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Journal of Chromatography A, 1334 (2014) 30–43

Contents lists available at ScienceDirect

Journal of Chromatography A

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

valuation of the kinetic performance of new prototype.1 mm × 100 mm narrow-bore columns packed with 1.6 �muperficially porous particles

abrice Gritti a, Stephen J. Shinerb, Jacob N. Fairchildb, Georges Guiochona,∗

Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USAWaters Corporation, Milford, MA 01757, USA

r t i c l e i n f o

rticle history:eceived 4 December 2013eceived in revised form 17 January 2014ccepted 20 January 2014vailable online 11 February 2014

eywords:ore–shell particlesass transfer mechanism

ddy dispersionongitudinal diffusionolid–liquid mass transfer resistancextra-column band broadening

a b s t r a c t

The mass transfer mechanism in three prototype narrow-bore columns (2.1 mm × 100 mm format)packed with 1.6 �m superficially porous particles was investigated using different instruments. Theheights equivalent to a theoretical plate of three small molecules were measured using a mixture ofacetonitrile and water as the eluent. The values reported include the contributions of longitudinal diffu-sion, eddy dispersion, and the solid–liquid mass transfer resistance. The bulk diffusion coefficients of theanalytes were measured using the capillary method, calibrated with thiourea in pure water. The reducedlongitudinal diffusion coefficient was determined from the results of a series of peak parking experiments.The solid–liquid mass transfer resistance coefficient and the intra-particle diffusivities of the analytes inthe porous region of the particles were estimated from Garnett–Torquato’s model of effective diffusion indense beds packed with core–shell particles. The eddy dispersion term, mostly due to trans-column andborder effects, was obtained by subtracting the longitudinal diffusion and the solid–liquid mass transferresistance terms from the total HETP obtained from the first and second central peak moments calculated

by numerical integration (Simpson’s approach) after baseline correction and systematic left and right cutsof the peak profiles. The results show that the eddy dispersion controls at least 66% of the overall columnHETP for small molecules beyond the optimum velocity. This work illustrates how important it is to useultra-low dispersive very high pressure liquid chromatography (vHPLC) systems to properly measure andto practically use the high efficiencies of narrow-bore columns packed with 1.6 �m core–shell particles

ide in

since these columns prov

. Introduction

The need to produce chromatographic columns packed withub-3 �m core–shell particles [1] has constantly increased sinceheir first commercialization in 2007 [2]. Six years later, at leasteven major column manufacturers commercialize conventional orarrow-bore columns packed with sub-3 �m core–shell particlesAdvanced Material Technologies, Phenomenex, Agilent Technolo-ies, Sigma–Aldrich/Supelco, ThermoScientific, Macherey-Nagel,nd Chromanik). Many analysts in a wide range of industries usehem to develop faster and more efficient separation methodshan those using columns packed with conventional fully porous

articles [3–5]. Scientists used them to unravel mass transfer mech-nisms in chromatography [2,6–27], to refine the general theory ofand broadening in packed columns [28], and to draw perspectives

∗ Corresponding author. Tel.: +1 865 974 0733; fax: +865 974 2667.E-mail addresses: guiochon@utk.edu, guiochon@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.2014.01.065

trinsic efficiencies higher than 400,000 plates per meter.© 2014 Elsevier B.V. All rights reserved.

regarding the evolution of the column efficiency in the near future[29].

Using the classical column format (4.6 mm I.D., 10–15 cm long),practitioners can benefit from exceptionally low minimum plateheights, often reported to be around 1.4 times the average particlesize [4]. These columns are nearly equivalent to those packed withsub-2 �m fully porous particles but have a much higher perme-ability, ranging from k0 = 4.6 × 10−11 cm2 for 2.7 �m Poroshell [30]to 5.8 × 10−11 cm2 for 2.6 �m Kinetex [31], and 6.4 × 10−11 cm2 for2.7 �m Halo [32]. The specific permeability of columns packed with1.7 �m, 2.5 �m, and 3.5 �m fully porous Bridge Ethylene Hybrid(BEH) particles are about 2.5, 4.0, and 7.8 × 10−11 cm2, respectively.Finally, columns packed with sub-3 �m core–shell are claimed tobe safely used with inlet pressures up to 600 bar.

The high efficiencies of columns packed with fine sub-3 �mcore–shell particles have some disadvantages. The widths of the

peaks eluted from them are so narrow that the instrument contri-bution to the total band width can no longer be neglected [17]. Aneasy solution is to reduce the detection cell volume and the diam-eter of the connecting tubes to 0.5 �L and 127 �m, respectively.

F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43 31

List of symbols

Roman lettersA(�) reduced eddy diffusion termB reduced longitudinal diffusion coefficient with ref-

erence to the interstitial linear velocityCi Sample concentration at time ti (s)Cp Reduced solid–liquid mass transfer resistance coef-

ficientDeff Effective diffusion coefficient of the packed bed

(m2/s)Dn Dean numberdp average particle diameter (m)ds mean Sauter particle diameter (m)Dm bulk molecular diffusion coefficient (m2/s)F(�m) hindrance diffusion factorFv flow rate (m3/s)h reduced plate heightH plate height (m)k′ retention factork1 zone retention factorKc Kozeny–Carman constant.k0 specific permeability (m2)Ka equilibrium Henry’s constant for the sample

adsorption-desorption between the solid phase inthe porous volume of the particle and the liquideluent phase

N column efficiencyL column length (m)Ptot total pressure drop (Pa)Pex system pressure drop in the absence of the chro-

matographic column (Pa)rc column inner radius (m)Sex external surface area of all the particles packed in

the chromatographic column (m2)t1 first discretized elution time (s)tN last discretized elution time (s)tleft elution time (adsorption) at 1.5% of the peak height

(s)tright elution time (desorption) at 1.5% of the peak height

(s)ti discretized elution time (s)tp parking time (s)tR retention time at the peak apex (s)�tp increment of the peak parking time (s)Rcoil coiled capillary tube radius (m)rtube capillary tube inner radius (m)Sc Schmidt numberu interstitial linear velocity (m/s)ucenter linear velocity in the center of the capillary tube

(m/s)us superficial linear velocity (m/s)V0 column hold-up volume (m3)

Greek lettersˇ parameter in Torquato’s model of effective diffusion

in packed beds defined by Eq. (6)εe external column porosityεp particle porosityεt total column porosity�e obstruction factor caused by randomly packed non-

� eluent viscosity (Pa s)�m ratio of the probe diameter to the average pore size�1 first moment (s)�′

2 second central moment (s2)�1,ex first moment recorded in the absence of the chro-

matographic column (s)�′

2,ex second central moment recorded in the absence ofthe chromatographic column (s)

� reduced interstitial linear velocity ratio of the effective diffusivity of the sample in the

porous region of the particle to its bulk diffusioncoefficient

2v,ex system volume variance (m6)

2v,tube

capillary tube volume variance (m6)� ratio of the solid non-porous core diameter to the

core–shell particle diameter

porous particles to the diffusion in the external bulkmobile phase

� i internal obstruction factor

�2 adjustable parameter in Torquato’s model of effec-tive diffusion Eq. (5)

This might decreases the system volume variance from about 10to 2 �L2 (depending on the applied flow rate) [17,33,34] but thisstill may be insufficient because 1.6–1.7 �m core–shell particles arenow packed in narrow-bore 2.1 mm I.D. columns. Injection devicesshould be designed to minimize the broadening of bands beforethey reach the column inlet and detection cells should not broadenbands exiting the column. Therefore, the kinetic performance ofnarrow-bore columns packed with sub-2 �m particles is expectedto depend much on the instrument used.

This work reports on the mass transfer kinetics of three columnspacked with prototype 1.6 �m RPLC-C18 core–shell particles. Theeluent used was an aqueous solution of acetonitrile (75/25, v/v) atroom temperature. The analytes were three small molecules (caf-feine, naphthalene, and anthracene). The diffusion coefficients ofuracil and naphthalene were measured using the calibrated capil-lary method. The heights equivalent to a theoretical plate (HETP)were derived by the moment method previously reported [35,36].Thus, the column HETP includes all the sources of dispersion takingplace in the column (radial heterogeneity, border effects [29]) andin the very high pressure liquid chromatography (vHPLC) instru-ment that may lead to the formation of non-Gaussian peaks (witheither peak fronting or tailing). The reduced longitudinal diffu-sion HETP term was measured with the peak parking (PP) method[37]. The solid–liquid mass transfer resistance HETP term was mea-sured by combining the results of the PP measurements and theGarnett–Torquato [38–41] model of effective diffusion in columnspacked with core–shell particles [28,42]. The overall eddy disper-sion HETP term was obtained by the subtraction method [43].The extra-column band broadening was measured by replacingthe chromatographic column by a zero dead volume (ZDV) unionconnector and the accuracy of this method for measuring the sys-tem variance was assessed. In particular, at a given flow rate, weexamine the effects of the sample concentration injected and of thesystem back pressure on the results of measurements of the bandspreading due to the instrument used.

2. Theory

2.1. Definitions

The core-to-particle diameter ratio is called �. The externalporosity of the packed bed is εe, Dm is the diffusion coefficient of theanalyte in the bulk mobile phase. The apparent analyte diffusivitythrough the porous shell of the particle is Dp = ˝Dm, being the

3 atogr

dsdp

p

k

�

wg

u

w

2

wiw[gt

h

t

2

f[p[

D

w

ˇ

aep

�

w

B

2

tt

C

2 F. Gritti et al. / J. Chrom

imensionless ratio of the sample diffusivity through the poroushell of the particles to its bulk diffusion coefficient. The effectiveiffusion coefficient along the heterogeneous packed bed (cores,orous shell, external eluent) is Deff.

The zone retention factor extended to the superficially porousarticle is written [28]:

1 = 1 − εe

εe[εp + (1 − εp)Ka][1 − �3] (1)

The reduced interstitial linear velocity, �, is written [44]:

= udp

Dm(2)

here u is the average interstitial linear velocity along the columniven by:

= Fv

εe r2c

(3)

here Fv is the flow rate and rc is the inner column radius.

.2. Reduced HETP equation

The temperature is assumed to be homogeneous across thehole column. The possible presence of significant frictional heat-

ng effects is neglected, which is the general case of columns packedith core–shell particles, even when heat friction power is high

15,16,45,46]. The overall reduced plate height is the sum of the lon-itudinal diffusion term, the trans-particle mass transfer resistanceerm, and the eddy diffusion term or:

= B

�+ A(�) + Cp� (4)

The explicit physico-chemical descriptions of each of these HETPerms are given in the next sections.

.2.1. The longitudinal diffusion termThe longitudinal diffusion term is derived from the effective dif-

usion coefficient of the analyte in a heterogeneous column bed40,41]. A physically relevant model of effective diffusion in randomacked beds is given by the composite Garnett–Torquato model38,42,47]. It is written:

eff = 1εe(1 + k1)

[1 + 2(1 − εe) − 2εe�2ˇ2

1 − (1 − εe) − 2εe�2ˇ2

]Dm (5)

ith

= ((1 − �3)/(1 + (�3/2))) − 1((1 − �3)/(1 + (�3/2))) + 2

(6)

nd �2 is an adjustable parameter estimated from the experimentalxternal obstruction factor for = 0, � = 0, and k1 = 0 (non-porousarticles). From Eq. (5), the expression of �e = Deff /Dm is given by:

e = 2(1 − (�2/2))3 − εe(1 + �2)

(7)

here �2 = 0.493 [48].The reduced B coefficient in Eq. (4) is then written [40]:

= 2(1 + k1)Deff

Dm(8)

.2.2. The solid–liquid mass transfer resistance termA general expression of the solid–liquid mass transfer resis-

ance coefficient (Cp) was derived for core–shell particles, using

he following coefficient provided by [7,6,49,50]:

p = 130

εe

1 − εe

(k1

1 + k1

)2[

1 + 2� + 3�2 − �3 − 5�4

(1 + � + �2)2

]1˝

(9)

. A 1334 (2014) 30–43

In this equation, was estimated from the Garnett–Torquatomodel of effective diffusion by combining Eqs. (5), (6) and (8).

2.2.3. The eddy diffusion termThe eddy diffusion term results from all sources of sample

dispersion in the interparticle column volume. It includes thecontributions of the homogeneous random packing or of analytedispersion along a hypothetical infinite diameter column (whichhas no wall, no inlet and outlet endfitting) [29,51], e.g., overdistances ranging from the interparticle distance (trans-channelvelocity biases) to a few particle diameters (short-range inter-channel velocity biases). It also includes the contributions of theso-called long-range trans-column velocity biases induced by thepresence of the solid cylindrical wall surrounding the bed and theinlet/outlet (distribution/collection) endfittings. The total reducededdy dispersion HETP term, A(�), is obtained by subtracting thereduced HETP terms Cp� and B/� from the expression of h in Eq. (4).

3. Experimental

3.1. Chemicals

The mobile phase used was a binary mixture of acetonitrileand water (75/25, v/v). Tetrahydrofuran (THF) was used as themobile phase for ISEC measurements. All these solvents wereHPLC grade from Fisher Scientific (Fair Lawn, NJ, USA). Acetoni-trile was filtered before use on a surfactant-free cellulose acetatefilter membrane, 0.2 �m pore size (Suwannee, GA, USA). Theeleven polystyrene standards (MW = 590, 1100, 3680, 6400, 13,200,31,600, 90,000, 171,000, 560,900, 900,000, and 1,870,000) werepurchased from Phenomenex (Torrance, CA, USA). Caffeine, naph-thalene, and anthracene were purchased from Fisher Scientific,with a minimum purity of 99%.

3.2. Instrument

Four different vHPLC instruments were used in this work. Theaccuracies of the flow rate delivered by the pump are all better than0.5% as measured by collecting the eluent in a 5 mL volumetric glassduring 10 min at 0.5 mL/min.

3.2.1. A 1290 Infinity HPLC system (Agilent Technologies,Waldbroen, Germany)

This liquid chromatograph includes a 1290 Infinity Binary Pumpwith solvent selection valves and a programmable auto-sampler.The injection volume is drawn into one end of the 20 �L injec-tion loop. The instrument includes a two-compartment oven anda multi-diode array UV-VIS detection system. The system is con-trolled by the Chemstation software. The sample trajectory in theequipment involves the successive passage of its band through theseries of:

• A 20 �L injection loop attached to the injection needle. The designof the First In, Last Out (FILO) injection system is such that theentire volume of sample drawn into the loop is injected into thecolumn. This ensures an excellent injection repeatability.

• A small volume needle seat capillary (115 �m I.D., 100 mm long),�1.0 �L, located between the injection needle and the injectionvalve. The total volume of the grooves and connection ports inthe valve is around 1.2 �L.

• Two 130 �m × 250 mm long Viper capillary tubes offered by themanufacturer (Thermo Fisher Scientific, Germering, Germany),placed one upstream, the second one downstream the column.Each tube has a volume around 3.3 �L.

atogr

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F. Gritti et al. / J. Chrom

A small volume detector cell, V() = 0.6 �L, VCell = 1.4 �L, 10 mmpath.

No solvent heat exchanger was used in the experiment. Thextra-column volume is equal to 1.0 + 1.2 + 3.3 + 3.3 + 1.4 = 10.2 �Lnd generates an extra-column peak variance that varies between

and 9 �L2 for small molecules when the flow rate is increasedrom 0.05 to 0.80 mL/min (injection volume = 0.25 �L). To improvehe performance of this Agilent system, Viper capillary tubes weresed. They allow a better reproducibility of the retention time andhe peak variances recorded [52] by avoiding the tube-column con-ection failures over the duration of the experiments that are oftenncountered with standard metallic and/or plastic endfittings atery high pressures (�1 kbar).

.2.2. The classic ACQUITY UPLC system (Waters, Milford, USA)This instrument for liquid chromatography includes a binary

ump with solvent selection valves and a programmable auto-ampler. All of the parts used have the standard configuration forhis instrument but the smaller injection loop. The injection vol-me is drawn into one end of a 1 �L injection loop. The instrument

ncludes a one-compartment oven and a tunable wavelength UV-IS detection system. The system is controlled by the Empoweroftware (Waters). The sample trajectory in the equipment involveshe successive passage of its band through the series of:

A 1 �L injection loop attached to the injection valve. The designof the injection system is such that only a fraction of the samplevolume drawn into the long needle is injected into the column.This ensures a minimization of the extra-column band spreading.A 127 �m × 450 mm long column stabilizer placed upstream thecolumn. It has a volume of around 5.7 �L.A 102 �m × 150 mm long outlet tube placed downstream the col-umn. Its volume is 1.2 �L.A small volume detector cell, 0.5 �L, 10 mm path.

The extra-column volume is equal to 5.7 + 1.2 + 0.5 = 7.4 �L andenerates an extra-column peak variance that varies between 1.5nd 4 �L2 for small molecules when the flow rate is increased from.05 to 0.80 mL/min (injection volume = 0.25 �L).

.2.3. The H-class ACQUITY UPLC system (Waters, Milford, USA)Two different H-class instruments were used. The first chro-

atograph (H-class ACQUITY 1) includes a quarternary solventanager (QSM), a flow through needle (FTN), a single column com-

artment, a photodiode array (PDA) detector and a programmableuto-sampler. The injection volume is drawn into one end of a

�L injection loop. The system is controlled by the Empower soft-are (Waters). The sample trajectory in the equipment involves

he successive passage of its band through the series of:

A 1 �L injection loop attached to the injection valve. The designof the injection system is such that only a fraction of the samplevolume drawn into the long needle is injected into the column.This ensures a minimization of the extra-column band spreading.A 102 �m × 317.5 mm long active pre-heater placed upstreamthe column. It has a volume of 2.57 �L.A 63.5 �m × 254 mm long outlet tube placed downstream thecolumn. Its volume is 0.80 �L.A small volume detector cell, 0.5 �L, 10 mm path.

The extra-column volume is equal to 2.57 + 0.80 + 0.50 = 3.87 �Lnd generates an extra-column peak variance that varies between.7 and 2.1 �L2 for small molecules when the flow rate is increasedrom 0.05 to 0.80 mL/min (injection volume = 0.25 �L).

. A 1334 (2014) 30–43 33

The second chromatograph (H-class ACQUITY 2) includes a QSM,a FTN, two column compartments, two column selection valves, aPDA detector and a programmable auto-sampler. There are twocolumn positions in each column compartment, selectable viaselection valves.

• A 1 �L injection loop attached to the injection valve. The designof the injection system is such that only a fraction of the samplevolume drawn into the long needle is injected into the column.This ensures a minimization of the extra-column band spreading.

• A 102 �m × 368.3 mm long tubing from the selection valve to thefirst column selection valve. It has a volume of 2.99 �L.

• A 102 �m × 317.5 mm long active pre-heater from the selectionvalve to the column inlet. It has a volume of 2.57 �L.

• A 102 �m × 482.6 mm long tubing from the column outlet to thesecond selection valve. It has a volume of 3.91 �L.

• A 102 �m × 482.6 mm long tubing from the second selectionvalve to the PDA flow cell. Its volume is 3.91 �L.

• A small volume detector cell, 0.5 �L, 10 mm path.

The extra-column volume is equal to 2.99 + 2.57 + 3.91 + 3.91 + 0.50 = 13.88 �L. It generates an extra-column peak variance thatvaries between 1.2 and 3.8 �L2 for small molecules when theflow rate is increased from 0.05 to 0.80 mL/min (injection vol-ume = 0.25 �L).

3.2.4. The I-class ACQUITY UPLC system (Waters, Milford, USA)This chromatograph includes a binary pump with solvent selec-

tion valves, a programmable auto-sampler and an active eluentpreheating by the column heater module. All the parts used arethose of the standard configuration of the I-class system, savethe smaller injection loop. The injection volume is drawn intoone end of a 1 �L injection loop. The instrument includes aone-compartment oven and a tunable wavelength UV-VIS detec-tion system. The system is controlled by the Empower software(Waters). The sample trajectory in the equipment involves the suc-cessive passage of its band through the series of:

• A 1 �L injection loop attached to the injection valve. The designof the injection system is such that only a fraction of the samplevolume drawn into the long needle is injected into the column.This ensures a minimization of the extra-column band spreading.

• A 76 �m × 317 mm long active pre-heater placed upstream thecolumn. It has a volume of around 1.4 �L.

• A 63 �m × 165 mm long outlet tube placed downstream the col-umn. Its volume is around 0.2 �L.

• A small volume detector cell, 0.5 �L, 10 mm path.

The extra-column volume is equal to 1.4 + 0.2 + 0.5 = 2.1 �L andgenerates an extra-column peak variance that varies between 0.2and 0.6 �L2 for small molecules when the flow rate is increasedfrom 0.05 to 0.80 mL/min (injection volume = 0.25 �L).

3.3. Columns

Three 2.1 × 100 mm columns packed with 1.6 �m prototypecore–shell particles were kindly given by Waters (Milford, MA,USA). The first column was packed with shell particles fromparticle batch 1. The second (A) and third (B) columns werepacked with shell particles from particle batch 2. Table 1 liststhe physico-chemical properties of these three columns, accord-

ing to manufacturer data and to data acquired in our laboratory. Afourth column (same dimension, batch 3) was also tested. It hadbeen packed using an optimized packing procedure for the 1.6 �mcore–shell particles.

34 F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43

Table 1Physico-chemical property of the three columns packed with 1.6 �m RPLC-C18 core–shell particles (batch 1 and batch 2).

Batch number Column Column’sdimension I.D.(mm) × length(mm)

Averageparticle sizea

(�m)

Totalb porosity(εt)

Externalporosityc (εe)

Particle/shellporosityd (εp)

Permeability(cm2)e (k0)

Kozeny–Carmanconstantf (Kc)

1 – 2.062 × 100 1.621 0.532 0.400 0.342 2.76 × 10−11 170

2A 2.073 × 100 1.615 0.526 0.395 0.367 2.68 × 10−11 164B 2.085 × 100 1.615 0.526 0.395 0.367 2.64 × 10−11 166

3 – 2.083 × 100 1.621 0.526 0.390 0.347 2.67 × 10−11 169

a Measured from calibrated Coulter Counter experiments.b Measured from the elution of toluene in THF.c Measured from ISEC experiments.

nitrile

fp

3

wlm1sbtl7G

obvsibtt(saTo

ε

Aa

3

a2wmT[

d Measured assuming a solid core diameter of 1.15 �m (� = 0.71).e Measured from the corrected pressure drop (<300 bar) using a mixture of acetof Determined from Eq. (25).

The PEEK capillary tube used for the measurement of the dif-usion coefficients (1/16 in o.d. × 0.0254 in i.d. × 50 ft long) wasurchased from IDEX Health & Science (Oak Harbor, WA, USA).

.4. ISEC experiments and column porosities

ISEC measurements were made on all four columns. Neat THFas used as the eluent. Eleven polystyrene standards with molecu-

ar weights between 500 and 2 million Daltons were used as probeolecules. They cover a wide range of molecular sizes, between

0 and 950 A. The flow rate was set at 0.10 mL/min and the sampleize set at 0.25 �L. The detection wavelength was set at 254 nm, theandwidth at 4 nm, and the sampling rate at 160 Hz. To minimizehe extra-column volume of the Agilent system, the inlet and out-et 130 �m × 250 mm Viper connecting tubes were replaced with5 �m × 250 mm Viper tubes (Thermo Fisher Scientific, Germering,ermany).

The external column porosities (εe) were derived by extrap-lating to a zero hydrodynamic molecular radius the exclusionranches of the ISEC plots of the elution volumes of the polymersersus their hydrodynamic molecular radius. The ISEC results arehown in Fig. 1. The accuracy of the ISEC experimental protocols within 1%. The size of the largest mesopores was estimated toe around 195 ± 10 A based on the deviation of the ISEC plot fromhe exclusion branch. This was confirmed by the low tempera-ure nitrogen adsorption and the plot of the Barret–Joyner–HalendaBJH) desorption (dV/d log D versus the D pore volume), whichhows the presence of large mesopores in the range between 150nd 350 A. The maximum of the BJH plot is observed for D = 105 A.he total column porosity (εt) was measured from the elution timef toluene in pure THF. The internal porosity (εp) was derived from:

p = εt − εe

(1 − εe)(1 − �3)(10)

ll the results for the total, the external, and the internal porositiesre listed in Table 1.

.5. Diffusion coefficients of the sample molecules

The bulk molecular diffusivities, Dm, of caffeine, naphthalenend anthracene were measured at a constant temperature of3.8 ± 0.3 ◦C. The mobile phase was a mixture of acetonitrile and

ater prepared by the pump mixer (75/25, v/v). The capillaryethod was used to measure these diffusion coefficients [53,54].

his method is valid only if all the following four conditions are met55–57]:

and water (75/25, v/v) at 23.8 ± 0.2 ◦C. Viscosity � = 0.571 cP.

1. The radial equilibration of the sample concentration is effec-tive along the tube of length L and of inner radius rtube, whichis achieved if [56]:

r2tube

3.82Dm

� L

ucenter(11)

where ucenter is the linear velocity in the center of the tube, whichis twice the average linear velocity.

2. The contribution of axial molecular diffusion to the total spatialvariance is negligible. This condition is achieved if [55]:

192D2m

r2tube

u2center

� 1 (12)

where ucenter is the linear velocity of the mobile phase in thecenter of the tube, which is twice the average linear velocity.

3. The extra-column peak variance 2v,ex is negligible compared to

the total variance of these peaks 2v,tube

:

2v,ex � 2

v,tube (13)

4. The product of the Dean number (Dn) squared by the Schmidtnumber (Sc) is smaller than 100 (no secondary flow circulationin the coiled tube) or [58]:

Dn2Sc � 100 (14)

The Dean number is defined by:

Dn = 2�urtube

�

√rtube

Rcoil(15)

where Rcoil is the radius of the coiled tube. The Schmidt numberis:

Sc = �

�Dm(16)

5. The diffusion coefficients measured are validated by comparingthe coefficient obtained for a standard compound for which thevalue of this coefficient are accurately known.

The flow rate was fixed at 0.050 mL/min, the tube lengthL = 15.24 m, the inner tube radius rtube = 0.0254 cm (1/100 in.), andthe coil radius R = 12 cm. So, ucenter = 49.6 cm/min. The injected vol-ume was 5 �L. The extra-column volume is the sum of the volumesof the needle seat capillary (1.3 �L), the grooves of the injectionvalve (1.2 �L) and the detector (1.6 �L). In the worst case, thesevolumes can be considered as mixing volumes, so, the maximum

extra-column volume variance is 52 + 1.32 + 1.22 + 1.62 = 30.7 �L2.Thus, the extra-column peak variance represents only 0.57, 0.96,and 0.67% of the total volume variance measured. The eluent viscos-ity is 0.57 cP, its density is 0.843 g/cm3. The Dean number is equal to

F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43 35

F ls repc

0ct

D

wt

(ta0acwDv2p

l1

3

i

ig. 1. ISEC results reported for the four columns used in this work. The black symboores.

.14. The Schmidt numbers were measured at 552, 361, and 470 foraffeine, naphthalene, and anthracene, respectively. Accordingly,he diffusion coefficient is given by the following relationship [55]:

m = 124

�1,t

�′2,t

r2tube (17)

here �1,t and �′2,t are respectively the first and the second central

ime moments of the recorded peak profiles.The radial equilibration times in the three columns

r2tube

/3.82Dm) are only 10.6, 7.4, and 9.2% of the shortest migrationime in the tube center (L/ucenter). The relative contributions ofxial molecular diffusion to the total spatial variance are 0.026,.061, and 0.036%. The products Dn2Sc are equal to 11.2, 7.3,nd 9.6, all values that are much smaller than 100. Finally, theapillary method was validated under standard conditions (pureater, T = 25 ◦C, by using thiourea infinitely diluted in pure water,m = 1.33 × 10−5 cm2/s [59,60]). The measurement provided aalue of 1.37 × 10−5 cm2/s (tube 1) and 1.35 × 10−5 cm2/s (tube) or a less than +3% relative error, which is acceptable for theurpose of this work. Thus, all the above four conditions are met.

As a result, the diffusion coefficients of caffeine, naphtha-ene, and anthracene were accurately measured at 1.23 × 10−5,.88 × 10−5, and 1.43 × 10−5 cm2/s, respectively.

.6. The peak parking experiments

The PP method was pioneered by Knox, first in gas [61], thenn liquid [37] chromatography. This method was used to measure

resent ISEC data obtained for the column packed with the 3.3 �m non-porous silica

the internal obstruction factor of columns packed with poroussilica-C18 particles [62], the intra-particle diffusion coefficients[42,63,64], and the bulk diffusion coefficients of various solutes indifferent liquid mobile phases [28,65,66].

In this work, 1 �L dilute solutions of caffeine, naphthalene,and anthracene (<0.5 g/L) were injected at constant flow rates of0.10 mL/min in the column. The column was eluted during the timenecessary for the sample bolus to reach exactly half the length ofthe column, at the constant temperature of 23.8 ± 0.3 ◦C. The flowwas then abruptly stopped and the sample left free to diffuse alongthe column during the parking time (values of 1, 15, 30, and 60 minwere used). All samples were detected at a wavelength of 263 nm.The detection bandwidth was set at 4 nm and the sampling rateat 20 Hz for all parking times. The slopes of the plots of the peakvariances, 2

t , versus the peak parking times, tp, provide a directestimate of the true effective diffusion coefficient along the column,as briefly explained in the theory section.

The first (�1) and the second central (�2) moments of the elutedbands were determined numerically by cutting the band profileson their left and right sides, as shown by Stevenson et al. [35,36].After baseline correction of the chromatogram, the first (t1, leftcut) and the last (tN, right cut) elution times were unambiguouslydetermined from the two elution times recorded when the sampleconcentration first increased (tleft) then decreased (tright) to 10% (in

the presence of a column) or 4% (in the absence of a column) of thepeak height:

t1 = tR − 1.5(tR − tleft) (18)

3 atogr

a

t

w

ttitptawraEa

�

�

waTpTsd

3

ats00rticiHc

aprtasb

mg

h

wac

6 F. Gritti et al. / J. Chrom

nd

N = tR + 2.3(tR − tright) (19)

here tR is the elution time taken at the apex of the peak profile.This method has the tremendous advantage of properly and sys-

ematically adjusting the integration window ([t1, tN]) regardlesshe degrees of peak fronting and tailing that may fluctuate in var-ous ways depending on the nature of the sample injected and onhe flow rate applied [67]. It is highly sensitive to any source ofre-asymptotic axial dispersion that leads to peak fronting and/orailing. The classical half-height peak width method would not beble to notice these peak deformation nor to account for them,hich is why it is considered as a highly inaccurate albeit quite

obust method. In contrast, the method used in this work is highlyccurate but less robust than the half-height peak width method.xamples are shown in Fig. 2 in the presence (right graphs) and thebsence (left graphs) of a chromatographic column.

The moments are provided by the following equations:

1 =∑i=N−1

i=2 (Ci−1 + 4Ci + Ci+1)ti∑i=N−1i=2 Ci−1 + 4Ci + Ci+1

(20)

′2 =

∑i=N−1i=1 (Ci−1 + 4Ci + Ci+1)(ti − �1)2

∑i=N−1i=2 Ci−1 + 4Ci + Ci+1

(21)

here N is the total odd number of data points recorded and i isn even integer, which increases from 2 to 4, 6, . . . and to N − 1.he numerical integration is based on the Simpson’s method (bestarabolic approximation of the local peak concentration profiles).he relative error on the true first and second peak moments ismaller than −0.1% and −1%, respectively (slight underestimationue to the finite time interval tN − t1).

.7. HETP measurements

All three compounds used (caffeine, naphthalene, andnthracene) were dissolved in the same sample vial in ordero allow a fair comparison between their corrected HETPs. Theequence of flow rates applied to the 2.1 mm I.D. columns was.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.50, 0.60, 0.70 and.80 mL/min (a total of twelve data points). The maximum flowate was chosen so that the frictional power dissipated throughhe column did not exceed 15 W/m. Eventually, the maximumnlet pressure used was about 830 bar. Under such frictional heatonditions, the columns are certainly not fully isothermal but thempact of the small radial temperature gradients on the columnETP remains practically negligible for 2.1 mm I.D. narrow-boreolumns packed with silica-based core–shell particles [15,16].

Depending on the flow rate, the sampling frequency wasdjusted between 5 and 160 Hz in order to record at least 140 dataoints for the whole band profile of caffeine, the thinnest and leastetained compound. Samples of 0.25 �L (each sample concentra-ion is smaller than 0.5 g/L) were injected into the three columnsnd the chromatograms recorded at a wavelength of 263 nm. A con-tant UV bandwidth of 4 nm was selected. The temperature was sety the laboratory air-conditioning system at 23.8 ± 0.3 ◦C.

The HETP data were all measured according to the integrationethod previously described and the reduced plate height h is

iven by:

= L

d

�′2 − �′

2,ex2

(22)

p (�1 − �1,ex)

here L is the column length, dp the mean particle size, and �1,exnd �′

2,ex are the first and second central moments of the extra-olumn band profiles measured by the same integration method.

. A 1334 (2014) 30–43

It should be emphasized that this method provides an excel-lent accuracy, although its precision is necessarily smaller than thatof the half-height peak width method, a procedure that providesan empirical parameter which is devoid of any physical meaning[44]. Provided that the protocol used to measure the extra-columnband broadening (ZDV union connector) is accurate, at worst,e.g., for flow rates when the relative contribution of the extra-column peak variances to the total peak variance is largest (seediscussion later), the accuracies are close to 8, 4, and 3% for non-retained compounds and for retained compounds with k′ = 1.2 and2.7, respectively [31,68]. However, due to the relatively small col-umn hold-up volume (V0 = 177 �L) compared to the extra-columnvolume (VExtra = 11 �L), the precision of the experimental reducedHETP plots is usually around ±25, 10, and 5% for retention fac-tors k′ = 0, 1.2, and 2.7, respectively. This explains the level of noiseobserved for the reduced HETP plots and the use of ultra-low dis-persive vHPLC systems, as discussed later in Section 4.

4. Results and discussion

4.1. Porosities of the columns

The total, internal, and external porosities of the three columnsused in this work are listed in Table 1. They are very close to eachother irrespective of the batch number (1 and 2) and the columnpacked (A and B). Remarkably, despite the difference in the columntube diameter between columns 2A (batch 2, column A) and 2B(batch 2, column B), their external and total porosities are exactlythe same, at 0.395 and 0.526, respectively. The porosities of theshells are close to 0.37 if it is assumed that the solid core diam-eter is 1.15 �m (� = 0.71). All these porosities are well within thestandard range of those measured for other brands of shell parti-cles [2,30–32]. Note that these porosities may be slightly affectedby the porosities of the inlet and outlet frits. Assuming that theirvoid volumes are 1.5 �L, the total, internal, and external porositywould drop by 0.01, 0.005, and 0.01, respectively. Thus, our mea-surements could overestimate the true column porosities by nomore than 0.01.

Fig. 1 shows that the slopes of the exclusion branches arelarger for columns packed with 1.6 �m shell particles than for4.6 × 100 mm columns packed with 3.3 �m solid silica cores. Asa first approximation, this slope is a third of the external surfacearea, Sex of the bed of particles per unit column volume [69]. Sincethe average particle sizes of the prototype particles studied aresmaller than the non-porous silica cores, the observation shownin Fig. 1 makes sense. The external surface areas available in thecolumns were estimated from the slope of the exclusion branchesat 0.872, 0.875, 0.883, 0.896, and 2.95 m2 for the 2.1 mm × 100 mmcolumns 1, 2A, 2B, 3, and for the 4.6 × 100 mm column packed withthe 3.3 �m silica cores, respectively. The expected surface area,assuming uniform (dp = Const) spherical particles are:

SA,ex = 6(1 − εe) r2c L

dp(23)

This equation provides theoretical surface areas of 0.742, 0.758,0.768, 0.769, and 1.77 m2 for the 2.1 mm × 100 mm columns 1, 2A,2B, 3, and for the 4.6 mm × 100 mm packed with the 3.3 �m silicacores, respectively. They are 15, 13, 13, 14, and 40% smaller thanthe corresponding experimental values, which could be explainedin part by the finite particle size distribution of these packing mate-

rials and the possible presence of particles smaller than averageinside the column. Remarkably, this relative difference is system-atically smaller for the prototype 1.6 �m core–shell particles (only−13 to −15%) than for the silica 3.3 �m core–shell particles (−40%),

F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43 37

15.0 15.5 16.0 16.5 17.0

50

100

150

200

CAFFEINE

32.5 33 .0 33 .5 34 .0 34 .5 35 .0

50

100

150

200

250

300

NAPHTHALENE

55 56 57

10

20

30

40

50

ANTHRACENE

0.5 1.0 1.5 2.0 2.5

100

200

300

400

500

600

0.5 1.0 1.5 2.0 2.5

200

400

600

800

1000

1200

1400

0.5 1.0 1.5 2.0 2.5

50

100

150

200

250

300

Fig. 2. Examples of peak profiles recorded in the absence (right graphs, extra-column peak profiles) and in the presence (left graphs) of the new 2.1 mm × 100 mm columnpacked with the prototype 1.6 �m core–shell particles. Flow rate: 0.80 mL/min, inlet pressure: 827 bar. T = 23.8 ± 0.3 ◦C. vHPLC system: optimized 1290 Infinity system. Thered segments on the left and right sides of the peak profiles locate the first and the last data point used in the calculation of the first and second central peak moments. Thedistance between the solid green line and the horizontal x-axis accounts for the error made in the calculation of these moments (the accuracy error is zero when the solidg and −n han thp nd, th

sa

4

s

k

reen line overlays perfectly the x-axis). These relative errors are less than −0.1%

umerical integration method provide an exceptionally high accuracy, far better teak width method. (For interpretation of the references to color in this figure lege

uggesting that the amounts of fine particles in batches 1, 2, and 3re relatively small.

.2. Permeabilities of the columns

The permeabilities of the three columns packed with 1.6 �m

hell particles were calculated according to the following equation:

0 = �L1

r2c ((�(Ptot − Pex))/�Fv)

(24)

1%, respectively, illustrating how the measurements of the peak moments by thee unacceptable accuracy (errors up to −50% at high flow rates) of the half-height

e reader is referred to the web version of the article.)

where � = 0.57 cP is the eluent (acetonitrile–water, 75/25, v/v) vis-cosity at room temperature (23.8 ± 0.3 ◦C), L is the column length(10 cm), rc is the inner column radius (see values in Table 1), Ptot

is the total pressure drop, including the system contribution, Pex isthe pressure drop generated by the vHPLC system in the absenceof column, replaced by a zero dead volume (ZDV) connector. Themaximum flow rate, Fv = 0.25 mL/min, was set so that the column

inlet pressure does not exceed 300 bar and the column tempera-ture remains constant (the frictional heat power per unit lengthis smaller than 1.5 W/m). The compressibility of the eluent canbe neglected under these conditions and the linear velocity of the

38 F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43

0.250.200.150.100.050.000

100

200

300C

orre

cted

pre

ssur

e dr

op [

bar]

Flow r ate [ mL/min]

Column Batc h 1Column A Ba tch 2Column B Ba tch 2Column Batc h 3

Ft

mcdT2bc

K

w

viabvpaomi

4

topcaupsutttaeatcov

0.80.60.40.20.00

4

8

12

Extr

a-co

lum

n pe

ak v

aria

nce

[µL2

]

Flow r ate [mL/min]

CaffeineNaphthaleneAnthrace ne

mobile phase a mixture of acetonitrile and water (75/25, v/v). Thecolumn was replaced with a ZDV union connector. At a fixed flowrate of 0.40 mL/min, the extra-column peak variance increasesfrom 0.6 to 1.7, 3.4 and to 8.3 �L2 from the I-class Acquity to

0.80.60.40.20.00

2

4

6

8

10

Varia

nce

[μL2 ]

Fv [mL/min]

1290 Infinity optimizedClassic AcquityH-class Acqu ityI-class Acquity

ig. 3. Plots of the corrected column pressure drop as a function of the flow rate forhe three columns used.

obile phase can be assumed to remain constant along the wholeolumn length. Fig. 3 shows the plots of the corrected pressurerop as a function of the flow rate for the three columns columns.he specific permeabilities were measured at 2.76, 2.68, 2.64, and.67 × 10−10 cm2 for the columns packed with batch 1, batch 2 (A),atch 2 (B), and batch 3 particles, respectively. The Kozeny–Carmanonstant Kc was measured according to:

c = ε3e d2

S

k0(1 − εe)2(25)

here dS is the mean Sauter diameter.We assumed that dS was given by the median diameter of the

olume-based particle size distribution. These diameters are listedn Table 1. Thus, the Kozeny–Carman constants were estimatedt 170, 164, 166, and 169 for the columns packed with batch 1,atch 2 (A), batch 2 (B), and batch 3 particles, respectively. Thesealues are consistent with those usually measured with columnsacked with larger fully porous particles [69–71]. In contrast, theyre smaller than those previously measured for some other brandsf 2.6–2.7 �m core–shell particles packed in the same column for-at [30–32]. This confirms that there is only a small amount of fines

n the packing materials used to make the three prototype columns.

.3. Extra-column volume contributions

The first vHPLC system used was the Agilent 1290 Infinity sys-em described in Section 3.2. The band spreading contributionf this instrument was minimized and made as reproducible asossible by using two finger tight 130 �m × 25 cm Viper capillaryonnecting tubes, a low-dispersive UV detection cell (V() = 0.6 �L),nd a 115 �m × 100 mm needle seat capillary. The injected vol-me was set at 0.25 �L. Fig. 4 shows plots of the extra-columneak variances measured by numerical integration of the first andecond central peak moments. It is noteworthy that these val-es are sensitive to the nature of the compound injected, throughheir diffusion coefficients. Unsurprisingly, naphthalene provideshe lowest extra-column band spreading volume because it hashe largest diffusion coefficient (1.88 × 10−5 cm2/s) of the threenalytes used. Large diffusion coefficients enable a faster radialquilibration of analyte concentration across the tube diameternd generate more symmetrical extra-column peak profiles than

hose of analytes with smaller diffusion coefficients [72]. The extra-olumn peak variance increases from about 2 �L2 at a flow ratef 0.05 mL/min (naphthalene) to a maximum value of 10 �L2 (thisalue is acceptable for HPLC columns but becomes significant for

Fig. 4. Plots of the extra-column peak volume variances of the three analytes usedin this work as a function of the flow rate. vHPLC system: optimized 1290 Infinitysystem.

narrow bore columns packed with sub-2 �m particles) at a flowrate of 0.80 mL/min (caffeine and anthracene).

The influence of the vHPLC system on the apparent column effi-ciency is significant for the very efficient narrow-bore 2.1 mm I.D.columns packed with 1.6 �m core–shell particles. Using the opti-mized 1290 Infinity system, the variances of the peaks of caffeine,naphthalene, and anthracene are between about 4 and 18, 10 and23, and 25 and 55 �L2, respectively. The largest relative contribu-tion of the system band spreading to the total band spreading wereestimated at 75% for caffeine at 0.15 mL/min, 50% for naphthalene at0.25 mL/min, and 35% for anthracene at 0.35 mL/min. In conclusion,it was the goal of this section to show and emphasize why the bandbroadening contributions of the HPLC system should be systemati-cally subtracted from the total peak variances observed in order toobtain the sole contribution of the chromatographic column.

Then, three other instruments were also used, the classicAcquity, the H-class Acquity, and the I-class Acquity instruments.Fig. 5 compares the extra-column volume variances of all fourUPLC instruments used. The sample was naphthalene and the

Fig. 5. Comparison between the experimental extra-column peak variances mea-sured on four different vHPLC systems as indicated in the graph. Flow rate range:0.05–0.80 mL/min. Analyte: naphthalene. Eluent: acetonitrile/water (75/25, v/v).T = 23.8 ◦C. The H-class instrument is the H-class ACQUITY 1.

F. Gritti et al. / J. Chromatogr

0.90.60.30.00

1

2

3

4

Flow rate [ mL/min]

Peak

var

ianc

e [μ

L2 ]

Fig. 6. Effect of the pressure adjusted by a specifically designed capillary restric-tor (see details in the text) on the extra-column peak variance of naphthalene ina mixture of acetonitrile and water (75/25, v/v) at room temperature. Five differ-ent pressures were generated: 33 bar (blue square symbols), 75 bar (purple circlesymbols), 286 bar (green upward triangle symbols), 582 bar (red star symbols) and5tv

ts

tToccZlcdfirepb

FtTS

28 bar (small blue diamond symbols). System H-class ACQUITY 2. (For interpreta-ion of the references to color in this figure legend, the reader is referred to the webersion of the article.)

he H-class Acquity, the classic Acquity and to the 1290 Infinityystems, respectively.

The impact of the high pressure in the pre-column tubing onhe extra-column band broadening was studied in the laboratory.he H-class Acquity 2 instrument was used for this purpose. Anriginal post-column tubing connection was used with one endonnected to the detector and fitted with a normally shaped metalollar and a standard PEEK screw. The other end, connected to theDV union connector, was made of a PEEK ferrule with a metal col-ar compressed by a metal screw. A progressive tightening of thisompression screw allows restriction of the flow by deforming andecreasing the tube inner diameter. The inlet pressure was variedrom 33 to 75, 286, 582 and to 528 bar. Fig. 6 shows the correspond-ng plots of the extra-column band variance (in �L2) versus the flow

ate for these five different pressure conditions. Except at the low-st pressure, the data in Fig. 6 confirm that the larger the systemressure, the larger the extra-column band broadening. This maye explained by optimization of the connection by its initial tight-

0.90.60.30.00

1

2

3

4

Peak

var

ianc

e [ μ

L2 ]

Flow rate [mL/min]

Thiou rea 100 mg/mL Thiou rea 50 mg/mL Thiou rea 25 mg/mL

ig. 7. Effect of the sample concentration on the extra-column peak variance ofhiourea in a mixture of acetonitrile and water (75/25, v/v) at room temperature.hree different injected concentration were used as indicated in the graph legend.ystem H-class ACQUITY 2.

. A 1334 (2014) 30–43 39

ening and by the effect of pressure on the peak distortion. FromP < 100 bar to P > 500 and at a constant flow rate of 0.8 mL/min,the system bandspreading increases from about 3.0 to 3.7 �L2 ora relative increase of 20–25%. Note that the impact of the sampleconcentration from C = 25 to 50 and to 100 �g/mL on the systembandspreading was tested with thiourea. The results shown in Fig. 7demonstrate the lack of effect of the sample concentration on theextra-column band broadening. Therefore, the difference betweenthe true (in the presence of the chromatographic column) and theexperimental (in the presence of the ZDV union connector) systembandspreading most likely stems from the difference of pressure inthe pre-column tubing connections.

In the next section we report on and compare the intrinsic per-formance of these three prototype columns, based on the results ofthe measurements of the individual HETP contributions of the B/�,Cp�, and A(�) terms after correction for the experimental contribu-tions of the HPLC system.

4.4. Intrinsic reduced plate height

4.4.1. Longitudinal diffusion and solid–liquid mass transferresistance HETP term

The reduced longitudinal HETP term was provided by the resultsof the peak parking experiments described in the experimental sec-tion. The reduced solid–liquid mass transfer resistance HETP termwas obtained by combining the PP results and the model of effec-tive diffusion of Garnett and Torquato [38,40,41,47]. The resultsare listed for the three prototype columns in Tables 2 (caffeine), 3(naphthalene), and 4 (anthrancene) along with the respective zoneretention factors k1, the effective diffusion coefficients Deff, the shelldiffusivity coefficients ˝, and the solid–liquid mass transfer resis-tance coefficients Cp. All the values make sense and are typical ofthose reported for endcapped RPLC-C18 bonded phases. The rela-tively small values of B (1.6, 2.4, and 3.8) compared to those (1.8,3.2, and 5.2) obtained for columns packed with particles having thesame values of but fully porous [28,73] is simply explained bythe presence of the impermeable solid core. The same remark holdsfor the Cp coefficients.

4.4.2. Total reduced plate heightFig. 8 shows the plots of the total reduced plate heights h versus

v, the reduced interstitial linear velocity, for caffeine, naphtha-lene, and anthracene by using the optimized 1290 Infinity system.The solid lines represent the sum of the reduced longitudinal andsolid–liquid mass transfer resistance HETP terms measured andreported in the previous section. Accordingly, the average distancebetween the symbols and these solid lines is a direct estimate ofthe total reduced eddy dispersion term. In the range of velocitybetween v = 0 and v = 15, the sums of the asymptotic trans-channeland short-range inter-channel reduced eddy dispersion HETP termsare smaller than 0.4h unit [29,74]. The residual eddy dispersionHETP term includes the combined effects of the trans-column pack-ing heterogeneity (center-to-wall velocity biases) and of the bordereffects (non-ideal sample distribution and sample collection at theinlet and outlet of the column, respectively). The former effect islargest for long columns, for small diameter columns still large bedaspect ratio, and for large retention factors [23,29,75]. The secondeffect is largest for short columns, for wide inner diameter columns,and for small retention factors [76,77].

As expected, the precision of the h data for caffeine (non-retained compound) is particularly low (±25%) at the lowest flowrates, where the extra-column band spreading accounts for about

75% of the total peak variance of caffeine. It is better for retainedanalytes, naphthalene (±10%) and anthracene (±5%) because theextra-column band broadening contributions are only 50 and 35%,respectively but remains important. The h plot of caffeine is very

40 F. Gritti et al. / J. Chromatogr. A 1334 (2014) 30–43

Table 2Diffusion coefficients (Dm), zone retention factor (k1), effective diffusion coefficients (Deff), reduced longitudinal diffusion coefficients (B), ratio of the shell diffusivity to thebulk diffusion (˝), and solid–liquid mass transfer coefficient (Cp) measured for the compound caffeine at T = 23.8 ◦C. The mobile phase composition is acetonitrile/water,75/25, v/v. The diffusion coefficient of caffeine is 1.23 × 10−5 cm2/s.

Batch number Column Column’s dimension I.D. (mm) × length (mm) k1 Deff (cm2/s) B Cp

1 – 2.062 × 100 0.34 7.30 × 10−6 1.59 0.15 0.0045

2A 2.073 × 100 0.34 7.18 × 10−6 1.57 0.15 0.0038B 2.085 × 100 0.34 7.28 × 10−6 1.59 0.16 0.0036

Table 3Diffusion coefficients (Dm), zone retention factor (k1), effective diffusion coefficients (Deff), reduced longitudinal diffusion coefficients (B), ratio of the shell diffusivity to thebulk diffusion (˝), and solid–liquid mass transfer coefficient (Cp) measured for the compound naphthalene at T = 23.8 ◦C. The mobile phase composition is acetonitrile/water,75/25, v/v. The diffusion coefficient of naphthalene is 1.88 × 10−5 cm2/s.

Batch number Column Column’s dimension I.D. (mm) × length (mm) k1 Deff (cm2/s) B Cp

1 – 2.062 × 100 1.99 7.70 × 10−6 2.45 0.49 0.0095

2A 2.073 × 100 1.98 7.72 × 10−6 2.45 0.49 0.0092B 2.085 × 100 1.99 7.66 × 10−6 2.44 0.48 0.0093

Table 4Diffusion coefficients (Dm), zone retention factor (k1), effective diffusion coefficients (Deff), reduced longitudinal diffusion coefficients (B), ratio of the shell diffusivity to thebulk diffusion (˝), and solid–liquid mass transfer coefficient (Cp) measured for the compound anthracene at T = 23.8 ◦C. The mobile phase composition is acetonitrile/water,75/25, v/v. The diffusion coefficient of anthracene is 1.43 × 10−5 cm2/s.

Batch number Column Column’s dimension I.D. (mm) × length (mm) k1 Deff (cm2/s) B Cp

1 – 2.062 × 100 3.92 5.52 × 10−6 3.92 1.13 0.0059

2A 2.073 × 100 3.88 5.59 × 10−6 3.81 1.14 0.0057B 2.085 × 100 3.93 5.44 × 10−6 3.74 1.10 0.0059

1510500

4

8

12

16

h=H

/dp Batch 1

Caff eineNaphtha leneAnthracen e

1510500

4

8

12

16

Caffei neNaphthalen eAnthracen e

Batch 2, A

h=H

/dp

1510500

4

8

12

16

CaffeineNaphthaleneAnthrace ne

Batch 2, B

h=H

/dp

ν ν

νFig. 8. Experimental corrected reduced plate height (h) as a function of the reduced interstitial linear velocity (�). The solid straight lines represent the contribution of the sumo(

f the reduced longitudinal eddy diffusion and solid–liquid mass transfer/resistance HETP75/25, v/v). T = 23.8 ◦C. The difference between the symbols and the solid lines represent

s. Small molecules. vHPLC system: 1290 Infinity system. Eluent: acetonitrile/waters the total reduced eddy dispersion HETP term.

atogr. A 1334 (2014) 30–43 41

scfuimrcn22pft

4

owt(scsia4Cw

HeaTtmaflab4tvnpbltdiuZsptout

hptfa0

0 2 4 6 8 100

2

4

6

hexpecte d, is othermal

νν=udp/Dm

h=H

/dp

Batc h 1Batch 2, co lumn ABatch 2, co lumn B

1290 Infinity

0 2 4 6 8 100

2

4

6

νν=udp/Dm

h=H

/dp

h=H

/dp

Batch 1Batch 2, column ABatch 2, column B

hexpe cted, isothe rmal

Classic Acquity

0 2 4 6 8 100

2

4

6New colu mn

Batch1

Batch2, column A

Batch2, column B

νν=u dp/Dm

hexpected, i sothe rmal

I-class Acquity

Fig. 9. Corrected reduced plate height (h) of naphthalene as a function of the reducedinterstitial linear velocity (�) measured on three different vHPLC systems as indi-cated in the graphs. The solid blue line represents the expected intrinsic HETP ofnaphtahlene with a reference eddy dispersion HETP term obtained from reference

F. Gritti et al. / J. Chrom

teep, revealing the negative impact of the border and trans-olumn effects on the column efficiency. These effects are largestor compounds having the smallest residence times in the col-mn. As the retention factor increases, the column performance

mproves due to the decrease of the eddy dispersion HETP. Thiseans that the border effects were practically eliminated when

etention factors increase, leaving solely the effects of the trans-olumn velocity biases. The minimum reduced plate heights ofaphthalene were then measured at 2.25 ± 0.23, 2.67 ± 0.27, and.51 ± 0.25 for columns 1, 2A, and 2B, respectively. The values are.76 ± 0.14, 2.81 ± 0.14, and 2.50 ± 0.13 for the most retained com-ound, anthracene. The minimum reduced plate height measuredor anthracene was slightly larger than the one measured for naph-halene, due to its larger B coefficient (3.82 versus 2.45).

.5. Effect of the HPLC instrument on the column efficiency

The corrected reduced plate heights of naphthalene were notnly measured with the 1290 Infinity. They were also measuredith less-dispersive instruments including the classic Acquity and

he I-class Acquity instruments for the four prototypes columnsblack symbols for batch 1, red symbols for batch 2A, and greenymbols for batch 2B, and orange symbols for the freshly packedolumn with batch 3). All these reduced plate height curves arehown in Fig. 9. The solid blue line represents the virtual referencentrinsic reduced plate height of naphthalene for B = 2.45, C = 0.0094nd for a total eddy dispersion HETP term, A(�), obtained for a.6 mm × 100 mm column packed with 2.6 �m core–shell Kinetex-18 particles [25]. A minimum intrinsic reduced plate height of 1.5as expected.

The most remarkable observation in Fig. 9 is that the correctedETP curves depend on the type of the instrument used. It wasxpected that the same kinetic performance would be obtained forll the columns after correction for the extra-column contributions.he results show that the smaller the system band spreading fromhe 1290 Agilent to the classic and to the I-class Acquity instru-

ents, the smaller the corrected total HETP. This is especially truet high flow rates and high reduced velocities. For instance, for aow rate of 0.8 mL/min and a reduced velocity of about 9, the aver-ge corrected reduced plate heights of the three columns (batch 1,atch 2A, and batch 2B columns) decreases from 5 (1290 Infinity) to

(classic Acquity) and to 2.5 (I-class Acquity). This is an experimen-al demonstration that measurements of the extra-column peakariance made by replacing the column with a ZDV union con-ector is (1) not accurate and (2) underestimates the true valuerovided by the chromatographic column. There are two plausi-le explanations for these underestimates: first, the pressure is

arger in the pre-column tubings in the presence of the column,he diffusion coefficients are smaller, and, according to the generalispersion theory of Aris along cylindrical tubes, the peak variance

s larger. Second, the solute concentrations in the post-column vol-me are smaller in the presence of the column than in that of theDV union connector. Therefore, the concentration gradients aremoother with the column than with the union connector and theeak variance along the post-column tube should be larger. In Sec-ion 4.3, it was shown that the most plausible explanation for thesebservations is the difference in pressure in the pre-column vol-me. The sample concentration injected has virtually no impact onhe bandspreading measurements.

In order to best estimate the true minimum reduced plateeights of columns packed with these new prototype core–shellarticles, an optimally packed column (batch 3) was tested on

he I-class instrument. The results are shown in Fig. 9 by theull orange stars. Remarkably, after correction for the smallestvailable extra-column peak variances (from only 0.04 �L2 at.05 mL/min to 0.60 �L2 at 0.80 mL/min), the minimum reduced

[25]. Eluent: acetonitrile/water (75/25, v/v). T = 23.8 ◦C. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthe article.)

HETP was measured at only 1.55. Assuming that the extra-column peak variance was underestimated by about 25%, aminimum intrinsic reduced HETP of 1.50 could be expectedfor these new prototype columns. This value is remarkable

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onsidering the narrow diameter of the column and the diffi-ulty to efficiently pack sub-2 �m particles. This value is only% larger than the minimum value of h reported for wider.6 mm × 100 mm columns packed with 2.6–2.7 �m core–shell par-icles [4,18,30–32].

. Conclusion

This detailed investigation of the mass transfer resistances inhree narrow-bore (2.1 mm × 100 mm) columns packed with pro-otype 1.6 �m core–shell particles from two different batchesor low molecular weight analytes (caffeine, naphthalene, andnthracene) confirms the major influence of the eddy dispersionerm on the overall efficiency of all columns.

Due to the importance of the extra-column volume of the290 instrument used compared to the column hold-up vol-me, the precision and accuracy that can possibly be achieved

n the determination of the column HETPs corrected for thenstrument contribution are limited. The precision of the mea-urements of the corrected reduced HETPs decreases from ±5 to25% from the most to the least retained compound. For this

eason, the accurate minimum reduced HETPs obtained for themall analytes could not be estimated accurately for the pro-otype columns. The average HETP are estimated at 2.47 ± 0.25naphthalene, B = 2.45) and 2.69 ± 0.14 (anthracene, B = 3.82) overhe three columns, for optimum reduced velocities of 3.0 and.5, respectively. The difference between the optimum reducedlate heights of naphthalene and anthracene is explained byhe difference between the longitudinal diffusion coefficients(3.82/3.5) − (2.45/3.0) = 1.08 − 0.81 = 0.27). This confirms that itsontribution to the optimum column performance is relativelymportant (>66%) compared to those of the B/� (<34%) and Cp�<1.5%) HETP terms.

Using an instrument having a low extra-column volumeontribution (I-class Acquity) and testing an optimally packedolumn provided a minimum reduced plate height of 1.50, aalue comparable to those usually found for columns packedith sub-3 �m core–shell particles in a wider column format

4.6 mm × 100 mm). This work shows that the measurement ofhe extra-column peak variance using a ZDV union connector inlace of the column underestimates the true extra-column peakariance by about 20–25%. This explains why the intrinsic mini-um reduced plate heights measured with the 1290 instrumentere found larger than those measured with the I-class instru-ent.The forthcoming challenge will be to pack uniform beds with

ub-2 �m particles while minimizing the wall effect in 2.1 mm I.D.olumns. A second challenge will be to develop an instrument giv-ng an extra-column contribution to peak broadening of the orderf 0.5 �L2 at 1 mL/min while contributing moderately to the extra-olumn pressure drop.

ote added in proof

The terms “standard” and “optimized” configurations used inhis paper refer to Agilent 1290 systems modified by the authorsith 140 and 130 �m connection capillaries, respectively, to pro-uce large system dispersion but do not refer to any configurationurrently available from Agilent Technologies.

cknowledgements

This work was supported in part by the cooperative agreementetween the University of Tennessee and the Oak Ridge National

[[[[[

. A 1334 (2014) 30–43

Laboratory with the support of the Waters Technologies Corpora-tion. We thank Paul Stevenson (Deakin University, Waurn Ponds,Victoria, Australia) for the home-made Mathematica program thatenabled us to measure systematically and accurately the first andsecond time peak moments.

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