194
Anal. Chem. 1989, 61, 194-198
Dependence of Surface Tension on Composition of Binary Aqueous-Organic Solutions Kenneth A. Connors* and James L. Wright School of Pharmacy, University of Wisconsin, Madison, Wisconsin 53706
A simple equation is derived relating the surface tension to the composltlon of aqueous sdutlons of organic cosoivents over the entire composnbn range. The baslc asmnptions are that the organic component (component 2) exists in the surface phase in two states, free and bound (adsorbed), and that the number of binding sites for component 2 in the surface Is proportional to the number of water molecules (component 1) in the surface. The resulting equation is y = y, [l bx,/(1 ax,)b,(y, 7,). I t is shown how this equation can be linearized. Literature data on 15 systems were analyzed and were found to be well described. From the parameter a can be calculated the binding constant K , for binding of the organlc component to the surface, and for 11 of the systems log K 2 was well correlated with log P,, where P, Is the octanoi-water partition coefficient. This behavior shows that the hydrophoMctly of these solutes Is the malor controlling factor in their surface activity. Very hydrophilic organics appear to possess an additional mechanism for binding to the surface.
+
-
-
-
The surface tension of solutions is of interest for several reasons. Most fundamentally, this quantity contains information on the structure and energetics of the surface region. The surface tension also appears as an important quantity in cavity theories of molecular association (1-4) and as a measure of eluent strength in liquid chromatography (5). There is a considerable history of theoretical investigations into the dependence of surface tension on solution composition, for with a successful theory it should be possible to extract, from experimental data, useful information about the nature of the surface; moreover it is of practical value to be able to describe quantitatively the composition dependence of surface tension. We are concerned with binary solutions of completely miscible liquids. Many theoreticians have developed equations relating the surface tension of such solutions to the surface tensions of the pure liquids. The methods of thermodynamics and of statistical mechanics have both been used. The resulting equations may be roughly classified as those that are fairly simple functions, and thus are easily applied to experimental data, and those that are rather complicated functions, whose applicability is limited. Among the complicated results are those of Siskova (6) and Randles and Behr (7). Many of the simple functions have the form y = y1
+ RT -In
ais
-
Al
alB
RT A2
a2B
y=y2+-ln-
degrees of generality, as exemplified by the work of Schuchowitzky (8),Belton and Evans (9), Guggenheim (IO), Hoar and Melford ( I I ) , Semenchenko (12),Feinerman (13),Sprow and Prausnitz (14),and Goldsack and Sarvas (15). Shereshefsky (16) and Eberhart (17)obtained equations based on the assumption that the surface tension is an average weighted by the surface concentrations, i.e. = 71x1s + 72x2s
This assumption is also used in the present paper, but with different results. Despite this abundance of published theoretical results, surface tension data on the very interesting binary solutions of water and organic cosolvents are seldom correlated or interpreted with the aid of these equations, probably because most of them are applicableprimarily to simple systems, such as mixtures of two organic liquids that do not show marked deviations from ideality. Aqueous solutions, however, are typically very nonideal, their surface tensions revealing high surface excesses of the organic component. In the present paper we develop a simple equation for the surface tension of binary aqueous-organic solutions over the entire composition range. We adopt a chemical model involving binding to the surface, so that this approach is related to the adsorption theory of Everett (18).
THEORY Derivation. We consider a solution of components 1 and 2, identifying solvent 1as water and 2 as the organic cosolvent. We adopt a physical picture in which the surface (S) region is a distinct phase (though not a homogeneous one); the other phase is of course the bulk (B)phase. All concentrations are expressed as mole fractions ( x ) . The assumption is made that the total concentration of component 2 in the surface phase (which is known to be enriched in 2 relative to the bulk) is the sum of concentrations of two states of component 2; one of these states is “free” and the other is “bound” (adsorbed). That is, the surface phase is postulated to be nonideal, and a chemical model of the nonideal behavior is adopted. Let n represent number of moles, with superscripts t, f, and b denoting “total”, “free”, and “bound”, respectively, and subscripts 1, 2, S, and B the component and phase. Then nSt =
nlSt + n2st
Dividing each equation by nst
a25
where y, yl,and y2 are the surface tensions of the solution, pure component 1, and pure component 2, respectively, Al and Az are partial molar areas, and ais, a2s,a l B , and a 2are ~ activities of components 1 and 2 in the surface (S) and bulk (B) phases. Such equations have been derived in various
where a primed quantity represents a total or apparent concentration. Equation 2 is the first basic assumption of the model. We adopt a conventional binding isotherm (Langmuir adsorption) to describe binding of component 2 to the surface, writing
0003-2700/89/0361-0194$01.50/00 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 3, FEBRUARY 1, 1989
(3) where K2 is the binding site constant and F is the fraction of sites on the surface that are occupied by component 2. We require a relationship between F and x2sb. Let Nt be the total number of binding sites and N the number of sites occupied by molecules of 2. Then, if each site can accommodate one molecule of 2, N = nSb, or F = N/Nt = nsb/Nt. The second basic assumption of this model is that the number of binding sites in the’surface is proportional to the number of molecules of component 1 (water) in the surface. We therefore write Nt = dxlS’. (If components 1 and 2 had identical sizes and shapes, d would be equal to nst, but this is not generally expected.) Then, since n2sb= n:xZSb, we get F = ~ s ~ x ~ ~or ~ / ~ x ~ ~ ’ , x2Sb
= kFx1s
(4)
where k = d/nst, and the prime superscript on xls is dropped because there is only one state of component 1. Combining eq 2, 3, and 4 gives an expression for x2s’
PI=
.--
P2x2B
195
(13)
x2B
These special cases follow from eq 13: (i) when P1= 1,P2= 1; (ii) when P1= 0, P2= 1/xm; (iii) when P2= 0, P1= l/xlB. There are three corresponding special cases of eq 12. Case i has already been described, since when Pl = 1,K 2 is zero, and eq 12 is obtained. Case ii means that K = m, with a = 1and b = 0; since P2= 1/X2B, we find that y = y1 when X2B = 0, but y = y2 when X2B # 0. The surface is completely organic except when no organic component is present in the system. This may be interpreted as an “organic phase transition”. The other limiting case of an “aqueous phase transition” arises when P2= 0; then y = yl,at all compositions except pure component 2. These limiting cases are not real, but they suggest limits for real systems. The partition coefficient P2is expected to have the value unity, because any process tending to make P2different from unity has been accounted for in the model (i.e., the binding phenomenon). This is a reasonable assumption, but it clearly is also a possible source of discrepancy, since nonideal behavior other than that explicitly accounted for may be present. Nevertheless, in the sequel we shall set P2= 1. For convenience we write x1 and x 2 for X1B and xzB, so the operating form of eq 11 is
Defining “partition coefficients” P1 = X l S / X l B and P2 = X22/%2B, and using X1B + X2B = 1, eq 5 is transformed to
APPLICATION TO DATA Evaluation of the Parameters. Define the “reduced surface tension” by eq 15
where
a=
K2P2 1 + K2P2
Y.
-Y
(7) and further define the quantity R by eq 16
(8) so b / a = k P l / P 2 . In the third basic assumption of the model, the surface tension of the solution, y, is written as an average of the surface tensions of the pure components, y1 and y2,weighted by the total surface concentrations of the components which may be written Equation 10 includes the nonideality of the surface phase through the inclusion of the total surface concentration, but it makes the assumption that the two states of organic component (free and bound) exert the same effect on the surface tension. Hansen and Sogar (19) have criticized eq 9, and its use is justified by the results. Combining eq 6 and 10 gives the desired relationship
Properties of the Equation. We note that when x2B = 0, y = yl,and when X2B = 1, y = y2 (since P2= 1 when Z2B = 1). Moreover, in an ideal system K2 = 0, P2= 1, so a = 0, b = 0, and eq 11 becomes = Y l X l B + 72x2B (12) From the definitions of Pl and P2we obtain P l X l B + P2X2B = 1 or
=
Yr~d/~2
(16)
where x2 is the mole fraction of component 2 in the bulk phase. [Note, by comparison of eq 10, 15, and 16, that y r d is an estimate of the concentration of component 2 in the surface phase and R is an apparent partition coefficient.] Equation 14 is the equation of a rectangular hyperbola, which can be rearranged into three linear plotting forms (20); in the present work eq 17 was used, because it is most sensitive to deviations from linearity. Adherence to eq 14 can be assessed by the
linearity of a plot according to eq 17, and the parameters a and b can be evaluated from the slope and intercept of the plot. An alternative approach is to carry out a nonlinear regression analysis of the data according to eq 14. From eq 7 and the assumption P2= 1we can estimate the binding constant K2, and since P1 = 1 when P2 = 1, k is obtained as the ratio b / a .
a K2 = 1-a
Results. Surface tension data on binary aqueous-organic solutions were taken from many literature sources (5,21-31). Plots according to eq 17 usually showed good linearity; for example, the correlation coefficient (r)for the methanol system is 0.9997 and that for the 2-methyl-2-propanol system is 0.99997. Some systems did not behave so well: r = 0.997 for acetonitrile, with definite curvature, and r = 0.966 for dimethyl sulfoxide (DMSO),with curvature in the opposite sense from
106
ANALYTICAL CHEMISTRY, VOL. 61, NO. 3, FEBRUARY 1, 1989
Table I. Surface Tension Parameters of Binary Aqueous-Organic Mixtures at 25 no.
organic cosolvent
1
methanol ethanol 2-propanol 1-propanol 2-methyl-2-propanol acetic acid propionic acid acetone acetonitrile dioxane tetrahydrofuran glycerol dimethyl sulfoxide formamide ethylene glycol
2 3
4 5 6 7 8
9 10 11
12 13 14
15
data source 5 21
5 22
5 23 24 26, 27 5 29 5 25 5, 28 30, 31 30, 31
OCnvb
a
b
0.899 (0.002) 0.963 (0.001) 0.984 (0.001) 0.990 (0.001) 0.992 (0.001) 0.967 (0.001) 0.987 (0,001) 0.978 (0.002) 0.956 (0.004) 0.951 (0.002) 0.984 (0.001) 0.958 (0.003) 0.869 (0.015) 0.698 (0.039) 0.793 (0.019)
0.777 (0.00s) 0.897 (0.010) 0.970 (0.008) 0.999 (0.023) 0.980 (0.008) 0.715 (0.002) 0.883 (0.005) 0.842 (0.014) 0.962 (0.023) 0.914 (0.006) 0.964 (0.009) 0.448 (0.007) 0.603 (0.022) 0.780 (0.047) 0.825 (0.028)
KZ
k
n
SO
8.9 25.3 61.5 99
0.86 0.94 0.99 1.01 0.99 0.74 0.89 0.86 1.01 0.96 0.98 0.47 0.69
13
0.3 0.5 0.6 1.6 0.8 0.4 0.3 1.0
124
29.3 75.9 44.5 21.7
19.4 61.5 22.8 6.6 2.3 3.8
17
13 11
13 16 9 17
13 10 13
1.2
0.2 0.6
11
0.1
1.12
23 18
0.8 0.4
1.04
22
0.6
Calculated from eq 14 by nonlinear regression. Quantities in parentheses are standard errors of the estimates. K2is calculated from a by eq 18, and k = b/a. bThe formamide and ethylene glycol data are at 20 "C;these data were read from published graphs. 'Standard deviation of the experimental points about the regression line, in dyn/cm; the degrees of freedom were taken to be n - 4, where n is the number of Doints. including the two Dure solvents.
1
1.0
\
07
;I
d2
d3
d.4
d.5
d.6
d7
d8
d9
'1
XI
0
Figure 3. Plot of eq 17 for the acetonltrlle-water system, data from ref 5. 0
01
02
03
05
04
06
07
08
09
I
XI
F@re 1. plot of eq 17 for the 2-methyC2propanoi-water system, data from ref 5.
XI
0
0
01
02
03
04
05
06
07
08
09
I
Figwe 4. Plot of eq 17 for the dbnethylsulfoxide-water system, data from ref 5 (open circles) and ref 28 (filled circles).
XI
Plot of eq 17 for the acetone-water system, data from ref 26 (open circles) and ref 27 (filled circles). Figure 2.
that seen for acetonitrile. Figure 1 shows the plot of eq 17 for 2-methyl-2-propanol. Figure 2, for the acetone system, is revealing in that it shows that interlaboratory variation can be significant. Figure 3 is the plot for the acetonitrile system, and Figure 4 shows the DMSO system, with data of two laboratories. It is evident that large systematic errors may exist and that curvature in these plots may be caused by such experimental errors as well as by a possible nonvalidity of the model equation. The uncertainties in parameter estimates tend to be larger when data from more than one laboratory are combined.
Table I lists the systems that were evaluated, with the parameters a and b, and the derived quantities K2and k. The parameters in Table I were obtained by unweighted nonlinear regression based directly on eq 14. Quasi-Newton minimization was used with the SYSTAT statisticalpackage, run on a Macintosh I1 computer. Initial parameter estimates for the nonlinear regression were obtained by the linear plotting method. Commonly about 10 iterations were required. Figure 5 illustrates the agreement between experimental values of the surface tension and values calculated with eq 14 and parameters in Table I. It is evident that eq 14 provides a reasonable description of the data, as is shown by the statistical measures in Table I. It is remarkable that, for many systems, the parameters remain essentially constant over the
ANALYTICAL CHEMISTRY, VOL. 61, NO. 3, FEBRUARY 1, 1989
197
t
Y
01 -3
I
0
0.1
0.2
0.3 0.4
0.5
0.6
0.7
0.8
0.9
I
I
xz
Flgure 5. Surface tension of 2-propanol-water mixtures as a function of mole fraction of 2-propanol. The line was drawn with eq 14 and
the parameters in Table I. Table 11. Comparative Performance of Several Surface Tension Equations (2-Propanol-Water System)
O n
equation
sum of squares of residuals”
this work, eq 14 Belton and Evans (9) Guggenheim (10) Eberhart (17) Shereshefsky (16) Feinerman (13) = 13.
3.68 (dyn/cm)* 166.8 166.8 4.65
10639 112.7
entire composition range from pure water to pure organic. In those systems exhibiting curvature in the plot of eq 17 it is possible that the parameters are subject to some composition dependence, but without a theoretical functional dependence for guidance, this possibility was not pursued, and it was judged best to treat a and b as constants. Comparison with Other Equations. As noted in the introduction, several other equations have been published that describe the surface tension of binary solutions. As a means of assessing the comparative effectiveness of eq 14, we have carried out regression analyses of a common set of data with several of these equations. The 2-propanol system was selected as the test system, and Table I1 gives the results. Clearly eq 14 is superior to the other equations that were examined, though the one-parameter equation of Eberhart (17)gives a surprisingly satisfactory result. This is accounted for by rearranging Eberhart’s equation into the form of eq 14, when it is found that Eberhart’s equation is a special case of eq 14, namely the case a = b. This is why Eberhart’s equation performs fairly well on the 2-propanol system (see Table I). Significance of the Parameters. The quantity K 2 was defined, in the derivation of eq 14, to be a binding constant for the association of the organic cosolvent (component2) with the surface region. If this is a valid interpretation, K2 should have some chemical meaning. This possibility was explored by plotting log K 2 against log P,, where PWtis the partition coefficient for the organic compound between 1-octanol and water. [Partition coefficients were obtained from the collection of Leo et al. (32))except for the tetrahydrofuran value, which is from Funasaki et al. (33).] This plot is shown in Figure 6. Clearly there is a strong correlation ( r = 0.974, n = 11) between log K 2 and log Pd for most of the systems. The equation of this line is log K2 = 0.92 log Po&+ 1.69 (19) Since log P, is generally considered to be a measure of hydrophobicity, Figure 6 shows that the binding (adsorption)
I
I
-I
-2 log
0
I
POSf
Flgure 8. Plot of log K 2 (Table I) against log P,,
where P, is the 1-octanoi-water partition coefficient. The numbers Identify systems as listed in Table I. of organic cosolvents to the surface is quantitatively related to their hydrophobicity. Moreover, with eq 19 the parameter K 2 is readily predicted because octanol-water partition coefficients are widely available. We now consider further the meaning of K 2 and its relationship to hydrophobicity. In the derivation of eq 14 it was assumed that the surface contains a number of binding sites proportional to the number of water molecules in the surface and that organic molecules bind to these sites. This led to eq 14, which was found to be an appropriate description. We now find, in the form of Figure 6 and eq 19, that the binding constant K 2 increases as the hydrophobicity of the organic species increases. Thus it seems unlikely that the organic solute binds directly to the water molecules in the surface. One interpretation is that the actual binding site is the airwater interface, air being more hydrophobic than water, and the number of such binding sites is proportionalto the number of water molecules in the surface. A simpler interpretation is that, since the number of water molecules in the surface is directly proportional to the number in the bulk, the more hydrophobic the organic cosolvent, the greater its tendency to leave the bulk phase, and thus to congregate at the surface. This is a conventional interpretation in terms of the hydrophobic “squeezing-out”effect; the surface enrichment of the organic component is caused not by attractive forces at the surface but rather by repulsive forces in the bulk; these are manifested in K2,which we interpret as a measure of binding at the surface. It is obvious, in Figure 6, that several substances with very small PWtvalues do not fall on the correlation line, showing large positive deviations. That is, these very hydrophilic substances partition into the surface phase more extensively than their hydrophobicities lead us to expect This observation suggests that there may be a second effect operating, namely an attractive interaction between hydrophilic solutes and water in the surface, and that the observed surface concentration results from the summing of this hydrophilic attractive effect and the hydrophobic repulsive effect. Thus the relationship between log K z and log PWtpossesses a minimum at (approximately) log Pd = -1.6, and the minimum value of K 2 is about 1.6.
LITERATURE CITED (1) Slnanoglu, 0. Molecular Associetkms In 6/0@y; Pullman, 8.. Ed.; Academic Press: New York, 1968; p 427. (2) Hallcloglu. T.; Sinanoglu, 0. Ann. N . Y . Acad. Scl. 1989, 158, 308. (3) Sinanoglu, 0.; Fernandez, A. 6bphys. Chem. 1885, 2 1 , 157, 167. (4) Connors, K. A.; Sun, S. J. Am. Chem. Soc. 1971. 9 3 , 7239. (5) Cheong, W. J.; Carr, P. W. J. Liq. Chromatog. 1987, 10, 561. (6) Siskova, M. Collect. Czech. Chem. Commun. 1972, 3 7 , 327. (7) Randles, J. E. B.; Behr, B. J. €/echoanal. Chem. Interfaciel Chem. 1972, 35, 389. (8) Schuchowttzky, A. (Zhukhovitskii, A.) Acta Pfiysicochim. URSS 1844, 19, 176, 508.
198
Anal. Chem. 1989, 67, 198-201
(9) Belton, J. W.; Evans, M. G. Trans. Faraday SOC. 1945, 47, 1.
Guggenheim, E. A. Trans. Faraday Soc. 1945, 4 1 , 150. Hoar, T. P.; Melford, D. A. Trans. Faraday SOC. 1857. 5 3 , 315. Semenchenko, V. K. Russ. J . fhys. Chem. 1973, 4 7 , 1630. Felnerman, A. E. Col/oklpolYm. Sci. 1874, 252, 582. Sprow, F. B.; Prausnltz, J. M. Trans. Faraday SOC. 1966, 62, 1105. Goklsack, D. E.; Sarvas, C. D. Can. J. Chem. 1981, 59, 2968. Shereshefsky, J. L. J. Col&id Interface Sci. 1967, 2 4 , 317. Eberhart, J. G. J. fhys. Chem. 1966, 7 0 , 1183. Everett, D. H. Trans. Faraday SOC. 1964. 60, 1803. Hansen, R. S.; Sogar, L. J. Colbid Interface Sci. 1972, 40, 424. Connors, K. A. Binding Constants: the Measurement of Moleculer Complex Stabilly; Wliey-Interscience: New York, 1987; Chapter 2. (21) Dunlcz, B. L. U . S . Gov. Res. D e v . Rep. 1986, 41(7), 37. (22) Timmermans, J. The Physico-Chemicai Constants of Binary Systems in concentrated Solutions; Interscience: New York, 1954; Vol. 4. (23) Glagoleva, A. A. Russ. J . a n . Chem. 1947, 17, 1047.
(10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
(24) Drucker, K. Z . fhys. Chem. Abt. A 1805, 777A, 209. (25) Ernst. R. C.; Watkins, C. H.; Ruwe, H. H. J. fhys. Chem. 1936, 4 0 , 627. (26) Howard, K.; McAllister, R. A. AIChE J. 1957. 3 , 325. (27) Toryanik, A. I.; Pogrebnyak, V. G. J. Struct. Chem. 1976, 77, 464. (28) Tommila, E.; Pajunen, A. Suomen Kemistil. B 1968, 4 1 , 172. (29) Hovorka, F.;Schaefer, R.;Driesbach, D. J. Am. Chem. SOC. 1936, 58, 2264. (30) Dorfler, H. D., ColloMfolym. Sci. 1879, 2 5 7 , 882. (31) Grabowska, A. Pol. J . Chem. 1985, 5 9 , 573. (32) Leo, A.; Hansch, C.; Elkins. D. Chem. Rev. 1971, 7 1 , 525. (33) Funasaki, N.; Hada, S.; Neya, S. J. Phys. Chem. 1885, 8 9 , 3048.
RECEIVED for review August 4,1988. Accepted November 14, 1988.
Electrosynthesis of Chromatographic Stationary Phases Ge Hailin and G. G . Wallace* Chemistry Department, The University of Wollongong,P.O. Box 1144, Wollongong,New South Wales 2500, Australia
Polymerlc statlonary phases can be syntheslred on a range of substrates electrochemically. For example, polypyrrde has been coated on vitreous carbon partlcles from a KCI solutlon electrochemlcally and used as a chromatographlc packing. The chemlcal and physlcal properties of polypyrrole/Cl on vitreous carbon have been Investlgated. Chromatogrephlc behavlor, lncludlng Ion exchange and reversed phase, has been found. The new polymeric material and column preparation technlques based on electrochemlcal polymerlzatlon may make these statlonary phases more stable, selective, and reproduclble and more easily prepared.
capillary or open tubular type columns. In each case the substrate employed to enable polymer growth should be mechanically stable as well as chemically inert and electrochemically conductive. For example, commercial carbon particles such as graphite or crushed reticulated vitreous carbon (RVC) have proven useful. Alternatively, metal substrates such as Pt, Au, some metal oxides, or even stainless steel may be employed. In the course of this work the feasibility of employing these polymers as stationary phases for ion-exchange or reversedphase chromatography has been established.
EXPERIMENTAL SECTION Polymeric materials have been widely used as stationary phases for gas and liquid chromatography due to their chemical and physical stability (1-4). Columns containing such polymers are usually prepared either by physical adsorption on a suitable support (e.g. silica or Celite) or by packing polymeric beads. The selectivity of such columns can be modified by varying the nature of the coating or the beads by copolymerization or by bonding appropriate functional groups to the polymer matrix. In recent times, electrochemical synthesis has proven useful for the synthesis of various polymers. Polymers such as polythiophene (5-7), polyaniline (8,9), polyfuran (6),and polypyrrole (10-14) have been successfully prepared. These polymers have previously been employed as sensors (15),energy storage devices (16),and semiconductors (17). Polypyrrole has, in particular, been intensively studied in recent years. The properties of this material make it ideal for preliminary studies into the electrochemical synthesis and application of new polymeric stationary phases. In this work, it has been established that electrochemical synthesis enables the following: (i) rapid and easily achieved column preparation; (ii) easy modification of the stationary phase; (iii) the production of a chemically and physically stable polymer; (iv) reproducible column production; (v) accurate control of stationary phase thickness and composition. It has also been demonstrated that the stationary phase can be grown either as beads (chemically or electrochemically) as a solid support for packed columns or on column walls for 0003-2700/89/0361-0198$01,50/0
Reagents and Standard Solutions. All reagents were of analytical reagent (AR)grade unless otherwise stated. LR grade pyrrole (Fluka) was redistilled before use. The aqueous solution used for polymer growth was 0.5 M KC1 and 0.5 M pyrrole. In some instances 0.1 M sodium dodecyl sulfate (SDS) was used as the supporting electrolyte for growing polymer. Acetate buffer was prepared by dissolving sodium acetate in water and then adjusting pH with acetic acid or sodium hydroxide. Methanol (HPLC grade) was obtained from BDH Chemicals. Water was distilled and then purified by a Milli-Q water system (Millipore). Instrumentation. All preliminary electrochemid experiments were performed by using a Princeton Applied Research (PAR) Model 173potentiostat/gdvanostat in conjunction with a Model 179 digital coulometer and a Model 175 potential controller. HPLC experiments were conducted with a Waters Model M-6000 A chromatography pump in conjunction with a Model 450 variable wavelength detector. A cell for polymer plating on the particle substrates was designed in this laboratory and is described later. Polymer-coated particles (
