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Journal of Chromatography A, 1355 (2014) 179–192

Contents lists available at ScienceDirect

Journal of Chromatography A

j o ur na l ho me page: www.elsev ier .com/ locate /chroma

article size distribution and column efficiency. An ongoing debateevived with 1.9 �m Titan-C18 particles

abrice Gritti a, David S. Bellb, Georges Guiochona,∗

Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USASupelco Analytical, Bellefonte, PA 16823, USA

r t i c l e i n f o

rticle history:eceived 15 April 2014eceived in revised form 6 June 2014ccepted 10 June 2014vailable online 23 June 2014

eywords:article size distributionolumn efficiencyass transfer mechanism

ddy dispersion

a b s t r a c t

The mass transfer mechanism in four prototype columns (2.1 and 3.0 × 50 mm, 2.1 and 3.0 × 100 mm)packed with 1.9 �m fully porous Titan-C18 particles was investigated by using two previously reportedhome-made protocols. The first one was used to measure the eddy dispersion HETP of these new columns,the second one to estimate their intrinsic (corrected for HPLC system contribution) HETPs. Titan particlesare fully porous particles with a narrow particle size distribution (RSD of 9.2%). The mean Sauter diameter(dSauter = 2.04 �m) was determined from Coulter counter measurements on the raw silica material (beforeC18 derivatization) and in the absence of a dispersant agent (Triton X-100) in a 2% NaCl electrolyte solution.The results show that these RPLC Titan columns have intrinsic minimum reduced HETPs ranging from 1.7to 1.9 and generate up to 290,000 plates per meter. The 3.0 mm i.d. columns are more efficient than the2.1 mm i.d. ones and short columns are preferred to minimize efficiency losses due to frictional heating

itan particles-Alkanophenones

at high speeds. This work also revealed that (1) the lowest h values of the Titan columns are observed atlow reduced velocities (�opt = 5); (2) this is due to the unusually small diffusivity of analytes across theporous Titan-C18 particles; and (3) the Titan columns are not packed more uniformly than conventionalcolumns packed with fully porous particles. Earlier and recent findings showing that the PSD has no directphysical impact on eddy dispersion and column efficiency are confirmed by these results.

. Introduction

The past and recent literature on the relationship between thefficiency of chromatographic columns and the particle size distri-ution (PSD) of their packing material is quite unanimous. Halasznd Naefe investigated the influence of various column parametersn peak broadening in HPLC for particles larger than 50 �m [1].hey concluded that the efficiency of 2,6-xylidine was hardly influ-nced by the width of the sieve fraction as long as it deviated fromhe arithmetic mean by less than approximately 40%. This resultas later confirmed by Done and Knox [2]. In the 1970s, Unger et al.

3] discussed the influence of the particle size (5–35 �m) of mate-ials with various PSDs and particle shapes. They concluded thathe column permeability and its efficiency were nearly unchangedhen the mean particle diameter was kept constant. The relative

tandard deviations (RSDs) of the different sieve fractions wereess than 25% for the smallest particle size (6 �m) and larger than0% for the largest size range (33 �m). A few years later, Unger

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

G. Guiochon).

ttp://dx.doi.org/10.1016/j.chroma.2014.06.029021-9673/© 2014 Elsevier B.V. All rights reserved.

© 2014 Elsevier B.V. All rights reserved.

and Messer [4] compared the performance of columns packed withspherical or irregular silica and alumina particles (1–10 �m) withvarious size distributions. They observed no significant differencein the minimum reduced plate heights. The RSDs of the various PSDsvaried from 20% (10 �m mean diameter) to 60% (2 �m mean diam-eter). In the 1980s, Dewaele and Verzele [5] evaluated the impactof the PSD of the packing material on the plate height in LC. Theyprepared a series of packing materials by mixing 3 and 8 �m parti-cles in different proportions. A linear increase in the plate numberwith increasing mass fraction of the 3 �m particles was observed,showing that a wider particle size distribution had no influenceon the column efficiency. More recently, Billen et al. [6] discussedthe impact of the PSD on the performance of sub-2 �m particlesand concluded that it was not the width of the PSD but ratherthe presence of fines that greatly determines the chromatographicperformance of packed columns. Finally, a series of columns werepacked with different mass fractions of 3 and 5 �m particles witha RSD of the PSDs adjusted between 17 and 43% but no impact ofthe RSD was observed on the reduced plate heights [7]. This study

even suggested that the presence of a small amount of 3 �m parti-cles amidst the larger 5 �m ones or vice versa led to smaller h valuesthan those measured for columns packed with only small or largeparticles.

180 F. Gritti et al. / J. Chromatogr. A

List of symbols

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

erence to the interstitial linear velocitycp sample concentration in the particle mesopores

(kg/m3)cs sample concentration in the stationary phase

(kg/m3)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)Fv 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 absence of the chromato-

graphic column (Pa)rc column inner radius (m)rtube PEEK capillary tube inner radius (m)tp parking time (s)tR retention time at the peak apex (s)�tp increment of the peak parking time (s)Sc Schmidt numberu interstitial 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)�e external column porosity�p particle porosity�t total column porosity�e obstruction factor caused by randomly packed non-

porous particles to the diffusion in the external bulkmobile phase

� eluent viscosity (Pa s)�1,t first moment (s)�′

2,t second central moment (s2)� reduced interstitial linear velocity

ratio of the effective diffusivity of the sample in theporous region of the particle to its bulk diffusioncoefficient

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

1355 (2014) 179–192

Yet, many lectures and discussions held at HPLC meetings andcommercial brochures suggest or assume that columns packed withparticles having a narrow PSD should a priori perform better thanthose packed with particles having a wide PSD. This myth is basedon the idea that particles having a tight PSD should pack orderly,as is systematically described in commercial brochures trying toexplain the well-known merits of the fine core–shell particles,which have very tight PSD around only 5% [8–19]. Unfortunately,irrespective of the PSD, the slurry packing process always producesbeds randomly packed at the scale of a few particle diameters.Coincidentally, core–shell particles produce more efficient columnsthan classical fully porous particles. This is what feeds the myth ofa correlation between particles RSD and column HETP. However,the reconstruction of packed beds [20–23] and numerical calcu-lations [24–26] demonstrated that short-range (over a distance ofa few particle diameters) eddy dispersion is larger for core–shellthan for conventional particles despite their tighter PSD. This isdue to the external porosity of columns packed with core–shellparticles (�0.40) being larger than that of those packed with fullyporous particles (�0.37). Also, detailed experimental investiga-tions [18,19,27–31] showed that the long-range (over distancescovering the column inner radius) eddy dispersion is significantlylower in beds of shell than in those of fully porous particles. Rhe-ological measurements mimicking the slurry packing process orreconstructing the bed of 2.1–4.6 mm i.d. columns and aiming atunravelling a correct physical explanation for this observation arestill lacking.

Yet, there are two important explanations suggested by theresults of rheological calculations [32] and of experiments car-ried out with capillary columns [33]. First, shear friction forces actbetween particles during bed consolidation. Rough core–shell par-ticles slip against each other and against the wall less easily thansmooth fully porous particles. For this reason, the distribution ofshear forces across the bed is less relaxed for core–shell than forfully porous particles while the strain distribution is lesser for theformer than for the latter. This process generates a more radiallyuniform structure for core–shell particles bed. The second explana-tion, that particle size segregation may take place across columns,the small particles accumulating near the wall, causing a radial bedstructure gradient, should be ruled out since all previous resultsshowed the marginal influence of the particle RSD on the columnefficiency.

The goal of this work is to rekindle discussions on the impactof particle PSD on the kinetic performance of chromatographiccolumns, based on results obtained with columns packed with newfully porous particles having a narrow PSD. Columns of differentlengths and diameters packed with Titan-C18 particles (Supelco,Bellefonte, PA, USA) were studied. The RSD of the PSD of theseparticles, the column porosities and specific permeabilities, theirapparent (including the system contribution to peak broadening)and intrinsic (measured independently of the system used [34]kinetic performance, and their eddy dispersion HETP terms [28,29])were accurately measured. Their performance is compared to thoseof commercially available columns packed with sub-2 �m particles(fully porous 1.8 �m Zorbax and 1.7 �m BEH and core–shell 1.7 �mKinetex). The possible impact of the tight PSD of the 1.9 �m Titanparticles on the column efficiency is then discussed in great detail.

2. Theory

2.1. Definitions

The external porosity of the packed bed is �e, Dm is the diffusioncoefficient of the analyte in the bulk mobile phase. The apparentanalyte diffusivity through the fully porous particle is Dp = ˝Dm,

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F. Gritti et al. / J. Chroma

being the dimensionless ratio of the analyte diffusivity throughhe porous particle to its bulk diffusion coefficient. The referenceoncentration gradient taken for the definition of the diffusion coef-cient Dp is the bulk concentration [35]. The effective diffusionoefficient along the heterogeneous packed bed (porous particlesnd external eluent) is Deff.

The zone retention factor k1 is written [36,37]:

1 = 1 − �e

�e[�p + (1 − �p)Ka] (1)

here �p is the particle porosity and Ka = cs/cp is the equilibriumatio of the stationary phase concentration to the pore concentra-ion.

The reduced interstitial linear velocity, �, is written [36]:

= udp

Dm(2)

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

= Fv

�er2c

(3)

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

.2. Reduced HETP equation

The possible presence of significant frictional heating effects isccounted for by its contribution, hheat to the reduced HETP. Theverall reduced plate height is the sum of the longitudinal diffu-ion term, the trans-particle mass transfer resistance term, the eddyiffusion term, and hheat or:

= B

�+ A(�) + Cp� + hheat (4)

he 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 Deff of the analyte in a heterogeneous column bed38,39]. A physically relevant model of effective diffusion in randomacked beds is given by the Torquato model [40,41] for fully porousarticles. It is written:

eff = 1�e(1 + k1)

[1 + 2(1 − �e) − 2�e�2ˇ2

1 − (1 − �e) − 2�e�2ˇ2

]Dm (5)

ith

= − 1 + 2

(6)

nd �2 is a parameter estimated from the experimental externalbstruction factor for = 0 and k1 = 0 (non-porous particles ando retention). For columns packed with particles having a narrowarticle size distribution and �e = 0.41, �e � 0.63 [42]. From Eq. (5),he expression of �e = Deff/Dm is given by:

e = 2(1 − (�2/2))3 − �e(1 + �2)

(7)

herefore, �2 is estimated at 0.495.

The reduced B coefficient in Eq. (4) is then written [38]:

= 2(1 + k1)Deff

Dm(8)

1355 (2014) 179–192 181

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

tance coefficient (Cp) was derived using the following coefficientprovided by [36,43]:

Cp = 130

�e

1 − �e

(k1

1 + k1

)2 1˝

(9)

In this equation, was estimated from the Torquato model ofeffective diffusion by combining Eqs (8), (5) and (6).

2.2.3. The eddy diffusion termThe eddy diffusion term A(�) results from all sources of sam-

ple dispersion in the interparticle column volume. It includes thecontributions of the homogeneous random packing or of analytedispersion along a hypothetical infinite diameter column (a col-umn with no wall, no inlet and outlet endfittings) [20,30], 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) when the HETP term related to frictional heating (hheat) can beneglected.

2.2.4. The frictional heating termThe origin of the reduced HETP term hHeat has already been

reported and explained in detail in Refs. [44–49]. When the fric-tion of the mobile phase against the surface of the packed particlesbecomes large, frictional heat is released all across the column vol-ume; its radial dissipation is accompanied by the formation of radialtemperature gradients. As a result, the sample molecules located inthe central region of the column progress faster than those presentin the peripheral region of the column and their diffusion coeffi-cient is larger. This is a significant source of band dispersion alongthe column.

2.3. Intrinsic and apparent plate heights

It is always delicate to measure the intrinsic plate height of acolumn because the unknown contribution of the HPLC systemshould be subtracted from the observable data. Replacing the col-umn with a ZDV union connector is not an accurate method [50,51].An alternative approach was recently proposed to access the intrin-sic performance of a chromatographic column. It is based on theelution of seven homologous compounds and on the following basictheory of band broadening.

The total volume variance of a chromatographic peak includesthe contributions of the instrument (its injector, valve, connectingtubes, detector, electronics) and of the column to the recorded bandwidth. Under isocratic conditions, it is given by [52–54]:

2v,Exp. = 2

v,ex + V20

Nint(1 + k′)2 (10)

where 2v,Exp. is the total volume variance measured, 2

v,ex is theunknown HPLC system volume variance, V0 is the column void vol-ume, Nint is the intrinsic column efficiency, and k′ is the retentionfactor given by:

k′ = VR − Vex − V0 (11)

V0

where VR is the elution volume and Vex is the extra-column volume.Eq. (10) assumes that the sample is dissolved in the same eluent asthe one used as the mobile phase.

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H

Apda

H

Ttd(tbeatuwvmtum

3

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3

bc1potsts

82 F. Gritti et al. / J. Chroma

By definition, the HETP Happ, (e.g., the overall apparent perfor-ance of the column and instrument as measured by the analyst)

s written:

app = L2

v,Exp.

V2R

(12)

ssuming that Vex � V0, substitution of Eq. (10) into Eq. (12)rovides the relationship between Happ, Hint = L/Nint, the columnimensions (V0 and L), the system variance in volume unit (2

v,ex),nd the retention factor k′:

app(k′) = Hint + L2

v,ex

V20

1

(1 + k′)2(13)

his result shows that, if under certain conditions of flow rate,emperature, and mobile phase composition, the intrinsic HETPepends weakly on k′ for a series of closely related compoundssame class of compounds such as a series of homologous analytes),he plot of the apparent HETP versus the reciprocal of (1 + k′)2 shoulde linear. Its y-axis intercept should provide Hint and its slope anstimate of the true extra-column volume variance 2

v,ex. The maindvantage of this approach for the determination of Hint and 2

v,ex ishat the column does not need to be replaced with a zero dead vol-me (ZDV) connector. This method is particularly recommendedhen the system volume variance is much larger than the column

olume variance. This concerns standard HPLC and vHPLC instru-ents used with narrow-bore columns. The main disadvantage is

hat the conditions mentioned above are not systematically metnder certain RPLC conditions (such as for too small or too highobile phase velocities).

. Experimental

.1. Chemicals

The mobile phase used was a binary mixture of acetonitrilend water (75/25, v/v). Tetrahydrofuran (THF) was used as theobile phase for ISEC measurements. All these solvents werePLC grade from Fisher Scientific (Fair Lawn, NJ, USA). Acetoni-

rile was filtered before use on a surfactant-free cellulose acetatelter membrane, 0.2 �m pore size (Suwannee, GA, USA). Theleven polystyrene standards (MW = 590, 1100, 3680, 6400, 13,200,1,600, 90,000, 171,000, 560,900, 900,000, and 1,870,000) wereurchased from Phenomenex (Torrance, CA, USA). The standardPLC checkout sample (1 mL ampoule) was purchased from Agilentechnologies. It contains 100.3 �g/mL (±0.5%) of acetophenone,ropiophenone, butyrophenone, valerophenone, hexanophenone,eptanophenone, octanophenone, benzophenone, and acetanilide.he solvent of this sample is a mixture of acetonitrile and water65/35, v/v, same composition as that of the mobile phase).cetanilide, acetophenone, valerophenone, and octanophenone

all >99% purity) were separately purchased from Sigma–AldrichSuwannee, GA, USA).

.2. Instrument

The 1290 Infinity HPLC system (Agilent Technologies, Wald-roen, Germany) was used to record the peak profiles of the nineompounds present in the RPLC checkout sample. It includes a290 Infinity Binary Pump with solvent selection valves and arogrammable auto-sampler. The injection volume is drawn intone end of the 20 �L injection loop. The instrument includes a

wo-compartment oven and a multi-diode array UV-VIS detectionystem. The system is controlled by the Chemstation software. Inhis work, the sample trajectory in the equipment involves theuccessive passage of its peak through the series of:

1355 (2014) 179–192

• A 20 �L injection loop attached to the injection needle. The designof this 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.

• A 130 �m × 50 mm long Viper capillary tubes offered by the man-ufacturer (Thermo Fisher Scientific, Germering, Germany) placedupstream the column. This tube has a volume of 0.7 �L.

• A 130 �m × 250 mm long Viper capillary tubes offered by thesame manufacturer placed downstream the 10 cm columns. Anadditional 130 �m × 50 mm long Viper capillary tube was placedin series downstream the column in order to connect the shorter5 cm long column. These two tubes have volumes of 3.3 and0.7 �L, respectively.

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

No solvent heat exchanger was used in the experiments. The elu-tion volume of the sample from the injection port to the detectioncell in the absence of a column is estimated at 1.0 + 1.2 + 0.7 + 3.3(or 4.0) +1.4/2 = 6.9 or 7.6 �L. To improve the performance of thisAgilent system, Viper capillary tubes were used and the shortestone was placed upstream the column. They allow a better repro-ducibility of the retention times and peak variances recorded [55]by avoiding tube-column connection failures over the duration ofthe experiments that are often encountered with standard metal-lic and/or plastic endfittings at very high pressures (�1 kbar) andwith different brands of chromatographic columns equipped withtheir own inlet and outlet endfittings. Placing a short tube upstreamthe column allows to minimize the extra-column band broaden-ing due to the impact of high pressures on the pre-column sampledispersion [56].

3.3. Columns

Four columns of dimensions 2.1 mm × 50 mm, 3.0 mm × 50 mm,2.1 mm × 100 mm, and 3.0 mm × 100 mm packed with 1.9 �mTitan-C18 fully porous particles were generously given by SupelcoAnalytical (Bellefonte, PA, USA). For the sake of comparison, threebrand new 2.1 mm × 100 mm commercial columns packed with1.8 �m Zorbax-C18 fully porous particles from Agilent Technologies(Little Fall, NJ, USA), 1.7 �m BEH-C18 particles from Waters (Mil-ford, PA, USA), and 1.7 �m Kinetex-C18 core–shell particles fromPhenomenex (Torrance, CA, USA) were purchased.

The PEEK capillary tube used to measure the diffusioncoefficients of acetophenone, valerophenone, and octanophenone(1/16 in o.d. × 0.0254 in i.d. × 50 ft long) was purchased from IDEXHealth & Science (Oak Harbor, WA, USA).

3.4. Determination of the particle size distribution

The particle size distribution of the Titan particles (batch8033) was measured by electrical sensing zone technique (Coultercounter principle) using the Elzone II 5390 V2.01 unit. The raw sil-ica and silica-C18 bonded particles were suspended in an aqueouselectrolyte solution containing 2% sodium chloride. Triton X-100(4-octylphenol polyethoxylate, n = 9–10) was added to disperse the

hydrophobic C18-bonded fully porous particles. The accessible sizerange goes from 0.50 �m to 50 �m. About 30,000 particles are ana-lyzed during the 30 s test. The Coulter counter measurements werecalibrated from the scanning electron microscopy (SEM) data.

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.5. ISEC experiments and column porosities

ISEC measurements were made on the four Titan columns. NeatHF was used as the eluent. Eleven polystyrene standards witholecular weights between 500 and 2 million Daltons were dis-

olved in pure THF and used as probe molecules. They cover a wideange of molecular sizes, between 10 and 950 A. The flow rate waset at 0.10 mL/min (2.1 mm i.d. column) and 0.20 mL/min (3.0 mm.d. column) and the sample size set at 0.25 �L (2.1 mm i.d.) and.50 �L (3.0 mm i.d.). The detection wavelength was set at 254 nm,he bandwidth at 4 nm, and the sampling rate at 160 Hz.

The external column porosities (�e) were derived by extrapolat-ng the exclusion branches of the ISEC plots of the elution volumesf the polymers versus their hydrodynamic molecular radius to aero radius. The ISEC results are shown in Fig. 2. The accuracy ofhe ISEC experimental protocol is ca. 1%. The size of the largest

esopores was estimated to be around 125 ± 10 A based on theeviation of the ISEC plot from the exclusion branches. The totalolumn porosity (�t) was measured from the elution time of toluenen pure THF. The internal porosity (�p) was derived from:

p = �t − �e

1 − �e(14)

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

.6. Measurement of the diffusion coefficients of the analytes

The bulk molecular diffusivities, Dm, of acetanilide, acetophe-one, valerophenone, and octanophenone were measured at theonstant temperature of 23 ± 0.5 ◦C. The mobile phase was a mix-ure of acetonitrile and water prepared by the pump mixer (75/25,/v). The capillary method was used to measure these diffusivities57–62]. The five conditions required for the validity of this methodre listed in Ref. [50]. They include a radial equilibration of the sam-le concentration along the capillary, a negligible contribution ofxial molecular diffusion to the total spatial variance, a negligiblextra-column peak variance compared to the total observed vari-nce, a product of the Dean number squared by the Schmidt numbermaller than 100 (no secondary flow circulation in the coiled tube),nd the validation of the method by using a standard sample.he diffusion coefficients measured were all validated by compar-ng the coefficient obtained for a standard compound (thiourea inure water at 298.15 K) for which its value is accurately knownDm = 1.33 × 10−5 cm2/s [63,64]).

Accordingly, the diffusion coefficient is directly given by theollowing relationship [59]:

m = 124

�1,t

�′2,t

r2tube (15)

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

ime moments of the recorded peak profiles and rtube is the inneradius of the PEEK capillary tube.

The diffusion coefficients of acetanilide, acetophenone,alerophenone, and octanophenone were then accuratelyeasured at 1.68 × 10−5, 1.77 × 10−5, 1.45 × 10−5, and

.24 × 10−5 cm2/s, respectively. From interpolation and by usinghe best fit of these experimental data to the empirical relationshipm = A/V˛

A (with VA the molar volume of analyte calculatedrom the average of the values given by the Shroeder and Le Bas

roup methods [65], A = 25.91 × 10−5 and = 0.542), the diffusionoefficients of propiophenone, butyrophenone, hexanophenone,nd heptanophenone were estimated at 1.64 × 10−5, 1.53 × 10−5,.37 × 10−5, and 1.30 × 10−5 cm2/s, respectively.

1355 (2014) 179–192 183

3.7. Peak parking experiments

The PP method was pioneered by Knox, first in gas [66], then inliquid chromatography [35,37,41,67–71]. This method is used hereto measure the reduced B and Cp coefficients in the van Deemterequation.

Samples of 0.75 and 1.50 �L of the RPLC checkout were injectedin the 2.1 mm and 3.0 mm i.d. columns at constant flow rates of0.20 and 0.41 mL/min, respectively. The column was eluted duringthe time necessary for the least retained compound (acetanilide) toreach exactly three quarters of the column length at the constanttemperature of 23 ± 0.5 ◦C. The flow was then abruptly stopped andthe sample left free to diffuse along the column during the parkingtime (values of 1, 15, 30, 45, and 60 min were used). All sampleswere detected at a wavelength of 254 nm. The detection bandwidthwas set at 4 nm and the sampling rate at 20 Hz for all parking times.The slopes of the plots of the peak variances, 2

t , versus the peakparking times, tp, provide a direct estimate of the true effectivediffusion coefficient along the column [37]:

Deff = 12

�2t

�tpu2

R (16)

where uR = u/(1 + k1) is the migration linear velocity of the analytes.The B and Cp coefficients are then given by Eq. 8 and 9. They are

listed in Tables 2 and 3.

3.8. HETP measurements

The retention time (tR) and the column efficiency (or the timepeak variance 2

t ) of the eluted peaks were automatically calcu-lated by the integration process of the Chemstation Software. Theintegration parameters were set manually as follows: slope sensi-tivity = 10 mAU/min, peak width = 0.01 min, height reject = 10 mAU.The sequence of flow rates applied to the 2.1 mm I.D. columns was0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10 and1.20 mL/min. The sequence of flow rates applied to the 3.0 mm I.D.column was 0.20, 0.41, 0.61, 0.82, 1.02, 1.22, 1.43, 1.63, 1.84, 2.04,2.24, 2.45 and 2.65 mL/min. The maximum inlet pressure used wasabout 800 bar. Under such frictional conditions, the columns arenot fully isothermal, so the impact of the small radial temperaturegradients on the column HETP are not fully negligible, especiallyfor fully porous particles [48,49]. Depending on the flow rate, thesampling frequency was adjusted between 10 and 160 Hz in orderto record at least 150 data points for the whole band profile ofacetanilide, the least retained compound. The injected sample vol-ume was set at 0.25 and 0.50 �L for the 2.1 and 3.0 mm i.d. columnand the chromatograms were recorded at a wavelength of 243 nm.A constant UV bandwidth of 4 nm was selected. The temperaturewas set by the laboratory air-conditioning system at 23 ± 0.5 ◦C.

The reduced plate height h is given by:

h = L

dSauter

2t

t2R

(17)

where L is the column length and dSauter is the mean Sauter diameterof the particle size distribution.

4. Results and discussion

4.1. Particle size distribution

The size distribution of the batch 8033 of Titan particles was

measured for the raw silica material in the absence and the pres-ence of Triton X-100 (this dispersant agent is not necessary forneat silica material) and for the C18-bonded material in the pres-ence of Triton X-100. Triton X-100 is required to disperse the

184 F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192

Table 1Physico-chemical property of the four columns packed with 1.9 �m fully porous Titan-C18 particles.

Batch number Column number Column’s dimension I.D.[mm] × length [mm]

Mean Sautersizea [�m]

Totalb

porosity (�t)Externalporosityc (�e)

Particle/shellporosityd (�p)

Permeability[cm2]e (k0)

Kozeny–Carmanconstantf (Kc)

8033 3193 2.1 × 100 2.04 0.621 0.390 0.379 4.21 × 10−11 1588033 3086 3.0 × 100 2.04 0.599 0.385 0.348 3.90 × 10−11 1647988 138343-03 2.1 × 50 2.04 0.605 0.368 0.375 3.75 × 10−11 1408056 140623-01 3.0 × 50 2.04 0.615 0.392 0.367 3.72 × 10−11 182

a Measured from calibrated Coulter Counter experiments on the raw silica Titan material without dispersant agent in the electrolyte solution.b Measured from the elution of toluene in THF.c Measured from ISEC experiments.d Determined from Eq. (14).e Measured from the corrected pressure drop (<300 bar) using a mixture of acetonitrile and water (75/25, v/v) at 23.0 ± 0.5◦ . Viscosity � = 0.571 cP.f Determined from Eq. (20).

Table 2Diffusion coefficients (Dm), zone retention factor (k1), effective diffusion coefficients (Deff), reduced longitudinal diffusion coefficients (B), ratio of the particle diffusivity tothe bulk diffusion (˝), and solid–liquid mass transfer coefficient (Cp) measured for the seven compounds acetophenone, propiophenone, butyrophenone, valerophenone,hexanophenone, heptanophenone, and octanophenone at T = 23.0 ± 0.5 ◦C. The mobile phase composition is acetonitrile/water, 75/25, v/v. The column is the 2.1 mm × 100 mmone packed with 1.9 �m Titan-C18 particles.

Compound Dm [cm2/s] k1 Deff [cm2/s] B Cp

Acetophenone 1.77 × 10−5 1.70 8.43 × 10−6 2.57 0.29 0.0294Propiophenone 1.64 × 10−5 2.30 7.32 × 10−6 2.94 0.38 0.0275Butyrophenone 1.53 × 10−5 3.02 6.02 × 10−6 3.16 0.43 0.0278Valerophenone 1.44 × 10−5 4.07 5.12 × 10−6 3.58 0.54 0.0253Hexanophenone 1.37 × 10−5 5.67 4.19 × 10−6 4.08 0.68 0.0226Heptanophenone 1.30 × 10−5 8.08 3.30 × 10−6 4.61 0.84 0.0202Octanophenone 1.24 × 10−5 11.73 2.59 × 10−6 5.32 1.06 0.0170

Table 3Diffusion coefficients (Dm), zone retention factor (k1), effective diffusion coefficients (Deff), reduced longitudinal diffusion coefficients (B), ratio of the particle diffusivity tothe bulk diffusion (˝), and solid–liquid mass transfer coefficient (Cp) measured for the seven compounds acetophenone, propiophenone, butyrophenone, valerophenone,hexanophenone, heptanophenone, and octanophenone at T = 23.0 ± 0.5 ◦C. The mobile phase composition is acetonitrile/water, 75/25, v/v. The column is the 3.0 mm × 100 mmone packed with 1.9 �m Titan-C18 particles.

Compound Dm [cm2/s] k1 Deff [cm2/s] B Cp

Acetophenone 1.77 × 10−5 1.34 8.13 × 10−6 2.15 0.19 0.0359Propiophenone 1.64 × 10−5 1.85 6.87 × 10−6 2.39 0.24 0.0362Butyrophenone 1.53 × 10−5 2.47 5.87 × 10−6 2.66 0.30 0.0347Valerophenone 1.44 × 10−5 3.37 4.83 × 10−6 2.91 0.36 0.0341

−5 3.29 × 10−6 3.08 0.46 0.03113.18 × 10−6 3.82 0.60 0.02662.48 × 10−6 4.39 0.76 0.0228

hscd

d

wisssab[

emcsathd

43210

2

4

6

8

10

12

14dSauter=2.26 μm

dSauter=2.13 μm

dSauter=2.04 μm

% i

n nu

mbe

r

Particle size [μm]

Raw Titan Raw Titan + Triton X-100 Titan-C18 + Triton X-100

Fig. 1. Coulter counter results for raw silica Titan (red color), raw silica Titan withTriton X-100 in the 2% NaCl electrolyte solution (green color), and Titan-C18 material

Hexanophenone 1.37 × 10 3.93

Heptanophenone 1.30 × 10−5 6.81

Octanophenone 1.24 × 10−5 9.96

ydrophobic Titan-C18 porous particles in the aqueous electrolyteolution containing 2% NaCl. Fig. 1 shows the corresponding parti-le size distribution (PSD) in number and the mean Sauter diameterS defined by [72]:

S =∑i=N

i=1 Nid3i∑i=N

i=1 Nid2i

(18)

here N is the total number of particles analyzed (N � 30, 000), dis a specific particle size, and Ni is the number of particles with aize in between di and di + �di (�di varies from 0.015 �m for themallest values of di around 1 �m to 0.25 �m for the largest particleize around 16 �m). The mean Sauter diameter is the most suit-ble average particle size to investigate the sample dispersion alongeds packed with particles having a non-uniform size distribution20].

The important result in Fig. 1 is that the PSD depends on the pres-nce of the dispersant agent in the electrolyte and on the surfaceodification (C18) of the porous silica particles. In fact, the effective

onductivity of porous silica particles immersed in the electrolyteolution decreases when Triton X-100 (a non-ionic surfactant) is

dded because it strongly interacts with the surface area of the par-icles. The same argument holds when the silica surface becomesydrophobic by attaching the C18 chains. Therefore, the observediminution of the cell conductivity upon passage of the particles

in the presence of Triton X-100 in the 2% NaCl electrolyte solution (blue color). Notethe shift of the size distribution from left to right when Triton X-100 is added tothe electrolyte and after derivatization of the raw silica with a hydrophobic C18

layer. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of the article.)

F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192 185

1000800600200

Acc

essi

ble

colu

mn

poro

sity

Polystyrene hydrod ymamic diameter DH [Å]4000

0.3

0.4

0.5

0.6 4.6 mm x 100 mm3.3 μm non -po rou s coresεe=0.41 5

2.1 mm x 100 mm1.9 μm Titan-C18εe=0.39 0

1000600200

Acc

essi

ble

colu

mn

poro

sity

Polystyrene hydrod ymamic diameter DH [Å]8004000

0.3

0.4

0.5

0.6 4.6 mm x 100 mm3.3 μm non -po rou s coresεe=0.415

3.0 mm x 100 mm1.9 μm Titan-C18εe=0.385

1000800600400200

Acc

essi

ble

colu

mn

poro

sity

Polystyrene hydrodymamic diameter DH [Å]0

0.3

0.4

0.5

0.6 4.6 mm x 100 mm3.3 μm non -po rous co resεe=0.415

2.1 mm x 50 mm1.9 μm Titan-C18εe=0.368

1000800600200

Acc

essi

ble

colu

mn

poro

sity

Polystyrene hydrod ymamic diameter DH [Å]4000

0.3

0.4

0.5

0.6 4.6 mm x 100 mm3.3 μm non -po rous co resεe=0.41 5

3.0 mm x 50 mm1.9 μm Titan-C18εe=0.39 2

F umns

c

traacfaaa

1ooppiX

4

Tclpiip�(

ig. 2. ISEC plots for the 10 cm (left graphs) and 5 cm (right graphs) long Titan cololumn packed with 3.3 �m non-porous silica cores.

hrough the aperture of the Coulter instrument is not the same foraw and for derivatized silica particles in the presence or in thebsence of Triton X-100 in the electrolyte solution. The particlesppear larger in the presence of Triton X-100 and of C18-bondedhains on their surface area. The mean Sauter diameter increasesrom 2.04 (raw Titan silica) to 2.13 (raw Titan silica + Triton X-100)nd 2.26 �m (Titan-C18 + Triton X-100). In the rest of this work, theverage particle size used for the calculation of the reduced velocitynd the plate height is dp = dSauter = 2.04 �m.

The RSD of the PSD of the raw Titan particles is 13.1%. It drops to0.2% after C18 derivatization and endcapping processes. The widthf the PSD of Titan-C18 particles is intermediate between thosef conventional fully porous particles (15–25%) and of core–shellarticles (�5%). The second remark made from Fig. 1 suggests theresence of doublet particles [15] shown by the shoulder (raw sil-

ca) or the tailing (raw Titan + Tritan X-100 or Titan-C18 + Triton-100) on the right side of the PSDs.

.2. Column porosities and permeabilities

The column porosities measured by ISEC are listed in Table 1.he external porosities are close for both the 2.1 and 3.0 mm i.d.olumns at 0.390 and 0.385, respectively. These values are slightlyarger than those measured for columns packed with fully porousarticles for which 0.35 < �e < 0.38. This should be advantageous

n terms of column permeability. This relatively large bed poros-

ty may be related to the imperfectly spherical shape of the Titanarticles observed in SEM (data not shown). The total porositiest are standard for C18-derivatized fully porous silica particles0.59 < �t ≤ 0.63). The internal porosities �p are around 0.35–0.38.

used in this work. The black symbols represent ISEC data obtained for a reference

The specific permeabilities of the two columns packed withTitan-C18 particles were measured according to the following rela-tionship:

k0 = �L1

r2c (�(Ptot − Pex)/�Fv)

(19)

where � = 0.57 cP is the eluent (acetonitrile–water, 75/25, v/v) vis-cosity at room temperature (23.0 ± 0.5 ◦C), L is the column length(10 cm), rc is the inner column radius (0.105 or 0.150 cm), Ptot is thetotal pressure drop, including the system contribution, Pex is thepressure drop generated by the vHPLC system in the absence of acolumn, replaced by a zero dead volume (ZDV) connector.

Accordingly, specific permeabilities of 4.21 and3.90 × 10−11 cm2 were found for the 2.1 and 3.0 mm × 100 mmcolumns packed with 1.9 �m Titan particles. The permeabilities ofnarrow-bore columns packed with sub-2 �m (1.7 �m BEH) fullyporous particles are around 2.5 × 10−11 cm2 [73,74]. The Titancolumns are then more permeable (+60%) than columns packedwith conventional 1.7 �m particles. This is due to a larger particlesize (2.0 versus 1.7 �m, +40%) and a larger external porosity (0.39versus 0.37, +20%).

The Kozeny–Carman constant Kc was obtained according to:

Kc = �3e d2

S

k0(1 − �e)2(20)

The Kozeny–Carman constants were 158 (2.1 mm i.d. column) and

164 (3.0 mm i.d. column). These values are consistent with thoseusually measured for columns packed with smaller or larger fullyporous particles [73,74,7]. In contrast, they are definitely smallerthan those (Kc � 210) previously measured for different brands of

186 F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192

25201510500

2

4

6

8 2.1 mm x 100 mm

Hap

p/dSa

uter

Reduced velocity ν

Ace tophenone , k1=1.7 Propiophenone, k1=2.3 Bu tyrophenone, k1=3.0 Valerophenone, k1=4.1 Hexanophenone, k1=5.7 Heptanophenone, k1=8.1 Oc tanophenone , k1=11.7

25201510500

2

4

6

8

3.0 mm x 100 mm

Hap

p/dSa

uter

Reduced velocit y ν

Acetophenone, k1=1.3 Propiophenone, k1=1.9 Bu tyrophenone, k1=2.5 Valerophenone, k1=3.4 Hexanophenone , k1=3.9 He ptanoph enon e, k1=6.8 Oc tanophenone, k1=10.0

Fig. 3. Plots of the apparent reduced plate heights of seven homologous compounds(n-alkanophenones) as a function of the reduced interstitial velocity for the two1co

suvfip3

4

4

rttTfc

orTtts

0.40.20.00

4

8

12

16

2.1 mm x 100 mm

Hap

p [μ

m]

(1+k')-2

0.1 mL/min 0.2 mL/min 0.3 mL/min 0.4 mL/min 0.5 mL/min 0.6 mL/min 0.7 mL/min 0.8 mL/min 0.9 mL/min 1.0 mL/min 1.1 mL/min 1.2 mL/min

0.40.20.00

4

8

12

16

3.0 mm x 100 mm

0.20 mL/min 0.41 mL/min 0.61 mL/min 0.82 mL/min 1.02 mL/min 1.22 mL/min 1.43 mL/min 1.63 mL/min 1.84 mL/min 2.04 mL/min 2.24 mL/min 2.45 mL/min

(1+k')-2

Hap

p [μ

m]

Fig. 4. Plots of the observed plate height Happ versus (1 + k′)−2 for the twelve appliedflow rates and a homologous series of n-alkanophenone samples. The linear extrap-

0 cm long columns packed with 2 �m Titan-C18 particles. (Top graph) 2.1 mm i.d.olumn. (Bottom graph) 3.0 mm i.d. column. Note the impact of the retention factorn the observed column performance.

ub-3 �m core–shell particles packed in the 2.1 mm × 100 mm col-mn format [75–77]. This most likely suggests that there is only aery small amount of fine particles in the Titan material, as con-rmed by both the Coulter counter data in Fig. 1 and the SEMhotograph (data not shown) there is no Titan particle among0,000 with a size smaller than 0.98 �m.

.3. Column performance

.3.1. 10 cm long Titan columnsThe performance of the 1.9 �m Titan-C18 RPLC columns will be

eported first without correction for the extra-column volume con-ribution due to the instrument (see Section 2 for details regardinghe connections between the injection port and the detector cell).he apparent or overall reduced HETP data are shown in Fig. 3or seven different homologous compounds present in the RPLCheckout sample.

The top graph in Fig. 3 shows plots of the reduced plate heightsf seven homologous compounds (n-alkanophenones) versus theeduced velocity for the 2.1 mm × 100 mm Titan RPLC column.

he variation of the retention factors from 0.70 (acetophenone)o 7.0 (octanophenone) explains most of the difference betweenhe seven reduced HETP plots. The larger the retention factor, themaller the apparent plate height because the contribution of the

olation of these plots to an infinitely large retention factor k′ provides the intrinsicHETP at a given flow rate. (Top graph) 2.1 mm i.d. column. (Bottom graph) 3.0 mmi.d. column.

vHPLC system to the observed peak variance becomes increasinglynegligible (see Section 2.3). The minimum observed reduced HETPmeasured for octanophenone is close to 2.0. The intrinsic perfor-mance of this column can be determined by applying a recentlyproposed protocol which is valid when the plots of the appar-ent HETP Happ versus (1 + k′)−2 are linear at different flow rates.This method is very useful because the classical one based on thereplacement of the column with a ZDV union connector is inac-curate and overestimates much the intrinsic HETP of narrow-borecolumns packed with sub-2 �m particles [34,51]. This is due to theeffect of the local pressure on the analyte dispersion in the pre-column volume: it is larger in the presence (high pressure) thanin the absence (lower pressure) of the chromatographic column[50,56]. The top graph in Fig. 4 shows the plots of the observed plateheight Happ versus (1 + k′)−2 for the twelve applied flow rates. Theplots of Happ versus (1 + k′)−2 are not linear for all seven homologouscompounds at the lowest flow rates (0.1 and 0.2 mL/min) when thelongitudinal diffusion is large and the intrinsic plate height dependson the retention factor (see the significantly different values of thereduced longitudinal diffusion coefficients B in Table 2) and at thelargest flow rates (1.0, 1.1, and 1.2 mL/min) for which frictionalheating is important and the observed plate heights of the mostretained compounds deviate strongly from the linear behavior. For

all other intermediate flow rates (0.3–0.9 mL/min), these plots arequasi-linear for at least six of the seven homologous compoundswith regression coefficients R2 larger than 0.998. The y-axis inter-cepts provide the different intrinsic plate heights Hint, which are

F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192 187

0.0 0.4 0.8 1.2 1. 60

2

4

6

8

Hin

t/dSa

uter

u [cm/s]

2.1 mm x 100 mmB/ν + Cpν:

Ace tophenone, k1=1.7 Prop iophenone, k1=2.3 Butyrophenone, k1=3.0 Valeroph enon e, k1=4.1 Hexanophenone, k1=5.7 Heptanophenone, k1=8.1 Octanophenone, k1=11.7

hmin=1.9

0.0 0.4 0.8 1.2 1.60

2

4

6

8 3.0 mm x 100 mm

hmin=1.7

B/ν + Cpν: Acetoph enon e, k1=1.3 Prop iophenone , k1=1.9 But yrophenone , k1=2.5 Va lerophenone, k1=3.4 Hexanophenone, k1=3.9 Heptanophenone, k1=6.8 Octanophenone, k1=10 .0

u [cm/s]

Hin

t/dSa

uter

Fig. 5. Plots of the intrinsic reduced plate height Hint/dSauter versus the interstitiallinear velocity (full purple stars) obtained by linear extrapolation of the HETP plotsshown in Fig. 4. The full circles represent the sum of the reduced longitudinal diffu-sion (B/�) and solid–liquid mass transfer resistance (Cp�) HETP terms for the sevenhcc

rtsmffratTrlc

caoch

0 5 10 150

2

4

6

8

k1=3

Zone retention fac tor k 1

Red

uced

B c

oeffi

cien

t

4.6 x 150 mm 5 μm Gem ini-C182.1 x 100 mm 1.9 μm Tita n-C183.0 x 100 mm 1.9 μm Tita n-C184.6 x 150 mm 3.5 μm BEH HILIC

Fig. 6. Comparison between the plots of the reduced longitudinal diffusion coef-ficient B as a function of the zone retention factor for most RPLC columns packedwith fully porous materials (5 �m Gemini-C18 is representative), with 2 �m Titan-

omologous n-alkanophenone analytes studied in this work. (Top graph) 2.1 mm i.d.olumn. (Bottom graph) 3.0 mm i.d. column. (For interpretation of the references toolor in this figure legend, the reader is referred to the web version of the article.)

epresented as full purple stars in the top graph of Fig. 5 as func-ions of the interstitial linear velocity. They are compared to theum of the reduced longitudinal diffusion (B/�) and solid–liquidass transfer resistance (Cp�) HETP terms measured independently

rom the peak parking method. The vertical distance between theull purple star symbols and the fully colored circles quantifies theeduced HETP due to the combined effects of the eddy dispersionnd frictional heating on the analyte band broadening. Remarkably,his term increases rapidly above 0.5 mL/min for the 2.1 mm i.d.itan column. This is when the effects of frictional heating becomeelevant, the heat power Pf being then larger than 5 W/m, whicheads to the formation of radial temperature gradients across theolumn [78,74]. The column efficiency eventually drops rapidly.

The same experimental data are given for the 3.0 mm i.d. Titanolumn in the bottom graphs of Figs. 3–5. The values of B and Cp

re listed in Table 3. As expected, the impact of the system volumen the apparent reduced HETPs is not as large as for the narrowerolumn. Yet, it is measurable and the minimum apparent plateeight is observed for the most retained analyte octanophenone

C18, and with 3.5 �m BEH HILIC particles. Note that the B coefficient of Titan columnis significantly smaller (−30%) that that of most commercial RPLC-C18 columns.

at only 1.8. This is a rather exceptional observation for a retainedcompound in RPLC since the minimum reduced plate height is usu-ally around 2.0–2.2 for columns packed with conventional fullyporous particles. The slope of the plots of the apparent HETP Happ

versus (1 + k′)−2 at different flow rates are smaller due to the 3.0 mmi.d. column having a twice larger hold-up volume V0 than the2.1 mm i.d. column (this slope is inversely proportional to V2

0 [34]).Remarkably, the intrinsic minimum reduced HETP of the 3.0 mmi.d. column is smaller than 2.0, at 1.7. It is remarkable to observe areduced plate height smaller than 2.0 for a compound retained ona RPLC column packed with fully porous particles. It is also note-worthy that this minimum reduced plate height is observed for asmall reduced velocity, only around 5. This is due in part to therelatively low values of the B and coefficients measured for theTitan-C18 particles, which are increasing with k1 in RPLC as shownin Tables 2 and 3. For instance, for k1 = 3 the coefficient wasaround 0.40 only.

For the sake of comparison, the intra-particle diffusivity ratio in the porous region of a large number of RPLC packing

materials was considered from the literature. What controls thevalue of of any RPLC packing material is the internal struc-ture (internal porosity, average pore size, specific surface area,surface coverage, and internal obstruction factor) irrespective ofits diameter (sub-2 �m or larger particles) or shape (spheres,cylinders, monolith, etc.). For instance, the intra-particle 1.7 �mKinetex-C18 (k1 = 1.3) [17], 5 �m Luna-C18(2) (k1 = 6.1) [7,79],2.6 �m Kinetex-C18 (k1 = 3.0) [75], 2.7 �m Halo-ES-C18 (k1 = 2.6)[76], 1.6 �m Cortecs-C18 (k1 = 3.9), [50], 2.7 �m Poroshell120-C18(k1 = 4.6) [77], Chromolith-C18 (k1 = 3.4) [80], 2.6 �m Accucore-C18 (k1 = 3.3) [81], 3.0 �m Hypersil-C18 (k1 = 5.0) [82], and 5.0 �mGemini-C18 (k1 = 3.0) [82] particles are equal to 1.0, 1.4, 1.6, 1.1, 1.2,1.6, 3.0, 1.0, 1.5, and 1.2 respectively. This seems to contrast withthe roughly three times smaller value of for Titan-C18 while theB coefficient is about 30% smaller at k1 � 3 (B = 3.0 versus B = 4.2).Fig. 6 compares the experimental reduced B coefficients of columnspacked with a standard RPLC material (5 �m Gemini-C18), with the1.9 �m Titan-C18, and with the 3.5 �m BEH-HILIC particles. The B

coefficient is minimum in HILIC due to the absence of surface diffu-sion [83,84], so, the B values of the BEH-HILIC column are a typicallow reference in LC. Clearly, the B terms of the Titan columns are

188 F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192

0 5 10 15 200

2

4

6

2.1 x 100 mm 1.9 μm Titan- C18

3.0 x 100 mm 1.9 μm Titan- C18

4.6 x 150 mm 5.0 μmLuna -C18

4.6 x 100 mm 2.6 μm Kine tex- C18

4.6 x 100 mm 1.7 μm Kine tex- C18

h Eddy

Reduced ve loc ity ν

Fig. 7. Comparison between the plots of the reduced eddy dispersion HETP terms ofthe 2.1 and 3.0 mm i.d. Titan columns and 4.6 mm i.d. columns packed with reference5 �m Luna-C18(2) and 2.6 �m Kinetex-C18 particles versus the reduced interstitiallinear velocity �. These overall reduced eddy dispersion HETPs were measured fromtaf

mfruisaocTpilp

stiet2ciodt5otutp2i

0.40.20.00

7

14

21

28 0.1 mL /min 0.2 mL /min 0.3 mL /min 0.4 mL /min 0.5 mL /min 0.6 mL /min 0.7 mL /min 0.8 mL /min 0.9 mL /min 1.0 mL /min 1.1 mL /min

2.1 mm x 50 mm

(1+k')-2

Hap

p [μ

m]

1.61.20.80.40.00

2

4

6

8

u [ cm/s]

Hin

t/dSa

uter

2.1 mm x 50 mm

hmin=1.9

Fig. 8. (Top graph) Plots of the measured plate height Happ versus (1 + k′)−2 for elevenapplied flow rates and a homologous series of n-alkanophenone samples using ashort 2.1 mm × 50 mm column packed with Titan-C18 particles. (Bottom graph) Plotsof the intrinsic reduced plate height Hint/dSauter versus the interstitial linear velocity

he subtraction method explained in Section 2 (hEddy = h − (B/�) − Cp�). Note the devi-tion of the eddy dispersion terms of the Titan columns at high speed is due torictional heating (hHeat).

uch smaller than those of standard RPLC columns packed withully porous particles. At a reduced velocity of 5 and for a zoneetention factor close to 3, this accounts for a (4.2–3.0)/5 = 0.25 hnit decrease, which is not negligible. This explains why the min-

mum reduced plate heights of the Titan-C18 columns can be asmall as 1.7. Nevertheless, the downside of smaller values of ˝nd B is a steeper C term, which is consistent with the small valuebserved for the optimum reduced velocity (�opt � 5) of the Titanolumns. The reasons explaining why the B values measured for theitan-C18 column are lower than those found for most RPLC-C18acking material are comprehensively discussed in the compan-

on paper [85]. They confirm that the explanation is the unusuallyow intensity of the internal obstruction factor in these Titan-C18articles.

A small reduced plate height of 1.7 could also be due to amall value of the eddy dispersion term. To answer this question,he reduced eddy dispersion HETP term of the 2.1 and 3.0 mm.d. Titan columns was measured from the subtraction methodxplained in Section 2 (hEddy = h − (B/�) − Cp�) and compared tohat of three reference columns packed with 1.7 �m Kinetex-C18,.6 �m Kinetex-C18, and 5 �m Luna-C18 particles [17,79,19] for aonstant zone retention factor of about 3.0. The results are shownn Fig. 7. First, it is important to realize that the steep increasef hEddy when � increases above 10 for the two Titan columns isue to frictional heating that is significant when the product ofhe flow rate and the pressure gradient along the column exceeds

W/m [78] and the column is kept under still-air conditions. Sec-nd, when frictional heating is negligible, this plot demonstrateshat the reduced eddy dispersion HETP term of the 3.0 mm i.d. col-mn packed with 1.9 �m Titan-C18 particles is slightly lower than

hat of the 4.6 mm i.d. column packed with 1.7 �m Kinetex-C18articles. Also, the eddy dispersion HETP term of the narrow-bore.1 mm i.d. Titan column is equivalent to that of a reference 4.6 mm

.d. column packed with the 1.7 �m Kinetex C18 particles. The graph

(full purple stars) obtained from the linear extrapolation of the HETP plots shownin the top graph. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of the article.)

shows that these narrow-bore Titan columns are as well packedas a reference 4.6 mm i.d. column packed with large 5.0 �m Luna-C18(2) particles. As expected for the 2.1 mm i.d. Titan column, itsreduced eddy dispersion HETP term is slightly larger than that of thewider 3.0 mm i.d. column because the column wall effects are moredominant in narrow-bore than in wide i.d. columns. On the sameline, the present work demonstrates that the Titan columns are notas uniformly packed as the reference columns packed with sub-3 �m Kinetex core–shell particles in a wide 4.6 mm i.d. columns. Itis always more challenging to pack fine particles into narrow tubesthan to pack larger particles into wider tubes.

The 3.0 mm i.d. Titan column performs better than the 2.1 mmi.d. column at high velocities. It should be emphasized that the opti-mum column performance is not observed over a wide range ofvelocities because the C term is steep. The optimum reduced veloc-ity is close to 5 whereas it is usually observed around 8 for sub-2 �mfully porous particles [74] and even above 10 for sub-3 �m RPLCcore–shell particles [13,17,18,27]. This is of great importance whenrunning fast gradients far above the optimum velocity [86].

4.3.2. 5 cm long Titan columnsThe previous section showed that frictional heating between the

eluent and the packed bed limits the efficiency of the 10 cm longTitan columns at linear velocities larger than 0.7 cm/s. Beyond this

F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192 189

0.40.20.00

7

14

21

28 0.1 mL/min 0.2 mL/min 0.3 mL/min 0.4 mL/min 0.5 mL/min 0.6 mL/min 0.7 mL/min 0.8 mL/min 0.9 mL/min 1.0 mL/min 1.1 mL/min

3.0 mm x 50 mm

(1+k')-2

Hap

p [μ

m]

1.61.20.80.40.00

2

4

6

8

u [cm/s]

Hin

t/dSa

uter

3.0 mm x 50 mm

hmin=1.8

vsatcipastiHalmfiaa(Rl(mAu

0.60.40.20.00

5

10

15

20

0.1 mL/min 0.2 mL/min 0.3 mL/min 0.4 mL/min 0.5 mL/min 0.6 mL/min 0.7 mL/min 0.8 mL/min 0.9 mL/min 1.0 mL/min

2.1 mm x 100 mm BEH old

(1+k')-2

Hap

p [μ

m]

1.61.20.80.40.00

2

4

6

8

10

u [cm/s]

Hin

t/dSa

uter

2.1 mm x 100 mm BEH old

hmin=2.2

Fig. 9. Same graphs as in Fig. 8 except for 3.0 mm i.d. columns.

elocity, the heat power Pf or product of the flow rate and the pres-ure gradient along the Titan columns is larger than about 7 W/mnd the efficiency is expected to decay rapidly due to the forma-ion of radial temperature gradients [46,47,78]. Shorter, 5 cm longolumns, were tested to minimize the impact of frictional heat-ng on the column performance at high velocities, because the heatower generated at a constant linear velocity decreases by a factor 2nd the radial temperature gradients are not fully developed alonghort columns [46]. Therefore, they affect less the column efficiencyhan the 10 cm long column. The results are shown in Fig. 8 (2.1 mm.d. column) and 9 (3.0 mm i.d. column). The plots of the apparentETP Happ versus (1 + k′)−2 required to measure the intrinsic HETPsnd the reduced intrinsic plate height as a function of the interstitialinear velocity are shown in Figs. 8 and 9. They show first that the

inimum reduced HETPs are nearly the same as those measuredor the 10 cm long columns at 1.9 (2.1 mm i.d.) and 1.8 (3.0 mm.d.). This suggests that the eddy dispersion HETP terms of both 5nd 10 cm long Titan columns are comparable. These minima arelso recorded for a small value of the linear velocity, at 0.3 cm/s�opt = 5) for which frictional heating is still negligible (Pf � 1 W/m).emarkably, the overall Cu terms are significantly flatter and more

inear for the 5 cm long columns than for the 10 cm long columns

see Fig. 5). The wider the column i.d., the higher the column perfor-

ance at large chromatographic velocities. This suggests that the(�) eddy dispersion term is smaller for 3.0 than for 2.1 mm i.d. col-mn. This confirms that wide-bore columns are more efficient than

Fig. 10. Same graphs as in Fig. 8 except for a 2.1 mm × 100 mm columns packedwith BEH-C18 particles.

narrow-bore columns because the contribution of the wall effectsto the overall band dispersion decreases [30].

4.3.3. Preliminary investigations of the reasons for the lowsample intra-particle diffusivity across Titan-C18

The low values of the B coefficients in the van Deemter equa-tion for the seven homologous n-alkanophenone compounds ismostly related to the low values of the intra-particle diffusivityDp = ˝Dm of theses analytes across the Titan-C18 particles. Accord-ing to the semi-empirical and validated models of diffusion acrossporous particles [41,83,84,87], the coefficient is proportional tothe particle porosity (�p = 0.35–0.38, it is a standard value) and tothe internal obstruction factor �p (this parameter can be estimatedfrom the intra-particle diffusivity of a non-retained compound[41]). is also strongly correlated to the specific surface area Sp ofthe porous particles and to the accumulation or excess amount ofacetonitrile (low viscosity, high diffusion coefficients) with respectto water (higher viscosity, lower diffusion coefficients) inside themesoporous volume of the particles (this can be estimated fromthe results of the minor disturbance method using RI detection[88–90]).

According to the manufacturer, Sp = 410 m2/g, which is evensomewhat larger than the average specific surface area of mostbrands of fully porous silica particles. This cannot explain a small

value for alone. Additionally, the material was endcapped andC18-derivatized with a surface coverage around 2.0 �mol/m2 (thecarbon percent is 13.5%), so, the minimum number of adsorbedlayers of acetonitrile is close to 3 as previously measured for

190 F. Gritti et al. / J. Chromatogr. A 1355 (2014) 179–192

0.40.20.00

5

10

15

20

0.1 mL/min 0.2 mL/min 0.3 mL/min 0.4 mL/min 0.5 mL/min 0.6 mL/min 0.7 mL/min 0.8 mL/min 0.9 mL/min 1.0 mL/min 1.1 mL/min

2.1 mm x 100 mm Zorbax

(1+k')-2

Hap

p [μ

m]

1.61.20.80.40.00

2

4

6

8

10

Hin

t/dSa

uter

u [cm/s]

2.1 mm x 100 mm Zorbax

hmin=2.0

0.60.40.20.00

4

8

12

16

0.1 mL/min 0.2 mL/min 0.3 mL/min 0.4 mL/min 0.5 mL/min 0.6 mL/min 0.7 mL/min 0.8 mL/min 0.9 mL/min 1.0 mL/min 1.1 mL/min

2.1 mm x 100 mm Kinetex

(1+k')-2

Hap

p [μ

m]

1.61.20.80.40.00

2

4

6

8

10

u [cm/s]

Hin

t/dSa

uter

2.1 mm x 100 mm Kinete x

hmin=2.3

F h 1.8 �p

siocwn˝fwffapmindwfbw

4

cfw1FtT

ig. 11. Same graphs as in Fig. 8 except for a 2.1 mm × 100 mm column packed witacked with 1.7 �m Kinetex-C18 core–shell particles (right graphs).

ilica-based particles [89]. The excess amount of acetonitrilen the pores is then expected to be standard. Finally, basedn the peak parking results recorded for the least retainedompound acetanilide (k′=0.28, Dm = 1.68 × 10−5 cm2/s), = 0.09,hich means that the value of in the absence of retention isecessarily smaller than 0.09. Since for a non-retained compounds,

� �p�pF(�m) (F(�m) is the hindrance diffusion factor around 0.8or small molecules and average pore size close to 100 A [41]), �p

ould be at most equal to 0.30. This can be compared to �p = 0.75or porous materials with an average mesopore size of 125 A butor a larger particle porosity around 0.70 [91]. �p was measuredt 0.53 in the porous volume of 100 A 2.6 �m Kinetex-C18 shellarticles and a shell porosity of 0.33 [41]. Definitely, further confir-ation and additional measurements are needed to estimate the

nternal obstruction factor in 1.9 �m Titan-C18 particles, using aon-retained compound (thiourea). Yet, the first conclusions to beerived from data related to the least retained compound in thisork (acetanilide) suggest that the internal tortuosity/constriction

actor is relatively small for Titan-C18 particles. This could proba-ly explain the low B terms measured for retained analytes in thisork.

.3.4. Comparison to benchmark columnsIn order to better appreciate the performance of these new Titan

olumns, the same approach was used to assess the intrinsic per-ormances of three 2.1 mm × 100 mm commercial columns packedith fully porous 1.8 �m Zorbax-C18 and 1.7 �m BEH-C18, and with

.7 �m Kinetex-C18 core–shell particles. The results are given inigs. 10 (BEH) and 12 (Zorbax and Kinetex). The measurements onhe BEH column show a hmin value of 2.2 and a flat Cu HETP term.he best performance was observed for the Zorbax column with

m Zorbax-C18 fully porous particles (left graphs) and a 2.1 mm × 100 mm columns

hmin = 2.0. Finally, the narrow-bore column packed with core–shellKinetex particles gave a minimum reduced plate height of 2.3 withthe flattest Cu HETP branch, which is specific to columns packedwith shell particles [18]. The impermeable silica core conductsheat better than aqueous/organic eluent mixtures, which mini-mizes the amplitude of radial temperature gradients across HPLCcolumns and maintains good column performance at high veloc-ity [48,49]. Overall, none of the 2.1 mm × 100 mm narrow-borecolumns packed with commercially available sub-2 �m particlesgenerate intrinsic reduced plate heights smaller than 2.0 or intrin-sic plate height smaller than 3.5 �m. The Titan columns studied inthis work provide minimum reduced plate heights smaller than 2.0(1.7–1.9 or 3.5–3.9 �m) and similar flat Cu branches for short 5 cmlong columns.

5. Conclusion

The kinetic performance of 3.0 and 2.1 mm i.d., 5 and 10 cm longcolumns packed with 1.9 �m fully porous Titan-C18 particles wereinvestigated in great detail. The minimum intrinsic reduced plateheights of these columns were smaller than 2.0, between 1.7 and1.9, which is unprecedented for analytical size columns (2.1 and3.0 mm i.d.) packed with fully porous particles. One of the particu-larities of these Titan particles is their relatively narrow particle sizedistribution with a RSD around 10%, which is intermediate betweenthe RSD of the PSD of core–shell particles (�5%, hmin � 1.4) and thatof classical porous particles (�20%, hmin � 2.0). This result suggests

a correlation between the RSDs of particle PSDs and the efficien-cies of columns packed with them. Analysts may be tempted tohastily believe that the uniformity of particle sizes is of fundamentalimportance in chromatography and because it controls the column

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F. Gritti et al. / J. Chroma

fficiency. This conclusion would challenge all past and recent find-ngs that the PSD of particle size distributions has no direct impactn column performance as long as its RSD is smaller than ca. 50%.

The conclusions of this work explain the reasons for thispparent contradiction. They showed that the sub-2 values ofhe minimum reduced plate heights of the Titan columns werebserved at a relatively low reduced velocity of 4–5 while in RPLCt is usually around 10. This is primarily due to a small longitudinaliffusion coefficient B (30% less than for most silica-C18 materials)

n the van Deemter equation. These small values provided by theeak parking method are directly related to the unusually small

ntra-particle diffusivities of retained analytes across the porousitan-C18 particles. For a retention factor close to 2, the intra-article diffusivities are about three times smaller for Titan-C18han for most other brands of silica-C18 porous materials. Theserst investigations suggest that the internal tortuosity/constrictionr obstruction factor in Titan-C18 particles is about twice smallerhan those of other brands of silica-C18 particles. The eddy disper-ion of the Titan columns was also shown to be close to that ofonventional column packed with fully porous particles.

The downside of a small B coefficient is a large C coefficient inhe van Deemter equation. Therefore, the range of velocity overhich the column efficiency is close to minimum is quite narrow.

his might be important when separations are carried out beyondhe optimal linear velocity value. The kinetic performance of the.1 mm × 100 mm columns packed with 1.9 �m Titan-C18 particlesre comparable to those of commercial columns packed with sub-

�m particles (BEH, Zorbax, Kinetex) with a minimum intrinsicETP in the range between 3.6 (Zorbax), 3.7 (BEH) and 3.9 (Kinetexnd Titan) �m. Yet, the Zorbax and Kinetex columns exhibit flatter Cerms at high velocities. The performance of the 3.0 mm × 100 mmitan column is superior, with a minimum HETP of only 3.5 �m.he Cu HETP term of a 5 cm long column is less steep than that of

10 cm long one because the frictional heating power is reducedy a factor 2 and the amplitude of the radial temperature gradientscross the column are lower.

cknowledgements

This work was supported in part by the cooperative agreementetween the University of Tennessee and the Oak Ridge Nationalaboratory with the support of the Waters Technologies Corpora-ion. We thank William Betz of the Particle Design Group of SupelcoBellefonte, USA) for the Coulter counter data and for fruitful dis-ussions.

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76] F. Gritti, G. Guiochon, Repeatability of the efficiency of columns packed withsub-3 �m coreshell particles: Part II. 2.7 �m halo-es-peptide-c18 particles in4.6 mm and 2.1 mm × 100 mm column formats, J. Chromatogr. A 1252 (2012)45–55.

77] F. Gritti, G. Guiochon, Repeatability of the efficiency of columns packed withsub-3 �m coreshell particles: Part III. 2.7 �m poroshell 120 ec-c18 particles in4.6 mm and 2.1 mm × 100 mm column formats, J. Chromatogr. A 1252 (2012)56–66.

78] F. Gritti, G. Guiochon, Optimization of the thermal environment ofcolumns packed with very fine particles, J. Chromatogr. A 1216 (2009)1353–1362.

79] F. Gritti, G. Guiochon, Speed-resolution properties of columns packed withnew 4.6 �m kinetex-c-18 core–shell particles, J. Chromatogr. A 1280 (2013)35–50.

80] F. Gritti, G. Guiochon, Measurement of the eddy dispersion term in chromato-graphic columns: III. application to new prototypes of 4.6 mm i.d. monolithiccolumns, J. Chromatogr. A 1225 (2012) 79–90.

81] F. Gritti, G. Guiochon, Effect of parallel segmented flow chromatography on theheight equivalent to a theoretical plate ii performances of 4.6 mm × 30 mmcolumns packed with 2.6 �m accucore-c18 superficially porous particles, J.Chromatogr. A 1314 (2013) 44–53.

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83] F. Gritti, G. Guiochon, Comparison between the intra-particle diffusivity in thehydrophilic interaction chromatography and reversed phase liquid chromatog-raphy modes. Impact on the column efficiency, J. Chromatogr. A 1297 (2013)85–95.

84] F. Gritti, G. Guiochon, Mass transfer mechanism in hydrophilic interaction chro-matography, J. Chromatogr. A 1302 (2013) 55–64.

85] F. Gritti, G. Guiochon, The rationale for the optimum efficiency of columnspacked with new 1.9 �m fully porous Titan-C18 particles—A detailed inves-tigation of the intra-particle diffusivity, J. Chromatogr. A 1255 (2014)164–178.

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88] F. Gritti, G. Guiochon, Thermodynamics of adsorption of binary aqueous organicliquid mixtures on a RPLC adsorbent, J. Chromatogr. A 1155 (2007) 85–99.

89] F. Gritti, Y. Kazakhevich, G. Guiochon, Effect of the surface coverage of end-capped c18-silica on the excess adsorption isotherms of commonly usedorganic solvents from water in reversed phase liquid chromatography, J. Chro-

90] F. Gritti, G. Guiochon, The distortion of gradient profiles in reversed-phaseliquid chromatography, J. Chromatogr. A 1340 (2014) 50–58.

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