physico-chemical properties of a solute X. Similarly, the quantity ESa depends on
the magnitude Ai and on the physicochemical properties of a solvent S. Summing up, we can write:
E Xa = f ( Ai ) ⋅ f ( X )
(45)
E Sa = f ( Ai ) ⋅ f (S )
(45a)
∆E = E Xa − E Sa = f ( Ai ) ⋅ [ f ( X ) − f (S )]
Equation 30a can be rewritten in the following way:
26
(46)
log
1 − R /f
R
/
f
= log
VaWa
+ log K th
Vm − VaWa
(30c)
Combining Eqs. 30c, 44a, and 46, we obtain the relationship:
log
1 − R /f
R
/
f
= log
VaWa
+ f ( Ai ) ⋅ [ f ( X ) − f (S )]
Vm − VaWa
(30d)
This equation can be rewritten in the concise form:
Rm/ = log
VaWa
+ α '⋅ f ( X , S )
Vm − VaWa
(30e)
where α' = f(Ai), and f(X,S) = f(X) - f(S). Thus α' is the function of the sorbent surface energy
independent from the properties of solute. It is known as the activity coefficient of the sorbent, and
determination of its numerical values can be regarded as quantification of sorbent activity.
The right-hand side of equation 30e consists of the three terms that define separate
contributions from the phase ratio, sorbent activity, and the so-called solute-solvent relationship
f(X,S) to the overall retention of solute. The numerical values of Rm, Vm, Va and Wa can be
established experimentally. Two unknowns in Eq. 30e, namely α' and f(X,S), cannot be determined
simultaneously from the same relationship. It was Snyder's (7) idea to overcome this difficult
problem in the following way.
Through intensive drying the sorbent can eventually achieve its full activity, which means
that each active center of a sorbent sample is free from any deactivating water molecules. The
activity coefficient α' of this sorbent is assumed as equal to l. Then the fully active sorbent can
further be used for determination of the solute-solvent relationship f(X,S) with a number of test
solutes. The respective results are collected for the sake of illustration in Table l (28). With the
numerical values of f(X,S) both known and independent from the degree of sorbent deactivation,
one can again utilize Eq. 30a for determination of α' with any given sorbent sample. Obviously, the
numerical values of f(X,S) have to be measured separately for each individual type of sorbent
(silica, alumina, cellulose, etc.) obtained in a given manufacturing procedure.
B. Quantification of Solvent Elution Strength
Solvent elution strength is among the most important factors governing solute retention. Solvents
with too little elution strength are incapable of moving solutes from the origin, while those that are
too strong push solutes with the mobile phase front. In other words, weak mobile phases cannot
27
significantly affect intermolecular interactions between solute molecules and the stationary phase,
while the strong ones practically annihilate such interactions. Therefore, the proper choice of a
single eluent, or eluent mixture, with respect to the analyzed substance and the stationary phase is
crucial for the general outcome of the chromatographic process.
Table 1 Numerical Values of f(X,S) for Test Solutes Chromatographed
in n-Hexane on Alumina and Silica
f(X,S)
Al2O3
SiO2
Styrene
2.34
1.71
Durene
2.30
1.80
Naphthalene
3.10
2.02
Azulene
3.56
2.35
Acenaphthylene
3.65
2.29
Phenanthrene
4.34
2.55
Anthracene
4.60
2.60
Pyrene
4.77
2.57
Fluoranthene
4.94
2.79
Chrysene
5.64
3.09
m-Terphenyl
4.78
3.13
Triphenylene
5.64
3.15
Benzanthracene
5.65
3.09
1,2- or 3,4-Dibenzopyrene
6.40
3.28
Test solute
Source: Data from Snyder (28)
Quantification of solvent elution strength is based on the Snyder-Soczewiński model of
adsorption chromatography. A possibility of appropriate quantification is offered by Eq. 46. For the
sorbent activity coefficient α' = l, Eq. 46 can be rewritten in the following form:
∆E = f ( X ) − f (S ) = f ( X , S )
(46a)
Equation 46a describes the difference between the adsorption energies of solute and
equivalent amount of solvent (one solute molecule can replace one or more solvent molecules on
the sorbent surface, depending on the stoichiometry of a given process). Thus ∆E can be regarded
as the net adsorption energy of the solute. With a simplifying assumption as to the monocomponent
mobile phase we can further write (7):
28
∆E = f ( X , S ) = S 0 − AS ε 0
(47)
where S0 [≡ EXa = f(X)] is the adsorption energy of the solute, AS denotes the cross-sectional area of
its molecule, and ε0 is the adsorption energy of solvent per unit of sorbent surface area
[ASε0 ≡ ESa = f(S)]. ε0 is usually referred to as solvent elution strength, or simply solvent strength.
Equation 47 is a function of three parameters, S0, AS and ε0, and therefore the question arises
how to conveniently express solvent elution strength in terms of ε0. Choosing an aliphatic
hydrocarbon as a test compound, one automatically attains the situation in which S0 ≈ 0. The
quantity AS can be evaluated from the molecular parameters of the test compound. Thus ε0 remains
the only unknown of the simplified relationship
∆E ≈ − AS ⋅ ε 0
(47a)
and it can be established experimentally.
Elution strength of the simplest liquid aliphatic hydrocarbon, n-pentane, is equal to 0, and
this particular solvent begins what is usually called the eluotropic series. Numerical values of
solvent elution strength ε0 determined for the most common chromatographic eluents on alumina
are collected in Table 2. To obtain the analogous set of data for silica, Snyder advises multiplying
the data from Table 2 by a factor of 0.77.
The concept of solvent elution strength ε0 is one way of quantifying solvent polarity. This
polarity is a very important factor in establishing the chromatographically advantageous equilibria
according to the following scheme:
solute
solvent
sorbent
Table 2 The Eluotropic Series of Solvents and Solvent
Elution Strength ε0 Determined on Alumina
Solvent
ε Al0 O
n-Pentane
0.00
n-Hexane
0.01
n-Heptane
0.01
Cyclohexane
0.04
Carbon disulfide
0.15
2
3
29
(48)
Carbon tetrachloridc
0.18
Isopropyl ether
0.28
2-Chlorpropane
0.29
Toluene
0.29
l-Chloropropane
0.30
Chlorobenzene
0.30
Benzene
0.32
Bromoethane
0.37
Diethyl ether
0.38
Chloroform
0.40
Dichloromethane
0.42
Tetrahydrofurane
0.45
1,2-Dichloroethane
0.49
Ethyl methyl ketone
0.51
Acetone
0.56
Dioxane
0.56
Ethyl acetate
0.58
Methyl acetate
0.60
1-Pentanol
0.61
Dimethylsulfoxide
0.62
Aniline
0.62
Nitromethane
0.64
Acetonitrile
0.65
Pyridine
0.71
2-Propanol
0.82
Ethanol
0.88
Methanol
0.95
Ethylene glycol
1.11
Acetic acid
>> l
Source: Data from Snyder (7).
Thus the solvent elution strength ε0 became a cornerstone of the new semiempirical strategy of
predicting multicomponent mobile-phase composition, and this problem will be discussed in the
Section V.D.l.
30
C. Quantification of Solvent Polarity and Selectivity
The main idea of this approach was to compare the variety of solvents mostly used as components
of mixed mobile phases in respect to their polarity and simultaneously as proton acceptors, proton
donors, and intermolecularly interacting dipoles. Three test solutes were selected, upon which the
polarity and selectivity scale was built: ethanol as a model proton donor, dioxane as a model proton
acceptor, and nitromethane as a model strong dipole. Upon an extensive experimental study by
Rohrschneider (29) delivering for the aforementioned three test solutes and over 80 solvents the
solubility constants Kg (the so-called gas liquid partition coefficients of the test solute distributed
between the gas phase and the solvent in a sealed flask and determined by gas chromatographic
analysis of the gas phase) Snyder managed to devise the chromatographically useful scale of the
polarity indices (P') and the selectivity parameters (xi) (13,14). The backbone of his approach was
the following given relationships:
( )
P ' = log K g//
ethanol
( )
+ log K g//
xe =
xd =
xn =
dioxane
( )
log K g//
nitrometha ne
(31)
ethanol
(32a)
dioxane
(32b)
nitrometha ne
(32c)
P'
( )
log K g//
P'
( )
log K n//
( )
+ log K g//
P'
Snyder's principal objective was to remove the dependence of the magnitude Kg on the
molecular weights of solvent and solute (14). The effect of the solvent molecular weight was
removed by multiplying Kg by the molar volume VS (ml/mole) of the solvent, leading to the
partially corrected magnitude K'g:
K g/ = K g ⋅ V S
(49)
The molecular weight effect of the solute on its K'g value can likewise be removed by
dividing K'g by the estimated K'g value (Kv) of an n-alkane whose molar volume is the same as that
of the solute:
K g// =
K g/
(50)
Kv
31
or
log K g// = log K g/ − log K v
(50a)
In this way Snyder "purified" the Rohrschneider's results from the effect of mass interaction,
thus better exposing the energetics of the differentiated intermolecular interactions between solute
and solvent.
Although solvent elution strength (ε0) and its polarity index (P') can be considered as the
two quasi-equivalent ways of quantifying solvent polarity, the physicochemical relevance of P' is
greater, simply because it offers a deeper insight in the nature of these forces which ultimately play
the most crucial role in the displacement mechanism of solute retention, or in the otherwise rather
neglected solute-solvent interactions. In the other words the two different solvents can be equally
polar (thus yielding the similar Rf values of the test solute), and yet considerably different, when
comparing the molecular-level role thereof in the process of retention. This difference usually
results in the differentiated selectivity of separation attained with aid of these two solvents.
D. Optimization of Mobile Phases
Optimization of resolution and selectivity is a practical goal in thin-layer chromatography. The
proper strategy is dictated by Eq. 24:
 K
R S = 0.25 2
 K 1
 
 − 1 ⋅ R f N ⋅ (1 − R f
 
)
(24)
From this relationship it follows that thin-layer efficiency (plate number N) and composition of
mobile phases (monitored through K2/K1 and Rf) can be optimized separately. Enhancement of
thin-layer performance in terms of raising N will be the subject of Section VI, while the approaches
aiming to optimize the composition of mobile phases will be discussed below.
1. Snyder's Approach (Solvent Elution Strength)
The most universal approach is a simple consequence of the idea of solvent elution strength,
introduced by Snyder (7). Combining Eqs. 44a, 46, and 47, we can view the thermodynamic
adsorption coefficient Kth as a function of solvent elution strength, ε0:
(
log K th = α ' S 0 − AS ε 0
)
(51)
If one solute developed in two different monocomponent mobile phases l and 2 using the
same sorbent, the following equations can be written:
32
(
= α ' (S
log K th (1) = α ' S 0 − AS ε 10
log K th ( 2 )
0
− AS ε 20
)
)
(51b)
)
(51c)
(51a)
and finally, subtracting Eq. 51b from 51a, we obtain
log
K th (1)
K th ( 2 )
(
= α ' AS ε 20 − ε 10
where ε10 and ε20 are solvent strength values for solvents l and 2, respectively. Equation 51c allows
comparison of the influence of solvents l and 2 on solute retention, which is indirectly expressed in
the form of the quantities Kth(1) and Kth(2) (see Eqs. 30a and 30b). Proper adjustment of the
numerical Kth values is really important for separation, and the optimum working conditions are
attained within the following range:
1 < K th ⋅
VaWa
≤ 10
Vm
(52)
The practical nature of Eq. 52 is better perceived if it is rewritten in the following way (see
Eq. 30b):
0.1 ≤ R f < 1.0
(52a)
Considering the large number of solutes and complex mixtures that are separated by TLC, it
is necessary to take advantage of multicomponent mobile phases for the better "fine-tuning" of the
necessary retention. The most commonly used are binary and ternary mobile phases, although in
some special cases four-component, or even more complex mixtures, cannot be avoided. To make
the choice of a multicomponent mobile phase less empirical, it would be useful to know in advance
its elution strength ε0. Unfortunately, the experimental determination of ε0 for these phases is
hardly possible, due to the endless combinations of components and their volume ratios.
In the early 1980s, Snyder (30-32) succeeded in deriving appropriate semiempirical
relationships to describe and allow calculation of elution strength ε0 of multicomponent mixtures.
The solvent strength εAB of a binary-solvent mobile phase can be related to the mole fraction
of the stronger solvent B (NB) in the mobile phase, the ε0 values of two pure solvents that constitute
the mobile phase (εA and εB) and the area nb required by a molecule of solvent B on the sorbent
surface:
ε AB
(
log N B ⋅10 α 'nb (ε B −ε A ) + 1 − N B
=εA +
α '⋅n b
33
)
(53)
The solvent strength εAB of a binary-solvent mobile phase can also be related to the
thermodynamic adsorption coefficients Kth of some solute in that mobile phase (KAB) and in pure
solvent (KA):
KA
K AB
=εA +
α '⋅ A S
log
ε AB
(54)
The quantity AS, which is the molecular area of the solute, can have any value, so let it equal
nb:
KA
K AB
=εA +
α '⋅n b
log
ε AB
(54a)
Relationships analogous to Eq. 54a are valid in the case of ternary, quaternary, and even
more complex mobile phases:
KA
Km
εm = ε A +
α '⋅n b
log
(54b)
where εm is the solvent strength of a multicomponent mobile phase and Km is the thermodynamic
adsorption coefficient of some solute in that phase.
In the case of simple solutes (e.g., aliphatic hydrocarbons) showing adsorption energies
S0 ≈ 0, the quantities εAB and εm can help to predict the Rf parameter. Combining Eqs. 30b and 51,
1
Rf ≈
10
−α '⋅ AS ⋅ε 0
VW
⋅ a a
Vm
(55)
where ε0 is the solvent strength of a multicomponent mobile phase (εAB for the binary phases and εm
for more complex ones).
Predictions of solvent elution strength ε0 and the retention parameter Rf made with the help
of Eqs. 53-55 cannot be regarded as error-free. The observed differences between the experimental
and calculated ε0 and Rf values are in the first instance due to the simplicity of the assumed
intermolecular interactions model in systems composed of solute, solvent, and mobile phase (see
Eqs. 45, 45a, and 46). In fact, the model discussed fully ignores self-association of solute and
solvent, as well as mixed intermolecular interactions simultaneously engaging the solute and the
mobile phase. For the aforementioned reason the most successful optimization of the mobile phase
can be attained for these solutes and solvents that are practically unable to interact intermolecularly
34
(such as hydrocarbons). Still, the importance of Snyder's approach is undeniable as an
easy-to-apply strategy for multicomponent mobile-phase optimization.
2. Snyder's Approach (Solvent Polarity and Selectivity)
Analogous to the eluotropic series presented in Table 2, Snyder managed to compare
solvents according to their polarity indices (P') (13,14). In Table 3 an example is given of this
alternative comparison, showing the polarity indices (P') and the selectivity parameters (xi) of the
selected common liquids.
Physicochemical relevance of the selectivity parameters concept gained a convincing
experimental confirmation in this sense that among the solvents of similar functionality the
strikingly great similarity of the selectivity parameters was observed (14) (see Table 4). This
observation can be translated into the language of the molecular-level phenomena as the best proof
of the predominant importance of functionality in the intermolecular interactions of the
solute-solvent and the stationary phase-solvent type.
Table 3 The Polarity Indices (P') and the Selectivity Parameters (xe, xd, and xn)
of the Selected Solvents
Solvent
P'
n-Hexane
0.1
Cyclohexane
0.2
Carbon sulfide
0.3
Carbon tetrachloride
1.6
Isopropyl ether
xe
xd
xn
2.4
0.48
0.14
0.38
Toluene
2.4
0.25
0.28
0.47
Chlorobenzene
2.7
0.23
0.33
0.44
Benzene
2.7
0.23
0.32
0.45
Diethyl ether
2.8
0.53
0.13
0.34
Chloroform
4.1
0.25
0.41
0.33
Dichloromethane
3.1
0.29
0.18
053
Tetrahydrofuran
4.0
0.38
0.20
0.42
1,2-Dichloroethane
3.5
0.30
0.21
0.49
Ethyl methyl ketone
4.7
0.35
0.22
0.43
Acetone
5.1
0.35
0.23
0.42
35
Dioxane
4.8
0.36
0.24
0.40
Ethyl acetate
4.4
0.34
0.23
0.43
Dimethyl sulfoxide
7.2
0.39
0.23
0.39
Aniline
6.3
0.32
0.32
0.36
Nitromethane
6.0
0.28
0.31
0.40
Acetonitrile
5.8
0.31
0.27
0.42
Pyridine
5.3
0.41
0.22
0.36
2-Propanol
3.9
0.55
0.19
0.27
Ethanol
4.3
0.52
0.19
0.29
Methanol
5.1
0.48
0.22
0.31
Ethylene glycol
6.9
0.43
0.29
0.28
Acetic acid
6.0
0.39
0.31
0.30
Water
10.2
0.37
0.37
0.25
Source: Data from Snyder (14).
Table 4 Similarity of Selectivity Parameters of Solvents of Similar Functionality
Average parameters values
xe
xd
xn
Alcohols
0.54 ± 0.03
0.19 ± 0.01
0.27 ± 0.02
Alkyl ethers
0.48 ± 0.05
0.15 ± 0.03
0.37 ± 0.02
Ketones
0.35 ± 0.01
0.22 ± 0.01
0.42 ± 0.01
Esters
0.34 ± 0.00
0.25 ± 0.01
0.41 ± 0.01
Phenyl alkyl ethers
0.27 ± 0.01
0.30 ± 0.02
0.43 ± 0.01
Aromatic hydrocarbons
0.25 ± 0.02
0.29 ± 0.02
0.46 ± 0.01
Solvent
functionality
Source: Data from Snyder (14).
Upon careful consideration of the selectivity parameters (xi) Snyder managed to divide
solvents into 8 classes of the similar compounds (see Table 5 and Fig. 8).
In the case of the liquid binary mixtures (composed of the solvents A and B) the respective
polarity index (P'AB) shows a straight-line dependence on its composition (13):
36
/
PAB
= φ A ⋅ PA/ + φ B ⋅ PB/
(56)
where φA and φB are, respectively, the volume fractions of the solvent A and B, and P'A and P'B are
the respective polarity indices of the individual solvents.
Optimization of the chromatographic process with aid of the Snyder concept of solvent
polarity and selectivity in fact means optimization of the separation selectivity. This goal can be
attained with help of the so-called isoeluotropic mixtures, i.e. of the mixed eluents which in spite of
composition different from that of the original eluent preserve equal elution strength.
Let us consider the adsorption and the normal-phase partition chromatography systems
employing binary mobile phases composed of the solvents A and B (with the nonpolar solvent A,
for which P ≈ 0). If we want to change the separation selectivity of this system, the simplest way is
to employ the isoeluotropic mixture in which solvent B is replaced by solvent C. The volume
fraction of solvent C can be estimated from the relationship:
φC = φ B ⋅
PB/
for φ A ⋅ PA/ ≈ 0
/
C
P
(57)
If we want to change selectivity of the mixed mobile phase in the reversed-phase partition
chromatography mode, we also need to employ the isoeluotropic mobile phase. The common
strategy is to replace the less polar component of the starting binary mixture by another solvent.
E.g., if the starting eluent was the methanol-water mixture, methanol has to be replaced by
acetonitrile or tetrahydrofuran. Then the volume fraction of the new solvent can be estimated from
the relationship:
φC = φ B
SB
SC
(58)
where S B = Pw/ − PB/ ; S C = Pw/ − PC/ ; the subscripts w, B, and C refer to water, solvent B, and
solvent C, respectively.
Table 5 Classification of Solvent Selectivity
Group
I
Solvents
Aliphatic ethers, tetramethylguanidine, hexamethyl phosphoric acid amide,
trialkyl amines
II
Aliphatic alcohols
37
III
Pyridine derivatives, tetrahydrofuran, amides (except formamide), glycol
ethers, sulfoxides
IV
Glycols, benzyl alcohol, acetic acid, formamide
V
Methylene chloride, ethylene chloride
VI
(a) Tricresyl phosphate, aliphatic ketones and esters, polyethers, dioxane
(b) Sulfones, nitriles, propylene carbonate
VII
Aromatic hydrocarbons, halo-substituted aromatic hydrocarbons, nitro
compounds, aromatic ethers
VIII
Fluoroalkanols, m-cresol, water, chloroform
Source: Data from Snyder (14).
Figure 8 Selectivity grouping of solvents (see Table 5) (14).
Other approaches for the prediction of binary-solvent mobile-phase strength have been described
by Polish workers (12, 19-27, 33-37) and by Scott and Kucera (15,16). Following is a brief review
of these approaches.
38
3. Soczewiński's Approach
Soczewiński's approach (12) to optimization of mobile phases for adsorption
chromatography can be regarded as a special case of the more general treatment of Snyder. It
assumes that the decisive step in the chromatographic process is hydrogen bonding between the
molecules of solute Z, solvent S, and the active centers A on the sorbent surface, leading to the
dynamic formation of complexes AZ, AS, and SZ:
Z+A
S+A
Z+S
KAZ
AZ
KAS
AS
KSZ
SZ
(59)
This premise permits application of the law of mass action, assuming further that solute and
solvent are not self-associated, that is, KZZ = KSS = 0.
When l : l complexes are formed (AZ, AS, and SZ) and the polar solvent S is diluted with an
inert solvent N (e.g., an aliphatic hydrocarbon), then a simple relationship is obtained for the
quantity Rm of solute Z:
R m = log
1− R f
Rf
= log
K AZ ⋅ x AS
x AZ
= log
x Z + x SZ
K AS ⋅ x S ⋅ (1 − K SZ ⋅ x S )
(60)
where x denotes molar fraction. For example, xAZ is the concentration of the molecules of solute Z
temporarily immobilized by hydrogen bonding with sorbent surface. It is assumed that the
probability of adsorption of solvated molecules (SZ) is much lower than that of molecules that are
nonsolvated (Z).
If it is additionally assumed that the solute is only weakly solvated by the solvent (xSZ = 0,
KSZ = 0), then Eq. 60 simplifies to:
R m = log
K AZ ⋅ x AS
K AS ⋅ x S
(60a)
Equation 61a can be rewritten in the following form:
R m + log
 1− R f xS
xS
= log
⋅
 R
x AS
x AS
f


 = log K AZ − log K AS


which is identical with Snyder's Eq. 46a, because
 1− R f xS
log K th = ∆E = log
⋅
 R
x AS
f

39




(60b)
S 0 = log K AZ
AS ε 0 = log K AS
4. The adsorption–partition model
Another approach was introduced to enable modeling of solute retention in TLC with
chemically bonded stationary phases (37). The authors of this model intended to reflect the
physicochemical nature of the retention process more closely than in any other approach currently
used. This retention model is capable of quantitative description of the two parallel processes
occurring in the course of solute migration through the stationary phase bed. One of these
complementary processes can be described as intermolecular interaction of a solute with the
chemically bonded organic ligands, according to the classical Snyder–Soczewiński model.
On the basis of this long-accepted assumption, the amount of the adsorbed solute can be
expressed as:
q1, = K ⋅ c1 where K = exp( p1 + p 2 ⋅ ϕ )
(61)
where q′ denotes the concentration of the solute molecules physically (e.g. as a result of dispersive
forces) connected to the chemically bonded ligands; c1 denotes the concentration of this solute in
the mobile phase; ϕ is the volume fraction of the active (i.e. strong) liquid component of the
mobile phase; and p1 and p2 are the equation constants.
The competitive process consists in intermolecular (mostly polar) interactions of a solute
with the free (i.e. non-bonded) silanols on the surface of the silica matrix. This complementary
mechanism was modeled with the aid of a simple stoichiometric isotherm, taking into the account
the adsorption both of the solute molecules and of the components of a mixed mobile phase:
q1'' =
q s K1c1
K1c1 + K 2 c2 + K 3 c3
(62)
where c1, c2, and c3 are concentrations of the solute and of the components of the binary mobile
phase, respectively, qs is the saturation capacity of solid phase, and K1, K2, and K3 are the
equilibrium constants for the solute and the mobile phase components, respectively. Because of the
typically very low concentrations of the solute, the first term in denominator can be ignored.
The overall mechanism of solute retention is given as a sum of the two contributions:


q s K1
c1
q1 = q1' + q2' =  exp( p1 + p2ϕ ) +
K 2 c2 + K 3c3 

40
(63)
It is well established that the retention coefficient k is proportional to the derivative of the
solute concentration in the solid phase with respect to the solute concentration in mobile phase:
k =Φ
∂q1
∂c1
(64)
The proportionality factor Φ (usually referred to as the phase ratio) is the volume ratio of
stationary phase to mobile phase.
Keeping in mind that the retardation factor Rf is defined as Rf = 1/(1+k) and assuming that
the mobile phase components form an ideal mixture, from Eqs 63, 64 the following relationship for
Rf can finally be derived (37):
Rf =
1
1
1 + exp( p1 + p 2ϕ ) +
p 3ϕ + p 4 (1 − ϕ )
(65)
where the phase ratio Φ is incorporated in the unknown terms pi. The performance of this model
was extensively tested on many experimental results (37) taken from the literature and relating to
(a) the chemically bonded 3-cyanopropyl stationary phase with 2-propanol–n-hexane as mobile
phase (NP TLC), (b) the chemically bonded octadecyl stationary phase with methanol–water as
mobile phase (RP TLC), (c) silanized silica with methanol–water as mobile phase (RP TLC), and
(d) silanized silica impregnated with paraffin oil as stationary phase and methanol–water as mobile
phase (RP TLC).
An outcome of this test led to the general conclusion that the fit of the experimental data to
Eq. 65 was outstanding. A typical comparison of experimental and theoretically predicted data is
shown in Fig. 9.
41
Rf
1 .0
0 .8
0 .6
0 .4
0 .2
0 .0
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
-1
φ [m o l L ]
Figure 9 Relationship between Rf and
ϕ for 1-naphthol chromatographed in system (a).
5. Other Approaches
The general approach to solute distribution between the stationary and mobile phases
proposed by Scott and Kucera (15,16) can also find application in the prediction of elution strength
with binary-solvent mobile phases. To demonstrate such a possibility, Eq. 33c is rewritten in the
following way:
F p f 3 (T )c p
Fd f 4 (T ) Ad
1
= /
+ /
/
/
/
K th F p f 1 (T )c p + Fd f 2 (T )c d F p f 1 (T )c /p + Fd/ f 2 (T )c d/
(33e)
Then it is assumed that in the case of binary mobile phases composed of one low-polar and one
semipolar or high-polar solvent, the polar forces acting in that mobile phase on solute molecule are
due basically to the polar component, while the dispersive forces are due mostly to the low-polar
component.
To examine the influence of different concentrations of polar or semipolar solvent in the
same dispersing medium (e.g., an aliphatic hydrocarbon) on solute retention, Eq. 33e can be given
in a simplified form:
1
= a⋅cp + b
K th
(33f)
where a and b are equation constants.
It is the minimum of two known concentrations of polar solvent (cp) that allow
establishment of numerical values of a and b for a given solute, stationary phase, and dispersing
42
(i.e., nonpolar) medium. With the numerical values of a and b already established, the Rf value for
any further concentration of the same polar solvent can be predicted according to the following
relationship (see Eq. 30b):
Rf ≈
V m (a ⋅ c p + b )
VaWa
(66)
If, on the contrary, it is intended to examine the influence of the changing dispersive forces
on solute retention, then Eq. 33e can be rewritten as
1
= a'⋅d + b'
K th
(33g)
where a' and b' are equation constants.
Polar interactions must be kept constant, which means that for a given phase system, cp of
the polar component must be kept constant. Dispersive forces are changed through changing the
low-polar component of the binary mixture (e.g., the hydrocarbon). For two different low-polar
components, numerical values of a' and b' (characteristic of a given solute, stationary phase, and
polar solvent) can be established. With these data, the solute Rf value for a binary mobile phase
with still another low-polar solvent can be predicted (cp of the polar component has to be
maintained constant). The basis of such prediction is furnished by the dependence:
Rf ≈
V m (a '⋅d + b')
V aW a
(66a)
Good correlation was observed between experimental Rf values and those predicted
according to the assumed theoretical model (15,16).
The Kowalska model of solute retention with use of the multicomponent mobile phases
(19-27) points out the fact that the generally accepted interpretation of the Rf coefficient does not
fully exhaust the potential physicochemical contents of this factor, the statement that anticipates the
eventual future models also immersed in the fundamentals of physical chemistry, but refraining
from the assumptions made by Martin and Synge, and by their successors.
Moreover, the relationships making part of the Kowalska model (e.g., Eqs. 40-43) are - contrary to
the relationships offered by the other approaches discussed in this chapter - more flexible and hence
more accurate, due to the fact that they (i) strongly depend on the chemical nature of the mixed
mobile phases, and (ii) couple together the Rf coefficient with the mobile phase composition in a
manner which is nonlinear by principle (the important feature that does not always occur with the
remaining models of solute retention, no matter how much this nonlinearity was closer to the
empirical practice of chromatography than the assumed straight-line simplifications). Thus it seems
reasonable to expect that Eqs. 40-43 can be employed in the interpretational methods of selectivity
43
optimization at least as successfully, as any other already established retention model, and
occasionally even significantly better than them.
E. Considerations on the Molecular Level
1. Role of Intermolecular Interaction Based of Chemical Potential Concept
Assuming the additive nature of chemical potential, the basic relationship of Kowalska's model (see
Section IV.E) can be rewritten in the following way:
ln x i f i =
∑ ∆µ
( k )i
k
(35a)
RT
where ∆µ(k)i is the partial change of the chemical potential accompanying the transfer of the kth
molecular fragment of the ith solute from the origin to the chromatographic system (calculated per
mole of the kth fragment). Thus ∆µ(k)i is an energetic measure of the efficiency of intermolecular
interactions between this fragment and the rest of the chromatographic system, considered as a
whole. Table 6 gives an example of the numerical values of ∆µ CH2 and ∆µ OH determined for a
homologous series of fatty alcohols on stationary phases of increasing activity using mobile phases
of increasing polarity.
As can be seen from Table 6, the energetic values, which are not dimensionless and relative
but on the contrary are absolute, are more persuasive and can be better integrated with general
knowledge of physical chemistry. Two border cases of ∆µ OH obtained on the low- and high-active
sorbent with use of a low- and high-polar mobile phase, can be considered. Values range from ca.
+15 to -15 kJ/mole, which coincide well with the absolute value of the hydrogen bond enthalpy for
alcohols. This fact can be interpreted in the following way. An alcohol sample on the origin of a
chromatogram can be regarded as a quasipure substance, forming chain-like self-associates:
R
R
R
R
O H O H O H O H
In this way practically each OH group is simultaneously involved in two hydrogen
bondings. Transfer of alcohol to the low-polar/low-active chromatographic system involves
dissociation of the chain multimers (disruption of two hydrogen bonds), followed by intermolecular
interaction with the sorbent active center (formation of one hydrogen bond). The balance of this
process is disruption of one hydrogen bond, which in energetic terms equals +15 kJ/mole.
44
Transfer of alcohol to the high-polar/high-active chromatographic system proceeds through
the identical initial stage, i.e., through dissociation of the chain multimers, which results in
disruption of two hydrogen bonds. Then the alcohol OH groups form one hydrogen bond to anchor
on the sorbent surface, and the remaining two with molecules of polar solvent (there is a maximum
of three hydrogen bonds in which one OH group can be involved). Thus, in this case the balance is
formation of one hydrogen bond, which corresponds to -15 kJ/mole. The scheme below in Fig. 10
furnishes an illustration of the aforementioned differentiated behavior of the OH group in
chromatographic systems differing profoundly in the activity of sorbents and the polarity of mobile
phases.
45
Table 6 Numerical Values of ∆µ CH and ∆µ OH for the Homologous Series of Fatty Alcohols on
2
Stationary Phases of Increasing Activity Using Mobile Phases of Increasing Polarity
∆µ CH2
Stationary phase
Mobile phase
∆µ OH
(kJ/mole) (kJ/mole)
Cellulose paper
Decalin
-0.57
+15.12
Cellulose powder
Decalin
-0.22
+11.16
Magnesium silicate
C6H6 + (CH3)2CO, 9:1 (v/v)
-0.28
-7.79
Alumina
C6H6 + (CH3)2CO, 9:1 (v/v)
-0.12
-12.46
Silica
C6H6 + CH3OH, 9:1 (v/v)
0
-15.31
Source: Data from Kowalska (38,39).
The example discussed in this section is a rare case, in which we can deduce on a molecular level
the nature of the chromatographic process investigated even if the applied model is macroscopic.
O
-15 kJ/mole
H
high polar/
high active
system
O
+15 kJ/mole
H
chain multimer
(quasi-pure substance at start)
O
H
low-polar/
low-active
system
Figure 10 Behavior of an OH group in chromatographic systems differing with respect to sorbent activity and
mobile-phase polarity.
2. Role of Intermolecular Interactions - Multilayer Adsorption
When higher fatty acids are chromatographed on cellulose powder with a non-polar mobile
phase the densitograms obtained are similar to those presented in Fig. 11 (43,44). Higher fatty acids
form associative multimers by hydrogen bonding, because of the presence of the negatively
polarized oxygen atom from the carbonyl group and the positively polarized hydrogen atom from
the carboxyl group. Direct contact of the higher fatty acids with an adsorbent results in forcible
opening of the rings of most the cyclic dimers (e.g., because of inevitable intermolecular
46
interactions as a result of hydrogen bonding with the hydroxyl groups of the cellulose), thus
considerably shifting equilibrium of self-association towards the linear associative multimers.
A
-1
0.5 mol L
-1
0.06
0.25 mol L
0.04
-1
0.1 mol L
0.02
0
0
20
40
80 d [mm]
60
Figure 11 Densitograms obtained for succinic acid. Sample concentrations were: 0.1, 0.25, and 0.5 mol L–1.
Stationary phase: cellulose, mobile phase: 1,4-dioxane.
The capacity of carboxylic acid analytes to form associative multimers (which can also be
viewed as multilayer adsorption) is a cornerstone of the approach introduced (43,44). This
phenomenon was depicted with the aid of the three similar isotherm models; the most convincing is
founded on the following premises:
•
Analyte molecules are adsorbed on the active sites of an adsorbent. The kinetic rates of
adsorption and desorption are infinitely fast.
•
Analyte molecules are adsorbed on a previously adsorbed monolayer. The kinetic rates of
dimerization and dimer dissociation (i.e. of the reverse process) also are infinitely fast.
•
This chain process of the stepwise building of the consecutive adsorption layers can be
continued ad infinitum.
These assumptions lead to the derivation of the isotherm equation (44):
KC (1 + 2 K p C + 3(K p C ) ....)
2
q = qs
1 + KC + KCK p C + KC (K p C ) ....
2
(67)
where K is the equilibrium constant for the adsorption–desorption process on the active sites of the
adsorbent, Kp denotes the equilibrium constant for dimerization, trimerization, etc., q is the
concentration of analyte on the adsorbent surface, qs is the saturation capacity, and C is the
concentration of analyte in solution.
47
The possibility of qualitative modeling of the experimentally observed peak profiles, presented
in Fig. 11, was evaluated on the basis of the model (43,44):
∂q
∂C
∂C
∂ 2C
∂ 2C
D
+w
+Φ
= Dx
+
y
∂t
∂x
∂t
∂x 2
∂y 2
(68)
with the assumed boundary conditions:
∂C
∂x
=
x =0 , x = x1
∂C
∂y
=0
(69)
y = 0 , y = y1
where w is the average flow rate of mobile-phase, C and q are, respectively, the concentrations
[mol dm–3] of analyte in the mobile phase and on the adsorbent surface, Dx and Dy are, respectively,
the effective diffusion coefficients lengthwise (x) and in the direction perpendicular to the plate axis
(y), Φ is the so-called phase ratio, and x1 and y1 are the plate length and width, respectively. It was
assumed that at time t = 0 analyte is concentrated in a rectangular spot at the start of the
chromatogram.
The simulation depicted in Fig. 12 was obtained by solution of model (Eq. 68) in conjunction
with isotherm (Eq. 67) and assuming three-layer adsorption as a maximum. Constants in the
equation of the adsorption isotherm, and the effective diffusion coefficients, were chosen to
reproduce the shapes of the lengthwise cross-sections of the chromatographic bands obtained in the
experimental densitograms (Fig. 11)
-1
A
0.5 mol L
0.08
0.06
-1
0.25 mol L
0.04
0.02
0.1 mol L
0
0
20
40
60
80
-1
d [mm]
Figure 12 Lengthwise cross-section of the simulated chromatogram, according to the model given by Eq. 68 in
conjunction with the isotherm given by Eq. 67. Concentrations of the applied solutions were 0.5, 0.25, and
0.1 mol L–1.
48
From Fig. 12 it is apparent that the adsorption fronts are considerably less steep than the
desorption fronts, and that the adsorption fronts simulated for different initial concentrations of the
spots overlap. Similar behavior is apparent in the typical experimental densitograms, given in
Fig 11. In all these densitograms the adsorption fronts for the different concentrations of acid also
overlap. The experimental Rf values determined in the two alternative ways, i.e. from the
concentration profile maxima and from the gravity centers of chromatographic bands, also decrease
with increasing analyte concentration (43,44). Such behavior of the Rf coefficients, qualitatively
consistent with the theoretical data presented in Fig. 12, cannot be explained by assuming classical
Langmuir, Freundlich, or similar isotherms.
Satisfactory qualitative agreement between the experimental and theoretical concentration profiles
of polar analytes suggests that their retention is substantially affected by lateral interactions, which
are probably even more complex than is assumed in this isotherm model. Overlapping of the
adsorption fronts and the behavior of the Rf coefficients can be explained only on the basis of
lateral interactions among the adsorbed molecules.
VI. ATTEMPTS TO ENHANCE THIN-LAYER PERFORMANCE
Enhancement of thin-layer performance is basically understood as elevation of the theoretical plate
number N for a given type of chromatographic plate. The quantity N was defined in Section III.A as
N=
l
H
(15)
From Eq. 15 it can be seen that an increase of N can be attained in two ways, i.e., through elevation
of l or lowering of H.
Prolongation of the migration path l is usually achieved through a continuous flow of the
mobile phase along the length of the chromatographic plate. This continuous development can be
done using the traditional stationary phases or supports.
Lowering of the quantity H cannot, however, be achieved while maintaining the basic
physical parameters of the chromatographic system unchanged. Suppression of the theoretical plate
height H can be done through lowering of the diameter of the solid bed particles dp (see Eqs. 17 and
19), and through lowering of the thickness of the stationary phase layer df (see Eq. 20). Practical
transformation of these conclusions into independent chromatographic techniques is briefly
sketched in the following sections.
49
A. High-Performance Thin-Layer Chromatography
It is not the aim of this section to present any details of the history or state-of-the-art procedures for
HPTLC. HPTLC is a relatively young thin-layer technique (established about 1974), which is still
undergoing improvements and gains in popularity. According to Kaiser (40), HPTLC involves the
combined action of several variables, including:
An optimized coating material with a separation power superior to the best HPLC separation
material
A new method of feeding the mobile phase
A novel procedure for layer conditioning
A considerably improved dosage method
A competent data acquisition and processing system
The secret underlying an optimized coating is a perfectly uniform surface of the thin layer.
This can be attained using fine-particulate sorbent materials in the adsorption mode, or very fine
and spherical nonporous SiO2 carriers with a bonded chemical phase in the partition mode. These
microparticulate solids additionally demonstrate a narrow distribution of particle dimensions (i.e.,
all particles are of practically equal size), which allows a much greater density of packing of the
HPTLC layers compared with normal ones. Thus, one can easily understand that the enhanced
performance of HPTLC is mainly due to lowering of the quantities dp and df (Eqs. 17, 19, and 20),
when compared with regular thin-layer chromatography. In other words, HPTLC takes advantage
of lowering of the quantity H.
B. Overpressured Thin-Layer Chromatography
The overpressured thin-layer mode of planar chromatography was introduced by Hungarian
scientists (41,42) in the 1970s. In overpressured thin-layer chromatography (OPTLC) the vapor
phase has been eliminated, the sorbent layer being completely covered with an elastic membrane
under external pressure. Thus the mobile phase migrates through the thin layer due to the "cushion
system" at overpressure. In this way OPTLC combines advantages of the continuous development
technique, mentioned before (elevation of l), with elimination of the free space in the
chromatographic chamber, which is also typical of the column techniques. This is done in an effort
50
to enhance the theoretical plate number N of a regular thin layer, although high-performance plates
are used as well.
C. Centrifugal-Layer Chromatography
Centrifugal-layer chromatography (CLC) (45) is a preparative circular chromatographic technique
in which the eluent flow is induced by centrifugal force. The sample is applied near the center of a
rotating disk covered with adsorption material. Concentric zones of substances migrate toward the
outside of the plate during elution. The circles elute sequentially from the disk and can be
recovered separately. Thus CLC can also be regarded as a continuous development mode (elevation
of l).
51
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