Langmuir 1993,9, 2071-2076
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Characterization of Polystyrene Latexes by Hydrodynamic and Electrophoretic Fingerprinting James H. Prescott,t Shaw-ji Shiau,t and Robert L. Rowell' Department of Chemistry, LGRT-102,University of Massachusetts, Amherst, Massachusetts 01003 Received August 10,1992.I n Final Form: June 11,1993 We report the first measurements of the new approach of hydrodynamic fingerprinting. The hydrodynamic fiigerprint is the isothermal contour diagram of the hydrodynamic size as a function of pH and pX (the logarithm of the conductivity (pSlcm)). The general applications of fingerprinting are discussed,and we compare hydrodynamic fingerprints with electrophoretic fingerprints on similar systems. The electrophoretic fiigerprint is the isothermal isomobility contour diagram in the pH-pX domain. Measurements are reported on five model polystyrene latexes with carboxyl or sulfate surface groups (ranging from 401 to 1050 nm) from the Interfacial Dynamics Corp. We find that the hydrodynamic size depends on pH, pX, and time, and is generallylarger than the electron microscopy size. The hydrodynamic fingerprint, like the electrophoretic fingerprint, is a characteristic pattern of a particular colloidal system. The advantages of the colloid system variable pX over the classical ionic strength are illustrated. The fingerprinting approach is a correlation of variables that can be used to spot errors and assess the general significance of a function of two independent or characteristic variables. Introduction The idea of representing the measurable electrophoretic mobility of colloidal particles as a function of pH and the logarithm of the conductivity was conceived at the University of Massachusetts in 1986.' In the first journal publication of the method, our collaborators coined the term 'electrophoretic fingerprinting"? We now defiie the electrophoretic fiigerprint as the isothermal isomobility contour diagram of the electrophoretic mobility as a function of pH and ph (the logarithm of the conductivity (pSlcm)). In the present work we report the first measurements of hydrodynamic fingerprinting3 where the hydrodynamic fingerprint is the isothermal contour diagram of the hydrodynamic size as a function of pH and PA. Both electrophoretic and hydrodynamic fingerprinting are representations of three measurable variables. In general, fingerprinting may be a probe to understand the interplay of a mixture of measurable and theoretical variable^.^ The method has also been applied to the acoustic mobilitye6 The present work builds on earlier experimental worke-8 and a theoretical prediction of the general a p p r ~ a c h . ~ Experimental Section Materials. Measurementa have been made on five ultraclean uniform latex microspherecolloidalsystems obtained at 4-10% ?Present address: Advanced Magnetics Inc., 61 Mooney St., Cambridge, MA 02138. t Present address: Du Pont Taiwan La., 7th F1. International Bldg., 8 Tung Hua North Rd., Taipei, Taiwan, ROC. (1)Morfeais, A. M. Ph.D. Thesis, University of Massachusetts, 1986. (2) Marlow, B. J.; Fairhurst, D.; Schutt, W. Longmuir 1988,4,776780. (3) Preecott, J. H.Ph.D. Thesis, University of Massachueetta, 1992. (4) Marlow, B. J.; Rowell, R. L. Langmuir 1991, 7, 2970-2980. (5) Marlow, B. J.; Rowell, R. L.Energy Fuels 1988,4, 125-131. (6) Rowell, R. L. In Scientific Methods for the Study of Polymer Colloide; Candeau, F., Ottewill, R. H., Eds.;Kluwer Academic Publishers: Dordrecht, "he Netherlands, 1990; pp 187-208. (7) Morfeais, A. A.; Rowell, R. L. Longmuir 1990,6,1088-1093. (8)Rowell, R. L.; Shiau, S.-.J.; Marlow, B. J. ACSIPMSE Roc. 1990, 62,52-56. (9) Rowell, R. L.; Shiau, S.-.J.; Marlow, B. J. In Particle Assessment and Characterization; Provder, T., Ed.; ACS Symposium Series 472; American Chemical Society: Washington, DC, 1991; pp 326-336.
Table I. Latex Designation and Diameter (nm) wt size at pH 7, low ph label IDC no." % b IDC size PA 2 size 4 401 8(1.9%) 450 460 C401 10-87-17 S489 2-94-35.188 8 489 11(2.2%h 525 530 3.5 984 50 (5.1%) C984 10-32-13 5686 10-2-2 10.4 686 15 (2.2%) 51050 10-86-15 8.4 1050 44 (4.2%) 0 Interfacial Dynamics Corp.10 Portland, OR, batch number and diameter reported by the manufacturer; a transmission electron microscopysize based on 600 measurements (ProductBulletin Vol. 12/90).b Concentration as supplied by IDC.
* *
solids concentration from Interfacial Dynamics Corp.lO (IDC). The batch numbers and manufacturer's nominal size are given in Table I which also includes selected size measurements from our work below. The latexes have extensive uses including "calibration standardsfor particlesizingequipment". According to the manufacturer, the latexes are made without surfactants, are ultraclean and ready for immediate use, and are rigid, amorphous polystyrene microspheres with a glass transition temperature around 100 "C. For our samplesthe surface charge groups were either carboxyl or sulfate. As an identifying label, we use a prefix C for carboxyl or S for sulfate followed by the manufacturer's nominal size (nm) as listed in Table I. The manufacturer's nominal size was based on measurements of 600 particles by transmission electron microscopy. Given in Table I are the mean diameter and the coefficient of variation in diameter obtained from the IDC report of the percent coefficient of variation. Electrophoresis. The electrophoreticmobility was measured with a Pen Kem System 3000 automated electrokineticsanalyzer which has been described elsewhere.6.11 The Pen Kem 3000 simultaneously measured electrophoretic mobility, pH, and conductivityat25"C. Typically,two drops of the standard latex were added to 250 mL of double-distilleddeionizedwater. The latex was dispersed at medium speed for 10 min using scale 5 of a Corning PC-351 hot plate/magnetic stirrer. The particle concentrations were in the range of 20-40 ppm. The pH was adjusted with HC1 or KOH, and the ph was adjusted with KCl. HC1, KOH, and KC1 were certified ACS grade from Fisher ScientificCo. The temperature of titrations and measurements was 25 "C. (10)Interfacial Dynamics Corp.,4814 NE 107thAve., Suite B, Portland,
OR 97220.
(11) Goetz, P. J. U.S. Patent 4,154,669.
0743-746319312409-2071$04.00/0 0 1993 American Chemical Society
2072 Langmuir, VoZ. 9, No. 8,1993
Prescott et al.
4
3 x2 Q
1
2
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s
'2
pc; Figure 1. Hydrodynamic surface (a) and corresponding hydrodynamic fingerprint (b) for surfactant-free carboxyl polystyrenelatex C401 for the aqueousHC1-KOH-KCl colloid system.
Hydrodynamic Size. The hydrodynamicsizemeasurements were made by photon correlation spectroscopy (PCS) using a Brookhaven BI-90.l2 Each diameter was the average of a minimum of five measurements. Working stock solutions were prepared by dilution of the samples as received from IDC using double-distilled water that had been filtered through Gelman Scientific0.2-pm polycarbonate membranes. The working stock solutions, from 0.5% to 2.0% solids by weight, were refrigerated at 4 "C in HDPE bottles. Prior to use, the working solutions were equilibrated to room temperature for 24-48 h. Samples for analysis were prepared by the addition of small (less than 0.20 mL) volumes of the working stock solutions to 4.0 mL of the pH-pX adjusted solution directly in the BI-90 sample cuvette. The supporting solutionshad been added to the cuvettes through 0.2-pm Gelman filters. The cuvettes were capped and sealed with parafilm to prevent contamination or evaporative loss. A particle weight fraction of approximately 5 X 106 had sufficient light scattering to give a measured hydrodynamic size that was independent of concentration. Measurements were made at 25 "C. Coincident with the samples for size measurements were separate measurements on 20-mEvolume preparations of the same colloidal solution for pH and conductivity. An Orion pH meter (model 399A, 10.02 pH unit) and a Horizon conductivity meter (model 1484, &2%)were used. Time Studies. The dependence of the hydrodynamic diameter on time was determined for latex S489. The sample was stored in the measuring cuvette at 4 "C between measurements. The samples were equilibrated a t room temperature for 24 h before sonication and size measurements. Data Analysis. The data are represented in three-dimensional perspective or two-dimensionalcontour diagrams, fingerprints (isomobilityor PCS size)in the pH-pX domain. The graphs were prepared using SURFER,a commercialsoftware package.'3
Results Hydrodynamic Size. Figures 1-3 are hydrodynamic size data taken from the Ph.D. thesis of J.H.P.3 In Figure 1we show the hydrodynamic surface and fingerprint of (12) BrookhavenInstrumentaCorp.,BrookhavenCorporatePark,750 Blue Point Rd., Holtaville, NY 11742. (13) Golden Graphics, 807 14th St.,P.O.Box 281, Golden, CO 80402.
PH Figure 2. Hydrodynamic surface (a) and corresponding hydrodynamicfingerprint (b) for surfactant+freesulfate polystyrene latex S489 for the aqueous HC1-KOH-KC1 colloid system.
+ ' 4
3
PA 2 1
PH Figure 3. Effect of a few bad data points: same data as for Figure 2 but with additional irreproducible data points (two bad points near pH 10, pX 3 and one bad point near pH 5.5, pX 3).
the carboxyl latex C401. The unstable regiona t high acid and strong electrolyte is clearlyshown by the sharp increase in size arising from aggregates. In the stable region, the hydrodynamic size is roughly constant but there are variations and a trend toward larger size a t the lowest electrolyte concentration is discernable. The hydrodynamic surface and fingerprint of sulfate latex S489 are shown in Figure 2. The domain of instability is somewhatsimilar to Figure 1but different in quantitative detail. The contour line pattern in the stable region differs from that of Figure 1,the significanceof which is discussed below. Careful inspection of the contour lines shows a
Langmuir, Vol. 9, No. 8, 1993 2073
Characterization of Polystyrene Latexes
7 '
0:
PH
iI10
'
Figure 4. Electrophoretic surface (a) and corresponding electrophoretic fingerprint (b) for surfactant-free carboxyl polystyrene latex C984 for the aqueous HC1-KOH-KC1 colloid system. An anomalous but small positive mobility was experimentally observed in the lowest pH, highest pX region.
n
"2
4
6
8
10
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Figure 6. Electrophoretic surface (a) and corresponding electrophoretic fingerprint (b)for surfactant-free sulfate polystyrene latex S686 for the aqueous HCl-KOH-KC1 colloid system.
O
.r( .r(
P
- 0
2
4
68
8 1 0 1 2 18 4
PH Figure 5. Numerically interpolated mobility-pH profiles for surfactant-free carboxyl latex C984 from the best-fit fingerprint At each pX data of Figure 4 at pX 2 (O),pX 3 (A),and pX 4 (0). the isoelectric point was pH 2.2.
small increase in size as the conductivity of the system decreases. In Figure 3 we show the effect of a few bad data points on the analysis. Two bad data points near pH 10, pX 3 result in a false maximum. A similar false maximum occurs at pH 5.5, pX 3 where one irreproducible data point gave rise to a maximum. The hydrodynamic surface and fingerprint of Figure 3 become the same as those of Figure 2 when the bad data are rejected. Electrophoretic Mobility. Figures 4-9 give electrophoretic mobility data taken from the Ph.D. thesis of S.-j.S.14 Figure 4 shows the electrophoretic surface and fingerprint of carboxyl latex C984. Two features of special interest are the mobility maximum at pH 5, pX 2 and the small region of positive mobility approached at high acid and high electrolyte concentration. The theoretical analysis of this latex system has been discussed in consider(14) Shiau, s.-j. PbD. Thesis, University of Masaachusetta, 1989.
PH
Figure 7. Electrophoretic surface (a) and corresponding electrophoretic fingerprint (b) for surfactant-free polystyrene latex S1050 for the aqueous HC1-KOH-KC1 colloid system.
able detail in earlier work4 and will be briefly discussed below. However, in the previoustheoretical consideration, the small region of positive mobility was not considered since the models used did not provide for a positive mobility. In Figure 5 we show numerically interpolated mobilitypH profiles for latex C984 obtained by computer from the best-fit fingerprint data of Figure 4. The self-consistency of the results supports the measurement of a small positive mobility at low pH and high pX. Figure 6 shows the electrophoretic surface and fingerprint of sulfate latex S686. The contour line pattern is clearly different from that of the carboxyl latex of Figures 4 and 5. The computer analysis shows a maximum in mobility at pH 5,pX 3 and a second, but smaller maximum at pH 9, pX 2.5.
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2074 Langmuir, Vol. 9,No. 8,1993
Table 11. Expansion of Surfactant-Free Sulfate Polystyrene Latex 9489 on Ageing
h
PH 4.23 5.62 6.58 11.37 5.16 5.32 6.28 11.42 8.30 11.63
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8
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Figure 9. Numerically interpolated mobility-pH profiles for surfactant-free sulfate latexes 5686 ( 0 )and 51050 (0) at very dilute electrolyte, pX 1. Data were obtained by computer interpolation of the best-fit fingerprint results of Figures 6 and 7.
In Figure 7 we show the electrophoretic surface and fingerprint of a larger sulfate latex 51050. The patterns, in either the surface or fingerprint representation, look strongly similar to Figure 6 in overall impact but seem to suggest differences in detail in different regions of pH-pX space. We show a comparison of the characterization of sulfate latexes of different size in a quantitative way by comparing numericallyinterpolated mobility-pH profiles for latexes 5686 and S1050 in Figures 8 and 9. Figure 8 shows a mobility-pH cut at intermediate electrolyte of constant pX 3. Small differences are shown which spread over a wide pH from 4 to 10. Figure 9 shows a mobility-pH cut at very dilute electrolyte of constant pX 1. There is no discernable difference between the two latexes, giving a common curve extending from pH 4 to pH 8.
Discussion Hydrodynamic Size. As we consider the representations of hydrodynamic size shown in Figures 1-3, we see four main points which may be summarized as follows: (1) The fingerprint is characteristic of a particular colloid system. (2) The carboxyl pattern differs from the sulfate pattern. (3) The in situ latex size size increases a t low electrolyte concentration. (4)The analysis is extremely sensitive to the measurements. Point 4 is the easiest to discuss because it is readily demonstrated by a comparison of Figures 2 and 3. A few irreproducible data points show striking differences in the patterns. Herein lie both a strength and a weakness in the methodology. The strength lies in the fact that it is easy to spot unusual data so that repeat measurements can be made to assess the reliability of the data. The
PA 1.60 0.36 1.09 3.28 2.17 2.20 2.15 3.33 3.87 4.00
dh (nm) initial after 12 dh (m) weeks 525 566 532 515 530 540 526 515 524 512 511 521 556 523 538 517 537 509 552 532
7% variation after 12 weeks 7.8 3.3 1.9 2.1 2.3 2.0 4.4 4.1 5.5 3.8
% increase in the mean particle volume 25.2 10.2 5.6 6.6 7.1 5.9 20.2 12.6 17.5 11.8
weakness lies in the possibility that much of the characteristic ripple structure in the patterns may be a consequence of experimentaluncertainties in the measurements. We discuss this point further below. Points 1-3 rest heavily on the reliability and selfconsistency of the data which we consider below. However, if the data are accepted as generally reliable, then point 3, the increase in latex size at low electrolyteconcentration, is a smallbut significant effect. We have noticed the same trend with every latex we have examined, and it appears that all polystyrene latexes will show a small increase in the in situ measured size as the conductivity approaches that of system-limited electrolyte, i.e., very nearly distilled water. We have summarized the properties of the latexes as given by the manufacturer in Table I along with a value for the hydrodynamicdiameter taken from the fingerprint at middomain pH 7, pX 2 and a limiting value for the hydrodynamic diameter a t very low ph. The in situ middomain size for the two latexes we have fingerprinted is significantly larger than the manufacturer's size which wm based on transmission electron microscopy measurement of 600 particles. This result is not new, but it is not inconsistent with widely dispersed literature on the subject. The new result is that the limiting in situ hydrodynamic size approached at very low pX was larger than the middomain size. Finally, over the entire pH-pX domain studied, the in situ hydrodynamic size was significantly larger than the manufacturer's TEM size for both latexes. Neither result was the focus of our research, but it is clear that the fingerprinting approach gives a clear, quantitative, and self-consistent characterization of the in situ colloidal state of the system. Time Dependence of Hydrodynamic Size. For one latex, the sulfate polystyrene latex S489,we have carried out a study of the time dependenceof in situ hydrodynamic size by numerical interpolation of a number of points in the pH-pX domain of the best-fit hydrodynamic fingerprint taken soon after preparation and after 12 weeks in a sealed container. The results of the analysis are given in Table 11. Severalpoints are clear from the data of Table 11: (1)All of the data are larger than the manufacturer's TEM size of 489 f 11 nm which is consistent with general knowledge. (2) All of the domain points selected showed a significant increase in size after 12-week equilibration. This is new. (3)The largest size noted, 566 nm, was 15.7% larger than the manufacturer's TEM size of 489 nm. (4) If the ripple structure in the hydrodynamic fingerprints were a consequence of random experimental error, then we would have observed random changes in the size. Clearly, there is a systematic increase in size upon ageing that is larger than the random uncertainty in size associated with a single measurement. We conclude therefore that some of the ripple structure in size in the pH-pX domain
Characterization of Polystyrene Latexes may be due to real differences in the state of equilibration of the samples. The increase in size does not appear to be due to doublets since doublets would be expected to give a larger increase in effective size. However, an averagingeffect over a small number of doublets cannot be ruled out. There are four points that support the idea of a real increase in size suggested by our data: (1)Doublets arising from the addition of electrolyte would cause an increase in hydrodynamic size with increasing pX. The data show exactly the opposite trend. (2) The expansion shown on ageing in Table I1 is greatest at lower electrolyte. (3) Doublet and aggregate formation is very obvious as shown in the off-scale regions of Figures 1 and 2 and the bad points in Figure 3. (4) Investigation of particle pairing in liquids has been investigated by Cooper et al. who found no evidence for the existence of pairs in suspensions of 343-nm polystyrene latex. They found only 0.3 % of the particles paired in highly diluted tap water for comparison. Electrophoretic Mobility Measurements. The measurements of hydrodynamic size and electrophoretic mobility were carried out independently by different researchers on different equipment at different times with different objectives. The focus was on exploring and understanding the new methodologyof fingerprinting. The work on electrophoretic finger~rintingl~ came first and inspired the consideration of hydrodynamic fingerprinting.3 Indeed, at that time, the hydrodynamic size was not considered as a function of pH and ph. It is clear that a desirable future work would be the exploration of the time dependence of the hydrodynamic and electrophoretic fingerprints on the same systems. As guidance for such as investigation, we report below our considerations of the electrophoretic fingerprinting data that have been obtained on model carboxyl and sulfate polystyrene latexes. The electrophoretic mobility of carboxyl latex C984 shown in Figure 4 shows a single maximum in the pH-pX domain centered at pH 5, pX 2. I t is a maximum along both the pH and ph coordinate, giving a dome-shaped region. In earlier work4we have used the single acid site dissociation model of Healy and White,lSJGthe GouyChapman exponential potential profiie for the double layer, and the electrophoretic theory (including relaxation) of O’Brien and White15J7to explore theoretical explanations of the fingerprint data of Figure 4. The principal results of that work may be summarized as follows: (1)A constant surface site density of 5 X 1013sites/cm2 (2.00 nm2/site) was employed. (2) The carboxyl pKa OF 3.5 was used. (3) A latex diameter of 980 nm was assumed (IDC, TEM value). (4) A two-step expansion of the shear plane was required to explain the electrophoretic maximum: (a) an expansion of about 1.5 nm from pX 5 to pX 3 and (b) a much sharper expansion of about 7 nm from pX 3 to pX 1. At this point we must note that we have used three different conventions in defining pX. In our earliest investigationsG9 we defined pX as the negative log of the conductivity (S/m) following the SI system. In the theoretical exploration4we defined pX as the logarithm of the conductivity (S/m). In the present work we have defined pX as the logarithm of the conductivity (pS/cm). In every case the scale is logarithmic, but the present convention sets the zero close to the conductivity of C02(16) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981. (16) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci., 1978, 9, 303. (17) OBrien, R. W.; White, L. R. J . Chem. SOC.,Faraday Tram.2 1978, 74, 1607.
Langmuir, Vol. 9, No. 8,1993 2075 equilibrated pure water. Increasingly positive simple whole numbers correspond to increasing conductivity. The advantage of the present scale is that in most of the foreseeable applications we avoid the thought process of ascale going through zero with a change of sign. We stress that pX is a measurable and characteristic variable that is useful in characterizing the conductivity (electrolyte content) of the medium suspending the colloid. In a general investigation of an unknown colloidal system, one has no knowledge of the concentration and nature of the electrolyte content of the medium so that the ionic strength is unknown. Accordingly, pX is a convenient and quantitative characteristic variable to measure and use to observe changes in the electrical state of the system. Since the colloid literature and indeed much of the physical chemistry of electrolyte solutions have historically used the ionic strengthI to characterize the concentration of a known added supporting electrolyte, we point out the simple relationship (shown in previous work4 to hold for a 1:l electrolyte where the cation and anion mobilities are equal): pX = PI+ constant (1) where pX is the positive logarithm of the conductivity. Clearly pX gives a more accessible characterization of the electrical state of the medium than either I or PI. Moreover, with the increasing availability of specific ion electrodes, the prospect of measuring the separate contributions to pX would argue for increasing use of direct measurements of pX wherever possible. We now return to a further consideration of point 4 above from the previous work? i.e., a two-step expansion in the shear plane comprising 1.5 nm over a two-decade decrease in X and 7 nm more over a further two-decade decrease in A. This order of expansion is very close to the in situ expansions noted for latexes C401 and S489 in Table I. It is regrettable that we did not have direct measurements of the in situ hydrodynamic diameters of the several latexes on which we report electrophoresis measurements. At that time we were not aware of the discrepancy of the manufacturer’s TEM size and the in situ hydrodynamic size, Nor were we aware of the possibility that the in situ hydrodynamic size could vary significantly over pH-ph space as shown in the fingerprints of Figures 1 and 2. From the foregoing discussion it is clear that some of the ripple structure in the best-fit hydrodynamic and electrophoretic fingerprints may be due to time-dependent and electrolyte-dependent shifts in the shear plane surrounding and defining the in situ colloidal particle size. In Figure 5, where we show mobility-pH profiles for carboxyl latex C984 obtained by numerical interpolation by computer (using SURFER) from the best-fit fingerprint of Figure 4, we note that the data show an unexpected isoelectric point a t pH 2.2. The curves for pX 2-4 all give an isoelectric point a t pH 2.2, and the respective slopes decrease in a regular fashion. We suggest that the small positive mobility observed below pH 2.2 is due to a positive charge acquired by hydrogen bonding of hydronium ions to the carbonyl of the undissociated carboxyl group. Clearly our data do not give a detailed mechanism for the attachment, but the positive mobility is strong evidence for the attachment of hydronium ions to the carboxyl polystyrene surface: (polystyrene)-C0,H-*.H30++ (polystyrene)-CO,H + H30+ The fingerprints for the sulfate polystyrene latexes shown in Figures 6 and 7 are clearly different from that
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2076 Langmuir, Vol. 9, No.8,1993
Theoretical investigations of such effects are beyond the of the carboxyl polystyrene latex shown in Figure 4. scope of the present work. The fingerprinting approach Neither of the sulfate fingerprints show an isoelectric point gives a good representation of the experimental data which or a positive mobility. It is not unreasonable that a positive could be used in further experimental and theoretical mobility might occur with a weak acid such as the carboxyl investigations of the possible existence of such artifacts. latex discussed above and that a strong acid latex would show only negative mobility under the same conditions. Conclusions Because of the time dependence of hydrodynamic size found for the sulfate latex 5489 given in Table 11, there We have presented the new experimental approach of may have been time-dependent effects in the data for the particle size measurement by hydrodynamic fingerprintelectrophoretic fingerprints shown in Figures 6and 7.Thus, ing. The hydrodynamic fingerprint is the isothermal the differences in the mobility-pH profiles for Figure 8 isohydrodynamic size contour diagram giving size as a may have, in part, been due to time-dependent effects. function of pH and pX (the base 10 logarithm of the The electrophoretic work (by S.-j.S.) was carried out before conductivity (pS/cm)). We have compared hydrodynamic the hydrodynamic work (by J.H.P.), and we were unaware fingerprints of surfactant-free, commercially available, of the possibility of time-dependent effects at that time. model latexes with electrophoretic fingerprints on similar The low electrolyte mobility-pH profiles of Figure 9 systems. show that both sulfate latexes have the same surface The principal contributions of the work are the folelectrochemistry. There is no evidence of any difference lowing: (1) The hydrodynamic fingerprint is one chararising from either particle size or time-dependent effects acteristic of the colloidalsystem. (2)The polystyrene latex at the very low electrolyte concentration. This suggests size is larger than the manufacturer’s TEM size which is that the low pX mobility-pH profile obtained by computer consistent with current knowledge, but the new finding is interpolation at constant ph may be a characteristic that the in situ size increases as pX decreases. (3) The property of a particular surface chemistry. fingerprint pattern is a sensitive function of the experiComparison with Other Work. The fingerprinting mental data. The function of hydrodynamic size in the approach is original with our laboratory so that it is not pH-pX domain is not a flat surface which would be the possible to make a full comparison with independent case if the manufacturer’s TEM sizes were universal measurements from other laboratories. constants. Bad data are easily identified. (4) The We have found no reports of independent measurements polystyrene latex in situ hydrodynamic size was found to of electrophoresis on the latexes studied. be significantlytime dependent, showing a general increase We have found several reports of measurements of with time. (5) The use of pX is advantageous over the particle size on IDC latexes, but nearly all of the reports widely used ionic strength especially because (a) pX is an gave no indication of the type or batch number of the in situ dynamic and characteristic, directly measurable latex used. There was no mention of a change in size with variable of the medium whereas ionic strength is a static electrolyte content of the medium, so we are the first to concentration variable that describes only the added and report the dependence of hydrodynamic size on pX. known electrolyte, (b) a complete knowledge of the The single exception is a paper by Berg et al.18 who electrolyte content is necessary in order to calculate the made measurements of the hydrodynamic size on a sulfate ionic strength whereas the conductivity is an experimental latex (0.486 f 1.0% pm manufacturer’s TEM diameter) variable that may be measured for any system whether of which we identify as batch 2-94-35from the manufacturer’s known or unknown electrolyte, and (c) the conductivity literature. This was apparently an earlier batch than our change may be monitored in real time by simple electrodes. IDC sulfate latex 2-94-35.188which is listed by the The prospect of employing specific ion electrodes is an manufacturer as having a TEM diameter of 0.489 f 2.2% attractive one for future applications. (6)The expansion (f0.011)pm. They also measured an IDC carboxyl latex of the hydrodynamic size with decreasing pX observed in with a TEM size of 0.401 f 1.85% pm which appears to the present work is in the same sense and very close to the be the same as the IDC latex 10-87-17, labeled C401 in our same numerical profile predicted in earlier theoretical work. Their measurements were carried out with a studies of electrophoretic fingerprinting. (7) For the Brookhaven Model BI-2030 at 24 “C and a fixed angle of carboxylic latex, a small positive mobility was noted at 90°. Thus, their instrument and software were essentially low pH which was attributed to charge reversal arising the same as ours. Their pH was adjusted to 7 “to ensure from hydrogen-bonded hydronium ions. (8)As in earlier total ionization of the carboxylgroups”. Their conductivity work, the electrophoretic fingerprint is also a characteristic was not stated. Their in situ hydrodynamic size was not of the colloidal system. (9)At low electrolyte concentraexplicitly given, but from their Figure 1 we estimate the tion, the mobility-pH profile (obtained by computer radius at 0.229 pm, giving a diameter of 0.458 pm. This interpolation of the electrophoretic fingerprint at constant is almost identical with the size of 460 nm for low pX we pX) appears to be a characteristic property of a particular show in Figure 1 and report in Table I. surface chemistry. It is important to note that our PCS measurements of Finally, we emphasize a point of broad relevance to all hydrodynamic size were carried out at low mass fraction work in which polystyrene latex size is important: the in (5 X 10“) where we have assumed that the measurements situ hydrodynamic size is larger than the manufacturer’s represent the average size of a uniform system of low TEM size, and the in situ size depends significantly on polydispersity. However, we cannot rule out the subtle time (ages) and electrolyte content (as readily measured effect of undetected pX-dependent artifacts such as the using PA). presence of a small amount of doublets, a double-layer effect, particle-ordering arising at low electrolyte, e t c . l B ~ ~ ~ Acknowledgment. We would like to thank the Pen Kem Instrument Co. for technical support and use of the (18) Aksberg, R.; Einarson, M.; Berg. J.; Odbert, L. Langmuir 1991, System 3000. We would also like to thank the Brookhaven 7, 43-45. Instrument Co. for technical support and use of the BI-90. (19) Schumacher, G. A,; van de Ven, T. G. M. Langmuir 1991,7,2060-
2065. (20) Virden, J. W.; Berg, J. C. J. Colloid Interface Sci. 1992,149,528535.
~~~~~
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(21) Cooper, D. W., Batchelder, J. S.; Taubenblatt, M. A. J. Colloid Interface Sci. 1991, 144, 201-209.
