Anal. Chem. 1994,66,4408-4415
Determination of Functional Groups on Particle Surfaces by Fluorescence and Reflection Spectroscopy J. W. Hofstraat,* 0. D. B. van Houwelingen, and E. B. van der To1 Akzo Nobel Central Research, Laboratories Arnhem, Department CRL, P.0. Box 9300, NL-6800 SB Arnhem, The Netherlands W. J. All. van Zeijl National Institute of Coastal and Marine Manaaement, Ministry of Transport, Public Works and Water Management, P.O. Box 20907, NL-2500 EX The Hague, The Netherlands
The application of fluorescence and rdection (absorption) measurements for the determination of functional groups on surfaces has been investigated. As an example, aminofunctionalized silica surfaces have been studied that were labeled with the strongly colored fluorodinitrobenzene (FDNB)and the fluorescent Lucifer YellowVS (LY).Both with reflection measurements and with fluorescence detection, amino groups could be quanti6ed with concentrations as low as 10 mmol/kg, which is significantly lower than the detection limit attainable with conventional titration approaches. At concentrations higher than 250 mmoVkg for the FDNB-labeled samples and above 50 mmoVkg for the LY ones, calibration curves become nonlinear. From the concentration dependence of the LY fluorescence, information can be derived on the structure of the labeled surface. Finally, it is shown that the fluorescent particles can also be examined individually by application of flow cytometry. On the basis of flow cytometric measurements, the concentration of functional groups, homogeneityof functionalization,and particle size distributions can be obtained. Functional groups on surfaces are a major determinant of special properties of particles, which may be used for a variety of applications. A few examples are as follows: (1) particles that are used in chromatographic systems, where functional groups may provide specific interactions with particular analytes, (2) lattices that are used for diagnostic purposes, where particles are bound to antibodies to invoke immunochemical diagnosis, (3) functionalized lattices applied in coatingswith improved properties, such as better blocking or water resistance, and (4)modified fiber surfaces with special adhesion properties. To be able to study the relationship between the structure of the surfaces of these particles and their activity, important information can be derived from the concentration and distribution of the functional groups. A number of analytical techniques are available to determine the concentration of functionalgroups. Most of these techniques have been developed for study of homogeneous systems but can in some cases be applied to heterogeneous systems as well, provided that the concentration of the functional groups is sufficiently high. The most direct measurements are based on 4408 Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
titrations, using a variety of detection principles (potentiometry, conductivity, colorimetry, etc.) .l Alternatively, strongly colored (absorption) or fluorescent probes can be used, which form specific, covalent, bonds with the functional groups. The application of such probes, which allow for spectroscopic determination of the functional groups, is well-known from biomedical as well as chromatographic applications. For determination of functional groups in homogeneous systems, the application of such labels is straightforward provided that the unreacted label does not interfere with the determination. Removal of unreacted label may require extensive chromatographic sample pretreatment.2~~In heterogeneous labeling, however, the use of absorption and fluorescence labels is not straightforward. As detection should also be done in the heterogeneous system, with a significant amount of strongly scattering particles, simple transmission or fluorescence measurements are not possible. Special detection techniques,which minimize the effects of interference due to light scatter, have to be developed. In this paper several spectroscopic detection techniques will be discussed, which can be applied to measure functional groups on particle surfaces. Both the application of absorption and of fluorescence probes will be discussed. The latter kind of probes has as advantage that information on the distribution of the functional groups can also be obtained. In combination with a flow cytometer, information becomes available on the concentration of functional groups per particle. The applicability of the spectroscopic techniques is demonstrated via study of silica particles with a modified surface that contains amino groups. EXPERIMENTAL SECTION Preparation ofM&ed Si Particles. Labeling. SpherosilXOA200B silica spheres were used. The particles are in the size range of 100-200 pm with a specific area of 203 m2/g and a 0.14 pm pore diameter. The spheres were functionalizedwith amino groups by reaction with (y-aminopropy1)triethoxysilane(y-APS). (1) Siggia, S.,Ed.Instrumental Methods of Otganic Functional Group Analysis; Wiley: New York, 1972. (2) Ichmose, N.; Schwedt, G.; Schnepel, F. M.; Adachi, K. Fluorometric Analysis in Biomedical Chemistty. Trends and Techniques including HPLC Applications; Wiley: New York, 1991. (3) Hofstraat, J. W.; Gooijer, C.; Velthorst, N. H. In Molecular Luminescence Spectroscopy: Methods and Applications, Pad 3; Schulman, S . G., Ed.; Wiley: New York, 1993; pp 323-443. 0003-2700/94/0366-4408$04.50/0 Q 1994 American Chemical Society
To activate the silica spheres, 100 g of Spherosil is kept in -400 mL water in an ultrasonic bath for 2 h at 80 "C. The water is replaced until the supernatant remains clear. Next, 40 mL of 4 mol/L HN03 is added and the solution is left for 2 h. The suspension is then rinsed over a glass filter until the pH of the water is constant. Finally, the Spherosil spheres are dried at 70 "C for 1 h and overnight under vacuum at 120 OC. For the silanization, 15 g of the activated and dried Spherosil is brought into 50 mL of toluene. To the suspension is added an accurate amount of y-APS. The flask is then stirred in an oil bath at 90 "C for 5 h and stirred overnight at room temperature. The samples are finally dried at 50 "C under vacuum. The maximum amount of amino groups that could be obtained (by application of a excess of y-APS) was 800 mmol/kg. Lower concentrations of amino groups were obtained by application of less PAPS. The reaction appeared to be quantitative. The concentrations of the amino groups on the particles were determined by titration. After deaeration,an excess of perchloric acid is added to the suspension with functionalized Si particles in acetic acid. After overnight reaction, the unreacted perchloric acid is titrated with tetrabutylammonium hydroxide. Titration could be applied for functional group concentrations above 50 mmol/kg. Comparison of the functional group concentration with the applied levels of y-APS showed that under the applied conditions the reaction was quantitative. Lower concentrations of functional groups were obtained by using lower levels of y-APS. The products of these reactions could only be analyzed by more sensitive, spectroscopic, methods. Two labels were applied for spectroscopic analysis. First, the amino groups were reacted with l-fluoro-2,4dinitrobemne("3). The FDNB reaction was done in an ethanolic solution of FDNB with sodium hydrogen carbonate buffer (PH 8-9) at 80 "C. This reagent is suitable for quantitative reaction with amino groups, even under heterogeneous Conditions! The reaction took 4 h. The unreacted reagent was removed by careful rinsing of the labeled particles with acetic acid (PH 3-4) and, subsequently,with acetone until a colorless eluate was obtained. FDNB gives a strongly colored product with maximum absorption at 417 nm. Second, the amino groups were labeled with the efficient fluorescent dye Lucifer Yellow vinyl sulfonate LY-VS.5 This reaction can be readily done in 0.1 M sodium hydrogen carbonate at room temperature; reaction time is -2 h. Excess reagent is removed by extensive rinsing with water over a glass filter. The filtrate was checked for fluorescence of LY. Spectroscopic Measurements. Diffuse reflection measurements were done on particles labeled with FDNB and with LY, using a Varian Cary 5 absorption spectrophotometerequipped with a so-called praying mantis accessory. The accessory can be placed directly into the Cary 5 sample chamber and contains optics to irradiate a particulate sample at normal incidence; the reflected radiation is collected over a fairly wide angle by application of big parabolic mirrors and coupled into the spectrophotometer. The reflection measurements were done on an "intinitely" thick layer, so that the absorption could be approximated via the Kubelka-Munk relatione5 In some cases, for the very concentrated samples, the material was diluted 1:9 with blank material. (4) Van Houwelingen, G. D. B.; Aalbers, J. G. M.; De Hoog, A J. Fresenius 2. Anal. Chem. 1980,300, 112-120. (5) Stewart, W. W. Nature 1981,292, 17-21. (6) Kubelka, P.; Munk, F. 2.Tech. Phys. 1931,12, 593-601.
Fluorescence emission and excitation spectra were recorded for particles labeled with LY. The spectra were recorded in a SPEX Fluorolog 2 fluorescence spectrophotometer. Emission was detected in a front face codguration, under an angle of 20" of the excitation light. The excitation spectra were obtained by monitoring the 535 nm emission; the emission spectra were obtained by excitation at 458 nm. Bandpass was 1.5 nm for excitation and emission. Flow Cytometry. Flow cytometry was done on a homebuilt flow cytometer,which has been designed in such a way that large particles, e.g., phytoplankton, can be analyzed.7.8 General reviews on principles and applications (mainly in the biomedical field) of flow cytometry have been published by, among others, Pinkelg and, more recently, Gilman-Sachs.lo For excitation, the 458 nm line of an Ar ion laser was used. For each individual particle, four parameters were determined: the time of flight O F; or length of the particle), the perpendicularlight scatter (PLSB; field of view 68-112") and the forward light scatter (FLSB; field of view 1-25'), both induced by the blue laser, and the fluorescence in the 525-645 nm range @BY; or fluorescence blue to yellow). To ensure that the particles remain homogenously suspended during the analysis, the samples are stirred continuously throughout the measurement. Data were recorded at high speed and stored in a Hewlett-Packard 9000330 minicomputer, awaiting further analysis. Analysis was done with the Apple Mackintosh DataDesk program. Typical measurements were done at a speed of 100 particleds; 10 O00 particles were examined per experiment, All experiments were done in duplicate. To check the accuracy of the measurements and to correct for possible fluctuations in the laser intensity or in the optical alignment, fluorescein containing standard beads from Flow Cytometry Standards Corp. were added to every sample prior to the measurement. Materials. Spherosil XOA200B silica beads were obtained from FWne Poulenc. The y-APS was from Aldrich. FDNB was purchased from Merck. Lucifer Yellow VS was from Aldrich. RESULTS AND DISCUSSION
Determination of amino groups on a modified Si surface was done using strongly colored (absorption) and fluorescent probes. The quantitative aspects could be verified-in the high concentration range-via well-known titration procedures. For low levels of functional groups and for analysis of levels of functional groups on individual particles, the titration method lacks sensitivity. It is just in this area where spectroscopic methods, in particular fluorescence, offer important advantages. As an example the application of flow cytometric analysis to analysis of single particles will be discussed. An important advantage of labeling techniques applied to heterogeneous systems, such as particles or surfaces in general, over the mostly applied labeling in homogeneous systems is that unreacted label can be removed effectively by simple filtration approaches. In homogeneous systems, removal of excess label requires in general careful chromatographic separations, extraction procedures or dissolution/precipitation, with the risk of loss of material. Such complications can be circumvented in hetero(7) Dubelaar, G. B. J.; Groenewegen, A C.; Stokdijk, W.; Van den Engh, G. J.; Visser, J. W. M. Cyiometty 1989,IO, 529-539. (8) Hofstraat, J. W.;De Vreeze, M. E. J.; Van Zeijl, W. J. M.; Peperzak, L; Peeters, J. C. H.; Balfoort, H. W. 1.Nuoresc. 1991,1,249-265. (9) F'inkel, D. Anal. Chem. 1982,54, 503A-519A (10) Gilman-Sachs, A Anal. Chem. 1994,66, 700A-707A. Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
4409
geneous systems. In heterogeneous systems, however, one has to be aware of possible spurious labeling due to aspecific interactions. In both the FDNB and in the LY systems examined in this study, no problems with unreacted label and no aspecific interactions were observed and reactions were found to be fast and complete. Absorption Probes. Absorption techniques can be readily applied to the analysis of functional groups. Strongly colored, and thus highly absorbing, dyes with reactive groups, which interact selectivelywith specific functionalities, are available for labeling. Two probes will be considered in this study, FDNB and LY, the latter probe also being strongly fluorescent. The reaction of the functionalized Si particleswith FDNB yields a yellow-colored material. Absorption maxima are at 360 nm and at 420 nm. As the labeled material is a suspension, and hence not transparent, no conventional determination of the absorption in the transmission mode can be applied. Scatter effects will result in significant additional loss of light. The approach to use is to measure accurately the reflection spectrum of the labeled particles. The praying mantis accessory of the Cary spectrophotometer allows for measurement of diffusely reflected radiation using perpendicular (“normal”) illumination of the sample. The absorp tion of light by the label results in a reduction of the level of the reflected light. From this reduction, the absorption and hence the concentration of the label and of functional groups can be determined. By application of the Kubelka-Munk approximation, which holds for optically infinitely thick (Le., not transparent) samples, the absorption of the heterogeneous sample can be quantitated, according to the formula
where k is the absorption coefficient (Iz = A t ) , s is the scattering coefficient, and R is the reflectance. Panels a and b of Figure lshow, respecively,the reflection curves and the Kubelka-Munk absorption curves obtained for the particles labeled with FDNB. The absorption of the labeled particles varies linearly with the concentrations of amino end groups as obtained by titration (range 50-500 mmol/kg) and as derived by the preparation procedure (range 10-50 mmol/kg, i.e., below the limit of detection for the titration procedure). The Kubelka-Munk absorption, F(R), has been plotted as a function of the concentration of amino end groups in Figure IC. The data shown have been obtained for 1:9 diluted samples. The diluted samples gave a more extended linear calibration curve. Linear regression analysis shows that the F(R) varies linearly with the concentration of end groups until -250 mmol/kg (Z= 0.993). The 504 mmol/kg sample shows significant deviation from linearity, which may be due to intermolecular interactions.The limit of detection is below 10 mmol/kg, i.e. much better than attainable with titration methods. A similar procedure has been applied to the labeling of LY. Although this probe is generally applied as fluorescence probe, it is strongly colored and should be useful as an absorptive probe as well. Reflection spectra, also recorded in the Cary praying mantis accessory, and Kubelka-Munk spectra are shown in panels a and b of Figures 2, respectively. The LY-labeled Spherosil samples are also yellow colored; they have an absorption maximum at 425 nm. The plot of F(R) vs the concentration of amino groups is shown in Figure 2c. The curve is h e a r (Z= 0.99) for concentrations up to -100 mmol/kg. At higher concentrations, 4410 Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
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Figure I. (a, top) Reflectionspectra and (b, middle) Kubelka-Munk spectra of FDNB-labeled Spherosil beads. Curves shown depict, from top to bottom, spectra obtained for samples with 504, 260, 148, and 76 mmol/kg amino groups, respectively. (c, bottom) Analytical curve obtained from the spectra shown in (a).
the F(R) shows a significantly stronger dependence on the end group concentration. The change in concentration dependence is accompanied by a broadening of the main absorption band. A possible explanation could be that at concentrations beyond 100 mmol/kg the way in which the LY molecules are positioned on the particle surface changes. The same concentration dependence was observed for 1:9 diluted samples, which indicates that the measured effects are due to interactions on the Si particles themselves. If this hypothesis is correct, an even stronger change in spectral behavior is expected for the fluorescence spectrum. In the following section, this point will be examined in more detail. Fluorescence Probes. LY-VS reacts readily with the amino end groups of the modified silica particles. Subsequently, the spectrum of the fluorescently labeled materials can be measured.
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Concentration aminogroups (mmolkg) Figure 2. (a, top) Reflectionspectra and (b, middle) Kubelka-Munk spectra of LY-labeled Spherosil beads. Curves shown depict, from top to bottom, 76, 40, 20, 10,and 0 mmol/kg; 148, 260, and 504 mmollkg are off-scale and have to be quantitated after dilution with blank beads. (c, bottom) Analytical curves obtained from the spectra shown in (a).
Fluorescence measurements were done with front face excitation and detection of the emitted light to minimize possible inner filter effects. The emission spectrum was obtained using 458 nm excitation, i.e., the same wavelength used in the flow cytometer. Excitation spectra were recorded while the emission at 535 nm was monitored. The excitation emission and spectra thus obtained are shown in panels a and b of Figure 3, respectively. Quantitative data are shown in Figure 3c. From the figures, it is obvious that three concentration regions can be discerned for the fluorescence behavior of LY on silica particles. In the first region, 0-40 mmol/ kg end groups, the fluorescence emission and excitation spectra have the same appearance and show a linear dependence of the concentration of end groups. The emission spectrum peaks at 535 nm; the excitation maximum is at 430 nm. The third region
starts beyond 76 mmol/kg end group and shows strong evidence of intermolecular interactions: strong red shifts and a significant loss in fluorescence intensity. In addition, in this concentration range, inner filter effect will play a role. In the second, intermediate, region the fluorescence intensity increases superproportional and shows a blue shift (compared to the low concentration range of 0-40 mmol/kg). The emission maximum of the 76 mmol/kg sample is at 520 nm, i.e., 15 nm blue shifted. The most obvious explanation for this behavior can be found in the mode of interaction of the LY groups with the silica surface. At a concentration of 50 mmol/kg -600 & is available on the surface per LY group (the specific surface area is 203 m2/g, according to the producer). The total surface area of the LY molecule is -150 k,so that interactions of the strongly polar probe molecules may become appreciable. At low surface concentrations, LY will interact with the polar silica surface. Several sites on the LY molecule are available for H-bonding with remaining unreacted silanol groups. Roumeliotis and Unger showed that after modification of silica surfaces a significant amount of SiOH groups remains.11The LY surface interactions may give rise to a red shift of the LY fluorescence. At higher concentrations, the surface coverage becomes very high, so that the fluorescent molecules can no longer interact optimally with the surface and the available space becomes limited. The molecules will tend to be lifted from the surface, which would lead to a reduced interaction and hence to the observed blue shift. At even higher concentrations the distance of the LY molecules rapidly decreases, so that intermolecular interactions and reab sorption processes will occur. From the measurements on the solid particles,these two phenomena cannot be distinguished.The high concentration phenomena give rise to significant reduction of the fluorescence quantum yield and a red shift of the fluorescence spectra, as observed in Figures 3a,b. Lochmuller and co-workers have shown for silica surfaces with chemically bonded pyrene groups that such interactions do occur: for the polynuclear aromatic hydrocarbon pyrene, with its extended n-electron system, intermolecular interactions become obvious via excimer fluorescence.*2Excimer formation seems less likely for the strongly polar LY molecule. On the basis of his study, Lochmuller concluded that the pyrene silane molecules react preferentially with silanol groups in a region where an already bound pyrene group is found. In this way, one can explain the observation that excimer fluorescence, a phenomenon characterized by a critical interaction distance of 3-5 A, is observed for average distances ranging from 34.9 to 12.3 LY is highly polar and dissolves well in the aqueous medium applied in this study. The results obtained in this study do not point to the occurrence of clusters of LY molecules on the silica surface, but to a more homogeneous distribution (see also the next section). Flow Cytometry. The functional group content of individual particles may be examined by application of flow cytometry. With this technique, the fluorescence intensity of individual particles can be measured. Hence, the homogeneity of the functional group level on the particles can be examined. Figure 4 shows typical bivariate plots obtained for flow cytometric analysis of the LYlabeled Spherosil beads. The measured intensities per particle are shown in the bivariate plots: every point in each of the figures
a.12
(11) Roumeliotis, P.;Unger, K K J Chromafogr. 1978,149, 211-224. (12) Lochmllller, C. H.;Colbom, A S.;Hunnicutt, M. L.;Harris, J. M. Anal. Chem. 1983,55,134-1348,
Analytical Chemistty, Vol. 66, No. 24, December 15, 1994
4411
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Concentration aminogroups (mmolkg) Figure 3. (a, top) Fluorescence excitation spectra of LY-labeled Spherosil beads; emission monitored at 535 nm. (b, middle) Fluorescence emission spectra of LY-labeled Spherosil beads; excitation done at 458 nm. (c, bottom) Analytical curves obtained from the spectra shown in (b). The curves are labeled as Sphxxx-LYvs, where xxx indicates the concentrationof amino groups on the particles in millimoles per kilogram. 441 2 Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
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Figure 4. (a, top) Bivariate plots obtained from flow cytometric analysis of LY-labeled Spherosil beads (148 mmoWkg amino groups). Each point in the plots represents a particular combination of the parameters shown, determined for a single particle. A total of 10 000 particles is shown, which cluster in three regions: in the right upper part the labeled Spherosil beads and in the left lower part the fluorescein-containing standard beads. The latter beads give two clusters, of single and double (sticking) particles. (b, middle) Analytical curve of the size-corrected averaged fluorescence intensity. The labels on the axes represent the plotted parameters: PLSR and PLSB are the perpendicularlight scatter induced by the red and blue lasers, respectively, FLSB is the forward light scatter induced by the blue laser, FBY is the yellow fluorescence induced by the blue laser, and TOF is the duration of the pulse measured for the FBY signal.
represents a measurement. The total number of particles analyzed is 10 000, which takes -2 min. A total of four parameters has been measured for every particle: the LY fluorescence,the length of the particle, forward light scatter, and perpendicular light scatter for the blue laser. The iigure also shows (in the left-hand corner) data obtained for fluorescein-containing standard beads. The standard beads are used for calibration of the measurements, i.e., to correct for possible variations in laser power or optical alignment. The data are presented as logarithmic values. By application of logarithmic amplifiers, the dynamic range of the detectors can be extended so that large particles (the Spherosil beads) and small particles (the standard beads) can be measured simultaneously. In contrast to the experienceswith homogeneous labeling, the excess of label is easily removed when in heterogeneous labeling situations. In the present case, the label was washed away over a filter. No aspecific adsorption of the label to
the particles was observed. Similar observations were made for labeling of phytoplankton parti~1es.l~ A number of observations can be made from the bivariate plots. First, the amount of fluorescence (and thus the LY concentration) per particle is highly variable: the fluorescence intensity across the clusters shown in Figure 4 varies over more than 1 order of magnitude. The large variation is also clear from the data presented in Table 1. The standard deviation, given for the linearized data, of the fluorescence parameter exceeds the average value! However, when the size of the particles is considered, which can be derived from the various scatter parameters or the TOF,the variability is strongly reduced. The FLSB offers the most direct information of the size: this parameter depends on (13) Hofstraac J. W.; Van Zeijl, W. J. M.;Peeters, J. C. H.; Peperzak, L. Anal. Chim.Acta 1994,290,135-145.
Analytical Chemistry, Vol. 66, No. 24, December 15, 1994
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Table 1. Flow Cytometric Data Obtained for Lucifer Yellow Labeled Functlonalized Spherosil Beads
sample (mmol of NHdkg) 0 10 20 40 76 148 260 504
single beads double beads a
M F (um)
FBYa (x lo4)
PUB" (x lo5)
FLSB" (x 106)
FBY/PLSB
FBY/FLSB
PLSB/FLSB
120 f 44b 128 f 49 93 f 43 88 f 44 119 f 48 144 f 57 36 f 64 34 f 60 5 f 2 13 f 2
1.4 f 2.1 2.5 f 3.7 1.6 f 2.2 5.1 f 7.8 36 f 38 388 f 360 85 f 236 74 f 210 0.10 f 0.05 0.22 f 0.11
4.7 f 2.7 4.7 f 2.5 2.7 f 1.9 2.6 f 2.0 4.5 f 2.7 5.4 f 2.9 1.4 f 2.6 1.3 f 2.5 0.18 f 0.05 0.39 i 0.07
5.2 f 3.1 5.4 f 2.9 3.0 f 2.1 2.9 f 2.2 4.9 f 3.2 4.4 i 2.4 0.99 f 2.1 0.92 f 2.0 0.039 i 0.004 0.089 z t 0.005
0.025 f 0.020 0.047 f 0.050 0.056 f 0.050 0.20 f 0.18 0.72 f 0.52 6.4 f 4.2 1.4 f 3.3 1.3 f 3.0 0.058 f 0.033 0.057 f 0.029
0.0022 f 0.002 0.0040 f 0.0043 0.0049 f 0.0043 0.017 f 0.015 0.065 f 0.044 0.79 f 0.55 0.19 i 0.41 0.18 f 0.38 0.025 f 0.013 0.024 f 0.012
0.097 f 0.038 0.092 f 0.038 0.10 f 0.056 0.11 f 0.063 0.10 f 0.046 0.13 f 0.037 0.41 f 1.06 0.44 f 1.29 0.45 f 0.11 0.43 f 0.08
Linearized values are indicated, given in arbitrary units. Data show average values and standard deviation.
the refractive index of the particle (which may be assumed the same for the particles of different sizes) and on the cell volume, as predicted from Mie's theoretical work.12 The bivariate plot of FBY vs FLSB shows a linear relationship, which indicates that most of the variation in fluorescence intensity can be attributed to size effects. The importance of the size effects on the average fluorescence can also be derived from Table 1: the samples with 20 and 40 mmol/kg have lower fluorescence than expected in relation to the other samples. The data measured for the sizedependent parameters show reduced values as well. The ratios of the fluorescence parameter to the "size parameters" FLSB and PLSB indeed show a significant reduction of the variability (see Table 1). The fluorescence intensity is expected to vary directly with FLSB, as the total volume determines the fluorescence intensity. In this context it should be remarked that, although the fluorophores are present on the surface of the particles, their concentration is mainly determined by their volume since the particles are highly porous. The size parameters FLSB and PLSB show similar values for the different samples up to -150 mol/kg: the ratio of the two parameters is 0.1 for all samples, except the two most concentrated ones. For 260 mmol/kg and for 504 mmol/kg, the data are strongly determined by interactions between the fluorophores and (re)absorption. The strong absorp tion by the particles causes primarily a reduction of the FLSB parameter; the PLSB parameter is less influenced by absorption. The size distribution of the particles can be estimated from the time-of-fight data. For most samples, the size range is very broad, -120 f 50 pm, in rough agreement with the product specification. The samples with 20 and 40 mmol/kg amino end groups show much smaller sizes (-90 f 40 pm), which strongly influences the fluorescence data, as discussed above. The samples with the highest concentration of amino end groups show a large reduction of the fluorescence signal; at the same time, the timeof-fight appears to be reduced due to reabsorption effects. After proper correction for the particle size effects, the flow cytometric data appear to give quantitative information in agreement with the bulk fluorescence measurements: the fluorescence intensity, weighed with the size parameter FLSB, is proportional to the concentration of amino groups up to -50 mmol/kg. A superproportional increase of the fluorescence intensity is observed for the range 50-150 Inmol/kg amino groups. This range is more extended than observed in the fluorescence spectrum, most probably because reabsorption phenomena will be less pronounced in the analysis of single particles. Two questions remain: how accurate is the flow cytometric analysis and how homogeneous is the labeling of the Spherosil 4414 Analytical Chemistry, Vol. 66, No. 24, December 75, 7994
particles. Both questions can be answered by considering the data obtained for the fluorescent standard beads, which are also given in Table 1. In the bivariate plots, the standard beads give two clusters: the left one due to single beads and the right, less populated one, due to double beads (Le., beads sticking together or coincident in the laser focus). The linearity of the detection is very well demonstrated by the exact doubling of all averaged parameter values determined for the double beads as compared to the single beads. The parameter ratios give the same values for the single and for the double beads, which also underscores the validity of the approach applied to correct for the size effects in the Spherosil measurements. Finally, the statistical analysis performed on the standard beads shows much better standard deviations (typically
