Theory and Mechanism of Thin-Layer Chromatography Teresa Kowalska, Krzysztof Kaczmarski, Wojciech Prus. Table of contents

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1 Theory and Mechanis o Thin-Layer Chroatography Teresa owalska, rzyszto aczarski, Wojciech Prus Table o contents I. INTODUCTION II. BASIC PHYSICAL PHENOMENA A. Capillary Flow B. Broadening o Chroatographic Spots C. Volatility o Solvents III. MEASUES OF CHOMATOGAPHIC SYSTEM EFFICIENCY A. Model o Theoretical Plates B. Van Deeter Equation C. Separation and esolution D. Selectivity o Separation IV. SEMIEMPIICAL MODELS OF PATITION AND ADSOPTION CHOMATOGAPHY A. Martin-Synge Model o Partition Chroatography B. Snyder-Soczewiński Model o Adsorption Chroatography C. Snyder Concept o Solvent Polarity and Selectivity D. Scott-ucera Model o Adsorption Chroatography E. owalska Model o Adsorption and Partition Chroatography F. owalska Model o etention with Use o Multicoponent Mobile Phase V. PACTICAL CONSEQUENCES OF ESTABLISHED MODELS A. Quantiication o Sorbent Activity B. Quantiication o Solvent Elution Strength C. Quantiication o Solvent Polarity and Selectivity D. Optiization o Mobile Phases. Snyder's Approach (Solvent Elution Strength). 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. ole o Interolecular Interactions Based o Cheical Potential Concept. ole o Interolecular Interactions - Multilayer Adsorption VI. ATTEMPTS TO ENHANCE THIN-LAYE PEFOMANCE A. High-Perorance Thin-Layer Chroatography B. Overpressured Thin-Layer Chroatography C. Centriugal-Layer Chroatography EFEENCES

2 Theory and Mechanis o Thin-Layer Chroatography Teresa owalska, rzyszto aczarski, Wojciech Prus 3 Silesian University, atowice, Poland zeszów Universiy o Technology, Poland 3 University o Technology and the Arts in Bielsko-Biała, Poland I. INTODUCTION Chroatographic theory describes the physicocheical relationships governing separations. Usually, seiepirical odels o the chroatographic process that have a relatively siple therodynaic background and give a bulk picture o the physical or cheical phenoena are involved. Macroscopic odels o the chroatographic process cannot irror the respective separation echaniss in any other way. Exceptions to this rule, i any exist, are rather negligible. It is iportant to keep in ind two acts. First, one always has to be aware o the coplexity o chroatographic processes, and consequently o liitations o the existing seiepirical odels. Second, one cannot orget that the study o chroatography theory has only begun relatively recently and that there is uch additional work to be done beore it reaches its ull potential. In this chapter, basic knowledge about iportant physical phenoena in the chroatography will be introduced (Section II), as well as the ain concepts regarding eiciency o separation (Section III). Further, the six overall seiepirical odels o partition and adsorption chroatography will be reviewed (Section IV), and their useulness in everyday laboratory practice will be discussed (Section V). Finally, the reader's attention will be drawn to attepts that have been ade to enhance perorance o thin-layer chroatography (TLC) (Section VI).

3 II. BASIC PHYSICAL PHENOMENA A. Capillary Flow Transer o a obile phase through the thin layer is induced by capillary orces. Stationary phases (in adsorption, size-exclusion, and ion-exchange chroatography) and supports (in partition chroatography) are all icroporous solids showing high speciic suraces (ranging ro ca. 50 g with celluloses to ca. 500 g with silica), and or this reason they can be regarded as capillary aggloerations. Solvents or solvent ixtures contained in the chroatographic chaber enter capillaries o a solid bed, attepting to lower both their ree surace area and their ree energy. The ree-energy gain E o a solvent entering a capillary is given by the ollowing relationship: γv n E () r where γ is the ree surace tension, V n denotes the olar volue o the solvent, and r is the capillary radius. Fro Eq. l it ollows that the capillary radius r is very iportant or capillary low, and a saller radius leads to ore eicient low. Preparation o the coercial stationary phases and supports cannot provide all pores o ideally equal diaeter, which results in certain side eects that contribute to broadening o the chroatographic spots. This proble will be discussed in the next subsection. B. Broadening o Chroatographic Spots The ost characteristic eature o chroatographic spots is that the longer the developing tie and the greater the distance ro the start, the greater their surace areas becoe. This phenoenon is not restricted to planar chroatographic ethods only, but occurs in each chroatographic technique. Spot broadening is due to eddy and olecular diusion, to the eects o ass transer, and to the given echanis o solute retention. Eddy diusion o solute olecules is induced by an uneven diaeter o the stationary phase or support capillaries, which autoatically results in an uneven low rate o the obile phase through the solid bed. In this way soe solute olecules displace aster, while others are retarded, copared with the average displaceent rate o the ajor portion o solute. 3

4 Molecular diusion has nothing to do with the presence o a solid bed in the chroatographic syste. It is the regular diusion in the obile phase, the driving orce o each dissolving process, and or this reason it needs no urther explanation. The eects o ass transer take place separately in the stationary and obile phases. First let us describe the eect in the stationary phase. It can occur that or soe energetic reason a raction o solute olecules is "captured" by the stationary phase a little while longer than the ajor portion o solute. Such retardation results in broadening o a chroatographic spot. Two dierent eects o ass transer are observed in the stagnant and lowing obile phase. Certain aounts o obile phase can be trapped within the partially closed pores, and only gradually and slowly are replaced by a resh portion o eluent. This is what we call the stagnant obile phase. I the solute olecules occasionally "dive" into such a blind pore, they will iss the ain strea o the lowing obile phase that carries the ajor portion o solute. With the lowing obile phase another phenoenon is observed. Those olecules that are in touch with the solid aterial ove ore slowly, while the others, passing through the center o the pores, displace ore quickly. This riction-induced inequality o the low rates additionally contributes to broadening o a chroatographic spot. Mechaniss o solute retention, which are also responsible or spot broadening, dier ro one chroatographic technique to another, and their role in this process is ar less siple than that o diusion and ass transer. All the aoreentioned phenoena, which jointly contribute to spot broadening, used to be described as an eective diusion. This is a convenient ter, which apart ro being concise and inorative, also underlines the act that these phenoena occur siultaneously. Spot broadening results in ass distribution o solute in a given chroatographic spot. This distribution is presented by a respective concentration proile, which in practice can be established densitoetrically. In Fig. l two exaples o such concentration proiles are shown. Nuerous eorts have been undertaken aiing to establish relevant theoretical odels that 4

5 conc. [gc ] a b Figure Two exaples o concentration proiles: (a) syetrical without tailing, and (b) skewed with tailing. could describe broadening o chroatographic spots and oration o the concentration proiles. The ost interesting odels are those that regard spot broadening as a two-diensional process. Two odels o two-diensional broadening o chroatographic spots were established by Belenky et al. (,) and by Mierzejewski (3). The coon basic concept that enabled elaboration o these two odels in Fick's second law, which describes the velocity o the concentration changes with a substance at a given point o a syste: δc divj δt () where c and t are concentration and tie, respectively, and J denotes the ass lux o the investigated substance. Upon the urther assuptions o Belenky's dynaic odel (,), the ollowing dependence was established, deining concentration o solute at tie t and at the given point o sorbent layer, described by the coordinates x and y (see Fig. ): 5

6 x y start direction o developent Figure The diused chroatographic spot. Illustration o Belenky's and Mierzejewski's odels o spot broadening. ( ) ( ) t D y t v D vt x v D D t q t y x c L L L L exp 4,, τ τ π (3) where q is the total aount o solute in a chroatographic spot; is the basic TLC paraeter introduced in Section III.C o this chapter; D L denotes the eective diusion coeicient that characterizes broadening o a chroatographic spot; v is the igration velocity o the chroatographic spot center; and τ is the paraeter representing a tie lag in establishing equilibriu between the obile and stationary phases (τ is also a unction o the particle size o a solid bed). Fro the ain dependence o Belenky's odel it ollows that the concentration o solute in the chroatographic spot is described by a two-diensional Gaussian distribution unction, which can be rewritten in a sipler or: ( ) + ax exp ),, ( x x y vt x c t y x c σ σ (4) where 6

7 c ax q 4π t DL D + v L τ (5) x DL v t σ + τ (6) σ y D L t (7) Mierzejewski's approach (3) to the proble was dierent. That author introduced our vectors, denoting speed o the two-diensional eective diusion o solute: two o the parallel to ρ the igration direction x but showing the opposite turns ( H x, and H σ x, ), and the analogous two vectors perpendicular to this direction ( H ρ y, and H σ y, ). His relationship or solute concentration at tie t, and at the point described by the coordinates x and y, is given below: c ( x, y, t) ρ σ where g H y t( H y H y, H y, ) ; x ls, j, and i x < l s, j. q ( + ) ( x l ) s exp ( j ) πgw 4g 4 6gw ( H H ) x, + y x, w ; H y x, (8) H x, ; l s v t. Additionally, i H As can be deduced ro Eq. 8, Mierzejewski's odel also describes the concentration o solute in the chroatographic spot by a two-diensional Gaussian distribution that can be presented in a sipler or: where c ( x, y, t) ( + ) ( x ) l ax exp s y c + σ x σ y q cax (0) 4πgw ( j ) σ x 8gw () (9) σ y g () As can be seen by observation o actual thin-layer chroatogras, any experiental concentration proiles can in act be described by the Gaussian distribution curves. 7

8 C. Volatility o Solvents Unlike the situation in colun chroatography, the thin-layer icroporous solid bed stays in unhindered contact with a usually voluinous space o the chroatographic chaber. The so-called sandwich chaber is an exception in this respect. Thereore, in thin-layer chroatography soe special easures need to be undertaken to acilitate achieveent o therodynaic equilibria between the obile-phase coponents in the gaseous and liquid ors. To ake this point clear, let us iagine that to an epty chroatographic chaber we siultaneously introduce obile phase and the chroatographic plate, autoatically initiating the chroatographic process. What happens then in the "ree" roo over the obile-phase surace? First it was occupied by air coponents and water vapors only, but ater adding solvent, or solvent ixture, it starts illing with the obile phase olecules. This process will last until saturation o the "ree" roo with the gaseous obile-phase coponents is copleted. Where do these gaseous obile-phase coponents coe ro? Partially ro the bulk liquid, and partially ro the chroatographic plate surace. In this way we obtain an unwanted change o the obile-phase coposition directly within the solid bed pores. One can iagine how uch this phenoenon aects separation, and how daaging it proves to be or reproducibility o the retention data. The ental experient presented above was aied at explaining the necessity o saturation o the chroatographic chaber with the gaseous obile-phase coponents prior to initiation o the chroatographic process proper. In other words, it was eant to deonstrate indispensability in this process o therodynaic equilibriu between the gaseous and liquid obile-phase coponents. Due to the, evaporation cannot aect the obile-phase coposition in either the bulk or or in the capillaries o the solid bed. Equation 3 gives the therodynaic condition o these equilibria: µ µ i,,..., n (3) i ( g ) i(l ) where µ i(g) and µ i(l) are the cheical potentials o the ith obile-phase coponent in the gaseous and liquid or, respectively, and n denotes the nuber o coponents. In Fig. 3 a schee o the chroatographic syste with the achieved therodynaic equilibria between the gaseous and liquid obile-phase coponents is presented. 8

9 Figure 3 Schee o therodynaic equilibria between the gaseous and liquid obile-phase coponents in a presaturated chroatographic chaber. III. MEASUES OF CHOMATOGAPHIC SYSTEM EFFICIENCY A. Model o Theoretical Plates The odel o theoretical plates originates ro the theory o distillation. It was adapted to chroatography in the pioneer work on the physicocheical oundations o this ethod accoplished by Martin and Synge (4,5). The utility o this odel in the highly sophisticated colun techniques, e.g., gas or high-perorance liquid chroatography, is long and indisputably recognized. The deand or the concept o theoretical plates in thin-layer chroatography seeed lesser in proportion to the coparatively lower separation eiciency o this ethod. In view o the recent and successul attepts to enhance eiciency in this ield also (see Section VI), the idea o theoretical plates applied to thin-layer chroatography or the irst tie becae really and ully relevant. Broadening o a chroatographic spot can be siply expressed in ters o the theoretical plate nuber N o the given chroatographic syste: 6 l z N (4) w 9

10 where l and z are the igration lengths o the obile phase and solute, respectively, and w is the chroatographic spot width in the direction o the obile-phase igration (see Fig. 4). Although the nuerical values o N attained or dierent solutes on the sae chroatographic plate proved to coincide airly well, they usually dier signiicantly ro the analogous values characteristic o another plate type. For this reason, the quantity N can be regarded as an approxiate easure o the separating eiciency o chroatographic plates. It is proportional to the igration length o the obile phase l, so that, the zw ratio being constant, an increase in l results in an increase o N and better separation. This proportionality o N and l is given by the ollowing relationship: l N (5) H where H is the so-called HETP value (i.e., height equivalent o a theoretical plate). The quantity H, or siply the plate height, easures the eiciency o a given chroatographic syste per unit length o the igration distance, l, o the obile phase. Sall H values ean ore eicient chroatographic systes and larger N values. The ain goal o eorts to enhance perorance o thin layers is the attainent o sall H values and axiu N values. As in other chroatographic techniques, the eiciency o a given TLC syste is better (i.e., H is saller) or: Saller particles o stationary phases or supports Lower obile-phase low rates Less viscous obile phases Saller solute olecules B. Van Deeter Equation In the preceding subsection the siplest easure o spot broadening was introduced in the or o the quantity H, or the plate height. One o the ost iportant chroatographic relationships, the Van Deeter equation, attepts to estiate the relative contributions o eddy and olecular diusion, and o the eects o ass transer, on H. It is an epirical equation, originally established or the colun chroatographic techniques, but valid also or thin-layer chroatography. The Van Deeter relationship can be written in the coplete version. H A u 0.33 B + + C u + D u u (6) 0

11 or sipliied, H A u B + C u u or D 0 (6a) where u is the low rate o the obile phase, and A, B, C, and D are the equation constants, easuring contributions o the dierent spot-broadening processes to the quantity H. The eects o eddy diusion and ass transer on the lowing obile phase are described jointly by A. The olecular diusion is relected in B, while C and D correspond to the eects o ass transer in the stagnant obile and stationary phases, respectively. The constants A, B, C, and D depend ostly on the paraeters o the icroporous solid, but they are also inluenced by the nature o the solute and obile phase, and by the working teperature o the chroatographic syste. Each constant o Eq. 6 can be deined as a unction o certain properties o the chroatographic syste. Let us briely review the appropriate epirical relationships. Giddings (6) proposed the ollowing expression or A: A λd p (7) where d p is the diaeter o a solid particle and λ depends on the icroscopic arrangeent o solid bed. B is given as: B γd (8) where D is the diusion coeicient o the solute in the obile phase, while γ is a correction actor irroring the nonlinearity o diusion due to the labyrinth arrangeent o icropores. C is described by the ollowing equation: d p C ω (9) D where ω is a proportionality actor. Siilar to γ in Eq. 8, it also depends on the labyrinthine arrangeent o icropores. D is described by the relationship d D σ (0) D s where d is the thickness o the stationary-phase layer, D s is the diusion coeicient o the solute in the stationary phase, and σ is a proportionality actor.

12 C. Separation and esolution The coeicient is the basic quantity used to express the position o solute on the developed chroatogra. It is calculated as the ratio: obile phase). distance o chroatographic spot center ro start () distance o solvent ro start Using sybols ro Fig. 4, can be given as z (a) l values are between 0 (solute reains on start) and.0 (solute igrates with ront o ront w z l start Figure 4 The thin-layer chroatographic paraeters used in calculation o the theoretical plate nuber N. The traditional (and so ar the only) ethod o deterination o the nuerical values o analyte coeicients quasi-autoatically assues the ollowing preconditions: (a) Circular (or ellipsoidal) chroatographic band shape; and (b) Gaussian distribution o the ass o the analyte in this band. On the basis o these assuptions, the position o a band on the chroatogra is deined

13 by easuring the distance between the origin and the geoetrical center o the band. Despite the considerable iprecision o this deinition or asyetric (i.e., tailing) and non-gaussian bands, two eatures o the deinition are very iportant: (i) The traditional deinition regards the center o a chroatographic band as the point at which the local concentration o the analyte is the highest. (ii) The traditional deinition also regards the center o the chroatographic band as the center o gravity o the ass distribution o the analyte in the band. For the ideal, circular bands with Gaussian analyte concentration proiles, the band centers described by assuptions (i) and (ii) are, in act, identical. For densitogras obtained ro non-circular (i.e. tailing) bands with non-gaussian concentration proiles, it can be stated that: The nuerical value o the coeicient or a given chroatographic band can be deterined or the axiu value o the concentration proile o the band (which is the point at which the local concentration o the analyte is the highest). The coeicient deterined according to this deinition can be denoted as (ax). Alternatively, the nuerical value o the coeicient can be deterined ro the center o gravity o the distribution o analyte ass in the band. With the non-syetrical chroatographic bands, this value cannot be identical with that obtained ro the axiu o the analyte concentration proile. The coeicient deterined in this second anner can denoted (int). To deterine the center o gravity o the analyte ass distribution in the chroatographic band one has to establish the baseline, reove the noise ro the densitogra, subtract the baseline signal, deine the beginning (i 0) and end (i k) o the chroatographic band, and, inally, calculate the position o its center o gravity by use o the relationship: d sr. k di + di I i k di + di di I S i ( d d ) i + d i i i ( d d ) i k di + d I i i d i + d i ( d d ) where S denotes the chroatographic band surace, and I(d i ) is the detector signal at a distance d i. With an increasing ipleentation o the thin-layer chroatographic laboratories with scanners, it sees quite iportant to reconsider deinition o the coeicient and the ways o its practical deterination. i i () 3

14 The ain goal o chroatography is separation o a given solute ixture. However, it can happen that the chroatographic spots o two adjacent solutes overlap to a saller or greater degree. Thereore, a deand arises or a easure o their separation. This deand is ulilled by introduction o the quantity s, called resolution. The resolution s o two adjacent chroatographic spots l and is deined as being equal to the distance between the two spot centers, divided by the ean spot width (Fig. 5); z z ront start w w a b Figure 5 Illustration o resolution in thin-layer chroatography: (a) chroatogra; (b) corresponding concentration proiles o chroatographic spots. z z s w (3) ( w ) The quantity s, serves to deine separation. When s l, the two spots are reasonably well separated. s values larger than l ean better separation, and saller than l poorer separation. In Fig. 6 an exaple is given o separation as a unction o resolution ( s ) and the relative spot concentration (understood as the ratio o the concentration proile axiu heights). Fro the exaple it becoes evident that spot overlap becoes ore disturbing when concentration o solute in one spot is uch greater than in the other. Utilizing the quantity, Eq. 3 can be rewritten in the ollowing way: 4

15 s s [ ] l () () (3a) 0.5 w ( w + ) where () and () are the values o the chroatographic spots l and, respectively. Assuing Gaussian concentration proiles o two closely spaced (i.e., overlapping) chroatographic spots, and ean value or both o the ( () () ), Snyder (7) anaged to transor Eq. 3 to the ollowing or: (I) (II) (III) 0.5 N ( ) (4) S 0.7 S 0.9 S. Figure 6 Separation as a unction o s and the relative spot concentration (the ratio o the concentration proile axiu heights). 5

16 where and are distribution coeicients o solutes l and between the stationary and obile phases ("distribution" is used in a general sense and eans partition, adsorption, or any other phenoenon, depending on the retention echanis o a particular chroatographic technique). Eq. 4 is the thin-layer chroatographic version o a undaental chroatographic relationship that allows discussion o spot resolution in ters o the inluence o, N, and Each o these three quantities is sensitive to changes in the dierent actors, and Eq. 4 akes discussion o their relative iportance or retention possible. Thus can onitor interdependence between the stationary and obile phases,. can onitor elution strength o the obile phase, and N depends on the length o the obile-phase igration and on the plate height (i.e., l and H, respectively). D. Selectivity o Separation Selectivity o separation is seldo reerred to in the case o thin-layer chroatography, although no serious reason can be given or avoiding this ter. To the contrary, selectivity o separation is a useul chroatographic notion, no atter which particular technique, colun or planar, is being considered. In the case o thin-layer chroatography, the separation actor α can be deined as: α (5) which reains in ull conority with the deinition used or the colun techniques. In act, the quantity α akes use o part o ter I in Eq. 4, describing resolution s o two overlapping chroatographic spots. It can be stated that with greater dierence between distribution coeicients o solutes l and ( and ), greater selectivity o separation (α) and better resolution ( s ) are observed. With the two chroatographic spots entirely overlap (α l) and the respective spot resolution s is nil. According to Snyder and irkland (8), several options or increasing α are available, and can be ranked in order o decreasing proise: Change o obile-phase coposition Change o obile-phase ph Change o stationary phase Change o teperature Special cheical eects 6

17 IV. SEMIEMPIICAL MODELS OF PATITION AND ADSOPTION CHOMATOGAPHY Partition and adsorption echaniss o solute retention are the two ost universal echaniss o chroatographic separation, both operating on a physical principle. In act, practically all solutes can adsorb on a icroporous solid surace or be partitioned between two iiscible liquids. It is the ain ai o the seiepirical chroatographic odels to couple the epirical paraeters o retention with the established therodynaic quantities generally used in physical cheistry. The validity o these odels or chroatographic practice can hardly be overestiated, because they oten and successully help to overcoe the old trial-and-error (or, elegantly said, epirical) approach to running the analyses. A. Martin-Synge Model o Partition Chroatography The basic principle o solute retention in partition chroatography is its distribution between the two iiscible liquids. Thereore, partition chroatography oten used to be called liquid-liquid chroatography, even i the liquid stationary phase was substituted by a cheically bonded one. Partition chroatography was irst aong the chroatographic techniques to gain therodynaic oundations, owing to the pioneering work o Martin and Synge (4,5), the 95 Nobel Prize winners in cheistry. It was their siple and siultaneously ruit-bearing idea to ascribe therodynaic eaning to the so-called retardation paraeter o the solute (i.e., ' or the therodynaic coeicient in thin-layer chroatography). The quantity ' is the idealized value, undisturbed by the disadvantageous side eects accopanying the real chroatographic process. ' is related to through the ollowing epirical dependence: ξ (6) where ξ is the disturbance actor [l ξ.6 (9)]. According to Martin and Synge, ' can be viewed as t t + t s n n + n (I) (II) (III) s + s (7) 7

18 where t and t s denote tie spent by a solute olecule in the obile and stationary phases, respectively, n and n s, are nubers o solute olecules equilibrially contained in the obile and stationary phases, and and s are the respective ole nubers. Ter I o Eq. 7 can be understood as the relative tie spent by solute olecules in the obile phase, while ters II and III denote the olar raction o solute in that phase. All the dependences are based on the assuption as to partition equilibriu gained by the syste. Equation 7 can urther be transored in the ollowing way: + s c V c V + c V s s cs V + c V s (7a) where c and c s are olar concentrations o solute in the obile and stationary phases, respectively, while V and V s are volues o these phases. The c s c ratio ro Eq. 7a can be expressed as c s (8) c where is the equilibriu constant o partition, or siply the partition coeicient. Cobining Eqs. 7a and 8, we obtain the inal or o the Martin-Synge dependence: V + V s (7b) This equation unites the retention paraeter o solute, ', with the established physicocheical quantity, its therodynaic eaning being µ p ln (9) T where µ p is the cheical potential o partition. The physical eaning o the partition coeicient is ully analogous to that ro the Nernst partition law, and consequently the nuerical values o obtained in the static experient correspond well with those established chroatographically (0). This act can be regarded as a avorable preise o the approaches aied at prediction o the retention paraeter on the basis o the known therodynaic characteristics o partition. 8

19 B. Snyder-Soczewiński Model o Adsorption Chroatography The basic principle o solute retention in adsorption chroatography is its distribution between the sorbent and the obile phase. For this reason adsorption chroatography is oten called liquid-solid chroatography. The seiepirical odel o adsorption chroatography, analogous to that in Section IV.A, was established only in the late 960s independently by Snyder (7,) and Soczewiński (). The authors assued that soe part o the obile phase rests adsorbed and stagnant on a sorbent surace. This adsorbed obile phase orally resebles the liquid stationary phase in partition chroatography. Thus, instead o an inconvenient necessity o discussing solute concentration on a solid surace, one can introduce a quantity expressing its concentration in the adsorbed obile phase. Otherwise the Snyder-Soczewiński odel beneits ro the partition chroatographic concept o viewing the quantities ' and th (where th is the adsorption equilibriu constant, or siply the therodynaic adsorption coeicient). The ain relationship o the Snyder-Soczewiński odel o adsorption chroatography is t t + t a n n + n a + a c c ( V VaWa ) ( V VaWa ) + cavawa (30) where V a is the volue o the adsorbed obile phase per ass unit o sorbent and W a is the considered ass o sorbent. The inal or o Eq. 30 is + th VaWa V V W a a (30a) where th c a c. In chroatographic practice, usually V a W a << V and th [V a W a (V -V a W a )] >>, and thereore Eq. 30a can be rewritten in a sipliied version: th VaW V a (30b) In ost cases Eq. 30b describes the experiental results well enough, and there is no urgent deand or its coplete or (i.e., or Eq. 30a). The approach to adsorption chroatography proposed by Snyder and Soczewiński proved eective in any respects and enabled quantiication 9

20 o the iportant chroatographic paraeters such as sorbent activity and the elution strength o solvents. These probles will be discussed ore extensively in Section V. C. Snyder Concept o Solvent Polarity and Selectivity The original Snyder-Soczewiński odel assues copetition between the solute and the solvent olecules to the active sites on the solid surace o stationary phase, its outcoe quantitatively related to the net energy o adsorption (i.e. to the dierence between the adsorption energies o the solvent and the solute; or ore details see Sections V.A and V.B). However, the net energy concept encopasses a ore detailed nature o these orces which are responsible or the process o adsorption. This deiciency is a particular shortcoing with the solvents which to a large extent govern solute retention, due to their overwheling excess over the solute olecules in the chroatographic systes. In order to develop a quantitative easure o the solvent's relative ability to interolecularly interact with the solutes as proton acceptors, proton donors, and strong dipoles Snyder established a new seiepirical odel (3,4) coupling the solvent's polarity index (P') with the so-called corrected gas-liquid partition coeicients or solubility constants ( g ") o the selected test solutes: ethanol (a odel proton donor), dioxane (a odel proton acceptor), and nitroethane (a odel strong dipole). The ain relationship o this approach is ( g ) + log( ) log( ) ethanol g dioxane g nitroethane P ' log + (3) where g " is a easure o the excess retention o the given solute (i.e. ethanol, dioxane, and nitroethane) relative to an n-alkane o equivalent olar volue. The individual ters o the trinoial given by Eq. 3 divided by the polarity index (P') are the selectivity paraeters, x e, x d, and x n : ( ) log g ethanol xe (3a) P' ( ) log g dioxane xd (3b) P' ( ) log g nitroethane xn (3c) P' The agnitudes x e, x d, and x n represent the raction o P' contributed by interactions associated with ethanol, dioxane and nitroethane, respectively. 0

21 Although the introduced concept o solvent polarity and selectivity cannot be regarded as a seiepirical odel o the adsorption or partition chroatography in its own rights, it certainly reains in the ainstrea o Snyder's viewing the role o the solvents in the process o retention as a valuable suppleent to the approach presented in the preceding subsection. D. Scott-ucera Model o Adsorption Chroatography The approach o Scott and ucera (5,6) aied to deine the equilibriu constant o solute distribution,, or exaple, th ro Eq. 30a, between the stationary and obile phases in ters o the balance o orces between the olecules o the solute and the olecules o each phase. They deined the distribution coeicient o a solute between the two phases in the ollowing way: rewritten as total orces acting on the solute in the stationary phase total orces acting on the solute in the obile phase orces between solute and stationary phase probability o interactions orces between solute and obile phase probability o interactions Considering the situation with respect to adsorption chroatography, Eq. 33 can be th F F p p ( Pp ) + Fd ( Pd ) ( P ) + F ( P ) p d d (33) (33a) where F p ' and F d ' are the polar and dispersive orces, respectively, between the solute olecules and the stationary phase; F p and F d are the polar and dispersive orces, respectively, between the solute olecules and the obile phase; and P p ', P d ', and P p, P d are the probabilities o the solute olecule interacting with the polar and dispersive oieties o the stationary and obile phases, respectively. The probability o interaction o a solute with one o the phases is soe unction o the absolute teperature, proportional to the concentration o the interacting oieties in each o the respective phases: th p ( T ) c p + Fd ( T ) cd ( T ) c p + F d 4 ( T ) c d Fp (33b) F 3 where c p ', c d ' and c p, c d are the concentrations o polar oieties and dispersive oieties in the stationary and obile phases, respectively, and T is the absolute teperature.

22 I the hypothesis is ade that the dispersive orces result ro ass interaction, then c d is proportional to the density o the dispersing ediu, which can be expressed as a concentration in ters o the ass per unit volue. Thus, c d Ad (34) where A is a constant and d is the density o the low-polar solvent. Inserting Eq. 34 in 33b, we obtain: th ( T ) c p + Fd ( T ) cd ( T ) c + F ( T )Ad Fp (33c) F p 3 p The authors urther assued that the dispersive orces on highly active sorbents, i present at all, do not have a signiicant eect on solute retention, which in the case o, e.g., silica, allows sipliication o Eq. 33c: th d Fp ( T ) c p ( T ) c + F ( T )Ad 4 (33d) F p 3 p d Correlations o the quantity th, as deined by Scott and ucera with the basic retention paraeter o solute, i.e., the coeicient, can be done with the help o Eq. 30a or 30b. 4 E. owalska Model o Adsorption and Partition Chroatography In owalska's approach (7,8) to adsorption and partition chroatography, the basic consequences were drawn ro the eect o spot broadening. The author pointed to the act that broadening o a chroatographic spot occurred due to the eective diusion, and in this respect it resebled dissolving. Thereore the change o the cheical potential accopanying the transer o solute ro the start to the chroatographic syste, µ i, could be given by the ollowing relationship: µ i ln xi i (35) T where x i and i are the olar raction and the activity coeicient o solute, respectively, in the chroatographic "binary solution". The "binary solution" concept assues two coponents o a syste, i.e., "solute" and "solvent". "Solute" is understood in a traditional way as a chroatographed substance, while stationary phase is eant as "solvent". The eects o the obile phase (and in partition chroatography o the support) are expressed in an indirect way through the activity coeicient.

23 The olar raction o solute, x i, is deined as x c i i (36) ci + cch where c i, and c ch are olar concentrations o the chroatographed substance and the stationary phase (i.e., o the "solute" and "solvent"), respectively, in the chroatographic spot; c i, and c ch, can urther be deined as n i c i and vi n ch c ch (37) vi where n i and n ch are the olar aliquots o "solute" and "solvent", respectively, contained in the chroatographic spot, and v i is the spot volue (see Fig. 7). Assuing therodynaic equilibria within the thin-layer chroatographic syste and the nonsyetrical way o expressing the cheical potential o the "solute", its activity coeicient i was derived as equal to c + c i (38) ch Figure 7 The chroatographic spot as a three-diensional structure (with volue v i ) in chroatographic "binary solution" odel. The approach proposed by owalska can be regarded as the only seiepirical odel o the chroatographic process based on the eect o spot broadening, and its practical useulness will be discussed in Section V. F. owalska Model o etention with Use o Multicoponent Mobile Phases 3

24 The owalska odel o adsorption and partition chroatography presented in the preceding subsection was not a proper retention odel siply because it did not couple any recognized retention paraeter o the solute with the therodynaic agnitude o the cheical potential. However, it positively ephasized the very speciic role played by the obile phase in transer o the solute olecules through the chroatographic syste. The olecular-level conclusions drawn with aid o that earlier approach (see Section V.E) plus the systeatically growing iportance o the cheically bonded stationary phases (applied in what is orally considered as partition, or synonyously liquid-liquid chroatography, but what in act is the liquid-solid or adsorption ode) gave rise to the uniied (adsorptionpartition) retention odel ocused on the chroatographic systes which eploy ulticoponent obile phases. The new odel was irst introduced in (9) and aied at a new physicocheical interpretation to the coeicient. Accepting the indisputable value o the coeicient or the theory and practice o chroatography, it ust in this place be underlined that the physicocheical contents o this actor have not as yet been suiciently studied and utilized. In (0) a new general deinition o the coeicient was given in the ollowing or: i χ β µ q (39) where i denotes the ixed obile phase oieties, χ is the volue raction o a given oiety, β denotes the degree o dissociation o the respective H-bonded oiety, µ is the respective standard cheical potential o the solute partitioning between the ith liquid oiety and stationary phase, and q is the respective proportionality coeicient. When entioning the obile phase oieties it needs explanation that in the discussed odel the recognized therodynaic concept was introduced o entally dividing the ulticoponent obile phases into the individual liquid oieties. For exaple, in the ethanol-water ixture the three ollowing oieties ay be distinguished: i i i stph i Pure ethanol (l); Pure water (); The ixed H-bonded ethanol-water oiety (3). Then the general deinition o the coeicient was elaborated into a nuber o the particular relationships reerring to the coon binary (and ternary) obile phases, eployed in the adsorption and partition chroatography. The ost iportant relationships are listed below: Mobile phases: Methanol-water and ethanol-buer (,): x A + x B + C (40) 4

25 where x and x are the volue ractions o ethanol and water (or buer), respectively, and A, B, and C are the equation constants with the proound therodynaic eaning. Mobile phases: Acetonitrile-water and acetonitrile-buer (3,4): x A + x B +.9 x n + x C + D (4) " where x and x are the volue ractions o acetonitrile and water (or buer), respectively, A, B, C, and D are the therodynaically relevant equation constants, and n" reers to the average sel-associated water cluster. Mobile phases: Tetrahydrouran-water and tetrahydrouran-buer (5,6): x A + x B x n + x C + D (4) " where x and x are the volue ractions o tetrahydrouran and water (or buer), respectively, A, B, C, and D are the therodynaically relevant equation constants, and n" reers to the average sel-associated water cluster. Mobile phases: Aliphatic alcohol-n-parain hydrocarbon (7): x A + x B + C (43) where x and x are the volue ractions o alcohol and hydrocarbon, respectively, and A, B, and C are the therodynaically relevant equation constants. V. PACTICAL CONSEQUENCES OF ESTABLISHED MODELS Consequences o the established odels are aniold, and their iportance is both theoretical and practical. In the ollowing subsections we ocus attention on the ain practical aspects o the approaches that have been introduced. A. Quantiication o Sorbent Activity Sorbent activity depends on the ollowing three paraeters: Speciic surace area Density o the ree (i.e., unoccupied) active centers per unit o sorbent surace area Energy o interolecular interactions between a solute olecule and a given type o sorbent active centers 5

26 Speciic surace area depends on the cheical structure o the sorbent (silica, aluina, cellulose, etc.) and on the technology o its anuacturing. It can be easured and expressed nuerically. The density o the ree active centers per unit o the sorbent surace area also depends on the cheical structure o the sorbent, and additionally on the nuber o olecules other than those o the solute or obile phase occupying sorbent active centers. These are ostly water olecules, which block (deactivate) active centers on a sorbent surace, and the degree o deactivation usually depends on the storage conditions o the precoated chroatographic plates. The density o the ree active centers can also be easured and expressed nuerically. The energy o interolecular interactions between a solute olecule and a given type o sorbent active centers depends as uch on the cheical nature o the sorbent as on the nature o the solute itsel. Thereore, with a given sorbent the energy o interolecular interactions diers ro one solute to another. As can be easily deduced, quantiication o sorbent activity cannot be done in the absolute, but in relative values only. The ost coplete approach to this proble was derived ro the Snyder-Soczewiński odel o adsorption chroatography, and it will be briely discussed here. way: The therodynaic adsorption coeicient th (see Eq. 30a) can be deined in the ollowing log where µ a is the cheical potential o adsorption. Sipliying Eq. 44, we can write: th µ a (44).303T log th E (44a) where E (that is, µ a.303 T) is the diensionless energy o adsorption. It equals the dierence between the energies o adsorption o the solute (E Xa ) and the solvent (E Sa ; a onocoponent obile phase is assued). The quantity E Xa is a unction o the sorbent surace energy A i and the physico-cheical properties o a solute X. Siilarly, the quantity E Sa depends on the agnitude A i and on the physicocheical properties o a solvent S. Suing up, we can write: E E Xa Sa ( A ) ( X ) (45) i ( A ) ( S ) (45a) i ( A ) [ ( X ) ( S )] E E E (46) Xa Equation 30a can be rewritten in the ollowing way: Sa i 6

27 log log V V W a a a V W a + log th (30c) Cobining Eqs. 30c, 44a, and 46, we obtain the relationship: log log V V W a V W a a a + [ S ( A ) ( X ) ( ) i ] (30d) This equation can be rewritten in the concise or: VaWa log + α ' ( X S ) (30e) V V W, a a where α' (A i ), and (X,S) (X) - (S). Thus α' is the unction o the sorbent surace energy independent ro the properties o solute. It is known as the activity coeicient o the sorbent, and deterination o its nuerical values can be regarded as quantiication o sorbent activity. The right-hand side o equation 30e consists o the three ters that deine separate contributions ro the phase ratio, sorbent activity, and the so-called solute-solvent relationship (X,S) to the overall retention o solute. The nuerical values o, V, V a and W a can be established experientally. Two unknowns in Eq. 30e, naely α' and (X,S), cannot be deterined siultaneously ro the sae relationship. It was Snyder's (7) idea to overcoe this diicult proble in the ollowing way. Through intensive drying the sorbent can eventually achieve its ull activity, which eans that each active center o a sorbent saple is ree ro any deactivating water olecules. The activity coeicient α' o this sorbent is assued as equal to l. Then the ully active sorbent can urther be used or deterination o the solute-solvent relationship (X,S) with a nuber o test solutes. The respective results are collected or the sake o illustration in Table l (8). With the nuerical values o (X,S) both known and independent ro the degree o sorbent deactivation, one can again utilize Eq. 30a or deterination o α' with any given sorbent saple. Obviously, the nuerical values o (X,S) have to be easured separately or each individual type o sorbent (silica, aluina, cellulose, etc.) obtained in a given anuacturing procedure. B. Quantiication o Solvent Elution Strength Solvent elution strength is aong the ost iportant actors governing solute retention. Solvents with too little elution strength are incapable o oving solutes ro the origin, while those that are too strong push solutes with the obile phase ront. In other words, weak obile phases cannot 7

28 signiicantly aect interolecular interactions between solute olecules and the stationary phase, while the strong ones practically annihilate such interactions. Thereore, the proper choice o a single eluent, or eluent ixture, with respect to the analyzed substance and the stationary phase is crucial or the general outcoe o the chroatographic process. Table Nuerical Values o (X,S) or Test Solutes Chroatographed in n-hexane on Aluina and Silica (X,S) Test solute Al O 3 SiO Styrene.34.7 Durene Naphthalene Azulene Acenaphthylene Phenanthrene Anthracene Pyrene Fluoranthene Chrysene Terphenyl Triphenylene Benzanthracene ,- or 3,4-Dibenzopyrene Source: Data ro Snyder (8) Quantiication o solvent elution strength is based on the Snyder-Soczewiński odel o adsorption chroatography. A possibility o appropriate quantiication is oered by Eq. 46. For the sorbent activity coeicient α' l, Eq. 46 can be rewritten in the ollowing or: ( X ) ( S ) ( X S ) E, (46a) Equation 46a describes the dierence between the adsorption energies o solute and equivalent aount o solvent (one solute olecule can replace one or ore solvent olecules on the sorbent surace, depending on the stoichioetry o a given process). Thus E can be regarded as the net adsorption energy o the solute. With a sipliying assuption as to the onocoponent obile phase we can urther write (7): 8

29 0 0 ( X, S ) S ε E (47) where S 0 [ E Xa (X)] is the adsorption energy o the solute, A S denotes the cross-sectional area o its olecule, and ε 0 is the adsorption energy o solvent per unit o sorbent surace area [A S ε 0 E Sa (S)]. ε 0 is usually reerred to as solvent elution strength, or siply solvent strength. Equation 47 is a unction o three paraeters, S 0, A S and ε 0, and thereore the question arises how to conveniently express solvent elution strength in ters o ε 0. Choosing an aliphatic hydrocarbon as a test copound, one autoatically attains the situation in which S 0 0. The quantity A S can be evaluated ro the olecular paraeters o the test copound. Thus ε 0 reains the only unknown o the sipliied relationship ε A S 0 E AS (47a) and it can be established experientally. Elution strength o the siplest liquid aliphatic hydrocarbon, n-pentane, is equal to 0, and this particular solvent begins what is usually called the eluotropic series. Nuerical values o solvent elution strength ε 0 deterined or the ost coon chroatographic eluents on aluina are collected in Table. To obtain the analogous set o data or silica, Snyder advises ultiplying the data ro Table by a actor o The concept o solvent elution strength ε 0 is one way o quantiying solvent polarity. This polarity is a very iportant actor in establishing the chroatographically advantageous equilibria according to the ollowing schee: solvent solute sorbent (48) Table The Eluotropic Series o Solvents and Solvent Elution Strength ε 0 Deterined on Aluina Solvent 0 ε Al O 3 n-pentane 0.00 n-hexane 0.0 n-heptane 0.0 Cyclohexane 0.04 Carbon disulide 0.5 9

30 Carbon tetrachloridc 0.8 Isopropyl ether 0.8 -Chlorpropane 0.9 Toluene 0.9 l-chloropropane 0.30 Chlorobenzene 0.30 Benzene 0.3 Brooethane 0.37 Diethyl ether 0.38 Chloroor 0.40 Dichloroethane 0.4 Tetrahydrourane 0.45,-Dichloroethane 0.49 Ethyl ethyl ketone 0.5 Acetone 0.56 Dioxane 0.56 Ethyl acetate 0.58 Methyl acetate Pentanol 0.6 Diethylsuloxide 0.6 Aniline 0.6 Nitroethane 0.64 Acetonitrile 0.65 Pyridine 0.7 -Propanol 0.8 Ethanol 0.88 Methanol 0.95 Ethylene glycol. Acetic acid >> l Source: Data ro Snyder (7). Thus the solvent elution strength ε 0 becae a cornerstone o the new seiepirical strategy o predicting ulticoponent obile-phase coposition, and this proble will be discussed in the Section V.D.l. 30

31 C. Quantiication o Solvent Polarity and Selectivity The ain idea o this approach was to copare the variety o solvents ostly used as coponents o ixed obile phases in respect to their polarity and siultaneously as proton acceptors, proton donors, and interolecularly interacting dipoles. Three test solutes were selected, upon which the polarity and selectivity scale was built: ethanol as a odel proton donor, dioxane as a odel proton acceptor, and nitroethane as a odel strong dipole. Upon an extensive experiental study by ohrschneider (9) delivering or the aoreentioned three test solutes and over 80 solvents the solubility constants g (the so-called gas liquid partition coeicients o the test solute distributed between the gas phase and the solvent in a sealed lask and deterined by gas chroatographic analysis o the gas phase) Snyder anaged to devise the chroatographically useul scale o the polarity indices (P') and the selectivity paraeters (x i ) (3,4). The backbone o his approach was the ollowing given relationships: ( g ) + log( ) log( ) ethanol g dioxane g nitroethane P ' log + (3) x x d e ( ) log g ethanol (3a) P' ( ) log g dioxane (3b) P' x n ( ) log n nitroethane (3c) P' Snyder's principal objective was to reove the dependence o the agnitude g on the olecular weights o solvent and solute (4). The eect o the solvent olecular weight was reoved by ultiplying g by the olar volue V S (lole) o the solvent, leading to the partially corrected agnitude ' g : g g V S The olecular weight eect o the solute on its ' g value can likewise be reoved by dividing ' g by the estiated ' g value ( v ) o an n-alkane whose olar volue is the sae as that o the solute: (49) g g (50) v 3

32 or log g log log (50a) g v In this way Snyder "puriied" the ohrschneider's results ro the eect o ass interaction, thus better exposing the energetics o the dierentiated interolecular interactions between solute and solvent. Although solvent elution strength (ε 0 ) and its polarity index (P') can be considered as the two quasi-equivalent ways o quantiying solvent polarity, the physicocheical relevance o P' is greater, siply because it oers a deeper insight in the nature o these orces which ultiately play the ost crucial role in the displaceent echanis o solute retention, or in the otherwise rather neglected solute-solvent interactions. In the other words the two dierent solvents can be equally polar (thus yielding the siilar values o the test solute), and yet considerably dierent, when coparing the olecular-level role thereo in the process o retention. This dierence usually results in the dierentiated selectivity o separation attained with aid o these two solvents. D. Optiization o Mobile Phases Optiization o resolution and selectivity is a practical goal in thin-layer chroatography. The proper strategy is dictated by Eq. 4: S 0.5 N ( ) (4) Fro this relationship it ollows that thin-layer eiciency (plate nuber N) and coposition o obile phases (onitored through and ) can be optiized separately. Enhanceent o thin-layer perorance in ters o raising N will be the subject o Section VI, while the approaches aiing to optiize the coposition o obile phases will be discussed below.. Snyder's Approach (Solvent Elution Strength) The ost universal approach is a siple consequence o the idea o solvent elution strength, introduced by Snyder (7). Cobining Eqs. 44a, 46, and 47, we can view the therodynaic adsorption coeicient th as a unction o solvent elution strength, ε 0 : log th 0 0 ( S A ε ) α' (5) I one solute developed in two dierent onocoponent obile phases l and using the sae sorbent, the ollowing equations can be written: S 3