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On the limits in size of Taylor dispersion analysis: representation of the different hydrodynamic regimes and application to the size-characterization of cubosomes Joseph Chamieh, Laurent Leclercq, Michel Martin, Sofia Slaoui, Henrik Jensen, Jesper Ostergaard, and Hervé Cottet Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b03806 • Publication Date (Web): 09 Nov 2017 Downloaded from http://pubs.acs.org on November 20, 2017
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On the limits in size of Taylor dispersion analysis: representation of the different hydrodynamic regimes and application to the sizecharacterization of cubosomes
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Joseph Chamieh1, Laurent Leclercq1, Michel Martin2, Sofia Slaoui3,4 Henrik Jensen3, Jesper Østergaard3, Hervé Cottet1,*
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ABSTRACT: Taylor Dispersion Analysis (TDA) is an absolute method (no calibration needed) for the determination of the molecular diffusion coefficient (D) based on the band broadening of a solute in a laminar flow. TDA is virtually applicable to any solute with size ranging from angstrom to sub-micron. The higher sizing limit is restricted by the occurrence of possibly two regimes: convective and hydrodynamic chromatography (HDC) regimes, which have different physical origins that should not be confused. This work aims at clearly defining the experimental conditions for which these two regimes can play a role, alone or concomitantly. It also calculates the relative error on D due to the HDC regime according to the solute to capillary size ratio. It is demonstrated in this work that HDC does not significantly affect the TDA measurement as far as the hydrodynamic radius of the solute is lower than 0.0051 times the capillary radius. Experimental illustrations of the occurrence of the two regimes are given taking polystyrene nanoparticles as model solutes. Finally, application of TDA to the sizing of large real-life solutes is proposed taking cubosomes as new drug nano-carriers of potential interest for drug delivery purposes.
IBMM, Univ. Montpellier, CNRS, ENSCM, Montpellier, France. Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), ESPCI Paris, CNRS, PSL (Paris Sciences et Lettres) Research University, Sorbonne Université, Université Paris-Diderot, 10 rue Vauquelin, 75231 Paris Cedex 05, France. 3 Department of Pharmacy, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark. 4 IUT Montpellier-Sète, Univ. Montpellier, Montpellier, France. 2
22 1. INTRODUCTION 23 Taylor dispersion analysis (TDA) is an absolute method allow24 ing determination of the molecular diffusion coefficient (D), 25 and hydrodynamic radius (Rh), based on the dispersion of an 26 injected band of solute under laminar flow1,2. The implementa27 tion of TDA in narrow bore capillaries (typically ~50 µm i.d.) 28 has recently gained interest due to several advantages3-6 such 29 as low sample consumption, short analysis time, wider range 30 of sizing (from angstrom to sub-micron) and straightforward 31 analysis without filtration. When the conditions of validity of 32 Taylor dispersion are fulfilled, D is related to the temporal 33 variance of the analyte, σt2, the average elution time t0 and the 34 capillary radius, Rc, of the tube according to7 : R2 t 35 (1) D= c 0
24 σ t2 36 The validity of equation (1) is conditioned to the assessment of 37 two requirements that were already pointed out in the seminal 38 work by Taylor8 . A first condition is that the axial (longitudi39 nal) diffusion is negligible compared to the dispersion due to 40 the parabolic velocity profile8 : Ru 41 (2) D > c 4 t0 57 Taking again a ratio of 1:10, Taylor proposed that inequality 58 (6) is considered as fulfilled if8 : R2 59 (7) t0 ≥ 2.5 c ( or τ ≥ 2.5 ) D 60 where τ = t0 D is a dimensionless characteristic diffusion Rc2 61 time. More recently, we demonstrated that the minimum value 62 of t0 can be expressed as a function of ε as9 :
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1
t0 ≥
3Rc2 80Dε
2 If one takes ε = 3%, inequality (8) becomes: 1.25Rc2 3 t0 ≥ ( or τ ≥ 1.25)
(8)
(9)
D
4 Combining the two conditions of validity with the Poiseuille 5 law leads to a given range of operating mobilizing pressure 6 that should be used for the application of eq. (1) which is 7 independent of the medium viscosity9 : 17 kbTL 0.34 kbT l L 8 (10) ≤ ∆P ≤
Rh Rc3 Rh Rc4 9 where T is the absolute temperature, kb is the Boltzmann con10 stant, L is the total capillary length, and l is the effective ca11 pillary length (to the detector). 12 Increasing the operating mobilizing pressure outside this upper 13 specified limit will first increase the experimental relative 14 error on D before deforming the peak shape from quasi15 Gaussian (Taylor dispersion regime) to a highly deformed 16 tailing profile representative of the convective regime with a 17 new peak appearing at an elution time corresponding to the 18 maximum flow experienced at the capillary centre. Okada et 19 al.10 used these two different regimes (Taylor and convective) 20 for separating two solutes having different partitioning coeffi21 cient with SDS micelles. The Taylor regime occurs when 22 inequalities (10) are verified, while the convective regime 23 progressively appears when decreasing τ to lower values than 24 1.25. The same group published separations of polystyrene 25 particles based on the same principle11. Interestingly, they 26 demonstrated experimentally that the peak deformation from 27 Gaussian to convective profiles occurs when τ ≤ 0.37. Similar28 ly, Adrover et al.12 simulated chromatograms and found a limit 29 for the peak deformation at τ ≤ 0.2. More recently, Latunde30 Dada et al. demonstrated that it is possible to fit the taylor31 grams in the convective regime to get the information on the 32 diffusion coefficient for single component or simple bimodal 33 mixture composed of small/large molecules13. Another ap34 proach for the data processing of taylorgrams obtained beyond 35 the limits of classical TDA was also recently proposed by the 36 same group14 based on the quantification of the degree of 37 radial diffusion that occurs between two spatially separated 38 detection points. However, this approach relies on a semi39 empirical relationship between the variation in the dimension40 less residence time ∆τ and a parameter f calculated from the 41 relative heights of the concentration profiles obtained at two 42 different detection points. Therefore, the absolute feature of 43 TDA (no required calibration), which is verified in ‘normal’ 44 conditions, is lost and the accuracy and simplicity of the 45 methodology is affected. 46 Another hydrodynamic regime, called hydrodynamic chroma47 tography (HDC), may also deform or displace the position of 48 the taylorgram. HDC is due to the exclusion of the solute from 49 the capillary wall leading to a solute average velocity larger 50 than the carrier average velocity given by the Poiseuille law. 51 This regime is only experienced for solutes having the highest 52 Rh/Rc ratio. It is more easily observed in thin capillaries (typi53 cally 25 µm i.d. or less), as reported by Belongia and Baygents 54 for nanoparticles15 and by Tijssen et al. for macromolecules16. 55 However, because the occurrence of HDC is related to the size 56 of the solute, it is sometimes confused with the non-convective 57 / convective transition11.
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58 The objective of this work is to clearly define the occurrence 59 of the different domains / regimes that could be encountered in 60 TDA according to the size of the solute and the experimental 61 conditions (applied mobilization pressure, capillary dimen62 sions). It notably aims at defining the differences in behavior 63 that can be encountered in TDA when going into the convec64 tive regime and/or hydrodynamic chromatography. The limits 65 and differences between these two regimes are not clearly 66 described in the literature. This work also sets the limit in 67 solute size for which HDC affects the size determination by 68 TDA. This question typically arises when dealing with large 69 solutes (typically in the order of a few hundred of nm or even 70 a few µm). Experimentally, we propose to illustrate the differ71 ent possible hydrodynamic regimes, with a clear description of 72 the crossover regions, taking well-defined nanoparticles as 73 model solute. In a second part of this work, an example of 74 TDA application to real life systems is proposed based on the 75 size-characterization of cubosomes. 76 77 2. EXPERIMENTAL 78 2.1. Chemicals and materials 79 Polybead® polystyrene nanoparticles (PS NP) of various 80 hydrodynamic radii (Cat# 08691, Rh = 20 nm; Cat# 07304, Rh 81 = 110 nm; Cat# 07307, Rh = 250 nm; Cat# 07310, Rh = 500 82 nm) and supplied as aqueous suspensions (at a concentration 83 of 2.5-2.6% (w/v) in water) were purchased from Polyscienc84 es, Inc. (Eppelheim, Germany). These particles have precise 85 monodisperse particle size distributions, according to the 86 supplier. Latex nanoparticles (Rh = 50 nm) in suspension at a 87 concentration of 25% (w/v) in water were kindly supplied by 88 CIBA (Basel, Switzerland). N,N-dimethylformamide (DMF) 89 and borax were purchased from Sigma-Aldrich (Saint-Quentin 90 Fallavier, France). 1,2-Dioleoyl-sn-glycero-3-phospho-rac91 glycerol (DOPG; purity: 99.2%) was purchased from Lipoid 92 GMBH (Ludwigshafen, Germany). Phytantriol (3,7,11,1593 tetramethylhexadecane-1,2,3-triol), with a nominal purity of 94 >96.4% from product specification as determined by gas 95 chromatography, was a gift from DSM Nutritional Products 96 Ltd. (Basel, Switzerland). Pluronic F127 was a gift from 97 BASF SE (Ludwigshafen, Germany). Sodium dihydrogen 98 phosphate monohydrate was obtained from Merck (Darmstadt, 99 Germany). 100 A 100 mM sodium borate buffer was prepared by dissolving 101 25 mM borax in water without any further pH adjustment (pH 102 9.20). A 67 mM sodium phosphate buffer was prepared by 103 dissolving NaH2PO4 • H2O in water followed by adjustment of 104 the pH to 7.40 with 5 M NaOH. The buffer was filtered 105 through a 0.20 µm cellulose acetate membrane (Sartorius AG, 106 Gottingen, Germany) prior to use. 107 2.2. Preparation of nanoparticle samples 108 For the experiments in the absence of DMF (used as a 109 small molecule standard), 10 µL aqueous suspension of 110 Polybead® PS NP (or latex nanoparticles suspension previous111 ly diluted ten times in water) were added to 40 µL water and 112 50 µL of 100 mM sodium borate buffer. For the experiments 113 in the presence of DMF, 10 µL aqueous suspension of 114 Polybead® PS NP (or latex nanoparticles suspension previous115 ly diluted ten times in water) were added to 30 µL water, 10 116 µL DMF (1% v/v in water) and 50 µL of 100 mM sodium 117 borate buffer. 118 2.3. Preparation of cubosome dispersion 2
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1 DOPG (18.7 mg) and Pluronic F127 (30.0 mg) were 2 dissolved in 0.067 M phosphate buffer with the aid of vortex3 ing at 50°C. Phytantriol (136.4 mg) was weighed into a vial 4 and the solution of DOPG with F127 was pipetted on top. The 5 concentration of F127 was 1% (w/w) and the total lipid con6 tent was at 5% (w/w) in the final dispersion. The resulting 7 mixture was ultrasonicated using an ultrasonic processor Q500 8 Sonicator, power 500 W, frequency 20 kHz (Qsonica, LLC, 9 Newtown, CT, USA) in pulse mode (1s pulse followed by 2s 10 break at 20-30% of maximum amplitude) to attain milky white 11 dispersions. Prior to TDA the cubosome dispersion was dilut12 ed with the phosphate buffer, pH 7.40, to achieve a final total 13 lipid concentration of 1% (w/w). The identification and char14 acterization of the internal nanostructure of the cubosomes 15 will be reported elsewhere. 16 2.4. Taylor dispersion analysis experiments 17 Analysis of the standardized nanoparticles and nanolatexes. 18 TDA experiments were performed on a PACE MDQ Beckman 19 Coulter (Fullerton, CA) apparatus. Capillaries were prepared 20 from bare silica tubing purchased from Composite Metal Ser21 vices (Worcester, United Kingdom). Capillary dimensions 22 were 60 cm (50 cm to the detector) × 50 µm i.d. (or 25 µm 23 i.d.). The temperature of the capillary cassette was set to 25°C 24 whereas the samples were kept at ambient temperature. So25 lutes were monitored by UV absorbance at 200 nm. The capil26 lary was conditioned by flushing with 1 M NaOH for 20 min, 27 0.1 M NaOH for 15 min, water for 5 min and finally sodium 28 borate buffer for 5 min. The conditioning procedure was re29 peated before injecting new nanoparticle sample. For each 30 given nanoparticle sample, the capillary was flushed with 31 sodium borate buffer for 5 min between repetitions. The sam32 ples were introduced into the capillary by hydrodynamic injec33 tion (20 mbar for 6 s for 50 µm i.d. capillaries and 80 mbar for 34 6 s for 25 µm i.d. capillaries). The mobilization pressure var35 ied from 7 to 1200 mbar, depending on the experiments 36 Application to the analysis of the cubosomes. TDA experi37 ments were carried out using a 3D-CE system (Agilent Tech38 nologies, Waldbronn, Germany). Detection at two windows in 39 a looped capillary was carried out applying an Actipix D100 40 UV area imaging detector and software version 1.4.911 41 (Paraytec Ltd, York, UK)17. The light source was a pulsed 42 xenon lamp and the wavelength applied was 214 nm. The two 43 detection windows were placed at 30 cm (1st detection point) 44 and 50 cm (2nd detection point) from the inlet end on a 100 cm 45 long uncoated fused silica capillary (Polymicro Technologies, 46 Phoenix, AZ) with 75 µm i.d. (360 µm o.d.). The new capil47 lary was conditioned by flushing with 1 M NaOH, water and 48 buffer for 30 min each. On a daily basis, the capillary was 49 flushed with 1 M NaOH and buffer for 5 min each before 50 starting experiments. Between runs, the capillary was flushed 51 with 1 M NaOH and buffer for 3 min and 2 min, respectively. 52 The samples were introduced into the capillary by hydrody53 namic injection (50 mbar for 7 s). The mobilization pressure 54 was 10 or 50 mbar. The temperature of the capillary cassette 55 was set to 25°C whereas the samples were kept at ambient 56 temperature.
Pe=40
106
Taylor regime
105 10
L/Rc
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Taylor Aris regime
4
103
e( 5P 2 . =1
102
1 τ=
) .25
c L/R
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Pure convection
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Pe 57 58 Figure 1. Illustration of the different regimes when a given 59 solute is mobilized in an open tubular column. L is the total 60 column length, Rc is the radius of the column and Pe is the 61 Péclet number. The red line shows the different regimes that 62 can be encountered in TDA when the Pe number is increased: 63 from Taylor-Aris, to Taylor, and finally convective regimes. 64 65 3. RESULTS AND DISCUSSION 66 3.1. Convective / non-convective transition in Taylor dis67 persion analysis: experimental illustration and graphical 68 representation 69 Figure 1 displays the different regimes that occur for a 70 solute band in an open-tubular capillary tube according to the 71 Péclet number and L/Rc ratio. The range in L/Rc typically 72 varies between 104 and 105 (red lines), either in the capillary 73 format (internal capillary diameter dc~25-100 µm; L~50-100 74 cm) with CE equipment or in the µHPLC format (dc ~500 µm; 75 L~10-20 m). The red zone corresponds to the ideal zone for 76 doing TDA for which the two conditions presented in the 77 introduction are fulfilled. Within this zone, the simplified 78 TDA equation (1) applies and the Gaussian peak shape should 79 be observed for a monodisperse sample. The limit set by Pe = 80 40 represents the transition between Taylor-Aris (i.e. Taylor 81 dispersion and axial diffusion) and pure Taylor regime as 82 expressed by eq. (5) [9]. The limits set by L/Rc = 1.25 Pe 83 corresponds to eq. (9) and represents the transition between 84 convective and non-convective pure Taylor regime. 85 Since the Péclet number depends both on the applied condi86 tions (mobilizing pressure, capillary dimensions) and on solute 87 size (or diffusion coefficient), it is convenient to visualize the 88 different regimes on a ∆P vs Rh plot for given capillary dimen89 sions that are typically used on CE instrumentation (dc = 50 90 µm and L = 60 cm, see Figure 2). The limiting lines between 91 the various operating regimes shown in Fig. 1 can now be 92 expressed in terms of ∆P by: ∆P =
93 94 and ∆P =
95
4Pecrit kbTL 3π Rc3Rh
(11a)
4 kbT l L 3πτ crit Rc4Rh
(11b)
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∆P (mbar)
1 where Pecrit and τcrit are the critical Pe and τ values discussed 43 pressures (τ ≤ 0.37). For the runs at mobilizing pressures of 7 2 above. In a log-log representation, these lines are seen to be 44 and 28 mbar, the calculated τ values where higher than the 45 requested 1.25 value (7.56 and 1.89 respectively), the elution 3 linear plots with a slope equal to -1. τ = 1.25 τ = 0.37 46 profiles were Gaussian, and the calculated Rh is 229 ± 4 nm (n 10000 Convection 47 =4). Convection Non Gaussian Non Gaussian 48 + HDC 49 Figure 4 shows the taylorgrams obtained for different sizes of 1000 50 PS NP mobilized at a constant pressure of 180 mbar. The 51 elution profiles remained Gaussian shaped up to a radius of 50 52 nm (τ = 1.47). For higher hydrodynamic radii, 110, 250 and Taylor regime 53 500 nm (τ = 0.67, 0.29 and 0.15 respectively) the peaks are 100 54 distorted. For samples having a τ value between 1.25 and 0.37 55 only a slight distortion is observed. For τ values lower than 56 0.37, the convective deformation of the peak becomes more 10 57 pronounced. For a better visualization of the transition be58 tween the two regimes (Taylor and convective), one may refer HDC 59 to Figure 2 where the Rh of the analyzed samples and the apregime 60 plied pressures are schematized with red dots on the horizontal 1 0.1 1 10 100 1000 10000 61 and the vertical arrows. The dots corresponding to τ values 62 between 1.25 and 0.37 presented a slight peak deformation. Rh (nm) 4 63 The dots with τ values below 0.37 presented distorted peaks, 5 Figure 2. Illustration of the different regimes possibly encoun- 64 while dots for τ higher than 1.25 presented Gaussian peak 6 tered in TDA experiments. ∆P is the applied mobilizing pres- 65 shape, as predicted by eq. (9). In the supporting information 7 sure. Capillary dimensions: 50 µm i.d. × 60 cm total capillary 66 section, Figures SI1 and SI2 display the ∆P=f(R ) representa8 length (50 cm effective length). The red dots represent the 67 tion showing the different regimes for different hcapillary i.d. 9 experimental conditions that were realized and that are pre- 68 (75 µm in Figure SI1 and 100 µm in Figure SI2; see Figure 5 10 sented in Figures 3 and 4. 69 for 25 µm i.d.). These graphs are very useful from a practical 11 70 point of view to visualize directly the occurrence of the Taylor 12 The experimental illustration of the change in the hydrody- 71 regime according to the solute’s R and the applied pressure h 13 namic regime can be performed both by changing the solute 72 ∆P. 14 size at a constant mobilizing pressure (horizontal red arrow in 15 Figure 2); or by changing the pressure for a given size (see 16 vertical arrow in Figure 2). Each red dot placed on Figure 2 17 represents one experimental condition that was investigated in 18 this work. 19 Figure 3A shows the analysis of polystyrene NP having a 250 20 nm radius at different mobilizing pressures, ranging from 7 21 mbar to 550 mbar. For better visual comparison, the height of 22 each peak was normalized by the maximum value at t0 (Figure 23 3B) and by changing the variable on the x-axis to correct the 24 variations in elution time due to different applied pressures. 25 Within the Taylor regime, the elution profile for a monodis26 perse sample is a Gaussian peak, as expressed by: Pe
=
40
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A y = y0 + e σ 2π
−( t −t0 ) 2σ 2
2
2
A 12 D = y0 + e Rc t0π
−( t − t0 ) 12 D t0 Rc2
27 (12) 28 where y is the detector response, y0 is an offset value, t is the 29 elution time, σ2 is the temporal variance of the peak and A is a 30 constant which is directly proportional to the total injected 31 quantity. From equation (12), it is clear that for a given capil32 lary radius Rc, the recorded signal y only depends on the diffu33 sion coefficient D if one changes the variable from t to 34 x = ( t − t0 ) t0 . Thus, within the Taylor conditions, the tay35 lorgrams y(x) obtained for a given sample at different mobili36 zation pressures should overlap, as far as Rc is kept constant. 37 As shown in Figure 3 (A and B), the peaks become slightly 38 distorted for ∆P = 90 mbar corresponding to a τ value of 0.6. 39 For higher applied pressures, the peaks present an abrupt in40 crease in absorbance on the left side, keeping the Gaussian 41 shape only on the right side of the elution profile. The distor42 tion on the left side is more pronounced for higher applied 4
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Mobilization ∆P 7 mbar 28 mbar 90 mbar 180 mbar 276 mbar 550 mbar
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17 horizontal arrow in Figure 2. Hydrodynamic injection: 21 18 mbar, 6s. Injected solute concentration: 2.5 % (w/v) in water.
Normalized Absorbance (a.u.)
19 3.2. Occurrence of the hydrodynamic chromatography 20 regime in Taylor dispersion analysis 4 21 The horizontal arrow in Figure 5 represents the position of the 0 5 10 Time (min) 22 PS NP samples having radii of 110 nm, 250 nm and 500 nm 3 23 that were analyzed at a constant mobilizing pressure of 28 24 mbar in a 25 µm i.d. capillary. At this applied pressure, a 2 25 hydrodynamic chromatography (HDC) separation, due to the 26 exclusion of the particles center of mass from the immediate 1 27 vicinity of the capillary wall, may occur for the analyzed sam28 ples. In fact, DMF used as a dead volume marker did not sepa0 29 rate from the 110 nm sample, but separated from the 250 nm 0 20 40 60 80 100 30 and 500 nm samples, as seen from the superimposed taylorTime (min) 31 grams in Figure 6. It can be noted that the peak apex of the 1 32 500 nm (and the 250 nm to some extent) NP are shifted to 2.0 Mobilization ∆P 33 lower elution times due to the HDC effect. This effect is hard7 mbar 34 ly observable on 50 µm i.d. capillaries. That is why a 25 µm 28 mbar 35 i.d. capillary was used for which the average detection time is 1.5 90 mbar 36 only 10% lower for the 500 nm NP compared to DMF (see the 180 mbar 276 mbar 37 taylorgrams in t/t0 scale in Figure 6). The peak broadening 550 mbar 38 (due to Taylor dispersion) is very pronounced due to the large 1.0 39 size of NP. However, in all cases, the peaks remain symmet40 rical because the TDA conditions are fulfilled. That is why 41 separations by HDC can only be implemented on very thin 0.5 42 capillaries (typically 10 or 5 µm), which then makes the detec43 tion more critical. Still, the HDC effect affects, not only the 44 mean elution time of the NPs, but also their temporal variance, 0.0 45 which both influence the accuracy of the diffusion coefficient -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 46 determination. It can be shown (see Supporting Information) 1/2 (t-t0)/t0 47 that the upper limit of the particle-to-column radius ratio lead2 3 Figure 3. Taylorgrams obtained for PS NP (250 nm) at differ- 48 ing to an error in the diffusion coefficient determination from 4 ent mobilization pressure in time scale (A) or in normalized 49 eq. (1) lower than ε is given as 5 scale (B). Capillary dimensions: 50 µm i.d. × 60 cm total Rh 6 capillary length (50 cm to the detector). Mobilization pressure = 0.17 ε 7 as indicated on the graph. The inset is the zoom of the area 50 Rc (13) 8 delimited by a dotted line. This series of experiments corre9 sponds to the illustration of the vertical arrow in Figure 2. 51 that is Rh/Rc lower than 0.0051 for an acceptable error of 3% 10 Hydrodynamic injection: 21 mbar, 6s. Injected solute concen- 52 on D, leading to Rh = 64 nm for Rc = 12.5 µm. Thus, the low53 est NPs analyzed in Fig. 6 are already outside of the domain 11 tration: 2.5 % (w/v) in water. 54 where the HDC effect does not affect significantly the deter1.2 Mobilizing ∆P = 180 mbar 55 mination of D. It should be noted that the HDC effect tends to DMF 56 maximize the diffusion coefficient, and hence minimize the 25 nm 1.0 50 nm 57 hydrodynamic radius. This is because it decreases the tem110 nm 58 poral variance more strongly than the elution time. Conse0.8 250 nm 59 quently, this effect on D can be present before a partial separa500 nm 60 tion between peaks is visually observed. 0.6 61 It must be stressed that, the peaks remain Gaussian in the case 62 of HDC, as far as the convective regime is not reached. It is 0.4 63 worth noting that the occurrence of both HDC and convective 64 regimes at the same time is possible, especially in the case of 0.2 65 large particles and high mobilizing pressure (see the green 66 zone in Figure 5). Therefore, if the flow rate is accelerated for 0.0 67 the 500 nm particle on the 25 µm i.d. capillary a combination 0 2 4 6 8 68 of HDC and ‘convective’-TDA conditions can be observed Time (min) 12 69 (see Figure SI3) that deforms the peak shape as discussed 13 Figure 4. Taylorgrams obtained for PS NP of different sizes at 70 earlier. However, the deformation of the peak due to convec14 the same mobilization pressure. Capillary dimensions: 50 µm 71 tion effect may mask the relatively small shift of the elution 15 i.d. × 60 cm total capillary length (50 cm to the detector). This 72 time due to the HDC phenomenon. 16 series of experiments corresponds to the illustration of the 2 1
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28 deviation is much less pronounced when the experiments are 29 conducted at 10 mbar (Figure 7B). The effect of changing the 30 experimental conditions on peak shape is readily apparent by 31 comparison of Figures 7A and 7B, and even within the exper32 iments upon inspection of changes of the peak shapes when 1000 Taylor regime 33 the sample is traveling from window 1 (30 cm) to window 2 34 (50 cm), due to the transition from convective to pure Taylor 35 dispersion regime. Table 1 depicts diffusion coefficient (as 100 36 determined from fitting a Gaussian to the UV traces and em37 ploying the difference in temporal variance and peak elution 38 time to calculate the diffusion coefficient19 using the Actipix 10 39 software), dimensionless residence time τ and the Péclet numHDC 40 ber for the experimental conditions at both detection points. regime 41 Clearly, from comparison of Figure 7A to Figure 7B, the TDA 42 conditions are better fulfilled at the lower mobilization pres1 0.1 1 10 100 1000 10000 43 sure (10 mbar). For a clear visualization of the position of the 44 experimental conditions relative to the TDA conditions, Figure Rh (nm) 1 2 Figure 5. Occurrence of HDC regime in Taylor dispersion 45 SI4 represents the experimental point as red dots on the ∆P vs 3 analysis. ∆P is the applied mobilizing pressure. Capillary 46 Rh plot. 4 dimensions: 25 µm i.d. × 60 cm total capillary length (50 cm 47 The apparent hydrodynamic radius of the cubosomes is 82.6 5 to the detector). The red dots represent the experimental condi- 48 nm (RSD 5%) as determined by TDA using a mobilization 6 tions that were realized and that are presented in Figure 6. The 49 pressure of 10 mbar. Table 1 shows that utilizing the applied 7 dashed blue line represents the Rh limit from which the HDC 50 setup with respect to capillary dimensions and pressure of 10 8 regime starts. 51 mbar Taylor conditions are fulfilled. Also, with respect to 52 error on D based on the occurrence of HDC, the error is less 110 nm 53 than 3% as the ratio Rh/Rc = 0.0022 (see eq. 13). The taylor250 nm 54 grams in Figure 7B indicate that TDA may be an attractive 1.0 500 nm 55 approach for size-characterization of cubosomes, which is 56 further corroborated by the above theoretical analysis. TDA is 57 proposed to constitute a viable alternative to dynamic light 58 scattering, laser diffraction and cryo-transmission electron 59 microscopy that are commonly used for cubosome characteri60 zation20. One advantage of TDA over DLS is the low sensitivi0.5 61 ty toward dusts, which makes the TDA analysis straightfor62 ward with no sample filtration. The size obtained by TDA 63 (165 nm diameter) is close, within experimental error, to the 64 size measurements performed using dynamic light scattering 65 (Zetasizer Nano ZS, Malvern Instruments, Malvern, UK) 0.0 66 providing a diameter of 155 nm with a polydispersity index of 0.4 0.6 0.8 1.0 1.2 67 0.134 for the investigated cubosomes. The close agreement 68 between the size obtained by the two independent methods t/t 69 also demonstrates the low polydispersity of the sample, since 0 9 10 Figure 6. Taylorgrams obtained for PS NPs of different sizes 70 TDA gives the weight-average Rh, while DLS measures a z11 (110, 250 and 500 nm Rh) on a 25 µm i.d. capillary illustrating 71 average value. 12 the occurrence of HDC regime in TDA. Capillary dimensions: 13 25 µm i.d. × 60 cm total capillary length (50 cm to the detec- 72 Table 1. Diffusion coefficient, dimensionless residence time τ 14 tor). Mobilization pressure: 28 mbar. Samples: 2.5 % (w/v) NP 73 and the Péclet number for the TDA of the Phyt/DOPG-based 74 cubosomes at two detection windows. 15 + 0.1% DMF as dead volume marker. Injection: 82 mbar, 6s. τ = 1.25 τ = 0.37
10000
=
A/Amax(DMF)
40
∆P (mbar)
Convection Non Gaussian + HDC
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Pe Mobilizing Pe D τ τ 16 3.3. Application to the size-characterization of cubosomes pressure (10-12 (×10-3) (×10-3) 17 by TDA 2 -1 m s ) (mbars) 18 Cubosomes are surfactant and lipid based nanoparticles, which 19 due to their special internal nanostructure hold potential as 10 (3) 2.97 2.71 4.51 3.0 3.0 20 drug nano-carriers18. Size-characterization constitutes an es50 0.54 0.9 15 15 21 sential activity in the development of cubosomes for drug (1) 75 Detection window 1 at 30 cm from injection point 22 delivery purposes. Taylorgrams obtained for the Phyt/DOPG- 76 (2) Detection window 2 at 50 cm from injection point 23 based cubosomes in 0.067 M phosphate buffer on a 75 µm i.d. 77 (3) Gaussian fitting on the whole peak using Actipix software (n=5) 24 capillary using two detection windows are presented in Figure 25 7 (red and black traces), for two different mobilizing pres26 sures. Figure 7 shows significant deviation from the Gaussian 27 shape at a mobilization pressure of 50 mbar (Figure 7A). The
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Absorbance (mAU)
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Analytical Chemistry
44 AUTHOR INFORMATION
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33 Supporting Information 34 The Supporting Information is available free of charge on the 35 ACS Publications website. 36 37 Calculation of the relative error on D due to the finite size of the 38 solute in TDA is provided in SI. Figures SI1 and SI2, different 39 regimes possibly encountered in TDA experiments (75 and 100 40 µm i.d.); Figure SI3, taylorgrams obtained for PS 500 nm at dif41 ferent mobilization pressures on a 25 µm i.d. capillary; Figure SI42 4, illustration of the different regimes encountered in TDA exper43 iments of cubosomes.
0.010 0.008
45 *Corresponding Authors 46 HC: Tel.: +33 4 67 14 34 27; Fax: +33 4 67 63 10 46. 47 E-mail:
[email protected] 48 49 ACKNOWLEDGMENTS 50 The authors would like to thank Anan Yaghmur from University 51 of Copenhagen for providing the cubosomes formulation. H.C. 52 gratefully acknowledges the support from the Institut Universi53 taire de France (Junior member, 2011-2016). HC is grateful for 54 the Institut Français au Danemark for its support in the French / 55 Danish collaboration.
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1 2 Figure 7. Taylorgrams of 1% (w/w) Phyt/DOPG-based cubo3 some dispersion at a mobilization pressure of (A) 50 mbar, (B) 4 10 mbar. Capillary dimensions: 75 µm i.d. × 100 cm total 5 capillary length (30 cm, black traces, and 50 cm, red traces, to 6 first and second detection window, respectively). Eluent: 7 0.067 M phosphate buffer, pH 7.40. Sample: 1% (w/w) 8 Phyt/DOPG-based cubosome dispersion in phosphate buffer. 9 Injection: 50 mbar, 7 s.
56 REFERENCES 57 (1) Taylor, G. Proc. R. Soc. London, Ser. A 1953, 219, 186-203. 58 (2) Aris, R. Proc. R. Soc. London, Ser. A 1956, 235, 67-77. 59 (3) Bello, M. S.; Rezzonico, R.; Righetti, P. G. Science 1994, 266, 77360 776. 61 (4) Sharma, U.; Gleason, N. J.; Carbeck, J. D. Anal. Chem. 2005, 77, 80662 813. 63 (5) Cottet, H.; Martin, M.; Papillaud, A.; Souaïd, E.; Collet, H.; 64 Commeyras, A. Biomacromolecules 2007, 8, 3235-3243. 65 (6) d'Orlyé, F.; Varenne, A.; Gareil, P. J. Chromatogr. A 2008, 1204, 22666 232. 67 (7) Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A. Int. J. 68 Thermophys. 1980, 1, 243-284. 69 (8) Taylor, G. Proc. R. Soc. London, Ser. A 1954, 225, 473-477. 70 (9) Cottet, H.; Biron, J. P.; Martin, M. Analyst 2014, 139, 3552-3562. 71 (10) Okada, T.; Harada, M.; Kido, T. Anal. Chem. 2005, 77, 6041-6046. 72 (11) Harada, M.; Kido, T.; Masudo, T.; Okada, T. Anal. Sci. 2005, 21, 73 491-496. 74 (12) Adrover, A.; Cerbelli, S.; Garofalo, F.; Giona, M. Anal. Chem. 2009, 75 81, 8009-8014. 76 (13) Latunde-Dada, S.; Bott, R.; Hampton, K.; Leszczyszyn, O. I. Anal. 77 Chem. 2015, 87, 8021-8025. 78 (14) Latunde-Dada, S.; Bott, R.; Crozier, J.; Trikeriotis, M.; Leszczyszyn, 79 O. I.; Goodall, D. J. Chromatogr. A 2016, 1472, 66-73. 80 (15) Belongia, B. M.; Baygents, J. C. J. Colloid Interface Sci. 1997, 195, 81 19-31. 82 (16) Tijssen, R.; Bos, J.; Van Kreveld, M. E. Anal. Chem. 1986, 58, 303683 3044. 84 (17) Østergaard, J.; Jensen, H. Anal. Chem. 2009, 81, 8644-8648. 85 (18) Yaghmur, A.; Glatter, O. Adv. Colloid Interface Sci. 2009, 147-148, 86 333-342. 87 (19) Chapman, A. J. S.; Goodall, D. M. Chromatography today 2008, 1, 88 22-24. 89 (20) Yaghmur, A.; Østergaard, J.; Larsen, S.; Jensen, H.; Larsen, C.; 90 Rappolt, M. In Liposomes, Lipid Bilayers and Model Membranes, Pabst, 91 G.; Kucerka, N.; Nieh, M.-P.; Katsaras, J., Eds.; CRC Press: Boca Raton, 92 FL, 2014, pp 341-360.
10 4. CONCLUSION 11 In this work, the limitations in size of TDA have been 12 clearly discussed and experimentally illustrated, taking into 13 account both the convective and the hydrodynamic chroma14 tography regimes. These two regimes are physically relevant 15 in TDA when increasing the solute size. They can occur alone 16 or concomitantly, depending on the experimental conditions 17 and the solute size. The occurrence of these two regimes can 18 be clearly identified and visualized on a log∆P vs log Rh plot. 19 While the convective regime tends to deform the Gaussian 20 shape of the taylorgram, HDC changes the elution time and 21 the variance of the elution profile. The relative error ε, due to 22 the HDC regime, on the determination of the diffusion coeffi23 cient D, has been calculated according to the Rh/Rc ratio. To 24 keep ε below 3%, it was found that Rh/Rc should be lower 25 than 0.0051 (i.e. Rh lower than 127 nm on a 50 µm i.d. capil26 lary). Regarding the influence of the convective regime, it was 27 previously found that ε is kept below 3% as far as τ is higher 28 than 1.259. Application to the sizing of cubosomes demon29 strated that it is possible to size nano-objects larger than 100 30 nm as far as the Taylor conditions are satisfied and the 93 31 Rh/Rc ratio is lower than 0.0051.
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