Study on steric transition in asymmetrical flow field-flow fractionation and application to characterization of high-energy material

Journal of Chromatography A, 1304 (2013) 211–219

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Study on steric transition in asymmetrical flow field-flow fractionation and application to characterization of high-energy material Haiyang Dou a , Yong-Ju Lee b , Euo Chang Jung c , Byung-Chul Lee d , Seungho Lee a,∗ a

Department of Chemistry, Hannam University, Daejeon 305-811, South Korea Gyungnam Department of Environmental Toxicology, Korea Institute of Toxicology, Jinju 660-844, South Korea c Nuclear Chemistry Research Center, Korea Atomic Energy Research Institute, Daejeon 305-353, South Korea d Department of Chemical Engineering and Nano-Bio Technology, Hannam University, Daejeon 305-811, South Korea b

a r t i c l e

i n f o

Article history: Received 12 May 2013 Received in revised form 17 June 2013 Accepted 19 June 2013 Available online 28 June 2013 Keywords: Asymmetrical flow field-flow fractionation (AF4) Steric transition Normal mode Steric/hyperlayer mode RDX particles

a b s t r a c t In field-flow fractionation (FFF), there is the ‘steric transition’ phenomenon where the sample elution mode changes from the normal to steric/hyperlayer mode. Accurate analysis by FFF requires understanding of the steric transition phenomenon, particularly when the sample has a broad size distribution, for which the effect by combination of different modes may become complicated to interpret. In this study, the steric transition phenomenon in asymmetrical flow FFF (AF4) was studied using polystyrene (PS) latex beads. The retention ratio (R) gradually decreases as the particle size increases (normal mode) and reaches a minimum (Ri ) at diameter around 0.5 ␮m, after which R increases with increasing diameter (steric/hyperlayer mode). It was found that the size-based selectivity (Sd ) tends to increase as the channel thickness (w) increases. The retention behavior of cyclo-1,3,5-trimethylene-2,4,6-trinitramine (commonly called ‘research department explosive’ (RDX)) particles in AF4 was investigated by varying experimental parameters including w and flow rates. AF4 showed a good reproducibility in size determination of RDX particles with the relative standard deviation of 4.1%. The reliability of separation obtained by AF4 was evaluated by transmission electron microscopy (TEM). © 2013 Elsevier B.V. All rights reserved.

1. Introduction Field-flow fractionation (FFF) is a family of elution-based separation techniques for particles and macromolecules [1]. Unlike chromatography, FFF requires no stationary phase and contains no packing material, which keeps shear degradation and absorption of the sample minimized [2,3]. Various sub-techniques of FFF have emerged depending on the type of the external forces employed [4]. Among them, Flow FFF (FlFFF) is considered to be the most versatile, because displacement of the sample components by the external field (cross-flow) is universal. FlFFF has been widely used for the separation and characterization of various types of particles and polymers [5–9]. In FFF, particles are eluted by a combination of various elution modes including the normal, steric, and hyperlayer mode [10–16]. In the normal mode, smaller particles are eluted earlier than larger ones. In the steric mode, the elution order is reversed from that in the normal mode [17,18]. There exists a range of particle size, called

∗ Corresponding author. Tel.: +82 42 629 8822; fax: +82 42 629 8811. E-mail addresses: [email protected] (B.-C. Lee), [email protected] (S. Lee). 0021-9673/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2013.06.051

‘steric transition region’, where particles are eluted by combination of the normal and the steric mode [11,19]. In the steric transition region, an ambiguity may be introduced into FFF data interpretation because two groups of particles having different sizes may elute together, one by the normal mode and the other by the steric mode. For accurate interpretation of FFF data, one must find a condition where the entire population of the sample is governed (or dominated) by only one type of the elution mode. And the steric transition phenomenon must be thoroughly understood to maximize the information from FFF. In FFF, the steric transition point (size at which the elution mode changes from normal to steric mode) can be varied by changing experimental conditions such as the field strength and flow rate. Effects of various experimental parameters on the steric transition phenomenon have been reported in SdFFF [11,17,18,20] and FlFFF [21], most of which were performed with standard samples for theoretical investigation. The cyclo-1,3,5-trimethylene-2,4,6-trinitramine, commonly called ‘research department explosive’ (RDX), is an ingredient used in various types of explosives and propellants [22,23]. It has been reported that the mean size and its distribution of the RDX particles play a critical role in the burning rate, sensitivity, and

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safety of RDX [24,25]. Generally, the shock sensitivity decreases with a reduction in particle size. In addition, the size of RDX particles significantly affects their run distances to detonation and initiating shock pressure. In the present study, effects of various parameters in asymmetrical FlFFF (AF4) analysis of RDX particles were investigated. The effects of the channel thickness and the flow rates on the steric transition were studied. Focused in this paper is optimization of AF4 for size characterization of RDX particles by considering the steric transition phenomenon. Finally, the separation mechanism and reliability of AF4 were evaluated by transmission electron microscopy (TEM). 2. Theory As mentioned earlier, there exist various elution modes in FFF [10,11,18,21,26–30], and accurate application of FFF requires complete understanding of those elution modes. 2.1. Normal mode of AF4 In the normal mode of AF4, particles are pushed to the accumulation wall by the field force, FF , which is expressed by [31]:

by ‘non-retained’ components to travel through the channel. In a typical trapezoidal channel of AF4, t0 can be determined by [36]: t0 =

(1)

(2)

where L is the channel length, z is the distance from the channel tip to the sample focusing point, and v is the time average channel flow velocity. The local average channel flow velocity, vz , can be expressed by [37]: vz =

Vin − |u0 | A(z) wb(z)

(3)

where Vin is the volumetric feed-flow rate, |u0 | is the cross-flow velocity at the accumulation wall, A(z) is the area of the accumulation wall from z to z, and b(z) is the channel breadth at point z. Full expression of R in FFF is given by [11,38]:



R = 6˛(1 − ˛) + 6 (1 − 2˛) coth

 1 − 2˛  2



− 2

(4)

where  is a dimensionless parameter that was adopted to accounts for deviation of R from that expected with  = 1 [15,21]. ˛ is the ratio of the particle radius a to the channel thickness w (˛ = a/w), and  is defined by  = l/w, which is expressed in AF4 by [36]: =

3dVc w FF = V0

L − z v

kTV 0 3dVc w2

(5)

in Eq. (5), k is the Boltzmann constant, and T is the temperature. When ˛ and  are small, Eq. (4) is reduced to

where  is the carrier viscosity, d is the particle diameter, Vc is the volumetric cross-flow rate, w is the channel thickness, and V0 is the void volume. It can be seen that FF is directly proportional to Vc . At the same time, the components diffuse away from the accumulation wall by Brownian motion, and eventually form an equilibrium layer between the two opposing transport processes. As the component size decreases, the thickness of the equilibrium layer (l) increases due to increasing diffusion coefficient (D), and experiences higher flow velocity. Thus smaller components are eluted faster than larger ones.

The first term of Eq. (6) is proportional to particle size, while the second term is inversely proportional to particle size. As a result, R decreases as d increases and reaches a minimum (Ri ), after which R increases with increasing d [11]. The diameter corresponding to Ri is called ‘steric transition point’, di . Ri and di are given respectively by [11]:

2.2. Steric mode of AF4

and

As the component size increases, diffusion by the Brownian motion decreases, and reaches a point where the Brownian motion is relatively low or almost negligible [30,32]. The particles are driven all the way down to (or close to) the accumulation wall and migrate down the channel at the rate corresponding to that of the fluid at the position of the particle center. Thus, larger ones occupy faster flow streamlines, and are eluted faster than smaller ones. The elution order is thus reversed from that of the normal mode.

Ri =

R = 6˛ + 6

 di =

2kTV 0 3Vc w

In the hyperlayer mode, the hydrodynamic lift forces (FHL ) are strong enough to counteract FF , resulting in a formation of a focused layer of particles (hyperlayer) at some distance away from the accumulation wall [33,34]. Lift forces are generated by the carrier liquid inertia and other effects by the presence of a particle moving in a fluid stream in the vicinity of channel wall (e.g. viscosity-dependent behavior that governs lubrication) [35]. 2.4. Retention ratio The retention ratio, R, is defined as the ratio of the void time t0 to the retention time tr (R = t0 /tr ). The void time t0 is time taken

1/2

6di w

(7)

(8)

Eq. (6) indicates R decreases as w increases as both the first and the second term are inversely proportional to w. Eq. (6) is further reduced to R = 6

(9)

in the normal mode, and to R = 6˛

2.3. Hyperlayer mode of AF4

(6)

(10)

in the steric or hyperlayer mode. It can be seen that R is inversely proportional to the particle size in the normal mode, while it is proportional in the steric or hyperlayer mode. The value of  yields information on the elution mode [20]. The  being higher than unity can be attributed to FHL driving the particles away from the accumulation wall – ‘hyperlayer mode’ [26]. The eventual particle elevation is that for which FHL is equal in magnitude but opposite in direction to the force applied on the particle by the external field, FF . High channel flow rate or low field strength encourages high particle elevation and thus high migration velocity and  values [39]. At sufficiently low channel flow rates and high field strengths, particles come close to the accumulation wall. As particles approach closer to the accumulation wall, their velocities are increasingly retarded relative to those of the surrounding fluid,

H. Dou et al. / J. Chromatogr. A 1304 (2013) 211–219

and  becomes lower than unity – ‘steric mode’ [10,30]. The  value of 1 will be realized only when the particles are raised some small height above the wall.

213

Carbon dioxide (CO2 ) (99.9%) used for recrystallization of RDX was obtained from Sebo Energy (Daejeon, Korea). The raw RDX particles were provided by the Agency for Defense Development of Korea (Daejeon, Korea).

2.5. Particle size determination by AF4 3.2. Recrystallization of RDX particles In the normal mode, the particle diameter d can be determined from tr using [40]: d=

2kTV 0 Vc w2 t 0

(11)

tr

In the steric or hyperlayer mode, however, direct determination of particle size is not possible as  varies with particle size and shape. It has been reported that  increases with channel flow rate and decreases with an increase of field strength [10,30]. Due to the complexity of , particle size determination in the steric or hyperlayer mode requires a calibration using size standards having the same shape as the sample particles. Generally, the calibration curve (log tr vs. log d) is expressed by [19]: logtr = −Sd logd + logtr1

(12)

where Sd is the size-based selectivity defined by Sd =   d(logtr )/d(logd), which is the negative slope of the calibration curve, and tr1 is a constant equal to the extrapolated value of tr of particles having unit diameter. Once Sd and tr1 are determined from the slope and y-intercept of the calibration curve, respectively, an AF4 fractogram (c(tr )) can be converted to the mass-based size distribution, m(d) by [19]:

The RDX particles were recrystallized as described previously [43]. This time a higher pressure drop was used. The raw RDX was dissolved in DMF at the concentration of 20 wt%. Then CO2 was delivered into the supercritical anti-solvent (SAS) recrystallization apparatus at a constant flow rate of 25 mL/min using a syringe pump until the desired pressure (10 MPa) was reached. Once the pressure and temperature (40 ◦ C) are equilibrated, the RDX solution was introduced into the CO2 phase in a vessel through a spraying nozzle. During spraying of RDX solution, a pressure drop of 15 MPa between the RDX solution phase and the CO2 phase was generated by controlling of length of the nozzle. Finally, the vessel was washed with CO2 to eliminate the solvent mixed with the supercritical CO2 and was depressurized. The recrystallized RDX particles in the vessel were then collected. The density of recrystallized RDX was determined to be 1.5 g/cm3 by pycnometer. 3.3. AF4 analysis of recrystallized RDX particles

where a and b are the width of the two peaks measured at one-half of their heights.

The AF4 was equipped with an Eclipse channel (Wyatt Technology Europe, Dernbach, Germany), which was assembled with a polyester spacer and a regenerated cellulose membrane (Art. No. 2920) having the molecular weight cutoff of 10 kDa. The channel thickness was determined from the retention time of ferritin. The channel geometry was trapezoidal with the tip-to-tip length of 13.5 cm and the breadths at the inlet and outlet of 2.5 and 0.3 cm, respectively. The carrier liquid was deionized water containing 0.02% (w/v) FL-70, a dispersing agent, and 0.02% (w/v) NaN3 , a bactericide. The carrier flow was delivered by an M930 pump (Young-Lin Instrument Co., Ltd., Seoul, Korea). The PS samples were prepared by diluting a droplet of PS standard suspensions with 1 mL of AF4 carrier liquid. The RDX samples were prepared by dispersing 20 mg of RDX particles in 10 mL of the same carrier liquid. Prior to their injection into the AF4 channel, the samples were sonicated in an FS60 ultrasonic cleaner (Fisher Scientific, Atlanta, USA) at a power of 100 W for 2 min to facilitate dispersion of the particles. The PS and RDX samples were injected by loading the 100 ␮L loop of a Rheodyne injector (Cotati, CA, USA) with a microsyringe. The sample was introduced into the AF4 channel by a syringe pump (KD Scientific Inc., FL, USA) at the flow rate of 0.2 mL/min. After focusing and relaxation of the sample, particles were eluted, and the eluted particles were monitored by a SPD-20 A UV/VIS detector (Shimadzu, Kyoto, Japan) at an operating wavelength of 254 nm.

3. Experimental

3.4. Transmission electron microscopy (TEM)

3.1. Materials and reagents

AF4 fractions were collected for 1 min period, and then were analyzed using a Tecnai G2 F30 field emission transmission electron microscope (FE-TEM) (FEI Company, Eindhoven, Holland) at the accelerating voltage of 200 kV. For sample preparation, a few of drops of collected fractions were allowed to dry slowly on nickel grids at room temperature.

m(d) = c(tr )Vch Sd tr1

 t (Sd +1)/Sd r tr1

(13)

where Vch is volumetric channel flow rate. The number-based size distribution, n(d), can be obtained from m(d)/d3 . 2.6. Resolution Resolution (Rs ) between two neighboring peaks is defined by [41]: Rs =

2(tr2 − tr1 ) w2 + w1

(14)

where tr1 and tr2 are the retention times of the two neighboring peaks, and w1 and w2 are the widths of the two peaks in the unit of time. In this study, a resolution parameter Rs∗ was used instead as a measure of resolution, which was defined by [42]: ∗ Rs(1,2) =

tr2 − tr1 a+b

(15)

Suspensions of polystyrene (PS) latex beads having mean diameters of 0.02, 0.04 0.1, 0.2, 0.4, 0.5, 2, 3, 6, 8, 12, 20 and 40 ␮m were purchased from Duke Scientific Corp. (Palo Alto, CA, USA). They were diluted with the AF4 carrier liquid for all AF4 experiments. Deionized water was obtained from a Milli-Q Plus Ultra-Pure Water system (Millipore, MA, USA). All of the following chemicals were of analytical reagent grade and were used without further purification. Dimethylformamide (DMF), ferritin (from horse spleen) and sodium azide (NaN3 ) were purchased from Sigma–Aldrich (St. Louis, MO, USA). FL-70, a mixture of anionic and non-ionic compounds, was purchased from Fisher Scientific (Fair Lawn, NJ, USA).

4. Results and discussion 4.1. Steric transition phenomenon in AF4 Retention ratios measured for a series of PS latex beads in AF4 at various w are shown in Fig. 1. The feedflow

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H. Dou et al. / J. Chromatogr. A 1304 (2013) 211–219 Table 2 Retention ratios and ’s measured from data shown in Fig.1.

0.8

Nominal diameter of PS latex beads (␮m)

0.6

w = 191

0.2 0.0 0.01

0.1

1

10

100

Diameter (µm) Fig. 1. Retention ratios measured for PS latex beads by AF4at various channel thicknesses. Symbols are R’s measured at w = 191 (), 273 (), and 408 ␮m (), respectively. Lines are theoretical plots calculated by Eq. (4) with  value of 1. Vin and Vc were 1.5 and 0.4 mL/min, respectively.

rate Vin and the crossflow rate Vc were kept constant at 1.5 and 0.4 mL/min, respectively. Symbols are retention ratios measured at w = 191, 273, and 408 ␮m, respectively, and the lines are theoretical plots calculated by Eq. (4) with  value of 1. Fig. 1 shows the trend expected by theory, where R decreases as the particle size increases (normal mode) and reaches a minimum (Ri ) at d around 0.5 ␮m, after which R increases with increasing diameter (steric or hyperlayer mode). As mentioned earlier, particles smaller than di are eluted by the normal mode and those larger are eluted by either the steric or hyperlayer mode. For the same particle size, R decreases as w increases as expected. In Fig. 1, theoretical plots were obtained with a fixed  value of 1, which is probably one of reasons for discrepancies between the measured and theoretical R values. As mentioned earlier,  varies with experimental conditions including the particle size. Ri ’s and di ’s observed in Fig. 1 are listed in Table 1. All theoretical values were calculated using Eqs. (7) and (8) with  value of 1. As V0 is proportional to w, di is expected to be independent of w if  stays constant (see Eq. (7)). As expected, di,theory is constant at 0.45 ␮m. On the other hand, Eq. (8) suggests Ri is inversely proportional to w. In Table 1, both Ri,theory and Ri,measured decrease as w increases as expected. At w = 273 ␮m, Ri,measured is in good agreement with Ri,theory . However, at 191 ␮m, Ri,measured is higher than Ri,theory , and, at 408 ␮m, Ri,measured is lower. Discrepancies between Ri,theory and Ri,measured seems to be related with the  value, which will be discussed later with Table 2. Measured R and  values are listed in Table 2, where  values are not shown for the normal mode. R (and thus ) values are also missing for those which were difficult to measure accurately either because the elution profiles were too broad (near the steric transition point) or because retention was too low (for larger particles). At w of 191 and 273 ␮m, all  values are greater than 1, indicating they are in the hyperlayer mode, while, at w of 408 ␮m, all  values are lower than 1, indicating they are in the steric mode. In the steric or hyperlayer mode (for particles having d larger than about

Table 1 Steric transition diameter (di ) and retention ratio (Ri ) observed for PS latex beads in Fig. 1 at various channel thicknesses (w). w (␮m)

di,theory (␮m)

di,measured (␮m)

Ri,theory

Ri,measured

191 273 408

0.45 0.45 0.45

0.48 0.46 0.48

0.015 0.010 0.007

0.025 0.011 0.003

0.02 0.04 0.1 0.2 0.4 0.5 1 3 6 8 12 20 40 a b

w (␮m)

w (␮m)

c

273

0.350 0.217 0.211 0.108 0.087 0.040 0.048 0.019 0.032 0.010 0.032 –b 0.054 –b 0.117 0.056 0.231 0.110 0.273 0.145 0.375 0.167 –c 0.286 –c 0.444

408

191

273

408

0.145 0.058 0.021 0.009 –b –b –b –b 0.032 0.045 0.069 0.112 0.202

–a –a –a –a –a 4.08 3.44 2.48 2.41 2.13 1.99 –c –c

–a –a –a –a –a –b –b 1.70 1.67 1.65 1.23 1.30 1.01

–a –a –a –a –a –b –b –b 0.73 0.77 0.78 0.76 0.69

Not determined. Could not measure due to too broad elution profile. Could not measure due to too low retention.

0.5 ␮m),  increases as w decreases due to increasing lift forces. This explains why Ri,measured is higher than Ri,theory at 191 ␮m, while Ri,measured is lower than Ri,theory at 408 ␮m. It is noted that, in the steric mode (at w = 408 ␮m),  does not change much with diameter. In the hyperlayer mode (at w = 191 or 273 ␮m), however, at the same w,  decreases gradually with increasing diameter. Fig. 2 shows plots of log tr vs. log d at various channel thicknesses, whose slopes are size-based selectivity (Sd ) as shown in Eq. (12). In Fig. 2, minute and micrometer were used as the units of retention time and diameter, respectively. It is noted that, in Fig. 2, data near the steric transition point were excluded. At the steric transition point, Sd becomes zero and no size-based separation as expected. Sd and resolution parameter (Rs∗ ) determined for neighboring particles from data shown in Fig. 1 are listed in Table 3. As shown in Fig. 2 and Table 3, in both the normal or steric/hyperlayer mode, the slope (and thus Sd ) gradually increases as w increases. This is because, as w increases, vz decreases at the same volumetric flow rate (see Eq. (3)), which generally yields improved selectivity. Resolution is proportional to Sd , and inversely proportional to the degree of band broadening [44], and hence, higher Sd will yield higher resolution if the band broadening remains constant. Unlike Sd , no particular trends in (Rs∗ ) with w were found in all elution modes, probably due to varying degrees of band broadening in different elution modes [45].

0.0 w = 191

-0.5

273

Log tr (min)

R

408 µm

0.001

 measured at

191

273

0.4

Rmeasured at

408 µm

-1.0

-1.5

Steric/Hyperlayer mode

Normal mode

-2.0 -2.0

-1.0

0.0

1.0

Log d (µm) Fig. 2. Plots of log tr vs. log d at various channel thickness.

2.0

H. Dou et al. / J. Chromatogr. A 1304 (2013) 211–219

215

Table 3 Size-based selectivity and resolution parameter determined for PS latex beads from data shown in Fig.2. Elution mode

Resolution parameter (Rs∗ )

Sd measured at w (␮m)

Normal mode

191

273

408

0.87

1.06

1.17

191

272

408

0.43

1.56

1.62

1.42

0.51

0.54

∗ Rs(0.1,0.2)

2.15

0.55

0.63

∗ Rs(3,6) ∗ Rs(6,8) ∗ Rs(8,12) ∗ Rs(12,20) ∗ Rs(20,40)

1.42

0.58

0.46

0.28

1.06

1.05

0.53

∗ Rs(0.02,0.04)

∗ Rs(0.04,0.1)

0.81

Steric/Hyperlayer mode

a

0.83

0.96

Rs∗ measured at w (␮m)

1.04

3.06

–a

1.05

0.51

–a

0.63

0.70

Could not measure due to too low retention.

0.3

with Vin . In the normal mode, no particular trend in Ri with Vin was observed as expected. In the steric mode, however, R tends to increase with Vin for the same diameter, due to flow rate-dependent lift forces. Increasing Vin leads to an increase in the lift forces, forcing particles placed further away from the surface of channel where the flow stream velocity is higher. Thus, particles are eluted faster, resulting in an increase in R. The change in R with Vin increases as the size increases due to the fact that the lift forces increases with size [28].

0.2

4.2. AF4 elution of recrystallized RDX particles

0.1

It was found from microscopic observations that the recrystallized RDX particles have a rather broad size distribution (with majority in micron sizes and some in submicron sizes) that may span across the steric transition point depending on experimental conditions. Thus there may be co-elution of two populations of different sizes, with smaller particles eluting by the normal mode and the larger ones by the steric mode, which leads to an overestimation in mean diameter. In this study, the steric (or hyperlayer) mode was chosen for AF4 separation as micron-sized particles are of higher interest. The effects of the channel thickness and flow rate on AF4 separation of recrystallized RDX particles were investigated. Fig. 5(a) shows AF4 fractograms of recrystallized RDX particles obtained with channels of three different thicknesses. Other conditions were the same as those used in Fig. 1. At w = 191 ␮m, the RDX particles were eluted without being separated from the void peak. As w increases, retention (and thus separation from the void peak) of the particles increases and, at the same time, the elution profile

0.7 Vc = 0.2

0.6

0.3 0.4 0.6 mL/min

R

0.5 0.4

0.0 0.01

0.1

1

10

Diameter (µm) Fig. 3. Retention ratios measured in AF4 for PS latex beads shown in Table 2 at various crossflow rates at w was 273 ␮m and Vin fixed at 1.5 mL/min.

0.7 0.6

Table 4 Steric transition diameter (di ) and retention ratio (Ri ) observed for PS latex beads in Fig. 3 at various flow rate combinations. Data from Fig. 3

Fig. 4

Vin (mL/min) 1.5

1.2 1.5 1.8 2.1

Vc (mL/min)

di (␮m)

Ri

0.2 0.3 0.4 0.6

0.69 0.51 0.46 0.26

0.015 0.011 0.010 0.006

0.47 0.51 0.48 0.47

0.010 0.012 0.011 0.010

0.3

Vin = 1.2 1.5 1.8 2.1 mL/min

0.5

R

In AF4, the crossflow provides the external field, and its flow rate is one of major factors affecting retention (and thus resolution) of particles [11,46–48]. Retention ratios measured for a series of PS latex beads in AF4 at various crossflow rates (Vc ) are shown in Fig. 3. The feedflow rate (Vin ) was fixed constant at 1.5 mL/min, and w was 273 ␮m. The steric transition diameter (di ) and retention ratio (Ri ) were determined using Peakfit 4.12 (Seasolve Software Inc., CA, USA) and are listed in Table 4. It can be seen that both Ri and di gradually decrease as Vc increases as expected from Eq. (7), which also agrees with previous reports [11]. Thus in AF4, higher Vc allows the range of the steric mode to be extended down to smaller particle size. Fig. 4 shows retention ratios measured for the same series of PS latex beads as in Fig. 3 at various Vin . w was 273 ␮m, and Vc was fixed constant at 0.3 mL/min. The steric transition diameter (di ) and retention ratio (Ri ) observed in Fig. 4 are also listed in Table 4. Unlike with Vc , the position of the steric transition point does not change

0.4 0.3 0.2 0.1 0.0 0.01

0.1

1

10

Diameter (µm) Fig. 4. Retention ratios measured for PS latex beads in AF4 at various Vin at w was 273 ␮m and Vc fixed at 0.3 mL/min.

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H. Dou et al. / J. Chromatogr. A 1304 (2013) 211–219

(a)

(a)

w = 191 µm

Vc = 0.2 0.3 0.4

UV/vis response

UV/vis response

void peak

w = 273 µm

0.6 mL/min

w = 408 µm 0

0

5

10

15

20

25

3

6

Retention time (min)

9

12

15

18

Retention time (min)

30 (b)

(b) Relative mass

w = 408 µm

Relative mass

Vc = 0.2 0.3

w = 273 µm

0.4 0.6 mL/min

0

20

40

60

Diameter (µm)

0

20

40

60

80

Fig. 6. AF4 fractograms (a) and size distributions (b) of recrystallized RDX particles obtained at various Vc . Vin was fixed at 1.5 mL/min and w was 273 ␮m.

Diameter (µm) Fig. 5. AF4 fractograms (a) and size distributions (b) of recrystallized RDX particles obtained at various w. Vin and Vc were the same as those used in Fig. 1.

(a) Vin = 1.2

Table 5 Mean diameters of recrystallized RDX particles measured from fractograms shown in Figs. 5–7. Data from

w (␮m)

Fig. 5

273 408

Fig. 6

273

Fig. 7

273

a

Vin (mL/min) 1.5 1.5

1.2 1.5 1.8 2.1

Number-based mean diameter.

Vc (mL/min) 0.4 0.2 0.3 0.4 0.6 0.3

dmean (␮m)a 1.52 4.61 1.76 1.36 1.52 1.28 1.39 1.35 1.13 1.11

UV/vis response

1.5

1.8 2.1 mL/min

0

5

10

15

20

25

Retention time (min)

(b)

Vin = 1.2 1.5

Relative mass

becomes broader, due to reduction in the linear flow velocity v by an increase in w at the same volumetric flow rate. Fig. 5(b) shows size distributions obtained from the fractograms shown in Fig. 5(a) using Eq. (13) and the calibration plot (Eq. (12)) established with micron-sized PS latex beads. The fractogram obtained at w of 191 ␮m is not shown as the separation from the void peak was poor. The number-based mean diameters of the recrystallized RDX particles measured from fractograms shown in Fig. 5(b) are listed in Table 5. It can be seen that the mean diameter obtained at w = 273 ␮m is much smaller than that obtained at w = 408 ␮m. At w = 408 ␮m, AF4 analysis of RDX particles is in the steric mode as indicated by  being smaller than 1 in Table 2. The elution profile was prolonged with tailing as shown in Fig. 5(a),

1.8 2.1 mL/min

0

10

20

30

40

50

60

Diameter (µm) Fig. 7. AF4 fractograms (a) and size distributions (b) of recrystallized RDX particles obtained at various Vin . Vc was fixed constant at 0.3 mL/min and w was 273 ␮m.

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Fig. 8. TEM images (a) and AF4 fractograms (b) of recrystallized RDX particles obtained at Vin and Vc of 1.8 and 0.3 mL/min, respectively. w was 273 ␮m. Inset shows fractions corresponding to TEM images.

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which seems to yield inaccurate size information. Thus w value of 273 ␮m was chosen in this study. Fig. 6 shows the AF4 fractograms and size distributions of RDX particles obtained at various Vc . Vin was fixed at 1.5 mL/min and w was 273 ␮m. Retention tends to increase as Vc increases, as expected. As mentioned earlier in Table 4, higher Vc allows the range of the steric mode to be extended down to smaller particle size. The number-based mean diameters of the recrystallized RDX particles measured from the fractograms shown in Fig. 6(b) are listed in Table 5. It is shown that the measured mean diameter decreases as Vc increases, probably due to prolonged elution of the particles, especially smaller ones, at higher Vc [49]. Fig. 7 shows the AF4 fractograms and size distributions of the same RDX particles obtained at various Vin . This time, Vc was fixed constant at 0.3 mL/min and w was 273 ␮m. The number-based mean diameters of the RDX particles measured from the fractograms shown in Fig. 7(a) are also listed in Table 5. As expected, the elution profile was shifted toward lower retention time as Vin increases. As shown in Table 5, the measured mean size tends to decrease as Vin increases. This may be explained by prolonged elution of relatively smaller particles. FHL is proportional to particle diameter. Thus, smaller particles are less affected by FHL , and are allowed to approach closer to the accumulation wall, resulting in prolonged elution. Moreover, there is no “ideal” standard for calibration of all types of samples. The variance in properties between standards (e.g. PS latex leads) and RDX particles could give rise to a discrepancy in size determination at some extent, but can be minimized through optimizing of operation conditions of AF4. This result suggests that, in the steric/hyperlayer mode of AF4, presence of FHL , to a certain extent, allows better elution of particles and more accurate size analysis through alleviation of the interaction between RDX particles and the surface of membrane. Care must be taken however as high Vin may lead to appearance of a new elution mode (Faxén-mode) [50], whose detailed discussion seems to be beyond the scope of this report. 4.3. Reproducibility of AF4 for analysis of RDX particles In order to evaluate the reproducibility of AF4, analysis was repeated 5 times at the same experimental condition, where w was 273 ␮m, and Vc and Vin were 0.3 and 1.8 mL/min, respectively. Also a set of fractions were collected at the time interval of 1 min for TEM analysis. AF4 fractograms and TEM images of the sample and some of collected fractions are presented in Fig. 8. TEM images confirm that particles are eluted by the steric/hyperlayer mode with larger particles eluting earlier than smaller ones. It seems most of particles are eluted by the hyperlayer mode with  larger than 1. Fig. 8(b) shows that AF4 has a good reproducibility with the relative standard deviation of mean diameter of 4.1% (n = 5). 5. Conclusion The RDX sample has a rather broad size distribution which may span across the steric transition point, and may give rise to coelution of two populations of different sizes with smaller particles eluting by the normal mode and larger ones by the steric/hyperlayer mode, which may lead to an overestimation of the mean diameter. The influence of operating conditions such as the channel thickness and flow rates in AF4 analysis of micron-sized particles was investigated. Results revealed that the position of the steric inversion point (di ) can be moved by varying Vc (di decreases with increasing Vc ), while it was not affected much by the channel thickness (w) or the feed flow rate (Vin ). As the channel thickness decreases, the linear flow velocity increases and resulted in a change in the elution mode from the steric ( < l) to the hyperlayer

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