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Journal of Chromatography A, 1333 (2014) 60–69

Contents lists available at ScienceDirect

Journal of Chromatography A

jo ur nal ho me pag e: www.elsev ier .com/ locate /chroma

apid development of core–shell column technology: Accurateeasurements of the intrinsic column efficiency of narrow-bore

olumns packed with 4.6 down to 1.3 �m superficially porousarticles

abrice Gritti, Georges Guiochon ∗

epartment of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USA

r t i c l e i n f o

rticle history:eceived 4 December 2013eceived in revised form 15 January 2014ccepted 18 January 2014vailable online 31 January 2014

a b s t r a c t

The intrinsic heights equivalent to a theoretical plate (HETPs) of 31 narrow-bore and wide-bore columnspacked with four different brands of core–shell particles were accurately measured on an optimizedvHPLC instrument (1290 Infinity system) that has an extra-column volume variance of 13.6 ± 0.3 �L2.These results were derived from the slopes of the linear plots of the apparent plate heights of each columnversus the reciprocal of (1 + k′)2 for seven homologous compounds with a linear regression coefficientlarger than 0.999. The results show that the kinetic performance of narrow-bore columns packed with

eywords:olumn efficiency

ntrinsic column efficiencyHPLC systemsomologous compoundsxtra-column band broadening

core–shell particles increases almost linearly with decreasing particle diameter. The optimum reducedplate heights increase slightly from 1.6 to 1.9 with decreasing particle sizes from 4.6 to 1.3 �m. Thisconfirms that wide-bore columns provide better efficiencies than narrow-bore columns.

© 2014 Elsevier B.V. All rights reserved.

ore–shell particles

. Introduction

Columns packed with sub-3 �m shell particles, also called pel-icular or superficially porous particles, are now solidly establishedn HPLC column technology since 2007. Their introduction pro-ided large improvements in the separation of small molecules1–6]. No fewer than ten manufacturers have developed their ownrands of core–shell particles, which are available in sizes between

and 1.3 �m. Several advanced theoretical [7–13] and experimen-al [3,4,6,14–21] investigations have allowed the elucidation of theeasons that explain their advantages in the separation of moleculesf widely different sizes. To summarize, the A, B, and C terms of thean Deemter HETP equation decrease when fully porous particlesre replaced with superficially porous particles. The decrease ofhe A term at high flow rates is the main explanation for this suc-ess. For small molecules, the efficiencies of narrow-bore columnsacked with 2.6 or 2.7 �m particles is similar to that of those packed

ith sub-2 �m fully porous particles but they require a much

ower back pressure [22,23]. They can be used with conventionalnstruments provided that the extra-column band broadening

∗ Corresponding author. Tel.: +1 8659740733; fax: +1 865 974 2667.E-mail addresses: guiochon@utk.edu,

uiochon@ion.chem.utk.edu (G. Guiochon).

021-9673/$ – see front matter © 2014 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.chroma.2014.01.061

contribution is minimized by replacing standard tubings with sim-ilar ones of smaller volumes and/or by focusing the injected sampleband at the column inlet [24–27]. For large molecules, the vanDeemter curves of these columns are flatter at high flow rates thanthose measured for fully porous particles [3,9,28,29], provided thatthe structure of the mesoporous volumes is similar in both types ofcolumns.

Most columns packed with core–shell particles are now avail-able in a narrow-bore diameter (2.1 mm) that allows savings onsolvents and samples. However, the contribution to band broad-ening of even advanced vHPLC instruments is large compared tothat of these columns. Measuring meaningful column efficien-cies is challenging because the contributions of instruments toband broadening differ from an instrument to the next. This isa source of endless discussions and arguments between columnmanufacturers, claiming exceptionally high column performance,and customers, complaining about the relatively poor column per-formance that they measure. Furthermore, determining the trueintrinsic efficiencies of narrow-bore columns is made difficult bythe current measurement process in which the volume variancesof the system estimated by using a zero dead volume (ZDV) union

connector are subtracted from the total recorded volume variance.It was recently shown [30,31] that the mere replacement of thechromatographic column with a ZDV union connector introducesa systematic error, of up to 40%. A non-invasive method should

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F. Gritti, G. Guiochon / J. Ch

e better. To solve these problems, a measurement process basedn plotting the apparent HETP (not corrected HETP for the systemariance) versus the reciprocal of (1 + k′)2 for a series of homolo-ous compounds was recently proposed [31]. If all the data pointsorm a straight line, the extrapolation to an infinite retention fac-or provides the true intrinsic HETP of the column for this class ofompounds.

The other result of this method is that it was proved to workell with standard, non-optimized HPLC and vHPLC system with

ystem volume variances as large as 40 �L2. Accurate estimates ofhe true efficiency of a new column can be made without minimiz-ng the system volume [25,26] or without developing new injectionechniques [27] to correct for most of the pre-column band broad-ning contributions. However, reducing as much as possible theontribution of the instrument used to band spreading is neces-ary. Analyst who seek to achieve the best performance from theodern columns available must understand this new requirement.nother advantage of this method is that it provides the true sys-

em volume variance provided that the column hold-up volume beccurately known [31,32]. This method was validated by showinghat it provided the same intrinsic efficiency for a given narrow-ore column, independently of the instrument with which it wassed to acquire the apparent column efficiency and the retentionactors of the probe compounds [31].

The goal of this work was to determine the intrinsic kinetic per-ormance of a large collection of columns packed with early (2.7 �malo and 2.6 �m Kinetex of 2007–2009) and recent core–shellarticles (1.6 �m CORTECS or 1.3 �m Kinetex in 2013). Thirtyne columns were tested including, 23 narrow-bore (2.1 mm.d.) columns. Four different brands of particles, Advanced mate-ial technologies, Phenomenex, Agilent Technologies, and Watersechnologies were studied. The alternative, non-invasive methodescribed above was applied. It permits accurate measurementsf the extra-column volume variances of HPLC instruments in theresence of a chromatographic column and that of the intrinsicfficiencies of modern narrow-bore columns. The justifications andxperimental conditions for the application of this protocol are dis-ussed in details. The impact of the column diameter and of thearticle size on the true column performance is finally discussed.

. Theory

.1. Band variance under isocratic and quasi-isocratic conditions

The total volume variance of a chromatographic peak includeshe contributions of the instrument (its injector, valve, connectingubes, detector, electronics) and of the column to the recorded bandidth. Under isocratic conditions, it is given by [26,33,34]:

2v,Exp. = �2

v,ex + V20

Nintrinsic(1 + k′)2 (1)

here �2v,Exp. is the total volume variance measured, �2

v,ex is thextra-column volume variance, V0 is the column void volume,intrinsic is the intrinsic column efficiency, and k′ is the retention

actor given by:

′ = VR − Vex − V0

V0(2)

here VR is the elution volume and Vex is the extra-column volume.ote that Eq. (1) assumes that the sample is dissolved in the sameluent as the one used as the mobile phase.

ogr. A 1333 (2014) 60–69 61

2.2. Relationship between the apparent and the intrinsic HETP

By definition, the HETP. H, (e.g., the overall apparent perfor-mance of the column and instrument as measured by the analyst)is written:

H = L�2

v,Exp.

V2R

(3)

Assuming that Vex � V0, substitution of Eq. (1) into Eq. (3) pro-vides the relationship between H, Hintrinsic = L/Nintrinsic, the columndimensions (V0 and L), the system variance in volume unit (�2

v,ex),and the retention factor k′:

H(k′) = Hintrinsic + L�2

v,ex

V20

1

(1 + k′)2(4)

This result shows that, if under certain conditions of flow rate,temperature, and mobile phase composition, the intrinsic HETPdepends weakly on k′ for a series of closely related compounds(same class of compounds such as a series of homologous analytes),the plot of the apparent HETP versus the reciprocal of (1 + k′)2 isexpected to be linear. Its y-axis intercept should provide Hintrinsicand its slope an estimate of the true extra-column volume variance�2

v,ex. The main advantage of this approach for the determination ofHintrinsic and �2

v,ex is that the column does not need to be replacedwith a zero dead volume (ZDV) connector. This method is partic-ularly recommended when the system volume variance is muchlarger than the column volume variance. This concerns standardHPLC and vHPLC instruments used with narrow-bore columns. Themain disadvantage is that the conditions mentioned above are notsystematically met under certain RPLC conditions.

3. Experimental

3.1. Chemicals

The mobile phase used was a binary mixture of acetonitrileand water (65/35, v/v). Small volumes of tetrahydrofuran (THF)were used for the ISEC measurements of the 2.1 mm × 50 mm col-umn packed with 1.3 �m Kinetex column. For the other columnsused, we used results obtained and published earlier. All the sol-vents used were HPLC grade from Fisher Scientific (Fair Lawn,NJ, USA). Acetonitrile was filtered before use on a surfactant-freecellulose acetate filter membrane, 0.2 �m pore size (Suwannee,GA, USA). The eleven polystyrene standards (MW = 590, 1100,3680, 6400, 13,200, 31,600, 90,000, 171,000, 560,900, 900,000,and 1,870,000) were purchased from Phenomenex (Torrance, CA,USA). The standard RPLC checkout sample (1 mL ampoule) was pur-chased from Agilent technologies. It contains 100.3 �g/mL (± 0.5%)of acetophenone, propiophenone, butyrophenone, valerophenone,hexanophenone, heptanophenone, octanophenone, benzophe-none, and acetanilide. The solvent of this sample is a mixture ofacetonitrile and water (35/65, v/v, same composition as that of themobile phase). Acetophenone, valerophenone, and octanophenone(all >99% purity) were separately purchased from Sigma–Aldrich(Suwannee, GA, USA).

The choice of these probe compounds was justified in an earlierpublication [31].

3.2. Instruments

A very high pressure liquid chromatograph (vHPLC) was used in

this work. This standard 1290 Infinity system (Agilent, Waldbroen,Germany) was slightly optimized. It includes a 1290 Infinity BinaryPump with solvent selection valves and a programmable auto-sampler. The injection volume (0.2 or 0.5 �L) is drawn into one end

62 F. Gritti, G. Guiochon / J. Chromatogr. A 1333 (2014) 60–69

Table 1Physico-chemical property of the narrow-bore column packed with 1.3 �m Kinetex-C18 core–shell particles.

Column SN Column’s dimension i.d.[mm] × length [mm]

Average particle sizea [�m] Totalb porosity (εt) Externalporosityc (εe)

Particle/shellporosityd (εp)

USGC001322 2.1 × 50 1.30 0.500 0.379 0.303

a Measured from Coulter Counter experiments.

otlrabtp

•

•

•

•

a

3

2wrcpUplaCoC2pc(t1t[eKta

b Measured from the elution of toluene in THF.c Measured from ISEC experiments.d Measured assuming a solid core diameter of 0.95 �m (� = 0.71).

f the 20 �L injection loop. This First In Last Out (FILO) injection sys-em design is such that the entire volume of sample drawn into theoop is injected into the column. This ensures an excellent injectionepeatability. The instrument includes a two-compartment ovennd a multi-diode array UV–vis detection system. It is controlledy the Chemstation software. In the present optimized configura-ion, the sample trajectory in the equipment involves the successiveassage of its band through the series of:

A smaller volume needle seat capillary (115 �m i.d., 100 mmlong), � 1.0 �L, located between the injection needle and theinjection valve. The same injection valve was used (1.2 �L).One 120 �m × 220 mm inlet metallic capillary tube. Its volume is2.5 �L. This capillary was replaced with a 130 �m × 250 mm Vipertube (Thermo Fisher Scientific, Germering, Germany) in order toconnect satisfactorily the CORTECS column. The volume of theViper tube is 3.3 �L.One 115 �m × 220 mm outlet metallic capillary tube. Its volumeis 2.3 �L.A small volume detector cell, V(�) = 0.6 �L, Vcell = 1.4 �L, 10 mmpath.

The total extra-column volume of this configuration is estimatedt Vex = 1.0 + 1.2 + 2.5 + 2.3 + 1.4 = 8.4 �L.

.3. Columns

A total of thirty one columns were used in this work: six.1 mm × 100 mm and two 4.6 mm × 100 mm columns packedith 2.6 �m Kinetex-C18 core–shell particles (Phenomenex, Tor-

ance, CA, USA), six 2.1 mm × 100 mm and two 4.6 mm × 100 mmolumns packed with 2.7 �m Halo Peptide ES-C18 core–shellarticles (Advanced Material Technologies, Wilmington, DE,SA), six 2.1 mm × 100 mm and two 4.6 mm × 100 mm columnsacked with 2.7 �m Poroshell120-C18 core–shell particles (Agi-

ent Technologies, Little Fall, NJ, USA), two 2.1 mm × 150 mmnd two 4.6 mm × 150 mm columns packed with 4.6 �m Kinetex-18 core–shell particles (Phenomenex, Torrance, CA, USA),ne 2.1 mm × 150 mm column packed with 1.7 �m Kinetex-18 core–shell particles (Phenomenex, Torrance, CA, USA), one.1 mm × 100 mm column packed with 1.6 �m CORTECS core–shellarticles (Waters, Milford, PA, USA), and one 2.1 mm × 50 mmolumn packed with 1.3 �m Kinetex-C18 core–shell particlesPhenomenex, Torrance, CA, USA) were offered by their respec-ive column manufacturer. Except for the column packed with.3 �m Kinetex particles, all the physico-chemical properties ofhese columns had already been measured and reported earlier30,31,35–40]. Table 1 lists the physico-chemical properties (total,

xternal, and internal porosities, and permeabilities) of the 1.3 �minetex-C18 column, according to data provided by the manufac-

urer (core size, particle size, column tube diameter) and thosecquired in our laboratory (ISEC and permeability data).

3.4. ISEC experiments and column porosities

ISEC measurements were made on the 2.1 mm × 50 mm columnpacked with 1.3 �m Kinetex-C18 shell particles. Neat THF was usedas the eluent. Eleven polystyrene standards with molecular weightsbetween 500 and 2 millions Dalton were used as probe molecules.They cover a wide range of molecular sizes, between 10 and 950 A.The flow rate was set at 0.10 mL/min and the sample size set at0.25 �L. The detection wavelength was set at 254 nm, the band-width at 4 nm, and the sampling rate at 160 Hz. To minimize theextra-column volume, the inlet and outlet connecting tubes were75 �m × 250 mm Viper tubes (Thermo Fisher Scientific, Germering,Germany).

The external porosities (εe) were derived by extrapolating toa zero hydrodynamic molecular radius the exclusion branches ofthe ISEC plots of the elution volumes of the polymers versus theirhydrodynamic molecular radius. The accuracy of the ISEC experi-mental protocol is about 1%. The total porosity (εt) was measuredfrom the elution time of toluene in pure THF. The internal porosity(εp) was derived from the classical relationship:

εp = εt − εe

(1 − εe)(1 − �3)(5)

All the results for the total, the external, and the internal porosi-ties are listed in Table 1.

3.5. Peak first and second central moments

The first and second moments of the eluted bands weremeasured by numerical integration of the whole concentration dis-tributions [17,41]. Details about the systematic selection of the leftand right cuts are given in [30].

3.6. Diffusion coefficients of compounds homologous ofn-alkanophenone

The diffusion coefficients of acetophenone (n = 2), valerophe-none (n = 5), and octanophenone (n = 8) were measured using thecapillary method. This method and its constraints were describedin [30,42,43]. The liquid used was a mixture of acetonitrile andwater (65/35, v/v) at room temperature (T = 23 ◦C). Its viscos-ity is 0.69 cP. For better precision, duplicate measurements weremade. The diffusion coefficients are 1.48 × 10−5, 1.20 × 10−5, and1.03 × 10−5 cm2/s, respectively. The accuracy and precision of thesedata are better than a few percents and 1%, respectively. At constanttemperature and liquid composition, the diffusion coefficients areinversely proportional to the molar volume VA (taken at the boilingpoint of the pure solute) elevated at an unknown power ˛:

Dm ∝ V−˛A (6)

According to the Wilke and Chang empirical correlation [44],

the exponent is 0.6. The volume VA was estimated from the aver-age value provided by the LeBas and Schroeder group contributionmethods [45]. Accordingly, the molar volumes of acetophenone(n = 2), valerophenone (n = 5), and octanophenone (n = 8) were

F. Gritti, G. Guiochon / J. Chromatogr. A 1333 (2014) 60–69 63

0.40.30.20.10.0

0

5

10

15

20

25

(1+k)-2

Hap

p [μμ

m]

2.1 x 100 mm Kinetex 2.6 μμm

#01

#02

#04

#05

#09

#20

Fig. 1. Plots of the apparent HETPs of seven homologous compounds (from theright to the left symbol: acetophenone, propiophenone, butyrophenone, valerophe-none, hexanophenone, heptanophenone, and octanophenone) versus the reciprocalof (1 + k′)2 at a flow rate of 0.5 mL/min. Columns: six 2.1 mm × 100 mm packed with2.6 �m Kinetex-C18 core–shell particles (the numbers are the last two digits ofthe column serial number). Eluent: acetonitrile/water, 65/35 (v/v). Injection vol-ume: 0.20 �L. Temperature: Tlab = 23 ◦C. vHPLC instrument: optimized 1290 Infinitysystem equipped with an inlet 120 �m × 22 cm, an outlet 115 �m × 22 cm metalliccapillaries, and a low-dispersion detection cell. Note the excellent linearity of thep

eTcna1r

3

uttcsslitpab

4

oFF(dl

0.40.30.20.10.0

2

4

6

4.6 x 100 mm Kinetex 2.6 μμm

(1+k)-2

HE

TP

[μμm

]

Happ

#17

Hint

#17

Happ

#07

Hint

#07

Fig. 2. Same graph as in Fig. 1 but for two 4.6 mm × 100 mm columns packedwith 2.6 �m Kinetex-C18 core–shell particles. Injection volume 0.5 �L, flow rate

integration of the whole concentration distribution, as explainedin references [41,46]. The peak volume variance increases slightlyfrom 10.6 ± 0.1 �L2 to 11.6 ± 0.4 �L2 and to 12.4 ± 0.5 �L2 from

0.0 0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

25

2.1 x 100 mm Halo-ES 2.7 μμm

Hap

p [μμ

m]

(1+k)-2

#312

#322

#323

#327

#329

#330

lot.

stimated at VA = 102.4, 135.1, and 167.8 cm3/mol, respectively.he best coefficient was found to be 0.74 and the diffusionoefficients of propiophenone (VA = 113.3 cm3/mol), butyrophe-one (VA = 124.2 cm3/mol), hexanophenone (VA = 146.0 cm3/mol),nd heptanophenone (VA = 156.9 cm3/mol) were estimated at.37 × 10−5, 1.28 × 10−5, 1.14 × 10−5, and 1.08 × 10−5 cm3/mol,espectively.

.7. Chromatographic conditions

The chromatographic conditions depend essentially on the col-mn i.d. The flow rates were set at 0.50 and 1.85 mL/min forhe 2.1 and 4.6 mm columns, respectively. Exceptions concernhe CORTECS (0.4 mL/min) and the 1.3 �m Kinetex (0.65 mL/min)olumns. These flow rates are close to the optimal flow rateselected by column manufacturer for their quality control tests. Theample solution injected was the RPLC check-out sample from Agi-ent technologies. The injection volumes were set at 0.2 (2.1 mm.d.) and 0.5 (4.6 mm i.d.) �L, respectively. The mobile phase washe same mixture of acetonitrile and water (65/35, v/v). The tem-erature was that of the laboratory, recorded at 23.0 ± 0.3 ◦C over

one week period. The UV wavelength was set at 243 nm and theandwidth at 4 nm.

. Results and discussion

For the sake of clarity, Figs. 1–11 are listed by nature and sizef the core–shell particles used: Figs. 1 and 2 (2.6 �m Kinetex),igs. 3 and 4 (2.7 �m Halo-ES), Figs. 5 and 6 (2.7 �m Poroshell),igs. 7 and 8 (4.6 �m Kinetex), Fig. 9 (1.7 �m Kinetex), Fig. 10

1.6 �m CORTECS), and Fig. 11 (1.3 �m Kinetex). They are called in aifferent order during a discussion based mostly on the linear/non-

inear behavior of the experimental plots of H versus (1 + k′)2.

1.85 mL/min. The plots are not linear due to the large hold-up volume V0 of thecolumn. Hint is the intrinsic HETP corrected for the extra-column contribution to thetotal band volume variance.

4.1. System band broadening using narrow bore columns

The mobile phase was a mixture of acetonitrile and water(65/35, v/v) at room temperature. The system band broadeningcontribution and its volume variance were estimated by replacingthe chromatographic column with a zero dead volume (ZDV) unionconnector. The solutes tested were acetophenone, valerophenone,and octanophenone. The flow rate was set at 0.5 mL/min. The maindrawback of this method is that its accuracy is unknown. The1290 Infinity system is equipped with metallic capillary connec-tors located before (120 �m × 22 cm) and after (115 �m × 22 cm)the column and with a low-dispersion detection cell (V(�) = 1.0 �L).For each injected compound, three consecutive replicate injectionswere performed. The peak variance was measured by numerical

Fig. 3. Same graph as in Fig. 1 but for six 2.1 mm × 100 mm columns packed with2.7 �m Halo Peptide-ES-C18 core–shell particles.

64 F. Gritti, G. Guiochon / J. Chromatogr. A 1333 (2014) 60–69

0.0 0.1 0.2 0.3 0.4 0.5

2

4

6

Happ

#316

Hint

#31 6

Happ

#29 7

Hint

#29 7

(1+k)-2

4.6 x 100 mm Halo-ES 2.7 μμm

HE

TP

[μμm

]

Fig. 4. Same graph as in Fig. 1 but for two 4.6 mm × 100 mm columns packed with21c

atadtte

tnifhhraii2(

F2

0.50.40.30.20.10.0

2

4

6

HE

TP

[μμ

m]

(1+k)-2

Hint

#36 8

Hint

#37 4

Happ

#36 8

Happ

#37 4

4.6 x 100 mm Poroshell120 2.7 μμm

Fig. 6. Same graph as in Fig. 1 but for two 4.6 mm × 100 mm columns packedwith 2.7 �m Poroshell-C18 core–shell particles). Injection volume: 0.5 �L, flow rate1.85 mL/min. The plots are not linear due to the large hold-up volume V0 of thecolumn.

0

4

8

12

16

Hint

#7 3

Hint

#7 5

HE

TP

[μμm

]

2.1 x 150 mm Kinetex 4.6 μμm

Happ

#7 3

Happ

#7 5

.7 �m Halo Peptide-ES-C18 core–shell particles. Injection volume 0.5 �L, flow rate

.85 mL/min. The plots are not linear due to the large hold-up volume V0 of theolumn.

cetophenone to valerophenone and to octanophenone, respec-ively. So, the diffusion rate across the system tubings, connections,nd valves barely affect the extra-column volume variance, whichepends little on the nature of the compound injected, providedhat the flow rate is sufficiently large. The band broadening throughhe system is then essentially controlled by the flow mechanism,ven for these highly diffusive, low-molecular-weight compounds.

Therefore, the system volume variance can be estimated fromhe series of results obtained for homologous compounds underon-invasive conditions, the column remaining connected to the

nlet and outlet capillaries of the instrument. It is directly derivedrom the slope of the linear plot of the apparent column plateeight versus the reciprocal of (1 + k′)2 for the series of sevenomologous compounds (acetophenone, propiophenone, buty-ophenone, valerophenone, hexanophenone, heptanophenone,nd octanophenone) for which the linear regression coefficient R2

s larger than 0.999 [31]. At a flow rate of 0.5 mL/min, the reducednterstitial linear velocity v of a 2.1 mm i.d. column packed with.7 �m particles having a bed porosity of 40%, increases from 11.0acetophenone) to 15.8 (octanophenone). This range of reduced

0.0 0.1 0.2 0.3 0.4

0

5

10

15

20

(1+k)-2

Hap

p [ μμ

m]

2.1 x 100 mm Poroshell120 2.7 μμm

#59

#60

#62

#63

#73

#74

ig. 5. Same graph as in Fig. 1 but for six 2.1 mm × 100 mm columns packed with.7 �m Poroshell120-C18 core–shell particles.

0 100 20 0 300 40 0

0

100

200

300

Octanophenon e

As10%

=0.87

Hep tanophenon e

As10%

=0.88

Hexanopheno ne

As10%

=0.90

Valerophenon e

As10%

=1.04

Butyrophenon e

As10%

=1.13

Prop iopheno ne

As10%

=1.23

Ace tophenon e

As10%

=1.35

Ab

so

rba

nc

e [

mA

U]

0.0 0.1 0.2 0.3

(1+k)-2

Fig. 7. (Top graph) Same graph as in Fig. 1 but for two 2.1 mm × 150 mmcolumns packed with 4.6 �m Kinetex-C18 core–shell particles. (Bottom graph) Chro-matogram of the RPLC-checkout sample recorded at a wavelength of 243 nm. Theasymmetry factors As10% at 10% of the peak height are reported in the graph for eachn-alkanophenone. The plots are not linear due to the peak fronting.

F. Gritti, G. Guiochon / J. Chromatogr. A 1333 (2014) 60–69 65

0.0 0.1 0.2 0.3 0.4 0.5

3

6

9

(1+k)-2

4.6 x 150 mm Kinetex 4.6 μμm

HE

TP

[μμm

]

Happ

#75

Hint

#7 5

Happ

#7 3

Hint

#73

0 100 20 0 300 40 0

0

50

100

150

Ab

so

rban

ce [m

AU

]

Time [s]

Octanophenon e

As10%

=1.09

Hepta nop henone

As10%

=1.10

Hex anop henon e

As10%

=1.12

Valerop henone

As10%

=1.14

Butyrophenone

As10%

=1.17

Propi oph enone

As10%

=1.20

Acetophenone

As10%

=1.25

Fig. 8. (Top graph) Same graph as in Fig. 1 but for two 4.6 mm × 150 mmcolumns packed with 4.6 �m Kinetex-C18 core–shell particles. (Bottom graph) Chro-matogram of the RPLC-checkout sample recorded at a wavelength of 243 nm. Theasymmetry factors As10% at 10% of the peak height are reported in the graph for eachnc

vpTvrltcvvHp

v(Csti(tw

0.0 0.1 0.2 0.3

0

5

10

15

2.1 x 150 mm Kinetex 1.7 μμm

(1+k)-2

HE

TP

[μμm

]

Happ

Hint

0 10 0 20 0 30 0 40 0

0

50

100

150

200

250

Octanoph enon e

As10%

=0.78

Heptanophenon e

As10%

=0.79

Hexanophenon e

As10%

=0.82

Valerophenon e

As10%

=0.88

Butyrophenon e

As10%

=0.96

Propiophenone

As10%

=1.25

Acetophen one

As10%

=1.39

Ab

so

rba

nc

e [

mA

U]

Time [s]

Fig. 9. (Top graph) Same graph as in Fig. 1 but for the two 2.1 mm × 150 mmcolumns packed with 1.7 �m Kinetex-C18 core–shell particles). (Bottom graph)Chromatogram of the RPLC-checkout sample recorded at a wavelength of 243 nm.The asymmetry factors As10% at 10% of the peak height are reported in the graph foreach n-alkanophenone. The plots are not linear due to the peak fronting.

0.0 0.1 0.2 0.3 0.4

0

3

6

9

12

(1+k)-2

HE

TP

[μμm

]

2.1 x 100 mm CORTECS 1.6 μμm

Fig. 10. Same graph as in Fig. 1 but for the 2.1 mm × 100 mm column packed

-alkanophenone. The plots are not linear due to the large hold-up volume V0 of theolumn.

elocities provides usually the maximum efficiency of columnsacked with core–shell particles for retained compounds in RPLC.his approach is valid only if the system contribution to the totalolume variance is much larger than that of the column in the wholeetention range of the test compounds. Otherwise, and particu-arly in RPLC-C18 with 4.6 mm i.d. columns, this plot will mirrorhe variation of the column HETP with the changing nature of theompounds (through the diffusion coefficient Dm or the reducedelocity v) and the retention factor k′: a non-linear plot of Happ

ersus the reciprocal of (1 + k′)2 is usually observed and the intrinsicETPs should be assessed for each individual homologous com-ound by the method of variance subtraction.

Figs. 1–5 show the plots of the apparent column plate heightsersus the reciprocals of (1 + k′)2 measured for six narrow-bore2.1 mm i.d.) columns packed with Kinetex-C18, Halo-ES-Peptide-18, and Poroshell120-C18 particles. For each column brand, theame batch of core–shell particles was used. The total porosities ofhese eighteen columns was previously measured from ISEC exper-ments and listed in references [35] (Kinetex), [36] (Halo), and [37]

Poroshell). These columns are representative of the efficiency dis-ribution of a much larger number of columns since two columnsere selected to have efficiencies in the center of this distribution,

with 1.6 �m CORTECS-C18 core–shell particles. Injection volume 0.2 �L, flow rate0.40 mL/min.

66 F. Gritti, G. Guiochon / J. Chromatogr. A 1333 (2014) 60–69

Table 2Experimental determination of the intrinsic HETP, Hintrinsic, and the extra-column volume variance �2

v,ex, using the method based on the elution of seven homologous com-pounds (acetophenone, propiophenone, butyrophenone, valerophenone, hexanophenone, heptanophenone, and octanophenone) and on the method based on the ZDV unionconnector (acetophenone, valerophenone, and octanophenone). Eluent: acetonitrile/water, 65/35 (v/v). Flow rate 0.5 mL/min. T = 23 ◦C. Columns: six 2.1 mm × 100 mm 2.6 �mKinetex-C18. System: 1290 Infinity system equipped with an inlet 120 �m × 22 cm and outlet 115 �m × 22 cm capillaries and a low-dispersion detection cell V(�) = 1.0 �L. Thevalues in parentheses (in the bottom raw and last three columns) are the relative difference between the extra-column volume variances measured using the two differentmethods.

Column SN R2 Hintrinsic [�m] �2v,ex [�L2] �2

v,ex [�L2] ZDV unionAcetophenone Valerophenone Octanophenone

#01 0.99994 4.62 13.59 10.6 11.6 12.4#02 0.99963 4.99 13.81#04 0.99988 5.27 13.17#05 0.99971 4.54 13.34#09 0.99982 5.36 13.76#20 0.99971 5.11 13.53

Average 0.99978 4.98 13.53

Standard Deviation 0.01% 6.8% 1.8%

Table 3Same as in Table 2 except the columns are six 2.1 mm × 100 mm 2.7 �m Halo-ES-Peptide C18.

Column SN R2 Hintrinsic [�m] �2v,ex [�L2]

#312 0.99953 6.30 13.28#322 0.99982 5.78 13.51#323 0.99964 5.99 13.86#327 0.99959 6.23 13.93#329 0.99975 5.58 13.83#330 0.99967 6.57 13.76

tttpanotlu(

Fw0a

Average 0.99967 6.07 13.69Standard Deviation 0.01% 6.0% 1.8%

wo to have efficiencies 2� larger than the average efficiency, andwo to have efficiencies 2� below this average. The most impor-ant feature in these graphs is the quasi-linear behavior of thelots, except those of the Poroshell120 columns (for which thepparent HETPs of the two most retained compounds, heptanophe-one and octanophenone, slightly deviate from the best linear fitbtained after discarding these two data points). Tables 2–4 report

he linear regression coefficients R2, the y-axis intercept of the bestinear fit to the data or the intrinsic HETP, and the system vol-me variance measured from the best slope combined with Eq.4). The average HETPs are then 6.07 �m for Halo-ES-Peptide-C18,

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

HE

TP

[μμm

]

(1+k)-2

2.1 x 50 mm Kinetex 1.3 μμm

ig. 11. Same graph as in Fig. 1 but for the six 2.1 mm × 50 mm columns packedith 1.3 �m Kinetex-C18 core–shell particles. Injection volume 0.2 �L, flow rate

.65 mL/min. The plots are slightly not linear due to the axial temperature gradientlong the column. The frictional heat power is equal to 16.6 W/m.

(−22%) (−14%) (−8%)

4.98 �m for Kinetex-C18, and 4.70 �m for Poroshell120-C18. Aunique extra-column volume variance was expected because, forthese three brands of columns, the same optimized 1290 vHPLCsystem, mobile phase, flow rate, and n-alkanophenone analyteswere used. So, in order to validate the method used, a unique valueof �2

ex had to be found experimentally despite the differences inthe hold-up volume V0 of the columns. The average values of thetotal porosities are slightly different, 0.505 (Kinetex), 0.567 (HaloES-Peptide), and 0.550 (Poroshell120). Finally, the average extra-column volume variances, �2

v,ex, were measured at 13.53 ± 1.8% (forKinetex), 13.69 ± 1.8% (for Halo ES-peptide), and 13.54 ± 2.6% �L2

(for Poroshell120). In contrast, these values were found to besmaller at 10.6 �L2 (acetophenone), 11.6 �L2 (valerophenone), and12.4 �L2 (octanophenone) when the columns were replaced witha ZDV union connector.

A linear plot was also found for the narrow-bore columns packedwith 1.6 �m CORTECS-C18 (see Fig. 10). Due to mechanical prob-lems to connect the metallic 120 �m × 22 cm inlet capillary of theinstrument and the inlet endfitting of the CORTECS column, theinlet capillary was replaced with a 130 �m × 25 cm Viper tubingthat adapts well to the inlets of all columns. The flow rate of theCORTECS column was decreased from 0.5 to 0.4 mL/min in orderto operate at the optimum flow rate [30]. The results are given

2 2

in Table 5. It is noteworthy that �v,ex decreases to 8.13 �L (at0.4 mL/min) which confirms the advantage of using Viper con-nections rather than classical metallic ferrules to minimize theextra-column system variance [47].

Table 4Same as in Table 2 except only five homologous compounds (acetophenone, propio-phenone, butyrophenone, valerophenone, and hexanophenone) were consideredand the columns are six 2.1 mm × 100 mm 2.7 �m Poroshell120-C18.

Column SN R2 Hintrinsic [�m] �2v,ex [�L2]

#59 0.99996 4.80 13.92#60 0.99999 5.00 12.98#62 0.99962 4.75 13.62#63 0.99998 4.50 13.37#73 0.99996 4.72 13.91#74 0.99963 4.41 13.42

Average 0.99986 4.70 13.54Standard Deviation 0.02% 4.6% 2.6%

Table 5Same as in Table 2 except the inlet capillary connector is a 130 �m × 250 mmViper, the flow rate is 0.40 mL/min and the column is one 2.1 mm × 100 mm 1.6 �mCORTECS-C18.

Column SN R2 Hintrinsic [�m] �2v,ex [�L2]

#0B01 0.99994 3.06 8.13

F. Gritti, G. Guiochon / J. Chromat

Table 6Same as in Table 5 except the flow rate is 0.65 mL/min, and the column is one2.1 mm × 50 mm 1.3 �m Kinetex-C18.

2 2 2

csctsatm1gHatoseT0ceob

4t

4Foc

iscHsanvv(tapuap2sc

nvuhpo

Column SN R Hintrinsic [�m] �v,ex [�L ]

#0B01 0.99989 2.35 9.21

A slightly non-linear plot was observed for the 2.1 mm × 50 mmolumn packed with the 1.3 �m Kinetex-C18 particles (Fig. 11). Theame experimental conditions as those applied for the CORTECSolumn were applied, except the flow rate of 0.65 mL/min in ordero operate close to the optimum flow rate. The reason for thelight non-linearity observed is directly related to the significantmount of heat produced due the friction of the eluent againsthe packed bed [48–50]. The pressure drop along the column was

easured at 750 bar for a frictional heat power Pf = Fv(�P/L) of6.25 W/m. The largest possible value for the axial temperatureradient, �T can be estimated from strict adiabatic conditions.ence, �T = (1 + ˛pT)(�P/cp,m) = 17.5 K (�p = −1.05 × 10−3 K−1

nd cp,m = 2.92 × 106 J/m3/K [51,52]). As a result, the retention fac-or of the most retained compounds is more affected than thosef the least retained homologous compounds and the plot appearslightly convex upward. For that all, the plot is almost perfectly lin-ar for the four most retained compounds. The results are given inable 6. It is again noteworthy that �2

v,ex decreases to 9.21 �L2 (at.65 mL/min) which again confirms the advantage of using Viperonnections rather than classical metallic ferrules to minimize thextra-column system variance [47]. Remarkably, the intrinsic HETPf these column is as low as 2.35 �m, a record for 2.1 mm narrow-ore column.

.2. Non-linear behavior of the Happ versus (1 + k′)−2 plots: howo evaluate Hintrinsic?

The plots of Happ versus (1 + k′)−2 are strongly non linear for all.6 mm i.d. columns, whatever the brand or the particle size (seeig. 8A, 2, 4, and 6) and for two 2.1 mm i.d. narrow-bore columns,ne packed with 1.7 �m, the other with 4.6 �m Kinetex-C18 parti-les (see Figs. 7A and 9A).

Regarding the wide 4.6 mm i.d. columns, the non-linear behav-or of these plots is explained by the system volume variance beingmaller than the column volume variance for all the homologousompounds used and for the strong dependence of their intrinsicETP on retention factors in RPLC-C18 [53–55]. The flow rate was

et at 1.85 mL/min, for which the extra-column volume variancesre equal to 10.5 �L2 for acetophenone, 10.3 �L2 for valerophe-one, and 11.1 �L2 for octanophenone. However, the true systemolume variance at 0.5 mL/min is 13.59 �L2. The average volumeariances measured when using a ZDV union connector were 11.53at 0.5 mL/min) and 10.63 �L2 (at 1.85 mL/min), respectively. So,he true system volume variance at 1.85 mL/min was correctednd estimated at 12.53 �L2. Accordingly, for 2.6–2.7 �m core–shellarticles packed in a 4.6 mm × 100 mm column, the column vol-me variance typically increases from about 10 to 200 �L2 (fromcetophenone to octanophenone). For the larger 4.6 �m Kinetexarticles packed in a 4.6 mm × 150 mm column, it increases from5 to 950 �L2. This confirms that the system volume variance ismaller than the column volume variance for all n-alkanophenoneompounds, even the less retained ones.

The unexpected non-linear plots observed for the 2.1 mm i.d.arrow-bore columns (Figs. 7A and 9A) may be due to the systemolume variance (13.6 �L2) being surprisingly smaller than the col-

mn variance for the two most retained homologous compounds,eptanophenone and octanophenone on the 1.7 �m Kinetex-C18articles; hexanophenone, heptanophenone, and octanophenonen the 4.6 �m Kinetex-C18 particles. A careful look at the peak

ogr. A 1333 (2014) 60–69 67

profiles recorded shows that the relatively poor efficiency of thesemost retained compounds is due to peak fronting. The peak asym-metry factor measured at 10% of the peak height decreases rapidlyand becomes smaller than unity with increasing retention factor.This is illustrated in Fig. 9B where these asymmetry factors arereported for each n-alkanophenone compounds. The same phe-nomenon of peak fronting is also observed for the narrow-borecolumn packed with 4.6 �m Kinetex-C18 particles (see Fig. 7B).This is not due to column overloading and an anti-langmuirianadsorption isotherm [56] but to trans-column flow heterogene-ity. Fronting is consistent with the average eluent velocity beingsmaller in the central region of the column than in the wall regionand with the local efficiency being lower near the wall than inthe column center [57]. In other words, the bed seems to be moredensely packed in the wall than in the center of the column. Mostoften, peaks are tailing and the opposite scenario is true as observedby local electrochemical detection [55,58]. For instance, in Fig. 8B,the deviation of the plots of Happ versus (1 + k′)−2 from linear behav-ior for the 4.6 mm i.d. column packed with the same 4.6 �m Kinetexparticles is not due to peak fronting (since all the peak asymmetryfactors exceed unity) but to the large influence of k′ on the A, B andC coefficients of the van Deemter HETP plot.

Therefore, in all cases in which the plots of Happ versus (1 + k′)−2

are strongly non-linear, the intrinsic HETP cannot be determinedfrom the extrapolation of the best linear fit function to zero. Thesystem volume variance must be determined first by using a col-umn for which the plot is linear and then subtracted it from theexperimental total volume variance. All these intrinsic HETPs areshown for each individual n-alkanophenone as full symbols inFigs. 2, 4, 6, 7A, 8A and 9A.

4.3. Summary of the column performance packed with core–shellparticles since 2007

The advantage of the method presented above is that it canbe used with any standard vHPLC instruments which have systemvolume variance as large as 10–15 �L2. Although these HPLC instru-ments do not permit analysts to perform excellent separationsnor to observe more than 20% of the intrinsic efficiency of 10 cmlong narrow-bore (2.1 mm i.d.) columns packed with sub-2 �mcore–shell particles for weakly retained compounds with k′ � 1,it still allows an easy and accurate measurement of the intrin-sic kinetic performance of modern narrow-bore, highly efficientcolumns.

It should be emphasized that the columns that we used wereavailable from the shelves of our laboratory and were not brandnew when tested. The eldest columns were received in 2009 whilethe most recent ones were first used in 2013. Additionally, the testconditions selected were not necessarily optimal for each individ-ual column tested since they differ in particle sizes (from 1.3 to4.6 �m). The goal of this work was simply to assess their overallkinetic performance for a specific class of small homologous n-alkanophenones in RPLC-C18 (with 0.20 < k′ < 10). Nevertheless, thecolumn plate heights measured are representative of the optimalcolumn performance because the Cv term of all columns were small.Operating these columns around their optimal reduced velocity(�opt � 10) usually provides the highest possible efficiency. Thesame mobile phase composition (acetonitrile–water, 65/35, v/v),temperature (room temperature or 23 ◦C), and class of small ana-lytes (homologous n-alkanophenone) were used for all columns.According to the experimental results in section 3.6, the diffusion

coefficients varied from 1.03 (octanophenone) to 1.48 × 10−5 cm2/s(acetophenone). This means that the range of experimental reducedvelocities varied from 6.9 to 9.9 for the 1.3 �m particles, from 10.6to 15.2 for the 2.6 �m particles and from 18.7 to 26.9 for the 4.6 �m

68 F. Gritti, G. Guiochon / J. Chromat

1 2 3 4 5 6 7 8 9 10 11

0

2

4

6

8

*Peak fronting

2.1 mm

2.1 mm

2.1 mm*

2.1 mm*

2.1 mm

2.1 mm

2.1 mm

4.6 mm

4.6 mm4.6 mm4.6 mm

Kin

ete

x 1

.3 μμ

m

CO

RT

EC

S 1

.6 μμ

m

Kin

ete

x 1

.7 μμ

m

Kin

ete

x 4

.6 μμ

m

Ki n

ete

x 4

.6 μμ

m

Po

rosh

ell120 2

.7 μμ

m

Po

rosh

ell120 2

.7 μμ

m

Halo

-ES

2.7

μμm

Halo

-ES

2.7

μμm

Kin

ete

x 2

.6 μμ

m

Kin

ete

x 2

.6 μμ

m

Hin

t [μμ

m]

Column group (i.d . and dp)

1 2 3 4 5 6 7 8 9 10 11

0

2

4

6

8

Fig. 12. Summary of the data collected in this work. Intrinsic HETPs Hint measuredfb4p

pu

gTitmrwttieittrlatdtT2ac

ftit1aefiaa

5

1

[[[[[[[[

or the different groups of columns available in the laboratory and mabufacturedetween 2009 and 2013. A group of column is described by the column i.d. (2.1 or.6 mm) and the particle size (1.3, 1.6, 1.7, 2.6, 2.7, and 4.6 �m) with which they areacked.

articles for the seven n-alkanophenone homologous compoundssed.

Fig. 12 shows the smallest intrinsic HETP recorded for eachroup of columns, defined by their diameters and particle sizes.his study confirms that 4.6 mm i.d. columns always provide largerntrinsic column efficiencies than 2.1 mm i.d. columns packed withhe same batch particle batch [17,59]. Detailed investigations of the

echanism of mass transfer in these columns showed that the long-ange eddy dispersion HETP term is larger in narrow-bore than inide-bore modern HPLC columns [13,17,35–38,59]. The explana-

ion is as follows. There is no evidence presented in the literaturehat trans-column velocity biases are more pronounced in 2.1 thann 4.6 mm i.d. columns. Actually, narrow-bore columns are moreasily operated under the asymptotic dispersion regime, character-zed by full radial equilibration of the sample concentration acrosshe column diameter. That is explained by the radial excursion dis-ance from the column center to its wall being smaller, the wall iseached faster in a narrow-bore than in a wide-bore columns. Tal-arek et al. [60] showed that, in the confined geometry of a tube, thexial dispersion coefficient under asymptotic conditions is largerhan that expected under the so-called transient pre-asymptoticispersion regime. This transient dispersion regime characterizeshe behavior of a column which is not fully radially equilibrated.herefore, the dispersive wall effects are smaller in 4.6 mm than in.1 mm i.d. columns because the former columns are operated in

dispersion regime that is closer to that of the infinite diameterolumn (free from wall and border effects).

Finally, this study confirms that, unless peaks are severelyronting due to packing issues, very fine core–shell particles downo 1.3 �m size (if not less) can be packed efficiently in 2.1 mm.d. columns. Their HETP decreases from about 7.5 to 4.5, 3.0 ando 2.3 �m with decreasing particle size from 4.6, 2.6, 1.6, and to.3 �m, respectively. This corresponds to reduced plate heights ofbout 1.6, 1.7, 1.9, and 1.8. This slight apparent loss of reducedfficiency is consistent with the smaller transverse dispersion coef-cient and the larger impact of the border effects regarding thesynchronous distribution and collection of the sample moleculescross the inlet and outlet column cross-section area.

. Conclusion

The intrinsic HETPs of modern efficient columns packed with.3–4.6 �m core–shell particles manufactured between 2009 and

[[[

[

ogr. A 1333 (2014) 60–69

2013 were measured on a standard vHPLC instrument with anexcellent accuracy. This task was achieved for narrow-bore 2.1 mmi.d. columns, the contribution of which to the volume variance of theelution bands is one order of magnitude smaller than the volumevariance of vHPLC system for weakly retained analytes. The intrin-sic HETP were measured by extrapolating for an infinitely retainedanalyte the linear plot of the apparent HETP versus the reciprocalof (1 + k′)2 measured for a series of homologous n-alkanophenonecompounds. The true value of the extra-column volume variancewas determined with a relative accuracy of less than a few per-cent from the best slopes of these quasi-linear plots. It was usedto assess the intrinsic HETPs of each homologous compounds onthe columns for which the plot was found non-linear due to eitherpacking issues or to large hold-up volumes.

This approach will be very useful for the measurement of theintrinsic HETPs of narrow-bore column packed with the finestcore–shell particles. The classical method used to measure theintrinsic HETP and the extra-column volume variances of instru-ments is based on replacing the column with a ZDV unionconnectors. This method fails because it systematically underes-timates the true system volume variances of small molecules byabout 10–30%. Inconsistent HETP data that depend on the instru-ment used are then generated. The advantage of this alternativemethod is that it allows column manufacturers and users to obtainthe same value for the intrinsic column performance. In the sametime, the slope of the plot provides the system performance used bythe customer, who may realize immediately how much of the fullkinetic performance of an efficient narrow-bore chromatographiccolumn can be achieved.

Acknowledgements

This work was supported in part by the cooperative agreementbetween the University of Tennessee and the Oak Ridge NationalLaboratory. We thank Joe DiStefano and Jack Kirkland (AdvancedMaterial Technologies, Wilmington, DE, USA) for the gift of theeight 2.7 �m Halo-ES-Peptide columns. We thank Jacob Fairchild(Waters, Mildford, MA, USA) for the gift of the CORTECS columnpacked with 1.6 �m core–shell particles; Tivadar Farkas and JasonAspach (Phenomenex, Torrance, CA, USA) for the preparation andgift of the 4.6, 2.6, 1.7, and 1.3 �m Kinetex columns; and Ron Majorsand Xiaoli Wang (Agilent Technologies, Little Fall, DE, USA) for thepreparation and gift of the 2.7 �m Poroshell 120 EC-C18 columnsused in this work.

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