Journal of Chromatography A, 1207 (2008) 122–129

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Journal of Chromatography A

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Monofunctional polymers in liquid adsorption chromatographyDetermination of the interaction parameter in the range ofweak interaction

Bernd Trathnigga,∗, Muhammad Imran Malika, Nguyen Viet Cuonga, Alexander M. Skvortsovb

a Institute of Chemistry, Karl-Franzens-University, A-8010 Graz, Austriab Chemical-Pharmaceutical Academy, Prof. Popova 14, 197376 St. Petersburg, Russia

a r t i c l e i n f o

Article history:Received 3 July 2008Received in revised form 8 August 2008Accepted 12 August 2008Available online 15 August 2008

Keywords:SeparationHomologous seriesReversed-phase liquid chromatography

a b s t r a c t

The main physical characteristics of monofunctionals in adsorption chromatography – the adsorptioninteraction parameter of the repeat units c and the interaction parameter of specific end group q – arediscussed. Both parameters are independent on column dimensions and pore diameter, and depend onmobile phase composition. In a plot of elution volumes Vn vs. the difference �V = Vn − Vn − 1 in elutionvolumes of consecutive non-functional or monofunctional oligomers, straight lines with the same slopeare obtained for sufficiently high molar masses. The intercept of these lines yield the accessible volumesof functionalized and non-functionalized oligomers. In the range of weak interaction, the interactionparameter of the repeat unit can be determined using monofunctional chains with strongly adsorbingend group. Scope and limitations of this approach are studied using monoalkyl ethers of polypropylene

Poly(propylene glycol)sAdsorptionMI

glycol as model polymers.© 2008 Elsevier B.V. All rights reserved.

1

ibpomasde

fg

uw

iiub

uenvm

rSu

0d

onofunctionalsnteraction parameter

. Introduction

Polymers and oligomers always contain end groups, which maynfluence their physical properties and also their chromatographicehaviour. While the end groups are typically neglected in higholymers, they can be highly important in functional polymers andligomers: functional polyethers and polyesters serve as prepoly-ers in polyurethane production, amphiphilic polyethers (such

s fatty alcohol ethoxylates) are in widespread use as non-ionicurfactants and emulsifiers, macromonomers are used in the pro-uction of graft copolymers (e.g for hydrogels, solid electrolytes),tc.

The properties of functional polymers depend strongly on theirunctionality (i.e. on the number and chemical nature of functionalroups) and molar mass distribution (MMD).

The functionality type distribution (FTD) can be determinedsing liquid chromatography at critical conditions (LCCC) [1–7],hich makes the chain “chromatographically invisible”.

∗ Corresponding author. Tel.: +43 316 3805328.E-mail address: bernd.trathnigg@uni-graz.at (B. Trathnigg).

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021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2008.08.040

The molar mass distribution of polymers and oligomers is typ-cally determined by size-exclusion chromatography (SEC), whichs based on entropic effects, while enthalpic interaction of repeatnits and end groups with the stationary phase should be negligi-le.

The influence of end groups can, however, be utilized in liq-id exclusion adsorption chromatography (LEAC) [8–12], where thend groups interact strongly with the stationary phase, while theon-functional homopolymer would elute in SEC mode. The indi-idual oligomers elute thus in SEC order, but with elution volumesuch larger than the dead volume of the column.Liquid adsorption chromatography (LAC) allows a much better

esolution in the separation of oligomers than SEC. In contrast toEC, the driving force in LAC is enthalpic interaction of the repeatnits with the stationary phase. As retention in LAC increases expo-entially with the number of adsorbing groups, gradient elution isften required to achieve complete elution of the sample.

In LAC (whether with isocratic or gradient elution), optimiza-ion of chromatographic conditions is often time-consuming, hence

arious attempts have been made to simulate LAC of polymers.his requires the knowledge of the parameters, which determinehe elution behaviour of a polymer. Some approaches are basicallympirical, while others are based on theoretical considerations8,13–17].

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ip

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E

B. Trathnigg et al. / J. Chrom

Predictions of retention in LAC require the knowledge of a fewarameters: the interaction parameter c (and its dependence onobile phase composition), the interstitial volume Vi and the pore

olume Vp of the column, the pore diameter D, or the pore surfacep. The theoretical predictions agree very well with the experimen-al results [8,13].

The interaction parameter c describes the interaction of theepeat unit with the surface of the stationary phase. It is measuredn inverse length (nm−1).

The value of c does not depend on D, Vp, Vi or on the degree ofolymerization n, but strongly depends on mobile phase composi-ion (for a given polymer–sorbent system).

In SEC, the interaction parameter is negative, in LCCC it equalsero. In LAC (where c is always positive), it is related to the averagehickness of the adsorption layer of a long polymer chain on theore surface: H = 1/c.

While the pore diameter, the interstitial volume and the poreolume can be determined by inverse SEC, the determination ofhe interaction parameter is not trivial. In recent papers, we haveescribed a simple method do determine these parameters [18–21],hich could be used in a data base for predictions of polymer chro-atography [21]. The interaction parameter can be determined

rom a chromatogram, in which a sufficient number of consecu-ive oligomers of the same homologous series are at least partiallyesolved. This procedure works well in the typical LAC range (cor-esponding to interaction parameters between 2 and 6 nm), whereuch a separation can be achieved.

In the range of very weak interaction a sufficient resolutionannot be achieved any more. The interaction parameter at weaknteraction is, however, important, as gradients often reach intohis range. The prediction of chromatograms with gradient elutionequires the knowledge of the interaction parameters also in thenal mobile phase composition, which may be close to the criticaloint of adsorption.

It must be mentioned, that near the critical adsorption pointCAP) significant deviations may occur, as the simple model ofhe slit-like pore does not take ino account the geometry of theores and possible polymer–polymer excluded volume interac-ions [22,23]. This range of c is, however, outside the scope of thistudy.

With non-functional homopolymers the determination of inter-ction parameters in the range of weak interaction is impossible, itay, however, be achieved by functional polymers with adsorbing

nd groups.In LAC of polymers, retention is influenced by the end groups, if

heir interaction with the surface of the stationary phase is strongerhan that of the repeat unit.

A separation of individual oligomers by LAC could be possibleven in the case of weak interaction of the repeat unit, if the inter-ction of the end group is strong enough. In analogy to LEAC, wherehe end group extends the SEC range, resolution in LAC may also benhanced by an adsorbing end group.

The aim of this paper was to evaluate the scope and limitationsf such an approach. Of course, the simple relations, which describeetention of polymers in the range of strong interaction quite well,ay no longer hold at weak interaction. Therefore it appeared nec-

ssary to study the elution behaviour of polymers without and withdsorbing end groups in the range of weak interaction.

. General relations for non-functional polymers

The elution volume Ve of a molecule in liquid chromatographys given by a general relation

e = Vi + KVp (1)

La

V

r. A 1207 (2008) 122–129 123

here Vi denotes the interstitial volume, Vp the pore volume, andis the distribution coefficient relevant to the change in Gibbs free

nergy, which results from the changes in enthalpy and entropy.All modes of liquid chromatography can be described by a the-

ry (using a model of a Gaussian polymer chain and a slit-like pore)or the distribution coefficient of flexible homopolymers capablef being adsorbed on the pore walls [2,5,8,24,25]. According to thisheory, the distribution coefficient K is a function of three param-ters: the pore width, D, the average radius of gyration R of theolymer coil, and the adsorption interaction parameter c of theepeat unit.

= 1 − 2D

(2R√

�+ 1

c

)+ 2

cDexp (cR)2[1 + erf(cR)] (2)

herein erf(cR) is the error function, and D > R.Combining Eqs. (1) and (2), the elution volume of non-functional

omopolymers can be expressed by

e = Vi + Vp

(1 − 4√

�

R

D

)− 2Vp

cD+ 2Vp

cDexp (cR)2[1 + erf(cR)]) (3)

n a column with a given pore diameter D, interstitial and pore vol-me (Vi and Vp), the elution volume of a polymer molecule dependsn the magnitude of c and R.

Eq. (3) can be applied in all regimes of liquid chromatogra-hy, provided D > R. It can be used to predict the chromatographicehaviour of non-functional polymers on a given stationary phase

n any mobile phase composition, if the interaction parameter c ofgiven structural unit in this mobile phase composition and thearameters Vi, Vp, and D are known.

For polymers with functional end groups (the interaction ofhich with the stationary phase is different from that of the repeatnit), a term describing the interaction of the end groups must be

ntroduced.In ideal SEC (which corresponds to c → − ∞) the terms con-

aining 1/c disappear, which yields Casassa’s well known relation26,27] for linear macromolecules in wide slit-like pores.

SEC = Vi + Vp

(1 − 4√

�

R

D

)(4)

n LAC, where c is positive (typically 2–6 nm−1), the first terms inq. (3) represent the accessible volume V∗

0 , which can be enteredy a polymer chain [18,19]:

∗0 = Vi + Vp

(1 − 4R

D√

�

)− 2Vp

cD= VSEC − 2Vp

cD(5)

vidently, the accessible volume V∗0 is always smaller than the void

olume V0 = Vi + Vp, and it is also smaller than the elution volumeSEC of a polymer molecule with the same size in ideal SEC.

Evidently, V∗0 depends on R, D, and c, there may, however, be two

imiting cases [19]:At very strong interaction (large c) and wide pores (large D) the

erm 2Vp/cD disappears, consequently V∗0 → VSEC.

For small molecules in wide pores (small R/D) VSEC → V0.With parameters typical for LAC on wide pore columns at strong

nteraction (small R/D, large cD) V∗0 can be considered to be inde-

endent on n.Combination of Eqs. (3) and (5) yields

e = V∗0 + 2Vp

cDexp(c2R2)[1 + erf(cR)] (6)

q. (6) holds in all regimes of liquid chromatography. In the typical

AC regime it can be simplified: at large cR the error function erf(cR)pproaches 1.0.

e = V∗0 + 4Vp

cDexp(c2R2) (7)

1 matog

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R

Tb

V

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l

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V

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rbsttp

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l

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l

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ilapo

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ot(as 0.5 nm (which corresponds to the ethylene oxide unit). The elu-tion volumes thus obtained for n = 1 to 20 were plotted accordingto Eq. (12): as can be seen in Fig. 1, perfectly straight lines areobserved for both pore sizes, the differences in elution volume are,however, rather small on the 30 nm column, and so the peaks of

24 B. Trathnigg et al. / J. Chro

he radius of gyration R can be expressed by the length a and theumber n of repeat units:

= a

√n

6(8)

aking into account Eq. (8), elution volumes in LAC can be describedy

e = V∗0 + 4Vp

cDexp

(n

c2a2

6

)(9)

q. (9) may also be written in terms of the retention factor [18,19]:

∗ = Ve − V∗0

V∗0

= 4Vp

cDV∗0

exp

(n

c2a2

6

)(10)

r, in logarithmic form

n k∗ = ln

(4Vp

cDV∗0

)+ n

c2a2

6(11)

his corresponds to the well-known equation ln k = A + Bn (Martin’sule) [28–32].

If the retention factors are calculated with the accessible volumeinstead of the void volume), perfectly straight lines are obtainedn a plot of ln k* vs. n (Martin’s plot), which is not the case other-

ise. From the slope in such a plot the interaction parameter cane calculated.

Based on Eq. (9), the accessible volume and the interactionarameter can be easily determined from the elution volumes ofsufficient number of consecutive oligomers of a (non-functional)olymer homologous series. As has been shown previously [18],here is a linear relation between the elution volume of the oligomerin LAC and the difference �Vn = Vn − Vn − 1 in the elution volumesf consecutive oligomers.

n = V∗0 + � �Vn (12)

n such a plot, the intercept represents the accessible volume,nd the interaction parameter c can be calculated from the slope= eB/eB − 1 (with B = c2a2/6).

While Eqs. (9)–(12) are approximations, which hold only in theange of strong interaction, Eq. (6) can be applied in all regimes ofiquid chromatography, provided D > R. It allows predictions of thehromatographic behaviour of polymers, if the parameters Vi, Vp,nd D and the dependence of the interaction parameter c of a giventructural unit on mobile phase composition are known.

A comparison of the theoretic prediction and the experimentalesult has shown, that the theory describes the chromatographicehaviour of polymers very well [13,15,24,25]. The main problem inuch predictions is just the determination of the parameters men-ioned above. The determination of the correct pore volume Vp andhe pore diameter D in SEC is not trivial, especially in mixed mobilehases [33].

Unlike in SEC, the elution volume in LAC depends only on theelation of these parameters, which corresponds to the pore surfacep, which is given (for slit-like pores) by Sp = 2VP/D. As has beenhown previously the pore surface can be determined in LAC ofon-functional chains from the slope in Martin’s plot (using thealue of the accessible volume V∗

0 and the interaction parameter crom Eq. (12). The length of the repeat unit (a) must be taken from

he literature. A possible error in a is not dramatic, as it cancels out,f the same value is used in the simulation.

n k∗ = ln

(2Sp

cV∗0

)+ n

c2a2

6(13)

Fe�

r. A 1207 (2008) 122–129

s has been shown previously [18], the surface area Sp can also bebtained from a plot of the difference in elution volumes �Vn (inogarithmic form) vs. the number of repeat units, n.

n �Vn = ln2Sp

�c+ Bn (14)

rom the slope B in these plots (according to Eqs. (13) and (14)) onean obtain the interaction parameter c, and from the intercept theore surface Sp. The equations given above were verified recently18–21] for various reversed phase columns. As has been discussedn these papers, there are the following situations:

For determination V∗0 and c using Eq. (12), a single chromatogram

n LAC mode is required, where a sufficient number of peaks is ateast partially resolved. No information on n is required, except thatll peaks belong to the same homologous series. Different series ofolymers (with the same repeat unit, but different end groups) falln one line.

For the determination of Sp and c using Eq. (13) or Eq. (14), oneust know the number of repeat units n for each peak. The inter-

ction parameter c is obtained from the slope. For non-functionalhains, the pore surface is obtained from the intercept.

After all, the most feasible procedure is the one using Eq. (12),s it does not require the knowledge of the oligomer number forach peak, which is often hard to achieve.

It must be mentioned, that the procedures described above (Eqs.11)–(14)) hold strictly only in the case of sufficiently strong inter-ction, as they are based on the assumption of a constant accessibleolume and a negligible contribution of the error function (i.e. thessumption of erf(cR) = 1.0). In the range of weak interaction, how-ver, deviations may occur for the lower oligomers: their retentionan only be described using Eq. (6).

For the determination of the interaction parameter this has con-equences: when data are plotted according to Eq. (12), deviationsrom the linear dependence may be observed at lower n. Hence one

ust be sure to use only data in a range, where the approximationsentioned above can be applied.We have thus calculated the elution volumes (based on Eq. (6))

f polymer homologous series on two hypothetical columns withypical dimensions (Vi = Vp = 1.0 ml) and different pore diameterD = 10 nm and 30 nm), the length of the repeat unit was assumed

ig. 1. Simulation of non-functionals on columns with D = 10 and 30 nm at differ-nt values of c: elution volume Vn vs. the difference in Ve of consecutive oligomersV = Vn − Vn − 1.

atogr. A 1207 (2008) 122–129 125

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V

R

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te

pts

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l

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t

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Ff

ta

wwtvt

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B. Trathnigg et al. / J. Chrom

he individual oligomers may not be sufficiently resolved in a realhromatographic experiment.

The resolution Rn of two peaks with the elution volumes Vn andn − 1 and the half width wn and wn − 1 is usually defined by

n = 2Vn − Vn − 1

wn + wn − 1(15)

n practice, one would like to achieve a separation to the baseline,hich corresponds to a resolution Rn = 2.0, while a higher value

f Rn would be just a waste of time. For the determination of thenteraction parameter, Rn = 1.0 may just be sufficient.

The resolution can also be expressed by

n =√

N

2Vn − Vn − 1

Vn + Vn − 1(16)

s the half width wn depends on the number of theoretical plates: wn = 4/

√NVn.

In order to demonstrate the influence of c and n on the resolu-ion, we have calculated Rn on the hypothetical columns using thexact equations assuming a plate number N = 5000.

As has been mentioned above, retention in LAC depends on theore surface area Sp = 2Vp/D. In our calculations we have assumedhe same pore volume (Vp = 1.0 mL) for all columns, therefore theorbent surface – and thus the retention – is proportional to 1/D.

With these assumptions, a resolution of 1.0 is achieved on the0 nm column at c = 2.0 nm−1 for n ≥ 10, and for n ≥ 17 on the 30 nmolumn. At c = 1.5 nm−1, oligomers with n ≥ 25 may be at least par-ially resolved on the 10 nm column, while no reasonable separationan be achieved on the 30 nm column (Fig. 2). At high n, the reso-ution approaches a constant value, which only depends on c, butot on D.

As follows from Eqs. (9), (11) and (16), the limiting resolution inAC (at high n) depends on the adsorption interaction parameter cnd on the number of theoretical plates N only:

im Rn =√

N

2(eB − 1)(eB + 1)

≈√

N

2c2a2

12(17)

n our hypothetical examples, the limiting resolution exceeds aalue of R = 1.0 at interaction parameters larger than 1.0–1.5 nm−1,

epending on the plate number of the column (see Fig. 3). Conse-uently, at very weak interaction (c < 1.0) no reasonable resolutionan be achieved on any column.

An interesting situation occurs with monofunctional chains: ifhe end group is adsorbed more strongly than the repeat unit,

ig. 2. Simulated resolution of non-functionals on the hypothetical columns as aunction of the number of repeat units for different values of the interaction param-ter.

gr(u

piqc

at

uw

qtpc

us

ig. 3. Simulation of limiting resolution on the (hypothetical) 10 nm column as aunction of the interaction parameter for different plate numbers N.

he retention of the individual oligomers will increase, which mayllow to enhance the LAC separation.

This corresponds in some way to the situation of LEAC [8,9],here the interaction parameter of the repeat unit is negative,hile that of the end group is positive, and thus results in an elu-

ion of the individual oligomers in SEC order, but far beyond the voidolume of the column, and with a dramatically higher resolutionhan in SEC.

Applied to LAC, such an approach would allow a separation ofhe individual oligomers even in the range of weak interaction.

In order to test this hypothesis, we have synthesized monoalkylthers of polypropylene glycol (PPG) with alkyl end groups fromutyl to octadecyl and studied their retention in different mobilehases [34]. From the chromatograms thus obtained, interactionarameters smaller than 2.0 nm−1 could be determined using theimplified equations (assuming a constant value of the error func-ion). In this paper, we have evaluated the scope and limitations ofuch an approach.

. Monofunctionals

The chromatographic behaviour of polymers with specific endroups depends not only on the interaction parameter c of theepeat unit, but also on the interaction of the functional groupswhich may be considerably different from that of the repeatnit).

According to the general theory of liquid chromatography ofolymers and oligomers with specific end groups [5,35], the

nfluence of specific groups can be expressed by the parameter= ı(e��/RT − 1), where ı is the interaction distance between spe-ific group and sorbent.

The parameter q measures the difference of the free energy ofdsorption �� (in RT units) between the functional end group andhe repeat unit.

The determination of the specific end group parameter q in liq-id chromatography was discussed in previous papers [25,36], inhich also the first experimental estimation of q was realized.

Similar to the adsorption interaction parameter c, the parameterhas a sense of a local interaction of the end groups with the sta-

ionary phase. It is independent on the number of the repeat units,ore size or pore volume, but strongly dependent on mobile phase

omposition (as the adsorption parameter c).

When the end group is more adsorption-active than the repeatnits, q is positive, when the end group has a lover affinity for theurface then repeat units, q is negative.

1 matogr. A 1207 (2008) 122–129

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V

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otaL

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u

26 B. Trathnigg et al. / J. Chro

The value q = 0 nm corresponds to a non-functional chain. As fol-ows from the theory [35], there is an exact equation for the elutionolume of a monofunctional chain:

m = V∗0,m + Sp

c(1 + qc) exp (cR)2[1 + erf(cR)]) (18)

his equation is similar to Eq. (3), with the factor (1 + qc) taking intoccount the influence of the end groups. It must be mentioned, thathe accessible volume V∗

0,m for monofunctionals is not exactly theame as that for non-functionals: it contains an additional term,hich is, however, not important for the determination of c using

q. (12).

∗0,m = V∗

0 − Vp

D

2√�

q

Rc(19)

sing the exact relation (Eq. (18)) we have calculated the elutionolumes for monofunctional chains with different q at D = 10 nmnd different interaction parameter. When the data thus obtainedre plotted according to Eq. (12), straight lines are observed forigher n, but considerable deviations from linearity at low n. This

s due to the fact, that Eq. (12) has to be modified for monofunc-ionals, for which an additional term has to be taken into account,hich disappears for non-functionals (where q = 0) and becomesegligible at sufficiently high n and c:

m = V∗0,m −

√6�

S(1 + qc)c2a

√n

+ � �Vm (20)

ig. 4 shows such a plot: for an interaction parameter of c = 1.5nd 2.0 nm−1 reasonable straight lines are obtained for higherligomers (with n = 5 or larger), the slope of which depends on c,ut is independent on q. For the lowest oligomers, a considerableurvature is observed. At c = 1.0 nm−1, no linear range is found atny n, and the differences in elution volume are by far too small tollow a sufficient resolution.

One may speculate, that the determination of the interactionarameter in the range of weak interaction (i.e.at small c and n)ould be solved by using polymers with strongly adsorbing endroups, for which a sufficient retention could be achieved even atrather low interaction parameter of the repeat unit.

Fig. 5 shows the same plot for c = 1.0–2.0 nm−1 and q = 20 nm. Inhis case, elution volumes are considerably larger (and so are the

ifferences), but the curvature at the lowest oligomers is still theame.

This means, that interaction parameters of 1.5 nm−1 and largeran be determined using this approach (without the lowest 2–5ligomers), in the case of weaker interaction only oligomers with 10

ig. 4. Simulation of monofunctionals with different end groups: elution volume Vn

s. The difference in elution volumes of consecutive oligomers �V = Vn − Vn − 1.

smni

F(o

ig. 5. Simulation of monofunctionals with different end groups: elution volume Vn

s. the difference in elution volumes of consecutive oligomers �V = Vn − Vn−1.

r more repeat units can be considered. In the case of c < 1.0 nm−1,owever, this approach cannot be applied any more.

This becomes even clearer in a different representation: Inplot of ln(�V) vs. the number of repeat units (see Eq. (14))

here will be considerable deviations from linearity in the rangef weak interaction (i.e. at small c and n), as can be seenn Fig. 6.

Straight lines with a positive slope are observed for higherligomers, while the slope decreases with n and is even nega-ive for the lowest oligomers! This means, that one must expect

peak pattern very different from the one typical for isocraticAC.

We have thus calculated the resolution of non-functionalsnd monofunctionals with q = 5 nm and q = 20 nm on the columnith D = 10 nm for different interaction parameters (c = 1.5 and

.0 nm−1). While for non-functionals the resolution increases with, it decreases for the functional molecules at low n and tendsowards the limiting resolution, which is the same for a given valuef c, regardless the magnitude of q (Fig. 7). For the functional chains,high resolution of the lowest oligomers is found, which decreasesith increasing n, and the resolution approaches the limiting valueuch faster than for the non-functionals.These predictions should now be proven by the experiment

sing a series of model polymers. For this purpose we have

ynthesized various monoalkylethers of polypropylene glycol byicrowave assisted anionic polymerization of propylene oxide with

-alkanols and sodium hydride as initiator, as has been describedn a recent paper [34].

ig. 6. Simulation of monofunctionals with strongly adsorbing end groupq = 20 nm) and D = 10 nm: difference in Ve of consecutive oligomers vs the numbern repeat units.

B. Trathnigg et al. / J. Chromatog

Fq

4

pt

dwSi(h

omputt

tudtcsa

m2san5e

dapd

(07wM

dptwf

i

os

st

md

pmte

5

iscmocs4aP

7olhdsPPG diols or monoallyl-PPG [34,37], which is formed by a chaintransfer reaction.

Fig. 9 shows a comparison of three chromatograms, which wereobtained on the Prodigy column in 75.79% (w/w) acetone: whileonly higher oligomers are resolved for PPG diols (about 20 repeat

ig. 7. Simulated resolution of non-functionals and monofunctionals with differentat D = 10 nm as a function of the number of repeat units at c = 1.5 and 2.0 nm−1.

. Experimental

The calculations of elution volumes, retention factors etc. waserfomed using the EXCEL program (version 2003; Microsoft, Seat-le, WA, USA), which also includes the error function.

Propylene oxide (PO) and all alcohols (butanol, hexanol, octanol,ecanol, dodecanol, tetradecanol, hexadecanol and octadecanol)ere purchased from Fluka (Buchs, Switzerland), PPG from

igma–Aldrich (Vienna, Austria). Sodium hydride (60% dispersionn mineral oil) from Aldrich was used as received. Lower alcoholsbutanol–decanol) were dried over anhydrous sodium sulfate whileigher alcohols were used as received.

The polymerization of PO was performed by anionic ringpening using alcohols and sodium hydride as initiator. All poly-erizations were performed in 2–5 ml (filling volume) microwave

rocess vials (Biotage,Upsala, Sweden), which were oven driednder vacuum prior to use. The alcohol and NaH were added tohe vials which were subsequently sealed with an aluminum crimpop and PTFE septum.

The calculated volume of PO was added with a syringe throughhe septum. The quantity of sodium hydride was 0.1% of total prod-ct, the quantities of alcohols and PO in different experimentsepended upon intended average number (2–10) of PO units inhe chain (calculated by molar ratios). The sealed microwave pro-ess vials were subsequently introduced into the cavity of theingle-mode microwave reactor (Biotage Initiator Eight EXP 2.0,bsorbance level: high).

At reaction temperatures of 160 ◦C the initial pressure in theicrowave process vial was typically in a range between 5 and

0 bar and decreased during the polymerization as PO was con-umed. All microwave-assisted polymerizations were carried outt 160 ◦C to complete conversion, as indicated by a drop of the inter-al pressure from initially 5–20 bar to zero. Typically reactions take0–80 min for complete conversion. After polymerization the activend was neutralized by adding an equimolar quantity of acetic acid.

Chromatographic measurements were performed using theensity detection system DDS70 (Chromtech, Graz, Austria). Datacquisition and processing was performed using the softwareackage CHROMA (Chromtech, Graz, Austria)., which has beeneveloped for the DDS70.

The mobile phase was delivered by a JASCO 880 PU pumpfrom Japan Spectrosopic Company, Tokyo, Japan) at a flow rate of

.5 ml min−1. Samples were injected manually using a Rheodyne125 injection valve (from Rheodyne, Cotati, CA, USA) equippedith an 50 �l loop. A Waters 2414 refractive index detector (Waters,ilford, MA, USA) was connected to the DDS 70. The columns and

Fw

r. A 1207 (2008) 122–129 127

ensity cells were placed in a thermostatted box, in which a tem-erature of 25.0 ◦C was maintained for all measurements using ahermostat (Lauda RM6, Lauda-Königshofen, Germany). Columnsere connected to two column selection valves (Rheodyne 7060,

rom Rheodyne).The measurements in this study were performed on the follow-

ng reversed phase columns (specifications given by the producer):Prodigy ODS3 (Phenomenex, Torrance, CA, USA): silica-based

ctadecyl phase; 250 mm × 4.6 mm; particle diameter = 5 �m; poreize = 10 nm, surface area: 450 m2/g, carbon load: 15.5%.

Spherisorb S5X C18 (Phase Separations, Deeside, Clywd, UK)ilica-based octadecyl phase; 250 mm × 4.6 mm; particle diame-er = 5 �m; pore size D = 30 nm.

Nucleosil 4000-7 C18 (Macherey-Nagel, Dueren, Ger-any): silica-based octadecyl phase; 250 × 4 mm; particle

iameter = 7 �m; pore size D = 400 nm.The HPLC solvents (acetone and water, both HPLC grade) were

urchased from Roth (Karlsruhe, Germany). Mobile phases wereixed by mass and vacuum degassed, their composition was con-

rolled by density measurement using a DMA 60 density meterquipped with a measuring cell DMA 602 M (A. Paar, Graz, Austria).

. Results and discussion

The predictions from theory had to be verified by experimentsn the relevant range of interaction parameters. We have cho-en polypropylene glycols and their monoalkyl ethers as modelompounds, as they can be easily synthesized, and acetone–waterobile phases on silica-based C18 columns, where the retention

f these samples can be varied in a wide range of mobile phaseomposition. We have used three columns with the same dimen-ions (250 mm × 4.6 mm), but different pore diameter (10, 30, and00 nm). As the expected effects should be most pronounced onnarrow pore column, we have run most chromatograms on the

rodigy ODS3 column, the pore diameter of which is 10 nm.Fig. 8 shows two chromatograms of PPG 425 in 50.03 and

0.83% (w/w) acetone: while a baseline separation of the individualligomers is achieved in the more polar mobile phase, the reso-ution is rather poor in 70% acetone. In the same mobile phase,owever, a monohexyl-PPG of approximately the same averageegree of polymerization is resolved very well. In front of the maineries appears a second series of peaks, which could either be the

ig. 8. Chromatograms of PPG 425 and a hexyl-PPG with the same average moleculareight, as obtained on the Prodigy column in different mobile phases.

128 B. Trathnigg et al. / J. Chromatogr. A 1207 (2008) 122–129

Fig. 9. Chromatograms of PPG 1000, a butyl- and a hexyl-PPG, as obtained on theProdigy column in 75.79% (w/w) acetone.

FV

uieeo

tPi

Fo

FP

wol

(wsb

trc(soa

Ppo

sw

ig. 10. PPGs with different functionality on the Prodigy column: elution volumen vs. the difference in Ve of consecutive oligomers �V = Vn − Vn − 1.

nits), a much better separation is achieved also for lower oligomersn the butyl- and hexyl-terminated PPGs (with nav = 10). When thelution volumes thus obtained are plotted vs. the differences in thelution volumes of consecutive peaks, the expected behaviour isbserved, as can be seen in Fig. 10.

When the solvent strength is further increased, the elution pat-ern changes considerably, as can be seen in Fig. 11: while hexylPGs are separated in 75.79% (w/w) acetone in the usual way (withncreasing differences in elution volume), the increase is much

ig. 11. Chromatograms of monofunctional PPGs with different end groups, asbtained on the Prodigy column in different mobile phases.

d

pau

FV

ig. 12. Resolution in LAC of PPGs with different functionality, as obtained on therodigy column in different mobile phases.

eaker for hexadecyl PPGs in 85.69% (w/w) acetone, and withctadecyl PPGs in 90.06% (w/w) acetone the difference is more oress constant (as could be expected from Fig. 6).

Fig. 12 shows a plot of the resolution of the individual peakscalculated by CHROMA) vs. the number of repeat units for PPGsith different functionality in different mobile phases: as can be

een, the experimental data show the same behaviour as predictedy the theory (see Fig. 7).

Fig. 13 shows a plot of the elution volumes vs. the differences inhe elution volumes of consecutive peaks (according to Eq. (12)):easonable straight lines with the same slope, but a different inter-ept are observed for PPG diols, hexyl and dodecyl PPGs in 79.96%w/w) acetone. In 90.06% acetone, however, the differences are con-tant for the higher oligomers and show an increase for the lowerligomers (as predicted). Obviously, no determination of the inter-ction parameter is possible in such a mobile phase.

When the interaction parameter of the PO unit (obtained fromPGs with different functionality) is plotted as a function of mobilehase composition, straight lines with the same intercept arebtained for all three columns, as can be seen in Fig. 14.

Obviously, the Spherisorb and the Nucleosil column fall on theame line, which indicates, that their surface is chemically identical,hile the the slope of the line for the Prodigy column is somewhatifferent (which may be due to a different end-capping).

Interaction parameters show a linear dependence on mobilehase composition in the range between c = 4.5 and 1.5 nm−1, thebsolute limit for the determination of the interaction parametersing the described approach will be c = 1.0 nm−1.

ig. 13. PPGs with different functionality on the Prodigy column: elution volumen vs. the difference in Ve of consecutive oligomers �V = Vn − Vn − 1.

B. Trathnigg et al. / J. Chromatog

Fc

6

optuaoesue

bc

pgavocmdc

A

vC

R

R

[[[[[[

[[[[[[

[[

[

[[[[[[[[

ig. 14. Dependence of the interaction parameter of the PO unit on three C18olumns with different ore diameter as a function of mobile phase composition.

. Conclusions

It has been shown, that the theory of LAC can predict retentionf polymers with different functionality very well. The requiredarameters are the characteristic volumes of a column (intersti-ial and pore volume), the pore diameter, the length of the repeatnit and its interaction parameter on a given stationary phase ingiven mobile phase. The dependence of interaction parameters

n mobile phase composition can be determined by plotting thelution volumes of oligomers (of the same polymer homologouseries) as a function of the difference in elution volumes of consec-tive oligomers. A comparison of the theoretical predictions withxperimental data showed excellent agreement.

This approach can be used in the range, where a sufficient num-er of peaks can be at least partially resolved. This is typically thease for interaction parameters larger than 2.0 nm−1.

In the range of weaker interaction (c < 2 nm−1) the interactionarameter can be determined using monofunctionals with an endroup, which is adsorbed more strongly than the repeat unit. Thisllows a determination of the interaction parameter down to aalue of c = 1.5 nm−1. For systems with a critical point (such as PEG

n alkyl-bonded phases in methanol–water or acetone–water) theomposition corresponding to the CAP (c = 0 nm−1) can be deter-ined in the usual way (from the elution volumes of samples with

ifferent molecular weight). This would allow the determination ofin the entire range of LAC.

[[[[

[

r. A 1207 (2008) 122–129 129

cknowledgements

B. T. thanks Dr. Alexei A. Gorbunov for fruitful discussions andaluable theoretical advice. M.I.M. thanks the Higher Educationommission of Pakistan for a Ph.D. Scholarship.

N. V. C. thanks Austrian Federal Ministery for Science andesearch for a Ph.D. Scholarship.

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