Article pubs.acs.org/Langmuir
Separation and Characterization of Poly(tetrafluoroethylene) Latex Particles by Asymmetric Flow Field Flow Fractionation with LightScattering Detection Melissa E. Collins, Erick Soto-Cantu, Rafael Cueto,* and Paul S. Russo Department of Chemistry and Macromolecular Studies Group, Louisiana State University, Baton Rouge, Louisiana 70803-1804, United States S Supporting Information *
ABSTRACT: Poly(tetrafluoroethylene) (PTFE) latex particles have been analyzed and sorted according to size using asymmetric flow field flow fractionation (AF4) coupled with multiple-angle light scattering (MALS). Characterization of fractions by regular and depolarized dynamic light scattering confirmed that smaller particles elute prior to larger ones, as expected for field flow fractionation. The measured radii of the optically and geometrically anisotropic particles are consistent with those determined from transmission electron microscopy (TEM). A certain amount of heterogeneity remains in the fractions, but their uniformity for use as diffusion probes is improved. Full characterization of PTFE colloids will require a difficult assessment of the distribution, even within fractions, of the optical anisotropy. A general method to obtain number versus size distributions is presented. This approach is valid even when an online concentration detector is not available or ineffective. The procedure is adaptable to particles of almost any regular shape.
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INTRODUCTION Poly(tetrafluoroethylene), or PTFE, is best known for its nonstick properties. Not easily or economically processed in the melt,1 PTFE is often molded from powders that are processed by sintering into many familiar solid objects. All feature the nonreactive, nonstick, hydrophobic, low-refractiveindex properties associated with fluoropolymers. PTFE’s hydrophobic properties have resulted in increased popularity as a coating with applications in biomedical materials and engineering.2,3 Commercial grades are not limited to powders, though. Aqueous dispersions are used in dip-coating, where several layers are applied for the desired thickness.4 PTFE particles can be sophisticated in structure,5 but they tend to be 0.2−0.5 μm in longest dimension. If not made with comonomers, they often assume the shape of distorted spheres or stubby cylinders.6 The PTFE polymer within the latex particles is partially crystalline; the resulting optical anisotropy proves useful in studies of particle dynamics.7−10 For example, the strong depolarized scattering arising from PTFE particles makes it simple to detect their rotational motion by depolarized dynamic light scattering (DDLS), even in a complex fluid (as long as the latter does not also depolarize very strongly). In such probe diffusion11 applications, variation in particle size complicates the determination of microrheological properties. A wide distribution of size usually contributes to poor colloid stability, too. The characterization of PTFE latex particles for size distribution poses significant challenges. For example, they are easily visualized by transmission electron microscopy (TEM), but sizing a large number of particles is slow, expensive, and tedious. Nor can TEM images speak to the © 2014 American Chemical Society
state of dispersion because particles often coalesce during drydown for TEM observation. A very large number of particles in their true state of dispersion is detected during typical dynamic light scattering (DLS) experiments, but the size distribution can only be estimated by inverse Laplace transformation algorithms, such as CONTIN.12,13 Such algorithms attempt to deal with the ill-posed nature of inverting multiexponential data corrupted by even small amounts of noise,14,15 but resolution is almost always poor, at least compared to chromatographic separation. TEM and DLS do not physically separate particles, which would improve their utility as diffusion probes of complex environments. Most PTFE particles are too large for separation by gel permeation chromatography (GPC) characterization using typical column sets. In this paper, the potential of asymmetric flow field flow fractionation (AF4) for routine characterization of PTFE particles is explored. Following a description of the experiments and some background, the visualization of the particles by TEM will demonstrate their anisotropic shape. A first pass at their characterization by AF4/MALS supplemented by single-angle batch-mode DLS as performed on a typical commercial instrument (a Malvern Zetasizer Nano ZS) follows. Extra details on these samples were sought using multiangle DLS and DDLS. A second pass at characterizing the particles takes advantage of added surfactant during the AF4/MALS separation and uses multiangle DLS and DDLS exclusively. Finally, the problem of determining size distributions without Received: December 21, 2013 Revised: February 15, 2014 Published: March 18, 2014 3373
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that are sensitive to after-pulsing effects (typically 0, because the largest particles in the distribution scatter less and less as q rises. This leaves only the scattering from smaller and faster-diffusing spheres, so Γ rises. In this case, the normalized variance μ2/Γ2 is expected to decrease with q, because the system appears to be more uniform than it is. For some objects, Dapp may rise with q2 (K > 0) due to the enhanced visibility of rotation and internal details as the system is investigated with finer spatial resolution (increased q). For cylindrically symmetric objects, which approximate the shapes studied here, end-over-end tumbling adds a second mode,17 the associated amplitude of which becomes detectable when qL > 3. In the present study, where the highest values of qL approach ∼5, the dimensionless parameter μ2/Γ2 from cumulants analysis rises with q to reflect the appearance of the new mode. Pronounced dependence of Dapp upon q2 was never observed in the present study. Flat Dapp vs q2 plots were obtained for PTFE particles right out of the bottle (after dilution; see the Supporting Information, Figure S3) and for early eluting fractions after AF4/MALS. The K parameter was found to increase with elution volume (Figure 5). The μ2/Γ2 plots for the fractionated material tend to exhibit a decreasing-thenincreasing behavior, but the effect is subtle (Supporting Information, Figure S6). An interpretation consistent with these observations is that cancellation of the finite size effect and the end-over-end tumbling effect, both of them weak, results in low values of K overall and K ≈ 0 for the unfractionated material. The perceptible increase of K with fractionation number is then attributed to the increasing visibility of the end-over-end tumbling for the longer particles
Figure 4. Decay rates from depolarized (Hv) scattering plotted against squared scattering vector magnitude: upper data set, fraction 5; lower data set, fraction 13. Error bars show the difference between oneexponential fits to data and third-order cumulants fits.
For uniform particles of low axial ratio, it is reasonable to expect Rh,r,Hv ≈ Rh,t,Hv, and this is indeed the case for fraction 5 (Rh,t,Hv = 1.07 × Rh,r,Hv = 56 nm, a modest 7% difference) but not for fraction 13 (Rh,t,Hv = 1.39 × Rh,r,Hv = 88 nm, a substantial 39% difference). Factors which may contribute to the rising disparity between Rh,t,Hv and Rh,r,Hv with fraction number include variation in depolarization ratio (which controls visibility in the Hv experiments) with elution volume, residual heterogeneity, and weak aggregation. Variation of the depolarization ratio across the distribution is relatively easy to dismiss because there is no reliable trend across the elution volume (Figure S2 of the Supporting Information). Evidence for residual heterogeneity was found in differences between third-order cumulants and one-exponential fits (not shown). The next potential explanation, weak aggregation, could result in “wagging”, the free movement of one end of one particle relative to another. In simple cumulant or one-exponential analysis, the extra motion would raise the average decay rate, even at q = 0, for these depolarized experiments. Such motion can easily lower the apparent Rh,r. It should lower the apparent Rh,t, too, but the major contributor to Rh,t remains translational motion, so the effect should be modest. Unfortunately, wagging is difficult to ascertain by scattering methods (if these particles were somewhat larger, wagging might be detected by direct visualization of the suspensions using an optical microscope). Improving the Conditions for Production and Testing of PTFE Particles: AF4 Flow Profiles, Sample Preselec3376
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these results are plotted as an overlay to the AF4/MALS measurements in Figure 7. Also shown is the trend for Rg,
Figure 5. The slope of Dapp vs q2 plots rises perceptibly with fraction number. Figure 7. Discrete points from multiangle DLS of fractions: orange squares, hydrodynamic radius from rotation (depolarized DLS); green squares, hydrodynamic radius from translation (depolarized DLS); red circles, hydrodynamic radius from translation (polarized DLS). Quasicontinuous curves: black, intensity at 90°; blue, radius from a nonlinear least-squares fit to the sphere form factor, as performed within the Wyatt software; purple, radius of gyration from linear fit to low-angle data.
that elute last. A second interpretation, indistinguishable from the first, is the already-discussed wagging. Finally, a reviewer suggested that the Uv measurements may contain a weak but significant contribution from the Hv signal; if so, the rotational term could raise the average decay rate by an amount that depends on scattering angle. The effect would be larger at low angles, and indeed, a modest upturn is seen for some of the runs. The near-equivalence of Uv and Vv results displayed in the Supporting Information (Figures S8 and S9) argues against the importance of the Hv contribution to the Uv signal, but in principle, depolarization is another factor to consider when evaluating the angular dependence of decay rates and μ2/Γ2 in the Uv mode, which is the most popular configuration on commercial instruments. Turning now to the depolarized results, they prove useful for confirming the ability of AF4 to separate the stubby PTFE cylindrical colloids. Figure 6 shows the Hv decay rate, ΓHv, against q2. Both the intercept and slope decrease almost steadily with fraction number. After conversion to hydrodynamic radii,
which was determined using only appropriately low scattering angles (such that qRg < 2, close to the Guinier approximation; Supporting Information, Figure S7). This plot is made possible by a Guinier plotting and fitting program written (in Visual Basic 6) to analyze the many slices from GPC/MALS or AF4/ MALS. The program makes it easy to exclude angles that are beyond the Guinier approximation. It is not always appreciated that the simple Guinier plot determines a well-defined size, Rg, independent of shape and without the need to know the zeroangle intensity. The relevant equation ln(I ) = ln(Io) −
q 2R g 2 3
(6)
is valid as long as qRg is sufficiently small. In the present case, typically five of the lowest scattering angles (out of 12 available) could be used. At the concentrations of this study, no correction for finite concentration effects is needed. The Rg values obtained exceed the apparent radius from a nonlinear fit of the data to the particle form factor for a sphere, which is one of the options available from the Wyatt software. Table 1 collects the various radii from polarized and depolarized results according to eqs 1−4. In agreement with Figure 7, when the first two columns (Rh,t from Uv DLS and Rh,t from Hv DLS) are compared, the Hv DLS experiments seem to yield larger sizes than the standard DLS measurements. One possible explanation for thislarger particles containing more crystalline content than small ones, leading to stronger Hv DLS signalsseems to be ruled out by the absence of a trend in depolarization ratio with elution order, described above. The appearance of larger sizes from the HvDLS measurements is just barely significant; on average, Rh,t,Hv = (1.14 ± 0.11) × Rh,t,Uv. Comparison of the second and third columns of Table 1 is more robust. For all fractions, the apparent hydrodynamic sizes derived from pure rotation (the
Figure 6. DDLS decay rates plotted against squared scattering vector for the fractions eluting at the indicated times (in minutes). 3377
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Because ci = νiMi, where νi is the number density of particles causing the scattering, eq 7 can be rewritten as
Table 1. Comparison of Rh for Uv and Hv DLS fraction/mL 39 40 41 42 43 44 45 46 47 un
Rh,t,Uv/nm 86 88 89 93 93 96 94 83 99 104
± ± ± ± ± ± ± ± ± ±
3 1 2 1 2 3 3 3 1 1
Rh,t,Hv/nm
Rh,r,Hv/nm
98 ± 4
108 ± 2
99 104 95 112 102 114
± ± ± ± ± ±
1 2 6 12 10 2
114 118 123 123 127 128
± ± ± ± ± ±
Ii ∝ νiMi 2Pi ∝ νiVi 2Pi
The second proportionality, connecting mass to volume Vi, implies uniform density throughout the particle for all particles. The form factor Pi ≅ 1 − q2Rg2/3 ≅ exp(−q2Rg2/3), regardless of the shape as long as we analyze only data in the Guinier limit [easily identified as the regime of angles where a plot of ln(I) vs q2 remains linear]. For each slice, a Guinier plot [ln(I) vs q2] provides Rg,i from the slope
1 1 4 6 6 1
R g, i =
−3 × slope
(9)
Now needed is a relationship connecting Rg to the dimensions of the PTFE particles, which can be modeled as spherocylinders. The relevant parameters are defined in Figure 8.
intercept) exceed those derived from translation (the slope) by a significant amount: Rh,r,Hv = (1.17 ± 0.08) × Rh,t,Hv. One possible explanation for the difference between Rh,r,Hv and Rh,t,Hv may be the deficiencies of a spherical model (eqs 3 and 4) applied to the conversion from Dt and Dr, respectively. The problem may be expected to be more severe for rotational diffusion than for translational, because the former is more sensitive to size (Dr ∼ size−3 while Dt ∼ size−1). The expressions given by Broersma27 and Tirado and de la Torre28 for cylinders and spherocylinders, respectively, were used to predict Dt and Dr for objects similar in length and axial ratio to those studied in this work. (Analysis of the TEM images from all fractions yields a length of 240 nm and width of 172 nm for an axial ratio of 1.4; the width is more narrowly distributed than the length.) The equations, which appear in the Supporting Information, are not thought to be very accurate for objects of low axial ratio, but indeed, the apparent spherical radius is ∼50% larger when obtained from calculated Dr values than when using Dt. Before concluding this section, a comment on the long tail observed in the intensity plot of Figure 7 is in order. This figure confirms that large particles elute last, and the most likely explanation for the tail is therefore large particles present at low concentration. Extracting Distributions without a Concentration Detector. When a concentration detector is unavailable or rendered ineffective by low concentrations (as in the present case), it is still possible to obtain a size distribution by taking advantage of the MALS data in the Guinier regime. The situation may be compared to inverse Laplace transform of DLS correlation functions. There, the path leading from a spread of correlogram decay rates to the affiliated size and associated amplitudes, all without any direct information about concentration, is well-traveled.29 In this section, we convert the intensity curve of Figure 7 and the associated Rg curve to a relative number vs length distribution. The intensity scattered into data slice i by a group of monodisperse particles is
Ii ∝ ciMiPi
(8)
Figure 8. Dimensions of a spherocylinder. L is the length of the cylindrical barrel, d = 2R is its diameter, and the overall length is Ltotal = L + d = L + 2R, where R is the radius of the hemispherical end-caps. In the analysis, L is determined for each data slice while R is taken as a constant.
For an object of uniform density and volume V, the radius of gyration is defined22 through Rg2 = V−1∫ V s2 dV, where s is the distance of an element from the center of mass. The necessary integral is easily evaluated for a spherocylinder, with the result 2
Rg =
12 3 R 5
+ 3R2L + RL2 + 4R + 3L
L3 4
(10)
Equation 10 agrees with an expression derived by Kaya and de Souza30,31 for objects with a dumbbell shape in the appropriate limit that the cylindrical bar and spherical end-caps have the same radius. For each slice, eq 10 was solved numerically for L using a grid search method with a resolution of 0.1 nm (Visual Basic for Excel was used for this). The total length and volume are, respectively, L total, i = Li + 2R (11) and Vi =
4 3 πR + πR2Li 3
(12)
The TEM images suggest a relatively constant diameter, d = 2R, so the particle length and volume are determined for each slice only by Rg,i. Because Pi = 1 at q = 0, a factor proportional to νiMi2 (and to νiVi2) is computed as eintercept. The number density of particles is then obtained, proportionately, as
(7)
where ci is the mass/volume concentration, Mi is the molecular weight, and Pi is the particle form factor, which depends on q. The missing proportionality factor contains the intensity that would be measured at zero scattering angle, if such a measurement could be made. It also contains optical parameters such as refractive index, wavelength, and contrast between the particle and solvent, usually expressed as the specific refractive index increment (dn/dc), Avogadro’s number, and the wavelength of incident light. None of these need to be specified to obtain a relative distribution.
νi ∝ e intercept /Vi 2
(13)
The resulting distribution appears in Figure 9. This distribution is based on ∼1 million particles detected as the sample flowed by the detector, which is far too many objects to size conveniently by TEM. Both the spherocylinderlike shape and the relative constancy of particle diameter come from TEM, though; it is the combination of TEM and AF4/ MALS which makes the analysis possible, but in a typical production environment the TEM images only need to be 3378
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were nominally spherocylinders with relatively constant diameter, but other simple shapes would be easily accommodated. The number of particles sampled is very large, essentially determined by how many objects flow by the detector during the AF4/MALS run.
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ASSOCIATED CONTENT
S Supporting Information *
Particle size analysis by TEM, depolarization ratios across the distribution, Dapp vs q2 trends, appearance of correlation functions, scattering envelopes and Guinier plots at several slices of the chromatogram, comparison of Uv and Vv correlation functions, comparison of DLS results from singleangle and multiangle instruments, and diffusion equations for axially symmetric objects. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
Figure 9. Number distribution estimated from experimental AF4/ MALS data using the approach outlined in the text, which takes advantage of the Guinier equation and large sample size in the AF4/ MALS experiment but does not require a concentration detector. A spherocylinder shape is assumed for the particles.
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the Gulf of Mexico Research Initiative, by the Donors of the American Chemical Society Petroleum Research Fund, and by the National Science Foundation through Grants 0606117 and 1005707 (DMR) for labwork and 0526949 (IMR) for equipment. We thank Ying Xiao from the Socolofski Microscopy Laboratory and Mr. Wayne Huberty, who confirmed selected Uv and Vv results. Finally, we thank the reviewers for helpful comments.
gathered if there is reason to suspect a change of shape. AF4/ MALS can handle the routine analysis. The lengths measured seem a little larger than observed by TEM for a limited number of particles, suggesting possible end-to-end aggregation in suspension, shrinkage of the particles during TEM preparation, or both. Because the PTFE particles are not smooth spherocylinders, an analysis similar to the one above was performed by choosing a simple cylinder shape in place of spherocylinders; this resulted in an average length ∼7% smaller.
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CONCLUSION PTFE latex particles can be separated and characterized for Rg by AF4/MALS in about 1 h. Larger particles eluted later than smaller ones, as expected for AF4. By DLS assessment, the fractions were rendered more uniform after passing through the AF4, which is a valuable result from the standpoint of probe diffusion studies. Although it was already known that PTFE particles are asymmetric in shape and optically anisotropic, the ratio of Rg to Rh suggests that the late-eluting species are either more extended or slightly aggregated. These differences could not be discerned by TEM as practiced here. In the case of aggregation, even more images would not help because particles tend to accrete during dry-down. None of the DLS methods applied was entirely satisfactory. Online DLS required correlation function acquisition times too long for the flow parameters chosen to separate the particles. The off-line measurements performed on the Malvern Zetasizer Nano ZS at a single, very high scattering angle are subject to the effects of end-over-end tumbling and optical anisotropy. Rather than try to assess these effects, multiangle depolarized DLS measurements were performed, but these readings, which detect only those particles that depolarize substantially, rely on the symmetric top approximation to obtain a size. Failure to adhere to that approximation probably explains the disagreements between Rh,t and Rh,r. The simplest tool in the lightscattering arsenalthe Guinier plotcan be applied to AF4/ MALS traces to obtain relative number vs length distributions, even without a concentration detector. The analysis took advantage of the information from TEM that PTFE particles
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