Effect of parallel segmented flow chromatography on the height equivalent to a theoretical plate....

Accepted Manuscript

Title: Effect of parallel segmented flow chromatography onthe height equivalent to a theoretical plate I- Performance of4.6 × 30 mm columns packed with 3.0 m Hypurity-C18 fullyporous particles

Author: Fabrice Gritti Georges Guiochon

PII: S0021-9673(13)00645-6DOI: http://dx.doi.org/doi:10.1016/j.chroma.2013.04.047Reference: CHROMA 354280

To appear in: Journal of Chromatography A

Received date: 23-2-2013Revised date: 13-4-2013Accepted date: 15-4-2013

Please cite this article as: Fabrice Gritti, Georges Guiochon, Effect of parallel segmentedflow chromatography on the height equivalent to a theoretical plate I- Performance of4.6 × 30 mm columns packed with 3.0 m Hypurity-C18 fully porous particles, Journalof Chromatography A (2013), http://dx.doi.org/10.1016/j.chroma.2013.04.047

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

http://dx.doi.org/doi:10.1016/j.chroma.2013.04.047

http://dx.doi.org/10.1016/j.chroma.2013.04.047

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Parallel segmented flow chromatography consists in splitting the exit flow of mobile phase

About half the stream flowing through the central region of the column is sent to the detector

The stream flowing along the less well packed wall region of the column is sent to waste

Elimination of the stream flowing along the wall cancels the effect of bed heterogeneity

The apparent column HETP and the signal to noise ratio are reduced by about 30 to 50%

*Highlights (for review)

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Effect of parallel segmented flow chromatography on1

the height equivalent to a theoretical plate2

I- Performance of 4.6 × 30 mm columns packed with3

3.0 µm Hypurity-C18 fully porous particles4

Fabrice Gritti and Georges Guiochon ∗,

Department of Chemistry, University of Tennessee

Knoxville, TN 37996–1600, USA

5

Abstract6

The mass transfer kinetics in short and wide 4.6 × 30 mm columns packed with 3.0 µm7

Hypurity-C18 fully porous particles were measured for three different configurations of the inlet8

sample distribution and outlet sample collection : (1) Both the inlet and outlet column endfit-9

tings are standard, (2) the inlet endfitting is standard while the outlet endfitting allows parallel10

segmentation of the exiting flow between a central and a peripheral region across the column11

diameter, and (3) both the inlet and outlet endfittings allow a parallel segmentation of the flow12

entering and exiting the column, respectively. The total reduced heights equivalent to a the-13

oretical plate (HETP) were carefully measured, using the first and second central moments of14

the elution band profiles, obtained by its accurate numerical integration. The longitudinal dif-15

fusion term was measured at the lowest experimental reduced velocity applied. The solid-liquid16

mass transfer resistance was estimated from measurements of the intra-particle diffusivity using17

the Torquato’s model of effective diffusion in packed beds. The trans-channel and short-range18

interchannel eddy diffusion HETP terms were taken from data obtained by solving numer-19

ically the Navier-Stokes equations and simulating advective-diffusive transport in20

computer-generated random sphere packings.21

∗Corresponding author: (e-mail) [email protected]; (fax) 865 974–2667.

http://ees.elsevier.com/chroma/viewRCResults.aspx?pdf=1&docID=28486&rev=1&fileID=1182756&msid=AA3897D6-0E1D-4CA7-B193-EE3E1617C8C2

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The results clearly show that the trans-column eddy diffusion HETP term can account for up22

to 85 % of the total intrinsic HETP (corrected for extra-column contributions) of the standard23

columns. Parallel segmented flow chromatography can reduce this contribution by half at high24

velocities, by eliminating most of the baseline peak tailing. This holds true irrespective of25

the retention factor of the analyte. It was found also that segmenting the inlet/outlet flow26

increases detection sensitivity by 25 to 50% for peaks with large to small retention factors,27

respectively. In practice, the advantage of parallel segmented flow chromatography in gradient28

elution (thin peak widths) is essentially limited by post-column bandspreading and diffusion in29

the dwell volume of the instrument used. Analyst should minimize post-column bandspreading30

(caused by connectors and detection cell volume) and synchronize the eluent composition in the31

peripheral and central inlet ports of the column, by using two separate pumps with appropriate32

dwell volumes.33

Keywords: Column efficiency; inlet and outlet segmented flow chromatography; eddy dispersion;34

trans-column eddy dispersion; Hypurity-C18; naphthalene;35

* Fax: 865-974-2667; email address: [email protected]

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1 Introduction37

Parallel segmented flow chromatography was recently suggested as an original way to increase38

the column efficiency and enhance the detection sensitivity, to allow multiplex detection, and to39

afford a better compatibility between the optimum flow rates required for HPLC separation and40

for mass spectrometry detection ?, 1–5. The principle is simple. The whole eluent stream is not41

sent directly to the detector but a specially designed endfittings splits the eluent stream into its42

central region, sent to the detector, and a wall region that is discarded. As a result, the outlet flow43

rate is smaller than the one delivered by the pump but adjusting the ratio of flow segmentation44

between the central and peripheral outlet ports provides a mean to increase the column efficiency45

by about 40-50%. Very substantial gains in separation performance were observed with46

4.6 × 100 mm columns packed with 5 µm particles 1: the number of theoretical plates47

and the sensitivity increased by 22 %. The peak elution volume was reduced by 85%48

allowing more efficient coupling in 2D systems. A 4.6 mm I.D. column can be tuned49

to operate as a virtual 2.1 mm I.D. column with a theoretical plate number 70% larger50

than that of a standard 2.1 mm narrow-bore column 2. The marriage between fast51

HPLC and MS is then definitely improved. Parallel segmented flow chromatography52

was also applied in gradient elution mode 3 with measurable gains in performance.53

This original approach discards the eluent percolating close to the column wall, the structure of54

which is known to differ from that in the central region of the packed bed. Column radial hetero-55

geneity exists not only for wide preparative chromatography columns 6–11 but also for analytical,56

narrow-bore columns packed with fully porous 12–22, core-shell particles ?, 23–31, and non-porous57

materials 32–39.58

As a matter of fact, fast analyses using short columns packed with fine particles are now run59

under what is called a pre-asymptotic transverse dispersion regime because the retention time60

is too short to allow complete radial equilibration of the stream composition 22,34,35. Transverse61

dispersion does play a beneficial role in randomly packed beds 35, contributing to radially homog-62

enize the sample concentration across the column diameter during migration of the sample zone.63

Transverse dispersion is usually the sum of a diffusive and a convective dispersion terms 40. Accu-64

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rate expressions of the transverse dispersion coefficient are now available by solving numerically65

the Navier-Stokes equations and simulating advective-diffusive transport in computer-66

generated random sphere packings 35. The diffusive term increases with increasing retention67

factors in RPLC due to an increase of surface diffusion 15,41. The convective term is proportional to68

the Peclet number, so, its contribution to the total transverse dispersion coefficient increases with69

increasing flow rate and average particle size, and with decreasing diffusion coefficient of analytes.70

Another potential advantage of this skimming outlet endfittings is to partially release the phys-71

ical constraint imposed by classical outlet endfittings, which force the whole outgoing eluent to72

converge towards a narrow hole in the column center. So, parallel segmented flow contributes to73

minimize the band spreading caused by the two endfittings (the inevitable border effects in actual74

columns) that are dominant for short and wide columns. An alternative to the parallel segmented75

flow endfittings would consist in designing new sample distributors and collectors that would com-76

pensate for retention time asynchronism from the center to the wall. This would be of main interest77

for short and wide preparative columns.78

The advantages of parallel segmented flow chromatography and its effect on the different HETP79

terms of the classical van Deemter equation have not yet been rigorously, quantitatively studied80

from experimental and theoretical viewpoints. It is obvious that this approach mainly affects the81

pre-asymptotic trans-column eddy diffusion term for which no general theory is available yet. In82

contrast, the theoretical properties and characteristics of (1) the longitudinal diffusion term (B/ν83

term) 42–47; (2) the solid-liquid mass transfer resistance term for packed spheres (Cpν term) 48–51;84

(3) the asymptotic trans-channel and short-range inter-channel eddy diffusion terms (A(ν)) 48,6285

derived for the bulk region of the packing material are well established and these theoretical results86

are in excellent agreement with experimental data 22. These contributions will not be affected when87

the eluent flow is split at the inlet and/or at the outlet of the column. The reason is that these88

HETP terms are defined over very short distances and involve only a limited number of packing89

particles. They are insensitive to the radial heterogeneity of the bed structure and to the border90

effects.91

The goal of this work was to assess the impact in isocratic and gradient elution chromatography92

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of parallel segmented flow on the column efficiency which includes all the mass transfer contributions93

except the following terms: B/ν, A(ν) (trans-channel and short-range interchannel eddy diffusion94

only), and Cpν. Short (3 cm ) and wide-bore (4.6 mm I.D.) columns packed with the same batch95

of 3 µm fully porous particles were tested. Three different system configurations combining two96

standard endfittings (inlet and outlet) and two segmented flow column endfittings (inlet and outlet)97

were fitted to one or both ends of the column. The segmentation flow ratio was set at 55% (at98

the peripheral port) because it was previously shown that this ratio was the optimum one for the99

maximization of the column efficiency 3–5. Three different retention factors were set by changing the100

eluent composition. This work required careful corrections of the extra-column band broadening101

contributions which differ whether the flow rate is segmented or not. The limits of operation of the102

new design are discussed in details.103

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2 THEORY104

2.1 Definitions105

The total, external and the internal porosities of the packed bed are εt, εe, and εp, respectively. Dm106

is the diffusion coefficient of the analyte in the bulk mobile phase. The apparent analyte diffusivity107

through the porous particles is Dp = ΩDm, with Ω the dimensionless ratio of sample diffusivity108

through the porous region of the particles to its bulk diffusion coefficient. The effective diffusion109

coefficient along the heterogeneous packed bed (porous particles and external eluent) is Deff .110

The zone retention factor, k1, is written 20,48:111

k1 =1− εeεe

[εp + (1− εp)Ka] (1)

This retention factor refers to the elution time of an analyte to the time that it spent in the112

interstitial column volume (εeπr2c ). The conventional retention factor, k

′, refers to the same elution113

time referred to the time spent in the total accessible pore volume (εtπr2c ).114

The reduced interstitial linear velocity, ν, is written 48:115

ν =udpDm

(2)

where u in the average interstitial linear velocity along the column given by:116

u =Fvεeπr2c

(3)

where Fv is the flow rate and rc is the inner column radius.117

2.2 Reduced HETP equation118

In the absence of significant amount of frictional heating (as is the general case with short columns,119

even at relatively high heat friction power because the radial temperature gradients are not fully120

developed 13,54–60), the overall reduced plate height is the sum of the longitudinal diffusion term,121

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the eddy diffusion term, and the trans-particle mass transfer resistance term or:122

h =B

ν+A(ν) + Cpν (4)

The following sections provide the explicit equations used in this work to express the B, A(ν), and123

the Cp terms that account for the contributions of these three terms. More detailed information124

on the derivation of these equations are available in 20,44,48,59,61,62.125

2.2.1 The longitudinal diffusion term126

The longitudinal diffusion term is derived from the effective diffusion coefficient of the analyte127

in a heterogeneous packing material 42,43,45,46,63,64. It includes the contributions of the diffusion128

processes taking place along the column, in the external and internal eluent volumes and along the129

surface of the stationary phase.130

A physical relevant model of effective diffusion in random packed beds is given by the Torquato131

model 43,44. This model describes the effective diffusion of packed fully porous spheres immersed132

in a homogeneous medium. It is written 45,46:133

Deff =1

εe(1 + k1)

[1 + 2(1− εe)β − 2εeξ2β

2

1− (1− εe)β − 2εeξ2β2

]Dm (5)

with134

β =Ω− 1

Ω + 2(6)

where ξ2 is an adjustable parameter that is estimated from the experimental external obstruction135

factor for Ω = 0 and k1 = 0 (non-porous particles). From Eq. 5, the general expression of γe =Deff

Dm136

as a function of εe and ξ2 is:137

γe =2(1− ξ2

2 )

3− εe(1 + ξ2)(7)

We made diffusion measurements after totally blocking the mesopores in the particles by filling138

them with liquid n-nonane. The results showed that the obstruction factor of a 4.6 × 150 mm139

column packed with 5 µm fully porous Gemini-C18 particles is 0.570 for an external porosity of140

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0.364 16. Accordingly, the value of ξ2 given by Eq. 7 and used for columns packed with fully porous141

particles is 0.627.142

The reduced B coefficient in Eq. 4 is then written 45:143

B = 2(1 + k1)Deff

Dm(8)

2.2.2 The solid-liquid mass transfer resistance term144

The general expression of the solid-liquid mass transfer resistance coefficient (Cp) is given by the145

following equation 48,53:146

Cp =1

30

εe1− εe

(k1

1 + k1

)2 1

Ω(9)

In this equation, the value of Ω is obtained by applying the model of effective diffusion (Eqs 5 and147

6) to the best experimental value of Deff estimated at the lowest reduced velocity applied (ν <148

0.3).149

2.2.3 The eddy diffusion term150

By construction, the eddy dispersion term A(ν) in Eq. 4 includes all the sources of band broadening151

along the column that are not caused by the apparent longitudinal diffusion along the column and152

by the mass transfer resistance across the stationary phase volume. It results from all sources153

of band dispersion that take place in the external column volume, between its inlet to outlet. It154

includes the contribution of the endfittings, the frits and the consequences of the random packing155

or of the analyte dispersion along a hypothetically infinite diameter column (which would have no156

wall, no inlet and no outlet endfitting) 22,62, over distances ranging from the interparticle distance157

(trans-channel velocity biases, hTS) to a few particle diameters (short-range inter-channel velocity158

biases, hIC). It also includes the contribution of the so-called long-range trans-column velocity159

biases (hTC) induced by the presence of the solid cylindrical wall surrounding the bed and the160

inlet/outlet (distribution/collection) endfittings. The presence of all these boundaries introduces161

physical constraints during the formation of the chromatographic bed (i.e., the slurry process)162

preventing the eluent streamlines from being parallel to the column axis. This contributes to add163

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trans-column velocity biases, which take place between the bulk center and the region close to the164

column wall or its ends. In practice, the axial dispersion coefficient of conventional HPLC columns165

cannot reach the asymptotic value, which is expected for infinitely long columns ?, 35, 65. So far,166

there is no available theoretical model predicting accurately the long-range eddy diffusion term167

of standard 2.1 × 4.6 mm I.D. columns in the transient dispersion regime, before the asymptotic168

regime is reached 19,22. It can only be estimated by subtraction method and is reported as such.169

Eventually, the overall eddy dispersion HETP term, A(ν), is simply written:170

A(ν) = hTS + hIC + hTC (10)

=1

12λ1

+ 1ω1ν

+1

12λ2

+ B2γeω2ν

+ hTC (11)

where λ1, ω1, λ2, and ω2 are eddy dispersion parameters that predict accurately the sample disper-171

sion in the homogeneous, random, bulk region of the bed packed with impermeable solid spheres172

under asymptotic conditions 62 according to the coupling theory of eddy diffusion of Giddings 48. It173

is noteworthy that Eq. 11 accounts for the impact of the effective diffusion coefficient174

through the packed bed (the B term) on the short-range interchannel eddy dispersion175

term. These parameters were obtained as functions of the bed porosity (external porosity) for176

monosized, non-porous particles (B = 2γe) and for different packing protocols 62. Because the177

effect of the particle size distribution on the analyte dispersion in the bulk region of the packed bed178

is small 66 and the bed porosity is always in the range 0.35 < εe < 0.41, accurate estimates of these179

four parameters is provided by the S × 2 packings in which each particle was randomly placed in180

n equal cubic cells defining the simulation box volume. More details on computer-generated beds181

are provided in reference 62.182

2.3 Transverse dispersion coefficient in packed beds183

Estimates of the transverse dispersion coefficient were recently refined for true packed beds (wide184

particle size distribution, non porous particles, no retention k1=0) by solving numerically the185

Navier-Stokes equations and simulating advective-diffusive transport in computer-186

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generated random sphere packings 35. The best fit between the simulated transverse reduced187

plate height data and the general mathematical expression (power law) of the transverse dispersion188

coefficient for reduced velocities in the range from 0.5 to 500 is :189

Dt

Dm= γe + 0.146ν0.758 (12)

At a first approximation, by assuming that the diffusive (γe) and the convective (0.146ν0.758)190

contributions to the total transverse dispersion coefficient remain additive and independent, for191

beds packed with fully porous particles (for which the external obstruction factor γe is replaced192

with the effective diffusion coefficientDeff

Dm

59) and under retentive conditions (k1 6= 0), the apparent193

transverse dispersion coefficient across the column becomes 22:194

Dt

Dm=Deff

Dm+

0.146

1 + k1ν0.758 (13)

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3 Experimental195

3.1 Chemicals196

The mobile phases were mixtures of acetonitrile and water (42.5/57.5, 62/38, and 90/10, v/v). All197

these solvents were HPLC grade from Fisher Scientific (Fair Lawn, NJ, USA). Acetonitrile was198

filtered before use on a surfactant-free cellulose acetate filter membrane, 0.20 µm pore size (Suwan-199

nee, GA, USA). Eleven polystyrene standards (MW=590, 1100, 3680, 6400, 13200, 31600, 90000,200

171000, 560900, 900000, and 1870000) were purchased from Phenomenex (Torrance, CA, USA) in201

order to perform inverse size-exclusion chromatography (ISEC) experiments on the standard Hypu-202

rity column. The RPLC checkout sample (1 mL) was purchased from Agilent Technologies (Little203

Fall, DE, USA). This mixture contains 100.3 µg/mL (± 0.5 %) of acetophenone, propiophenone,204

butyrophenone, valerophenone, hexanophenone, heptanophenone, octanophenone, benzophenone,205

and acetanilide dissolved in a water/acetonitrile (65/35, v/v) matrix. Naphthalene was purchased206

from Fisher Scientific, with a minimum purity of 99%.207

3.2 Apparatus208

All the measurements were performed on a 1290 Infinity HPLC system (Agilent Technologies,209

Waldbronn, Germany) liquid chromatograph. This system includes a 1290 Infinity Binary Pump210

with Solvent Selection Valves and a programmable auto-sampler. The injection volume is drawn211

into one end of the 20 µL injection loop. The instrument includes a two-compartment oven and a212

multi-diode array UV-VIS detection system. The system is controlled by the Chemstation software.213

Three different system configurations (called S for standard, O for outlet segmented flow, and IO214

for outlet and inlet segmented flow) were applied in this work. They are described in Figure 1:215

1- Standard conditions: system configuration S216

Under standard conditions, e.g. in the absence of split flow, the sample trajectory in the217

equipment involves the successive passage of its band through the series of:218

• A 20 µL injection loop attached to the injection needle. The design of the First In -219

Last Out (FILO) injection system is such that the entire volume of sample drawn into220

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the loop is injected into the column. This ensures an excellent injection repeatability.221

• A small volume needle seat capillary (115 µm I.D., 100 mm long), ' 1.0 µL, located222

between the injection needle and the injection valve. The total volume of the grooves223

and connection ports in the valve is around 1.2 µL.224

• Two 130 µm× 250 mm long Viper capillary tubes offered by the manufacturer (Thermo225

Fisher Scientific, Germering, Germany), placed one before, the second after the column.226

Each tube has a volume of around 3.3 µL. The arrangement of the injection valve and227

detection cell in the 1290 Infinity system does not enable the use of shorter 130 µm ×228

60 mm long Viper capillary tubes.229

• A standard volume detector cell, V (σ)=1.0 µL, 10 mm path.230

2- Post-column split flow : system configuration O231

The same system configuration as the one described above was used, except that the post-232

column flow is split into two separate directions. The first connector tube (130 µm × 250233

mm long Viper capillary tube) conveys the part of the sample eluted in the central region234

of the column to the detector. The second tubing (115 µm × 220 mm long metal capillary235

tube) collects the part of the sample eluted along the column wall to the waste bottle.236

According to the optimum split flow reported by Camenzulli et al. for 4.6 × 100237

mm columns packed with 5 µm particles 1, the parallel segmentation flow ratio was238

set at 55% (wall) for all the experiments made with this configuration. So, the flow rate from239

the column outlet to the detector was 45% of the total flow rate.240

3- Post-column and inlet split flow : system configuration IO241

The same system configuration as the previous one was conserved, except that the eluent242

flow coming from the pump and the Jet weaver mixer was split into two streams prior to243

entering the injection valve. The inlet of a ZDV T union connector was connected to the long244

(' 50 cm) green tubing (254 µm I.D.) coming from the Jet weaver 35 µL mixer installed in245

the 1290 HPLC pump unit. A short 130 µm × 50 mm long Viper capillary tube connects246

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the first outlet of the T-union to the injection valve. A 115 µm × 340 mm metal capillary247

tube coupled in series with a 130 µm × 50 mm long Viper capillary tube connects directly248

the second outlet of the T-union to the peripheral inlet port of the column. To measure the249

extra-column time and variance contributions to the total retention time and peak variance,250

a four port union was installed. Two inlets received the eluent streams from the injection251

valve (prior to the central column inlet) and from the second stream of the pump flow. The252

two outlets of the four ports union split the main flow into two streams, one to the detector253

cell, the second to the waste bottle.254

The segmentation flow ratio was measured at 56.5% at the inlet wall of the column for all255

the mobile phase compositions applied in this work. It was kept as close as possible to the256

outlet split flow ratio (55.0 %). So, the inlet flow rate in the central region of the column is257

43.5% of the total flow rate.258

The total dwell volume of this instrument was measured from step gradient experiments made259

by the manufacturer at 170 µL. It includes the volume contributions of the connecting tubes (green260

tubings, I.D. = 254 µm, ' 75 µL), of the jet weaver V35 mixer (35 µL), of the injection loop (40261

µL), and of the syringe (20 µL). No solvent heat exchanger was used in these experiments. The262

extra-column volume is close to 13 µL and generates an extra-column peak volume variance under263

standard conditions (no split flow) that varies between about 4 (90.0% acetonitrile in water at 0.05264

mL/min) and 30 µL2 (42.5 % acetonitrile in water at 4.00 mL/min) for naphthalene molecules265

when the flow rate is increased from 0.05 to 4.00 mL/min (injection volume of 1 µL). Figure 2266

shows the complete variation of the true extra-column peak variances of naphthalene as a function267

of the flow rate and of the mobile phase composition.268

3.3 Columns269

Three 4.6 × 30 mm prototype columns packed with the same batch of 3.0 µm Hypurity-C18 fully270

porous particles were generously offered by their manufacturer (Thermo Fisher Scientific, Runcorn,271

UK). One column is assembled with standard column endfittings at both ends. A second one272

was equipped with a special outlet endfitting that allows the parallel flow segmentation of the273

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sample molecules eluted at the column outlet. The fraction of the eluent stream eluted along the274

peripheral region of the column flows directly into the waste bottle while the other fraction flows to275

the detector. The last column was equipped with the same special endfitting at both ends. The inlet276

flow coming from the pump and the outlet flow are segmented. A fraction of the total inlet stream277

is sent to the peripheral inlet of the column, by bypassing the injection valve. The other fraction278

of the flow, the one sent to the central region of the column, flows through the injection valve. So,279

the sample injected into this third column flows only through the central region of the column.280

More detailed information on these prototype column endfittings can be found in references 1–5 or281

obtained from the manufacturer (Thermo Fisher Scientific, Runcorn, UK).282

The external, total, and internal porosities of the standard 4.6 × 30 mm column were measured283

by ISEC (see more details in the next section) at 0.391, 0.720, and 0.540, respectively. Note that284

these porosities are not necessarily the same for the three different columns because the slurry285

packing process is a random process and the endfittings are different. It is noteworthy that the286

external porosity of the short standard column packed with 3.0 µm fully porous particles appears to287

be significantly larger than that measured for longer columns (10-15 cm long) packed with smaller288

and tougher to pack 2.5 µm fully porous particles (0.34 < εe < 0.37) 19. This strongly suggests289

that the inlet and outlet frits used in this column cause a significant hold-up volume inside the290

column. Commercially available 0.5, 2.0, 10, and 20 µm stainless steel frits (same diameter, 4.78291

mm, and same thickness, 1.88 mm) have void fractions of 19.2, 23, 26.9, and 28.8%, respectively.292

They generate hold-up volumes of 6.46, 7.75, 9.14, and 9.69 µL3. The total external volumes of293

the short Hypurity column was initially measured at 195 µL. Assuming that two such 0.5 µm frits294

were used in the Hypurity column, the relative contribution of the frit volume (2 × 6.5 = 13.0 µL)295

to the total external volume would be about 6.7 %. Therefore, the presence of the frit generates296

higher than expected values for the external and total porosities of the column. After correction for297

the frit contribution, the true external and total porosities of the column would be 0.371 and 0.712,298

values in better agreement with those measured for longer columns. Because the exact nature of299

the frits used and their variance contributions to band spreading are unknown, the retention times300

and the peak variances reported in this work include the contributions of the inlet and outlet frits.301

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The average mesopore size of the derivatized material was assessed at about 170 A from the302

intersection of the exclusion and retention ISEC branches.303

3.4 Inverse size-exclusion chromatography (ISEC)304

ISEC measurements were made only with the standard 4.6 × 30 mm Hypurity-C18 column. Neat305

THF was used as the eluent. Eleven polystyrene standards with molecular weights between 500306

and 2 millions Dalton were used as probe molecules. They cover a wide range of molecular sizes,307

between 10 and 950 A. The average mesopore size before C18 derivatization of the fully porous308

Hypurity particles was 175 A according to the manufacturer. After C18-derivatization followed309

by trimethylsilane (TMS) endcapping, the average size decreased to about 165 A 67–69. The flow310

rate was set at 0.50 mL/min and the sample size set at 2 µL. The detection wavelength was set311

at 254 nm with a bandwidth of 4 nm. The external porosities (εe) were derived by extrapolating312

to a zero molecular weight the exclusion branch of the ISEC plot of the elution volumes of the313

polymers versus their hydrodynamic molecular radius. The accuracy of the ISEC experimental314

protocol is within 1%. The total porosity (εt) was measured from the elution time of toluene in315

pure tetrahydrofuran. The internal porosity (εp) was derived from:316

εp =εt − εe1− εe

(14)

3.5 Diffusion coefficients of naphthalene317

The bulk molecular diffusivities, Dm, of naphthalene were measured with the peak parking (PP)318

method in a series of seven different mixtures of acetonitrile and water (42.5/57.5, 51.0/49.0,319

58.0/42.0, 65.0/35.0, 75.5/24.5, 83.0/17.0, and 90.0/10.0, v/v) at room temperature (24.1 ± 0.5320

oC). All the experimental details (column used, packed with non-porous silica particles, reference321

standard compound, thiourea in pure water) regarding the PP can be found in references 20,70–72.322

The relative error made on the true value of the bulk diffusion coefficient is less than 4% 61,73,74.323

It is mostly due to the errors made in the measurements of the external obstruction factor of the324

column packed with non-porous particles and of the eluent viscosities. They are equal to 1.08 ×325

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10−5, 1.48 × 10−5, and 2.60 × 10−5 cm2/s for the volume fractions of acetonitrile of 0.425, 0.62,326

and 0.90, respectively.327

3.6 HETP measurements328

The same sequence of flow rates was applied to all three columns. The flow rate was increased329

successively from 0.05 to 0.10, 0.25, 0.50, 0.75, 1.00, 1.50, 2.00, 3.00 and to 4.0 mL/min. Depending330

on the flow rate, the data acquisition frequency was adjusted between 2.5 and 160 Hz in order to331

record at least 120 data points for the whole elution band of naphthalene. Samples of 1 µL of a332

naphthalene solution (concentration < 0.5 g/L in the mobile phase) were injected into the three333

columns and the chromatograms recorded at a wavelength of 290 nm, with a constant UV bandwidth334

of 4 nm. The temperature was set by the laboratory air-conditioning system at 24.1 ± 0.5 oC.335

For the same sequence of flow rates, the extra-column contributions of the 1290 Infinity HPLC336

instrument to the retention time and time variance were measured in the three system configurations337

(S, O, and IO). Due to the split flow (O and IO configurations) and the subsequent reduction of338

the flow rate from the column outlet to the detector cell, the system first and second time moments339

are larger than those measured under the standard configuration S.340

The first and second central moments were all measured by the numerical integration method.341

The peak area was measured by the Simpson integration method. The results were systematically342

corrected for the dispersion due to extra-column band broadening in the absence of the column343

(replaced with a ZDV union connector or a ZDV splitter). All the details for the measurement of344

the HETP data and their accuracy are given in 75–77. The first and second central moments of the345

eluted band profiles were measured from the following discrete sums :346

µ1 =∑i=N−1

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

(15)

µ′2 =

∑i=N−1i=1 (Ci−1+4Ci+Ci+1)(ti−µ1)2∑i=N−1

i=2 Ci−1+4Ci+Ci+1(16)

where N is total odd number of data point and i is an even integer, which increases from 2 to 4, 6,347

... and to N − 1.348

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The first (left cut, i=1) and last (right cut, i=N) elution times in these sums were determined349

from the elution times recorded when the sample concentration first increased (left) then decreased350

(right) to less than 0.1% of the peak height after linear baseline correction. This method has the351

advantage of properly and systematically adjusting the integration window regardless of the degrees352

of peak fronting and peak tailing that may fluctuate in various ways depending on the nature of353

the sample injected and the flow rate applied. It is highly sensitive to packing heterogeneity or354

any source of flow heterogeneity in the column which would not be perceptible by the classical355

half-height peak width method.356

The intrinsic reduced plate height h, corrected for the extra-column volume contributions, is357

given by :358

h =L

dp

µ′2 − µ

′2,ex

(µ1 − µ1,ex)2(17)

where L is the column length (3 cm), dp the mean particle size (3.0 µm), and µ1,ex and µ′2,ex359

are the first and second central moments of the extra-column band profiles measured by the same360

numerical integration method (discrete Simpson’s sums).361

The accuracy of these h values is around 10% and 4% under non-retained and retained condi-362

tions, respectively.363

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4 Results and Discussion364

This section is divided into three main parts. The first one reports on the extra-column contribution365

on the band broadening observed with small molecules like those of naphthalene under standard366

conditions (no split flow) and under parallel segmented flow chromatography. A second part reports367

on the corrected reduced plate heights of the column used and on the detection sensivity measured368

with the three system configurations, S (standard), O (outlet split), and IO (inlet and outlet369

split flow). Finally, the advantages/disadvantages of parallel segmented flow chromatography are370

illustrated in the case of the gradient separation of nine small molecules.371

4.1 Extra-column contributions372

Figure 2 shows the volume variances measured for naphthalene in the system configuration S for373

three different mobile phase compositions (42.5, 62.0, and 90.0% acetonitrile in water, v/v). For374

these measurements, the column was replaced with a zero dead volume (ZDV) union connector.375

At low flow rates (< 0.5 mL/min), the higher the diffusion coefficient, the smaller the volume376

variance due to the faster radial equilibration of the concentration gradients across the diameters377

of the different connecting tubes. The smallest volume variance was measured at 4 µL2 for a378

90/10 acetonitrile/water mobile phase and a flow rate of only 0.05 mL/min. At larger flow rates,379

the band-spreading is no longer controlled only by the diffusion coefficient. The volume variances380

increase up to 30 µL2 for the largest flow rate of 4 mL/min.381

In configurations O and IO, the flow rate cannot be defined as in configuration S due to the inlet382

and/or outlet split flow. In configuration O, a three-ports ZDV union connector (a T) splits the383

outlet flow into two parallel streams. About 45% of the inlet flow rate passes through the detection384

cell. Therefore, the flow rate in the outlet Viper tubing and in the detection cell is less than half385

the one passing through the needle seat capillary, the injection valve, and the inlet Viper tubing. In386

configuration IO, a four ports union connector was used (a Q). Two inlet ports receive the streams387

coming from the inlet Viper tubing (' 45% of the total flow rate) and the bypass of the injection388

valve path (' 55% of the total flow rate). The two outlet ports split the total flow rate in the389

same way as done in the O configuration. Therefore, the elution times and the time variances are390

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necessarily larger in configurations O and IO than those in the standard configuration because the391

average flow rate along the column is about 1.5 (O configuration) and 2 (IO configuration) times392

smaller than the constant flow rate in standard conditions. Figure 3 shows the relative increases393

of the first and second central moments of naphthalene compared to the same moments measured394

in the standard configuration for three different retention factors.395

Three different mobile phase compositions were tested in order to generate three different re-396

tention factors on the same column. The first moments are about 50 and 100% larger for the397

configurations O and IO, respectively, than for configuration S because the sample molecules de-398

tected and/or injected are transported at a flow rate 45% lower than the total flow rate from the399

ZDV union connector to the detector and/or from the needle seat to the ZDV union connector. This400

segmentation flow ratio was determined by collecting the different eluent flows and measuring the401

time it took them to fill a 5 mL volumetric glass. The first time moments of naphthalene recorded402

confirmed fully these independent measurements. The relative increases of the second central time403

moments are significantly larger than those of the first moments when the flow rate increases from404

0.05 mL/min (+50-90% in the O configuration and +150-200% in the IO configuration) to 4.0405

mL/min (+100-200% in the O configuration and +250-600% in the IO configuration). To illustrate406

this problem, the extra-column peak profiles recorded at the constant total flow rate of 4 mL/min407

are shown in Figures 5, 6, and 7, for the three different mobile phase compositions and for the three408

different configurations.409

The extra-column volume visited by the sample molecules is always the same, at about 13 µL410

while the column hold-up volume is only 359 µL. It represents 3.6% of the total column hold-up411

volume volume. At worst, the elution times of non-retained compounds should be larger by about412

2% in configuration 0 and by 4% in configuration IO than they are in configuration S, with no413

split flow. This relative increase of the retention time is practically negligible and is not detectable414

in fast chromatography. In contrast, the extra-column volume might affect seriously the peak415

variance of non-retained or weakly retained compounds. For instance, consider the elution profiles416

of uracil at a constant flow rate of 2 mL/min on the Hypurity column. In configuration S (no split417

flow), the overall second central time moment is 0.102 s2. In the IO configuration, the variance418

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of the same peak is 0.126 s2 while the respective extra-column contributions are 0.014 and 0.059419

s2. After correction for these extra-column peak variances, the intrinsic column performance in420

the IO (0.126-0.059=0.067 s2) is better than in the S (0.102-0.014=0.088 s2) configuration. This421

demonstrates that, even though the intrinsic kinetic performance of the column may be better in422

one configuration than in the other, analysts may not be able to perceive the advantage due to the423

extra-column effects. In conclusion, the determination of the intrinsic kinetic performance, i.e., or424

the corrected reduced HETPs of naphthalene for the 4.6 × 30 mm Hypurity column under different425

system configurations necessitates significant corrections for the extra-column band broadening426

effects. This task is necessary for weakly retained compounds and was carefully performed.427

4.2 Intrinsic column HETP428

The goal of this section is to assess quantitatively the possible advantages of parallel segmented429

flow chromatography on the intrinsic kinetic performance of a short 4.6 mm × 30 mm Hypurity430

column. The reduced plate heights of naphthalene were measured with three different mobile431

phase compositions providing different retention factors equal to about 9.8 (ϕCH3CN=0.425), 2.3432

(ϕCH3CN=0.62) and 0.5 (ϕCH3CN=0.90). These strong, moderate and low retention might lead to433

different conclusions.434

4.2.1 Strong retention : 42.5% acetonitrile435

Figure 4A shows the corrected reduced HETPs of naphthalene in the S (black color), the O (red436

color), and the IO (green color) configurations. Because the retention factor is relatively important,437

the apparent longitudinal diffusion coefficient is large due to the importance of surface diffusion438

in RPLC 16,41. It is noteworthy that the configuration has virtually no impact on the B term of439

the van Deemter plots (B=15.7). As the flow rate tends towards zero, the column tends toward440

radial equilibrium and the effective axial diffusivity controls band broadening. Segmenting such441

an infinitesimally small flow rate at the inlet and/or at the outlet of the column cannot affect442

the dominant effective diffusion process. Molecular transport by convection is negligible. Neither443

does flow segmentation have any influence on the solid-liquid mass transfer resistance coefficient444

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Cp because the external porosity εe and the nature of the Hypurity-C18 particles (all the columns445

were packed with the same batch of particles so the average particle size dp and the intra-particle446

diffusivity ΩDm are the same) are the same irrespective of the flow configuration. Therefore, any447

significant differences in the h data necessarily reveals a change in the eddy dispersion A(ν) HETP448

term (the trans-column eddy diffusion HETP term) from one to another mode of operation (S, O,449

and IO configurations).450

Differences between the h plots are clearly visible for reduced interstitial linear velocities larger451

than about 3.5. The optimum reduced velocity increases from about 10 (S configuration) to 16452

(O and IO configurations) because the contribution of the eddy diffusion HETP term to the total453

reduced HETP decreases when the flow is segmented. The minimum reduced plate height observed454

decreases considerably, from 5.1 to only 3.5 and 3.1, when the flow is segmented at the column455

outlet. Therefore, discarding the eluent streamlets in the column wall region from the stream to456

the detector appears to be highly advantageous when analyte molecules do not have enough time to457

disperse uniformly across the column diameter. Indeed, Eq. 13 shows that the effective transverse458

dispersion coefficient varies from 4.29 to 5.26 × 10 −6 cm2 when the reduced velocity increases from459

0.36 to 28.4, respectively. Knowing the retention times tR at all flow velocities provides the radial460

distance r(ν) =√

4DttR and gives a fair estimate of the average radial excursion of one analyte461

molecule during its migration along the column. Calculations show that r(ν) decreases from 0.28462

cm (ν=0.4) to 0.04 cm (ν=28.4). The column inner radius is 0.23 cm. The transverse random463

walk of the analyte is equal or smaller than the column radius (r(ν) ≤ rc) for ν > 0.5. This result464

is consistent with the enhanced deviation of the h data from those measured after segmenting the465

inlet and/or the outlet flow as shown in Figure 4A. The transcolumn velocity biases across the466

short Hypurity column are relatively important and become less relaxed with increasing flow rate.467

The contribution of convective dispersion to the overall transverse dispersion remains too small at468

high flow rates because the average particle size is only 3.0 µm. The optimum column efficiency469

increases by about 50%. At the highest flow rate applied (4 mL/min), the efficiency gain is as large470

as 75%.471

The difference between the h plots measured in the O and the IO configurations are rather small.472

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They are maximum for velocities around the optimum velocity. The column efficiency increases by473

about 15%. At larger flow rates, the improvement is not significant due to the limited precision of474

the measurements (± 4 %). Probably, analyte molecules injected in the column center tend to be475

redistributed radially at large flow rates and the IO configuration seems to be quasi-equivalent to476

the O configuration.477

Figure 5 illustrates the main advantage of the IO configuration over the O and S ones. It478

compares the extra-column band profiles (two ports ZDV union in black, three ports ZDV union479

in red, and four ports ZDV union in green for the S, O and IO configurations, respectively) and480

the overall band profiles recorded in the presence of the column. The flow rate was set at 4.0481

mL/min. The figure shows a potential increase in detection sensitivity (see the green chromatogram482

in the right graph) when injection is made in the central region of the column (configuration IO)483

rather than across the whole cross-section area as in S and O configurations (see black and red484

chromatograms). Because the same amount of naphthalene is locally injected in the central region485

of the column, the mass injected is concentrated in the central zone of the column, in a smaller486

volume, and a higher peak is recorded. Remarkably enough, even though the extra-column band487

spreading is larger in the O and the IO configurations than in the S one (see chromatograms in488

the left graph), the highest peak height is systematically observed for the IO configuration. The489

sensitivity is improved by as much as 25% for a retention factor of about 10. The gain in column490

efficiency is mostly due to the removal of the baseline peak tailing (see and compare the black signal491

with the red or green signals) which is due to the analyte molecules migrating more slowly in the492

peripheral region of the column. As a consequence, the second peak moment is markedly reduced,493

giving a higher column efficiency.494

4.2.2 Moderate retention : 62% acetonitrile495

Figure 4B shows the same h plots and chromatograms as does Figure 4A, except that for the496

increase of the volume fraction of acetonitrile from 42.5% to 62%. The retention factor drops from497

9.8 to 2.3, the reduced B coefficient decreases significantly, from 15.7 to 6.5, and hmin becomes498

4.3, 3.5, and 2.9 in the S, O, and IO configurations, respectively. The optimum reduced velocity499

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increases from 3.4 (S configuration) to 6.5 (IO configuration) and 7.8 (O configuration) because500

the contribution of the reduced eddy diffusion HETP term to the total reduced HETP decreases501

when the flow is segmented. This is due to the variation of the eddy dispersion term A(ν), which502

compensates less for the decrease of the B/ν term at a much smaller reduced velocity.503

The effect of parallel segmented flow on the intrinsic column performance for a moderate reten-504

tion factor of k′=2.3 is similar to that previously described for k

′=9.8. The transverse dispersion505

coefficients increase from 8.10 × 10−6 to 1.15 × 10−5 cm2 as the reduced velocity increases from506

0.26 to 20.9. The average radial distance r(ν) decreases from 0.21 cm (ν=0.26) to 0.03 cm (ν=20.9).507

The decreases in the retention times (× 0.3) more than compensate for the increases of the diffusion508

coefficients (× 1.4). So, the average radial distance sampled by analyte molecules is nearly twice509

smaller. The standard h data differs from those measured in O and IO configurations for ν > 2.510

The intrinsic optimum column efficiency is increased by 50% after splitting the flow rate at both the511

inlet and the outlet of the column using a constant flow segmentation ratio of 45% in the column512

center. It is nearly doubled at the maximum flow rate applied (4 mL/min). Again, Figure 6 shows513

that this is due to the quasi-complete elimination of the tailing part of the reference peak (black514

peak profile).515

Detection sensitivity had increases by 25% from S to IO configurations for k′=9.8. It is 50%516

larger for k′=2.3. It is noteworthy that the peak area under the red and green profiles differ because517

the sample injected is distributed differently and so is the analyte mass eluted through the column518

center region. Figures 5, 6, and 7 do demonstrate that more analyte is detected under IO than519

under O or S configurations, which both follow the standard injection process. Thus, it is impossible520

to directly compare the areas of the black and either the red or the green peaks. Indeed, the eluent521

mass flow rate is 2.2 times larger for the black than that for the red and the green chromatograms.522

So, the peak area under the black signal (configuration S) is 2.2 × lower than if the same amount523

were eluted at the same flow rate as the red and green peaks (configurations O and IO). The peak524

integration of these three signals shows that 100%, 74%, and 48% of the total mass injected is525

detected for the S, IO, and O configurations.526

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4.2.3 Weak retention : 90.0 % acetonitrile527

Figure 4C shows h data and chromatograms similar to those in Figures 4A and 4B, except that528

the volume fraction of acetonitrile is now 90%. The retention factor of naphthalene is only k′=0.5.529

Compared to the values reported in the previous section, the reduced B coefficient decreases to530

2.9, the transverse dispersion coefficients increases from 1.39 to 2.25 × 10−5 cm2 as the reduced531

velocity increases from 0.15 to 11.9, the retention time decreases by more than 2 but the range of532

radial dispersion distances, r(ν), remains virtually unchanged (0.19 to 0.03 cm). As a result, the533

h data in Figure 7 differ little from those shown in Figure 6, except for the longitudinal diffusion534

term observed for the smallest reduced velocity. The optimum velocity increases from about 2 to535

6 after flow segmentation. This confirms again that the contribution of eddy diffusion decreases536

significantly for the lowest reduced velocities when the eluent near the column wall is rejected537

before detection. The minimum reduced plate height hmin deceases from 4.1 (S configuration) to538

3.5 (O configuration) and to 3.0 (IO configuration). The same maximum gain in intrinsic column539

efficiency (+ 90%) is observed at the highest flow rate (4.0 mL/min) and the sensitivity increases540

by as much as 45%.541

It is noteworthy that for low retention factors, the half-height peak width of naphthalene is542

not smaller in the O and IO configurations than the one recorded under standard conditions.543

In fact, they may even be larger as shown in Figure 7. The peak shape is more symmetrical544

when flow is segmented and so the overall peak variances are very similar or only slightly smaller.545

Therefore, analysts may not necessarily see the advantage of segmenting the flow for poorly retained546

compounds, even though the intrinsic performance is improved. This can be solved only by further547

minimizing the sample band broadening that takes place before and after the column, by minimizing548

the detection cell volume, the I.D. of connecting tubes, and the injected volume.549

4.3 Trans-column eddy diffusion550

Figure 8 compares the plots of the measured trans-column reduced plate height (hTC) as a function551

of the reduced velocity (ν) for the three configurations shown in Figure 1. The comparison was made552

for three retention factors (k′

equal to 9.8, 2.3 and 0.5) by increasing the acetonitrile concentration553

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from 0.425 to 0.62 and 0.90, respectively. The parallel segmented flow ratio was fixed at 55%554

because this ratio was found to provide the largest gain in column efficiency as reported earlier 1–3.555

The reduced plate height hTC was obtained by subtracting the sum of (1) the simulated reduced556

plate heights hTS (trans-channel eddy diffusion) and hIC (short-range eddy diffusion) 62 (λ1=0.46,557

ω1=0.0042, λ2=0.23, ω2=0.13, and γe=0.62 for εe=0.39 in Eqs. 11 and 7); (2) the longitudinal558

diffusion reduced HETP term Bν (B derived from Eq. 4 for the smallest values of ν 1); and559

(3) the solid-liquid mass transfer resistance HETP term Cpν (Eq. 9) from the experimental h560

values measured. The B coefficients were measured for the lowest experimental reduced velocities561

(νmin= 0.36, 0.26, and 0.15 for acetonitrile volume fractions of 42.5, 62.0 and 90.0 %, respectively).562

Accordingly B=15.7, 6.5, and 2.9, respectively. The values of Ω (or the ratio of the effective intra-563

particle diffusivity to the bulk diffusion coefficient) was obtained by combining Eqs 5, 6, and 8.564

Accordingly, Ω=4.90, 1.47, and 0.37, respectively. Finally, Cp=0.0039, 0.0101, and 0.0238.565

The experimental results are clear: the trans-column eddy diffusion HETP term of columns566

operated with parallel segmented outlet and/or inlet flow is much lower than that of columns using567

standard inlet/outlet endfittings. For 4.6 × 30 mm columns packed with 3 µm particles, this568

HETP term is about twice lower at the highest applied flow rate (4 mL/min). This reduction569

of the trans-column eddy diffusion term is similar for all three retention factors. An important570

practical consequence is that the HETP curves of these columns is quasi-flat at high flow rates. In571

this study, h remains equal to 3.0 for flow rates between 1.0 and 4.0 mL/min. Local injection of572

the sample in the central region of the column is also beneficial at intermediate reduced velocities,573

close to the optimum velocity although the efficiency gain remains moderate (15% maximum). At574

high flow rates and for large retention factors, the advantage of parallel segmented inlet flow is575

nearly negligible because analyte molecules are redistributed across the whole column diameter576

through transverse dispersion before they reach the column outlet. Therefore, parallel segmented577

inlet/outlet flow and parallel segmented outlet flow columns are quasi-equivalent in the velocity578

range ν=20-30.579

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4.4 Gradient application580

The gradient elution separations of the nine compounds in the Agilent RPLC check-out sample581

with the same column operated in the three configurations were compared. The mobile phase582

composition was linearly increased from ϕ=0.40 to 0.95. The gradient volume VG was set at six583

times the column hold-up volume (VG=6 × 0.359 cm3= 2.154 cm3. The volume gradient slope was584

βv=0.209 cm−3. Three different flow rates were used : 0.25 mL/min (diffusion regime), 1.0 mL/min585

(maximum column efficiency), and 4.0 mL/min. The expected peak capacity were estimated from586

the peak standard deviation σi of the fully resolved peaks i=1, 2, 3, 6, 7, 8, and 9 :587

Pc = 1 + 7t9 − t1∑

i σi(18)

Figure 9 shows the gradient chromatograms recorded under S (red color), O (blue color), and588

IO (green color) configurations. The segmented flow ratio was set at exactly 55.0% at both the inlet589

and outlet of the column. Remarkably, all the peaks, except the non-retained one are fronting when590

the inlet flow is split. The corresponding peak capacities were 81 (0.25 mL/min), 94 (1.0 mL/min),591

and 112 (4.0 mL/min) in the IO configuration but 108, 114, and 107 in the S configuration. The592

relatively poor performance of the IO configuration in gradient elution is probably explained by the593

lack of synchronism of the mobile phase compositions entering the wall and the central regions of594

the column. First, the dwell volume of the tubing from the split union to the central column inlet595

is 0.7 µL (short Viper connector) + 1.2 µL (first injection valve groove) + 20 µL (syringe) + 40596

µL (injection loop) + 1.0 µL (needle seat capillary) + 1.2 µL (second injection valve groove)+ 3.3597

µL (long Viper connector) = 67.4 µL. The flow rate through the central inlet port is only 45% of598

the total flow rate. Secondly, the dwell volume between the split union and the peripheral column599

inlet is: 3.5 µL (long metallic connector) + 0.7 µL (short Viper connector) =4.2 µL only. The flow600

rate along this channel is 55% of the total flow rate. So, the sample needs 0.55×67.40.45×4.2 ' 20 less time601

to reach the peripheral than the central region of the column.602

This time differential causes a difference of the mobile phase composition between the wall and603

the center regions of the column. The stronger eluent strength in the wall region can locally desorb604

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faster a small fraction of the strongly retained compounds with the largest radial excursion r(ν)605

from the central region of the column. This could potentially explain the systematic peak fronting606

observed for all retained samples. For a total flow rate of 4 mL/min, the central-to-peripheral time607

differential is about 2.2 s and peak fronting is clearly seen in the green chromatogram in Figure 9.608

The larger the retention factor, the more pronounced peak fronting. Two solutions are possible:609

(1) two independent pumps can be used to feed eluent independently to the peripheral and central610

column inlets. Synchronizing the eluent delivery at these two inlet ports knowing their respective611

dwell volume will remain difficult but it is definitely doable. (2) a known hold-up volume which612

would not increase the pressure resistance could be cautiously added to exactly compensate the613

time differential. Note that an advantage of the center-to-wall differential is the sharp rear of all614

retained peaks observed because the wall region is flushed with a stronger eluent than the column615

center. Only analyte molecules retained in the central region are detected. Also, as observed under616

isocratic conditions, the sensitivity is increased by 50 and 35% for the least and the most retained617

analytes, respectively.618

The peak capacities observed in the O configuration (109, 130, 121) are all larger than those619

measured in the standard flow conditions (108, 114, 107). As expected from the previous inves-620

tigations under isocratic conditions, the gain in peak capacity is maximal (+15%) at the largest621

flow rates, which significantly diminish the transcolumn eddy diffusion term. It is noteworthy that622

the gain in peak capacity is mostly due to the elimination of the peak tailing observed with the623

standard column. Indeed, the half-height peak widths are even slightly larger in the O than in624

the S configuration, by an average of + 10 and + 20% at 1.0 and 4.0 mL/min, respectively. This625

stresses the importance of minimizing the extra-column brand spreading that takes place down-626

ward the column (outlet connector and detection cell volume) when large flow rates are applied.627

As previously shown in section 4.1, the extra-column peak time variance can be multiplied by a628

factor up to 3 at the maximum flow rate of 4 mL/min. This cannot be neglected anymore with629

column packed with fine 3 µm particles.630

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5 Conclusion631

The intrinsic (HETPs and column efficiency corrected for extra-column volume contributions) and632

the overall (gradient elution) kinetic performances of short (3 cm long ) and wide (4.6 mm I.D.)633

columns packed with the same batch of porous particles were measured for three different configu-634

rations of the inlet sample distribution and outlet eluent collection. The test analyte was the small635

molecule naphthalene eluted with a series of acetonitrile-water mixtures (42.5/57.5, 62.0/38.0 and636

90.0/10.0, v/v). The first and reference configuration is the standard column with no split flow637

and two classical end-fittings fitted to both ends of the column. The second configuration allows638

parallel segmentation of the outlet flow rate: 55% of the eluent being collected in the wall region639

and wasted while 45% of the eluent stream in the center region is collected for detection. The640

third configuration allows an additional, second split of the flow rate at the column inlet (same641

segmentation flow ratio of 55%) in order to inject the sample in the column center.642

The results show that parallel segmented flow columns provide more efficient separations than643

the same columns equipped with standard end-fittings. The maximum efficiency gain (+90 to644

100%) is observed at the largest flow rates (4 mL/min), with inlet/outlet parallel segmented flow.645

The outlet parallel segmented flow column generates a comparable maximum efficiency gain of 70646

to 90%. In RPLC, these efficiency gains at the optimum flow velocity were measured at 65, 50,647

and 35% for retention factors of 9.8, 2.3, and 0.5, respectively. The detailed, careful analysis of all648

the reduced HETP terms involved in the overall mass transfer mechanism (longitudinal diffusion,649

solid-liquid mass transfer resistance, trans-channel eddy diffusion, short-range inter-channel eddy650

diffusion and trans-column eddy diffusion) clearly demonstrates that the fundamental explanation651

for this column technology improvement is directly related to a significant reduction of the trans-652

column eddy diffusion HETP term. Additionally, the local injection of the sample in the central653

region of the column allows achieving higher sensitivity (25 to 50%) than the classical injection654

across the whole column diameter. From a practical viewpoint, the advantage of segmented flow655

columns is visible at the bases of peak profiles due to the practical elimination of nefarious peak656

tailing.657

In gradient elution, the peak capacities of columns operated in flow segmentation were 15%658

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larger than those measured for standard columns at high flow rates. This is about 60% smaller659

than expected based on the intrinsic efficiency gain of the parallel segmented flow columns. The660

most important limitation in gradient elution is the bandspreading along the outlet connector (3.3661

µL) and the detection cell (V (σ)=1 µL) at very high flow rates. These parts account for about662

15-20% of the average peak width recorded in gradient elution. A second limitation concerns the663

inlet parallel segmented flow column. Careful attention should be paid to synchronisation of the664

eluent composition in the peripheral and central inlet ports of the column. This is necessary to665

avoid serious peak fronting in gradient elution.666

From a more fundamental viewpoint, this work confirms that the trans-column reduced plate667

height is the limiting mass transfer resistance phenomenon in modern HPLC columns. Even at668

moderately large reduced velocities encountered for small molecules (15 < ν < 30, naphthalene),669

this HETP term controls about 85% of the total plate height of the short columns studied in this670

work. Parallel segmented flow allows minimization of its contribution to the plate height at high671

velocities, so the intrinsic column efficiencies become closer to that of the infinite diameter column.672

The minimum and incompressible reduced plate heights are 0.90, 0.85 and 0.80 for retention factors673

of 10, 2.5, and 0.5 in RPLC columns using fully porous particles and assuming no-slip flow condition674

at the particle surface. Still, the same issue remains: HPLC systems can let columns to provide675

their best performance unless instrument manufacturers provide (1) the ability to inject directly676

the sample into the very column inlet and to sharply cut the rear part of the injected volume; and677

(2) a direct connection of a small detector cell to the column outlet through a movable detection678

port system.679

Important new questions subsist regarding the potential impact of this new method, parallel680

segmented flow, in modern column technology. Will the influence on the apparent column efficiency681

of short columns be also observed with columns packed with smaller particles (2.6 µm) or particles682

of different nature (core-shell particles) of with monolithic columns? What of the impact of the683

column length on the benefit of segmented flow? Longer columns might favor the faster radial684

equilibration of analyte concentration across the column diameter. Those are the purposes of685

current investigations that will be reported later.686

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6 Acknowledgements687

This work was supported in part by the cooperative agreement between the University of Tennessee688

and the Oak Ridge National Laboratory. We thank Andrew Shalliker and Harald Ritchie (Thermo689

Fisher Scientific, Runcorn, UK) for the generous gift of the Hypurity columns and of the necessary690

column fittings.691

References692

[1] Camenzulli, M.; Ritchie, H. J.; Ladine, J. R.; Shalliker, R. J. Chromatogr. A 2012, 1232, 47.693

[2] Shalliker, R.; Camenzulli, M.; Pereira, L.; Ritchie, H. J. J. Chromatogr. A 2012, 1262, 64.694

[3] Camenzulli, M.; Ritchie, H. J.; Shalliker, R. J. Chromatogr. A 2012, 1270, 204.695

[4] Camenzulli, M.; Ritchie, H. J.; Ladine, J. R.; Shalliker, R. Analyst 2011, 136, 5127.696

[5] Camenzulli, M.; Goodie, T. A.; Bassanese, D. N.; Francis, P.; barnett, N.; Ritchie, H. J.;697

Ladine, J. R.; Shalliker, R. Rapid Commun. mass Spectrom. 2012, 1232, 47.698

[6] Camenzulli, M.; Ritchie, H. J.; Ladine, J. R.; Shalliker, R. J. Sep. Sci. 2012, 35, 410.699

[7] Farkas, T.; Guiochon, G. Anal. Chem. 1997, 69, 4592.700

[8] Farkas, T.; Sepaniak, M. J.; Guiochon, G. AIChE J. 1997, 43, 1964.701

[9] Yun, T.; Smith, M. S.; Guiochon, G. J. Chromatogr. A 1998, 828, 19.702

[10] Yew, B. G.; Ureta, J.; Shalliker, R. A.; Drumm, E. C.; Guiochon, G. AIChE J. 2003, 49,703

642–664.704

[11] Shalliker, R. A.; Wong, V.; Broyles, B. S.; Guiochon, G. J. Chromatogr. A 2002, 977, 213.705

[12] Mriziq, K. S.; Abia, J. A.; Lee, Y.; Guiochon, G. J. Chromatogr. A 2008, 1193, 97.706

[13] Baur, J.; Kristensen, E.; Wightman, R. Anal. Chem. 1988, 60, 2334.707

30

of 47

Accep

ted

Man

uscr

ipt

[14] Gritti, F.; Martin, M.; Guiochon, G. Anal. Chem. 2009, 81, 3365.708

[15] Gritti, F.; Guiochon, G. J. Chromatogr. A 2010, 1217, 6350.709

[16] Gritti, F.; Guiochon, G. AIChE. J. 2011, 57, 346.710

[17] Gritti, F.; Guiochon, G. AIChE J. 2011, 57, 333.711

[18] Gritti, F.; Guiochon, G. AIChE J. 2010, 56, 1495.712

[19] Abia, J.; Mriziq, K.; Guiochon, G. J. Chromatogr. A 2009, 1216, 3185.713




[23] Gritti, F.; Guiochon, G. Anal. Chem. 2013, doi: 10.1021/ac3033307.717


[25] Gritti, F.; Leonardis, I.; Shock, D.; Stevenson, P.; Shalliker, A.; Guiochon, G. J. Chromatogr.719

A 2010, 1217, 1589.720

[26] Gritti, F.; Leonardis, I.; Abia, J.; Guiochon, G. J. Chromatogr. A 2010, 1217, 3219.721

[27] Guiochon, G.; Gritti, F. J. Chromatogr. A 2011, 1218, 1915.722




[31] Gritti, F.; Guiochon, G. LC-GC North Am. 2012, 30, 586.726

[32] Gritti, F. Chromatography Today 2012, 3, 4.727

[33] Bruns, S.; D., S.; B.M., S.; Tallarek, U. J. Chromatogr. A 2012, 1268, 53.728

31

of 47

Accep

ted

Man

uscr

ipt

[34] Gritti, F.; Horvath, K.; Guiochon, G. J. Chromatogr. A 2012, 1263, 84.729

[35] Khirevich, K.; Holtzel, A.; Seidel-Morgenstern, A.; Tallarek, U. J. Chromatogr. A 2012, 1262,730

77.731

[36] Daneyko, A.; Khirevich, S.; Holtzel, A.; Seidel-Morgenstern, A.; Tallarek, U. J. Chromatogr.732

A 2011, 1218, 8231.733

[37] Daneyko, A.; Hlushkou, D.; Khirevich, S.; Tallarek, U. J. Chromatogr. A 2012, 1257, 98.734

[38] Bruns, S.; Tallarek, U. J. Chromatogr. A 2011, 1218, 1849.735

[39] Hormann, K.; Muellner, T.; Bruns, S.; Holtzel, A.; Tallarek, U. J. Chromatogr. A 2012, 1222,736

46.737



[42] Tallarek, U.; Bayer, E.; Guiochon, G. J. Am. Chem. Soc. 1998, 120, 1494.740

[43] Miyabe, K.; Guiochon, G. J. Chromatogr. A 2010, 1217, 1713.741

[44] Landauer, R. J. Appl. Phys. 1952, 23, 779–784.742

[45] Torquato, S. Random Heterogeneous Materials. Microstructure and Macroscopic Properties;743

Springer: New York, 2002.744

[46] Torquato, S. J. Appl. Phys. 1985, 58, 3790.745


[48] Gritti, F.; Guiochon, G. Chem. Eng. Sci. 2011, 66, 3773.747


[50] Giddings, J. Dynamics of Chromatography; Marcel Dekker, New York, NY, 1965.749

[51] Kucera, E. J. Chromatogr. 1965, 19, 237.750

32

of 47

Accep

ted

Man

uscr

ipt

[52] Lapidus, L.; Amundson, N. R. J. Phys. Chem. 1952, 56, 984.751

[53] Kaczmarski, K.; Guiochon, G. Anal. Chem. 2008, 79, 4648.752

[54] Khirevich, S.; Daneyko, A.; Holtzel, A.; A., S.-M.; Tallarek, U. J. Chromatogr. A 2010, 1217,753

4713.754

[55] Gritti, F.; Guiochon, G. Anal. Chem. 2008, 80, 5009.755








[63] Davis, H. J. Am. Ceram. Soc. 1977, 60, 499–501.763

[64] Garnett, J. C. M. Philos. Trans. R. Soc. London, Ser. B 1904, 203, 385.764

[65] Guiochon, G.; Felinger, A.; Katti, A.; Shirazi, D. Fundamentals of Preparative and Nonlinear765

Chromatography, 2nd ed.; Academic Press, Boston, MA, 2006.766

[66] Taylor, G. Proc. R. Soc. Lond. A 1953, 219, pages = 186,.767

[67] Bruns, S.; Grinias, J. P.; Blue, L. E.; Jorgenson, J. W.; Tallarek, U. Anal. Chem. 2012, 84,768

4496.769

[68] Daneyko, A.; Holtzel, A.; Khirevich, S.; Tallarek, U. Anal. Chem. 2011, 83, 3903.770

[69] Rustamov, I. Farcas, T.; Ahmed, F.; Chan, F.; LoBrutto, R.; McNair, H.; Kazakevich, Y. J.771

Chromatogr. A 2001, 913, 49.772

33

of 47

Accep

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Man

uscr

ipt


[71] Gritti, F.; Kazakhevich, Y.; Guiochon, G. J. Chromatogr. A 2007, 1169, 111.774

[72] Knox, J.; Scott, H. J. Chromatogr. 1983, 282, 297.775

[73] Knox, J. H.; McLaren, L. Anal. Chem. 1964, 36, 1477.776





[78] Stevenson, P.; Gritti, F.; Guiochon, G. J. Chromatogr. A 2011, 1218, 8255.781

[79] Stevenson, P.; Gao, H.; Gritti, F.; Guiochon, G. J. Sep. Sci. 2013, 36, 279.782

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7 List of symbols783

Roman letters784

A(ν) Reduced eddy diffusion term785

B Reduced longitudinal diffusion coefficient with reference to the interstitial linear velocity786

Ci Sample concentration at time ti (s)787

Cp Reduced solid-liquid mass transfer resistance coefficient788

dp Average particle diameter (m)789

Deff Effective diffusion coefficient of the analyte in the packed column (m2/s)790

Dm Bulk molecular diffusion coefficient (m2/s)791

Dt Transverse dispersion coefficient of the analyte across the packed column (m2/s)792

Fv Flow rate (m3/s)793

h Reduced plate height794

hTS Reduced trans-channel eddy diffusion plate height795

hIC Reduced short-range eddy diffusion plate height796

hTC Reduced trans-column plate height797

k′

Retention factor798

k1 Zone retention factor.799

Ka Equilibrium Henry’s constant for the sample adsorption-desorption between the solid800

phase in the porous volume of the particle and the liquid eluent phase.801

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L Column length (m).802

rc Column inner radius (m)803

ti Discretized elution time (s)804

u Interstitial linear velocity (m/s)805

VG Gradient volume (m3)806

Greek letters807

β Parameter in Torquato’s model of effective diffusion in packed beds defined by Eq. 6808

βv Volume gradient slope (m−3)809

εe External column porosity810

εp Particle porosity811

εt Total column porosity812

γe Obstruction factor caused by randomly packed non-porous particles to the diffusion in the813

external bulk mobile phase814

µ1 First moment (s)815

µ′2 Second central moment (s2)816

µ1,ex First moment recorded in absence of the chromatographic column (s)817

µ′2,ex Second central moment recorded in absence of the chromatographic column (s)818

ν Reduced interstitial linear velocity819

Ω Ratio of the effective diffusivity of the sample in the porous region of the particle to its820

bulk diffusion coefficient821

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ω1 Diffusion eddy dispersion coefficient related to trans-channel velocity bias822

λ1 Flow eddy dispersion coefficient related to trans-channel velocity bias823

ω2 Diffusion eddy dispersion coefficient related to short-range inter-channel velocity bias in824

columns packed with non-porous particles825

λ2 Flow eddy dispersion coefficient related to short-range inter-channel trans-column velocity826

bias in columns packed with non-porous particles827

ϕCH3CN Volume fraction of acetonitrile in water828

ξ2 Adjustable parameter in Torquato’s model of effective diffusion Eq. 5829

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Inlet Outlet

PumpInjectionValve

DetectorWasteBottle

Fv

Fv

Fv

STANDARD OUTLET FLOW

OUTLET

SPLIT FLOW

STANDARD INLET FLOW

STANDARD INLET FLOW

OUTLET

SPLIT FLOW

INLET

SPLIT FLOW

Figure 1: Schematics of the standard (top), outlet split (middle) and inlet and outlet split (bottom)flow modes applied during the operation of the 4.6 × 30 mm column packed with 3.0 µm Hypurity-C18 fully porous particles.

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0 1 2 3 40

10

20

30

Volu

me

varia

nce

[L2 ]

Flow rate [mL/min]

CH3CN=42.5% CH3CN=62.0% CH3CN=90.0%

Figure 2: Volume variance of the 1290 Infinity system under standard configuration (no split flow)for three different mobile phase compositions. Compound: naphthalene. Room temperature.

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0 1 2 3 40

100

200

300

400

500

600

CH3CN=0.425

1st moment, outlet split flow

2nd moment, outlet split flow

1st moment, inlet and outlet split flow

2nd moment, inlet and outlet split flow

Rel

ativ

e in

crea

se [

%]

Flow rate [mL/min]

0 1 2 3 40

100

200

300

400





CH3CN=0.62

Rel

ativ

e in

crea

se [

%]

Flow rate [mL/min]

0 1 2 3 40

100

200

300




CH3CN=0.90

Rel

ativ

e in

crea

se [

%]

Flow rate [mL/min]


Figure 3: Relative increases of the first and second central time moments of naphthalene when thesystem is used under the configurations O (outlet split, green and blue colors) and IO (inlet andoutlet split flow, black and red colors) with respect to those measured under standard conditions.

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0 10 20 300

10

20

30

40

50

CH3CN=0.425

h=H

/dp

Reduced velocity

Standard column Oulet split flow Inlet-Outlet split flow

0 10 20 300

10

20

30

40

50

Reduced velocity

h=H

/dp


CH3CN=0.62

0 10 20 300

10

20

30

40

50

CH3CN=0.90


Reduced velocity

h=H

/dp

Figure 4: Experimental corrected reduced plate height plots, h versus ν, for three different config-urations of the 1290 Infinity system as indicated in the legend. The volume fraction of acetonitrilein the mobile phase increases from 42.5 % (A), 62.0 %(B), and to 90.0 % (C). The retention factorsdecrease from k

′=9.8 to 2.3 and to 0.5. Column: 4.6 × 30 mm Hypurity-C18. Room temperature.

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50 60 700

25

50

75

CH3CN=0.425

Abs

orba

nce

[mA

U]

Time [s]

Standard column Outlet split flow Inlet-Outlet split flow

0.0 0.5 1.0 1.50

400

800CH3CN=0.425

Abs

orba

nce

[mA

U]

Time [s]


Figure 5: Experimental extra-column (left) and column (right) band profiles of naphthalenerecorded for three different configurations of the 1290 Infinity system as indicated in the legend.The volume fraction of acetonitrile in the mobile phase is 42.5 %. The retention factors is k

′=9.8.

Column: 4.6 × 30 mm Hypurity-C18. Room temperature. Flow rate : 4 mL/min. Injection volume: 1 µL.

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15 20

0

100

200CH3CN=0.62

Abs

orba

nce

[mA

U]

Time [s]


0.0 0.5 1.0 1.50

400

800CH3CN=0.62

Abs

orba

nce

[mA

U]

Time [s]



′=2.3.


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7 8 90

100

200

300 CH3CN=0.90

Abs

orba

nce

[mA

U]

Time [s]


0.0 0.5 1.0 1.50

400

800

CH3CN=0.90

Abs

orba

nce

[mA

U]

Time [s]



′=0.5.


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0 10 20 300

2

4

6

Reduced velocity

hTC


CH3CN=0.425

0 10 20 300

2

4

6

hTC

Reduced velocity

CH3CN=0.62


0 10 20 300

2

4

6

hTC


CH3CN=0.90

Reduced velocity

Figure 8: Experimental plots of the reduced transcolumn plate height, hTC versus ν, for threedifferent configurations of the 1290 Infinity system as indicated in the legend. The volume fractionof acetonitrile in the mobile phase increases from 42.5 % (A), 62.0 %(B), and to 90.0 % (C). Theretention factors decrease from k

′=9.8 to 2.3 and to 0.5. Column: 4.6 × 30 mm Hypurity-C18.

Room temperature.

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Figure 9: Gradient chromatograms recorded for the three different system configurations (see thelegend and the three different colors in the graph) presented in Figure 1. Column: 4.6 × 30 mmHypurity-C18. Room temperature. Flow rate : 4 mL/min. Injection volume : 1 µL. Analytes :Agilent RPLC check-out samples (see experimental section for more details).

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Effect of parallel segmented flow chromatography on the height equivalent to a theoretical plate....

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