Anal. Chem. 1988, 6 0 , 2812-2818
2812
Rapid Characterization of Linear and Star-Branched Polymers by Concentration Gradient Detection Darrell 0.Hancock a n d Robert E. Synovec* Center for Process Analytical Chemistry, Department of Chemistry, BG-10, University of Washington, Seattle, Washington 98195
Linear polystyrenes tn methylene chloride (CH,CI,) were used to calibrate a flow-through devlce that measwes the concentratlon gradient, more specifically the refractlve Index gradient (RIG), of inlected solutions. The rapld and simple method measures M,, weight average mdecular weight. The detected RIG response Is proportional to l/u:, where u,' Is the volumetric variance of the eluting polymer concentration profiie. Cabations between VU,? and M,O." are of Injected sdute mass and imkpendent of the sdute-solvent refractlve Index semltlvlty factor dn/dC. If the number average molecular welght, M,, Is measured by a suitable technlque, changes In the potydkperslty parameter MJM, of less than 0.10 polydispersity unlts were effectlvely monitored. Star-branchedpolystyrenes In CH,& were analyzed with the device and compared with the calibration of the ilnear pdystyrenes. Resuits of the study with concentratlon gradient detection by the flow-through devlce were compared to slze-exclusionchromatography data. For a given molecular weight the star-branched polymers are scaled to the hear polymers by the shrlnkage factor g = (3f 2 ) / f 2 , where f equals the number of branches. I n a good solvent the hydrodynamic radius of a starpolymer Rh,, scaled to the hydrodynamlc radius of a Hnear polymer Rh,, by Rh,, = 9'"RhJ for a given weight average molecular welght. Thus, the correlatlons through the molecular hydrodynamlc radius are used to compensate for branching In the M, determination. Potential use of the flow-through concentratlon gradient detectlon technique for on-llne process monttorlng Is addressed.
-
INTRODUCTION Characterization of synthetic polymers is an important industrial and academic concern ( 1 ) . A wide variety of analytical techniques are employed, including ultracentrifugation, dynamic light scattering, size-exclusion chromatography (SEC), gas chromatography, viscometry, osmometry, end group analysis by nuclear magnetic resonance, mass spectrometry, and infrared and Raman spectroscopy (1-3). Many of these analytical techniques are very time-consuming and, in terms of process control applications, off-line techniques (4, 5 ) . For process analysis it is essential to develop rapid polymer characterization techniques that are on-line, in-line, or noninvasive (5). Polymer molecular weight and polydispersity often require continuous monitoring to achieve a consistent product. Ideally, one desires to measure the polymer molecular weight and polydispersity directly, such as in SEC coupled with both light scattering and concentration profile detection, typically by UV-vis absorbance and/or refractive index detection (6-8). Elaborate schemes using chromatographic data, through correlations to solute translational diffusion coefficients, have been developed for molecular weight determinations (9-12). Furthermore, field-flow fractionation (FFF) has been developed as a means to characterize polymer and particulate solutions, with subsequent 0003-2700/88/0360-2812$01.50/0
correlation to molecular or particle weight (13-15). In many ways, SEC and FFF are complementary due to differences in optimum molecular weight ranges of operation (2, 14). Polystyrenes are excellent synthetic polymers for new analytical methodology development and theoretical study. Recent interest in understanding the hydrodynamic and molecular characteristics of branched polymers relative to linear polymers has led to many interesting studies (16-24). In much of this theoretical work comparisons were made between polymer behavior in 0 solvents vis-a-vis good solventa (20,221. Much of the consistency between polymer theory and experimental observation pertains to polymer behavior in 0 solvents, while analytical applications must resort to good solvents in practice, such as in SEC (25)and hydrodynamic chromatography (26). Observing and characterizing differences in polymer branching offer an excellent test for any analytical method that claims applicability as a process monitor. In this work, both linear and star polystyrenes are examined by a rapid, simple, and unique flow method that employs refractive index gradient (RIG) detection, previously applied as a liquid chromatography detector (27). The RIG detector sensitivity is highly dependent upon the variance of the solute elution profile, as pointed out by Pawliszyn (28, 29). He demonstrated the capability of RIG detection in the selective mode, when coupled with modulated solute absorbance (30). Our flow method takes advantage of the hydrodynamic properties of dilute polymer solutions to sensitively distinguish polymers based upon translational diffusion differences, which influence the solute elution profile variance. A nonabsorbing wavelength for the polymers is used. In developing this flow method, coupled with RIG detection, one must consider all contributions to solute broadening, or dispersion, since both flow and spontaneous translational diffusion are coupled (31-35). We have designed a flow method with RIG detection that accuratelymeasures equivalent linear polystyrene size with similar precision as SEC, although no separation is required with the described method. Both linear and star polystyrene "standards" are employed to test the applicability of the method vis-a-vis SEC examination of the same standards. Utility of the described flow method with RIG detection as an on-line process monitor is addressed. Specifically, changing polymer polydispersity, through the polydispersityparameter MJM,,, is effectively monitored by the technique, with data for this capability reported. A correlation technique between the experimental data and M , is presented, that is independent of polymer concentration (injected mass) and independent of polymer refractive index (RI). EXPERIMENTAL SECTION The apparatus applied in this work is shown in Figure 1. The RIG detector was configured as in previous work (27). The 780-nm, 3-mW output from a single-mode diode laser (Physitec Corp., DL25, Norfolk, MA), with a 10-m coherence length (minimum), was intensity modulated at 20 kHz via a TTL waveform (Wavetek, Model 190,San Diego, CA) which was also synchronized to a lock-in amplifier (Princeton Applied Research 0 1988 American Chemical
Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, I988
2813
Table I. Physical Constants for Linear and Star Polystyrenes LI
WT
COMP
A,
C T
Ca---@
IL
Figure 1. Experimental apparatus for the flow method with RIG detection: DL, diode laser; MO, microscope obJecttve:WT, wave generator: LI, kck-in amplffler;PO, photodiode: COMP, computer or chart recorder: S, syringe pump: IL, Injection loop: T, tubing (0.007 In. 1.d. Teflon): C, flow cell; W, waste.
Corp., Model 5204, Princeton, NJ). The modulated diode laser output was focused at a focal length of 60 cm to a spot size of 200 pm at a z-configurationcell (made in-house) via a microscope objective, f 16.85, which was designed for the diode laser system. Previously, we have optimized this apparatus to achieve excellent capabilities in RIG detection (27). The flow cell, as described previously ( 2 3 ,had a 1-cm bore length with a 800 pm i.d., producing a volume of 5.0 pL. After the diode laser beam passed through the flow cell, it was imaged onto a photodiode (Hamamatau, S1723-05,Hamamatau City, Japan) having a 1cm x 1cm active surface. The voltage output from the photodiodewas sent to the lock-in amplifier to obtain the in-phase, and subsequently demodulated analytical signal, synchronized by the waveform generator. The analytical signal was sent to either a personal computer (IBM Corp., IBM-XT, Armonk, NY)via a laboratory interface board (MetraByte, DASH-16, Taunton, MA), or a chart Austin, TX) or simulrecorder (Houston Instruments, D-5000, taneously to both devices. In contrast to previous work in which SEC was demonstrated with RIG detection (27), the sample was introduced to the RIG detector flow cell by 85 cm of 0.007 in. i.d. Teflon tubing (20 pL), instead of a chromatographycolumn. For these studiea, methylene chloride, CH2C12,was used as the solvent and was delivered by a syringe pump (ISCO, LC-2600, Lincoln, NE) through an injection valve (Rheodyne, Model 7125, Cotati, CA) fitted with a 4.0-pL injection loop for subsequent sample introduction into the tubing prior to RIG detection. A volumetric flow rate of 107 pL/min was used, except where noted otherwise in the text. Under the experimental conditions, calculations demonstrate that injection of a “plug” of dilute polymer, i.e., pseudo-delta function, will arrive at the flow cell entrance (Figure2, ref 27)with negligible dispersion, or band broadening, relative to the ensuing diffusion upon careful expansion into the flow cell (31,32,36). Note that the flow cell diameter (800 pm) is 4.5 times that of the introduction tubing (178pm). Thus, the spontaneous expansion of the solute profile as it enters the flow cell, which is governed by hydrodynamic behavior, dominates over all other broadeningmechanisms. This broadening effect is dependent upon the translational diffusion properties of the solute in the solvent. The net result is to encode solute size properties into the detected solute concentration profile, which is sensitively monitored by RIG detedion. Note that the solute profile expands into the flow cell under ordered-flow or nonturbulent conditions at the flow rate used. Thus,the system is not functioning as a well-stirred reactor but, rather, is diffusion and convection controlled. The primary evidence for these conclusions is 3-fold. First, observation of the RIG effect via optical detection requires ordered flow such that the RIG of the effluent entering the flow cell is preserved during optical probing (27-30). Second,if the solute concentration profile entering the flow cell is Gaussian, the observed RIG signal with our device is appropriately the derivative of a Gaussian or nearly so, both for high-performance liquid chromatography (HPLC) (27) and with the flow method presented here. Third, the vol-
polystyrene desigcategory nation linear linear linear linear linear linear linear Star
star star
L1 L2 L3 L4 L5 L6 L7
Mw,O gmol-1
S2
S3
852800
s1
E$
3 250 1.05 9 000 1.04
34 500 68000 170000 500000 1130000 90 200 367300
Mn, branches,“ g mol-’
-8
2 2 2 2 2 2 2 12
-8 -8
6 6
1.05 1.06 1.04 1.08 1.06
ge
-f -f -f -f -f -f -I
LOO0 1.000 1.000 1.000 1.000
7000 59 200 116700
0.236 0.444 0.444
1.OOO
1.OOO
Weight average molecular weight, M,, quoted by manufacturer. Polydispersity, Mw/M,, quoted by manufacturer. Nominal number of branches quoted by manufacturer, defined as 2 for a linear polymer. dNumber average molecular weight, M,, of branches quoted by manufacturer. e Shrinking factor calculated with f using eq 14. f M , of branches not defined for linear polystyrenes. #Overall polydispersity of star polystyrenes was not quoted by manufacturer. umetric variance, C T ~of, the detected RIG signals is observed to be dependent upon solute molecular weight. The detection mechanism depends upon the solute concentration gradient as a function of distance, dC/dr, within the probe beam cross section (29). Recent calculations suggest that, via expansion, dC/dx is magnified within the flow cell (37),so the transit time through the flow cell sufficiently affects dC/& due to solute diffusional properties. The transit time through the flow cell is only a few seconds depending upon volumetric flow rate. Polystyrene standards were obtained from outside sources for this work. The linear polystyrenes were identical with those examined earlier (25)and were considered quite reliable (Polymer Laboratories, Amherst, MA). Three star polystyrenes were examined (Polysciences,Inc., Warrington, PA). Although the star polystyrenes were “standards” with quoted weight average molecular weights and nominal number of branches, our studies will show that each ”standard” is more appropriately considered a mixture. Salient physical data and labeling of both the linear and star polystyrenes are listed in Table I. Essentially, the linear polystyrenes are applied as calibranta for the flow method with RIG detection (Figure 1). The star polystyrenes act as a good test of the analytical method. In order to compare the results of the studies with the apparatus shown in Figure 1, SEC was employed to make comparisons between the linear and star polystyrenes. The results of both analytical methods were then compared. The SEC system was similar to that applied in previous work (25). The SEC system consisted of the same syringe pump as in Figure 1, and also the same injection loop. The SEC column was a 250 X 4.6 mm Macrosphere, 300 8, pore, 5 pm, C8 (Alltech, Deerfield, IL) connected to a W-vis absorbancedetedor (ISCO Model V4,Lincoln, NE), with a 5-mm path-length cell, operated at 254 nm. The output of the absorbance detector was sent to a chart recorder, and the retention times of all eluting peaks were measured and converted to retention volumes. SEC data were collected until the precision of peak retention volume was better than 1.0%.
RESULTS AND DISCUSSION Calibration of RIG Detection System. Both linear and star-polystyrenes were analyzed by the flow-through RIG detection system shown in Figure 1. Analysis time for a single injection was about 12 s for the conditions used. In order to correlate experimental data to molecular properties, one must consider solutions of polymers at dilute concentration in a good solvent (20,22,25,26,38).From previous SEC work, we have shown for well-developed chromatographic peaks the experimentally measured concentration gradient signal VC is inversely related to the solute concentration profile variance 2 (27). Contrary to the SEC work with the RIG where column
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
broadening dominated 2, measurement of polymer solutions in the flow-throughsystem (Figure 1) requires a more thorough consideration of u2 contributions within the system. If we assume a delta function at injection and consider all contributions to u2,one obtains UT2
+ ut2 + Qfc2
= ui2
(1)
where uT2 is the total variance for a given solute, comprised of u: (injection variance), ut2 (variance due to broadening in the inlet tubing), and uf: (flow cell variance). It is not practical to solve eq 1 rigorously for our system, but rather, to derive an empirical relationship that containsthe salient relationships between molecular and hydrodynamic properties. For this work, RIG signals were measured from the base line to the first relative maxima (or minima). In this case the RI of the polymers was greater than the RI of the solvent CHzClzand the measurement was from base line to relative maxima (maximum slope). In general eq 1, suggests several contributions to uT2, while for this work uf: (flow cell variance) dominated. The : q term was found to be dominated by random diffusion, as solutes enter the flow cell under the experimental conditions. Thus, uf,2 is related to solute hydrodynamic properties through the translational diffusion coefficient, D, by (39) = 2Dt
gf:
(2)
where t is the time allowed for diffusion from an initial delta function. Since the linear polystyrenes were applied as the standard to study the star polystyrenes, one must relate eq 2 to a solution for VC, the experimental data. For linear polymers in a good solvent, one notes from polymer theory (18) that
D
0:
Mw-3/5
(3)
where M , is the weight average molecular weight (2) defined by (4)
where Ci is the concentration in grams per milliliter of a polymer at the exact molecular weight Mi. It is useful to define the number average molecular weight, M,, given by
Polydispersity is defined in the usual manner polydispersity = M,/M,
(6)
which is a useful parameter when characterizing polymers (2, 3). Generally, polydispersity is determined by the polymerization mechanism and reaction conditions. Equations 4-6 will be utilized shortly, through application with the RIG detection system. Equation 3 has been supported by other workers using CHZClz,or other good solvents and polystyrenes (18,26, 38). Furthermore, note that
D
0:
(7)
Rh-'
where R h is the polymer hydrodynamic radius. Experimental results have shown that the detected RIG signals, VC, are linearly related to M,o.Bo and fit the empirical expression
+
VC = aMwo,60 b
(8)
where a and b are experimentally determined constants. Our choice of the exponent on M , is consistent with the experimental work of others, where D is inversely proportional to MWo.@'where the theoretical exponent 315 ranges experi-
450
I
400-
i
a z
350-
v)
300-
c3
/=
_"
0
1000
2000
3000
4000
Figure 2. RIG (VC) signal @V) versus M$" for linear polystyrenes (0),uncorrected star polystyrenes (+), g-factor-corrected star polystyrenes (W), and SECpredicted star polystyrenes (X). The solid line corresponds to eq 8.
mentally from about 0.55 to 0.65 for polystyrene in a good solvent (26,38). Comparison of eq 3 and 7 in the context of eq 8 suggests that the experimentally measured RIG signals, VC, are linearly correlated with the solute hydrodynamic radius, Rh, by VC = a'Rh
+ b'
(9)
where a'and b'are also experimentallydetermined constants. For this work, it is understood that eq 9 is the intrinsically correct expression, but correlations are made through eq 8, in terms of M,, inferred relative to the linear polystyrenes. From a physical point of view, one realizes that the differences in VC signals, at constant solute RI and injected mass, are due to differences in their frictional properties. The results for the linear polystyrenes (Table I), L1 through L6, are shown in Figure 2 ( O ) , where the RIG signals, VC, are plotted as a function of Mw0,"(eq 8). For this calibration, a = 0.084 /IV mol3l5g-3/5and b = 178.7 MV. Indeed, eq 8 is supported for the range of linear polystyrenes studied. Error bars on VC data were omitted in Figure 2 for clarity. The average relative standard deviation of VC for a given linear polystyrene measured by the flow system was 4.7% (six trials each) in Figure 2. Other results plotted in Figure 2 are related to the star polystyrenes and will be explained shortly. Each linear polystyrene was injected at a concentration of 5 X lo4 g mL-l; thus it was possible to assume operation at "infinite dilution" since eq 2 is related to the diffusion coefficient,D(C), as a function of concentration, C, by (22)
D ( C ) = D ( 1 + KDC)
(10)
where the KD values are on the order of 100 mL g-' or less for polystyrenes in the M , range of 109 to 106 g in a good solvent. Taking the worst case of KD = 100 mL g-' and assuming no solute dilution at the peak prior to detection, the error in assuming infinite dilution according to eq 10 was no worse than about 5%. This is essentially the same amount of error as associated with the experimental uncertainty. If the KDC term is not negligible, the consequence of eq 10 is to produce a nonlinearity in VC signals as a function of injected mass for a given molecular weight. This was tested by using linear 170000 g mol-' polystyrene at injected masses ranging from 2500 ng down to 10 ng. The data fit the linear regression equation VC = 0.433m
+ 2.96
(11)
where m is the injected mass in nanograms, 0.433was the slope with units of microvolts per nanogram, and 2.96 was the y
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988 0.041
200
2815
I
-I
a
z i?cn + z
w 0 0.03-
z 4
LT
100
a >
wD
---
I
0.02i
- 1
a U
(3
0.01
C 1000 2000
3000
4000
"
0
5000
"
0.60
Mw Correlation between the RIG (VC)signal, in arbltrary units,
Flgwr 3. for Unear polystyrenes (0). Same Row system as for Figure and Mwo.W 2 except a flow rate of 32 pLlmln and a 0.5-pL injection loop were used.
intercept in microvolts. Ideally, the y intercept should be zero for this calibration. The error a t zero injected mass is 6.8 ng, consistent with the detection limit of about 10 ng. Equation 11 displayed a correlation coefficient of 0.990 over 2 orders of magnitude in injected mass. Meanwhile, the volumetric variance, u: for 170 000 8; mol-l polystyrene was essentially constant at 83 pL2 (i5%) over the polystyrene concentration range examined to obtain eq 11. The other linear polystyrenes behaved similarly. Correlations between M, and either VCor .:a There are two problems associated with correlating VC data to M$6. First, VC data for solutes at unknown concentration must be corrected due to injected mass differences as suggested by eq 11 (concentration dependence). Second, VC data for solutes of unknown RI must be corrected since VC is proportional to dn/dC, a RI sensitivity factor for a solute in a given solvent system (27). The second problem is not quite so critical since polymers within a given sample often have roughly the same RI over a wide molecular weight range (40); thus dn/dC may be assumed constant for many polymer studies. The first problem, i.e., concentration dependence, is more critical. If one considers eq 2 and 3, a possible solution is evident. Essentially, since uf: is proportional to D (eq 2), and D is proportional to M,-3/6 (eq 3), then one should observe experimentally that 1/u: is proportional to Mw8l5, where u: is the volumetric variance of the RIG signal where the peak-to-peak interval is measured as 20, (28). A plot of 1/u: as a function of M,o.Bo should be linear and independent of solute concentration as discussed briefly following eq 11. Measurements of u, were made for the linear polystyrenes for the flow method system operating at 32 pL/min and with a 0.5-pL injection loop instead of the 4.0-pL injection loop. It is useful to show the plotted result. In Figure 3 is shown the standard VC versus MWo.@' plot for L3 through L7 according to eq 8. The average relative standard deviation of VC for a given linear polystyrene was 2.1%. A plot of l/u: versus M,o.60 is shown in Figure 4 for the same RIG signals used to prepare Figure 3. Clearly, 1/u: versus M$@' is quite linear, and furthermore, the calibration is independent of solute injected mass, to the extent that eq 10 is satisfied. The average relative standard deviation of u,2 was 10% for each polymer prior to calculating l/u: and plotting. The observation that Figure 4 appears more linear than Figure 3 is strong evidence that the concentration independence of 11:. versus MWo.@' calibrations may be a powerful tool in polymer characterization. Polydispersity Measurements of Linear Polystyrene Mixtures. From eq 4-6 and 8, it is clear that one may obtain
"
1000 2000
"
3000
4000
5000
M ;6 Flgure 4. Correlation between 110: pL-', labeled as IlVARIANCE, and Mwa~ea for the linear polystyrenes (0). Same experimental data as for Figure 3.
Table 11. Data for Polydispersity Study at Constant Injected Mass and M , with M , Varied
M,/M,"
1.04 1.19 1.53 1.92 2.29 2.65
weight fractions of each polymerb L2 L5 L6 O.OO0 0.004 0.011 0.018 0.025 0.032
1.000 0.900 0.700 0.500
0.300 0.100
0.OOO
0.096 0.289 0.482 0.675 0.868
vc,'
%
FV
sd
RSD'
292 313 326 363 383 403
10.0 6.0 10.0 3.8
3.4 1.9 3.4 2.8 1.0
8.0
2.0
11.2
Polymer solutions prepared by using L2, L5, and L6 (Table I); Mn = 170000 g mol-' (constant), so each mixture is 2.9 pM (constants) and.5 X lo4 g/mL injected concentration (constant), Le., M, is varied. *Linear polystyrenes designated according to Table I. cLinear regression of data yields a correlation coefficient of 0.99. dStandard deviation, s, of three replicate measurements. e (s/VC) x 100%. information concerning the polydispersity of polymers and polymer mixtures by using the apparatus in Figure 1. This was facilitated by preparing linear polystyrene mixtures from 9000, 170000, and 500000 g mol-' linear polystyrene (L2, L5, L6) such that each mixture was exactly 5 X lo4 g mL-' total concentration, holding M , constant (eq 5) at 170000 g mol-', and varying M , (eq 4) by varying the relative weight fractions of the three polystyrenes (2). It was assumed that the three linear polystyrenes were reasonably monodisperse for this study, which was consistent with the data in Table I. Six solutions of varying polydispersity (eq 6) were measured by the RIG detection method and VC signals measured. The results are presented in Table 11. Weight fractions of each polystyrene used to prepare each solution are also listed. The V C signals were linear with polydispersity over the range tested, fitting the expression
VC = 67.85 p V
(5)+
226.6 pV
(12)
with a correlation coefficient of 0.99. Note that polydispersity changes on the order of 0.10 units were confidently measured within the precision of the data. This is good evidence that the apparatus, Figure 1,may prove useful for routine process analysis of polymer systems. In practice, since the flow method measures M,., only, another technique is necessary to measure M , to obtain M,/M,. Thus, in light of the injected mass calibration (eq ll),the linear polystyrene diffusion calibration shown in Figure 2, and the polydispersity measurement study (Table 11, eq 12), it is
2816
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
now possible to study the star polystyrenes "blind" with the flow-through technique. It is assumed in this work that all the polystyrenes, both linear and stars, have the same refractive index and density, nominally 1.60 and 1.05 g mL-', respectively (27,40). Indeed, within experimental uncertainty this is a reasonable assumption, and found to not detract from our studies and conclusions. This assumption allows one to compare directly (at constant injected mass) the RIG signal, VC,as a concentration gradient. Alternatively, 1/u; correlations with M,o.eo could have been used to study the star polymers without worry of injected mass differences as shown by Figure 4. Correlations between VC and M,o.eo (eq 8) were applied in the star polymer studies since slightly better precision was obtained with the experimental data. In future applications, either approach may be suitable with l/u; correlations with M,"6 inherently superior since the calibration is independent of injected solute mass and independent of dn/dC. Examination of Star Polystyrenes by RIG Detection Method. Salient data for the three star polystyrenes studied in the work are listed below the linear polystyrenes in Table I. Note that what one has to work with is an overall weight average molecular weight M,, along with the average number of branches, or arms, f, with the number average molecular weight M, of the branches. These data will be referred to, with respect to experimental results. The star polystyrene VC signals were measured with the flow-through RIG detection system, as for the linear polystyrenes, a t constant injected mass. Initially, with no correction for molecular size, Le., Rh (hydrodynamic radius), the VC data for the star polystyrenes were plotted in Figure 2 (+) as a function of Mwo.eo, using the manufacturers M , values given in Table I. As to be expected, since the VC signal is correlated physically to diffusional properties, relating VC to R h by eq 9 is more appropriate. For star polymers at a given molecular weight, the dominating factor in comparing the two polymer shapes is the shrinkage factor, g, given by (22)
v)
m
a
J
w
K
::-:I_ 0
2
4
6
8
TIME,min Figure 5. UV-vis absorbance detection at 254 nm following SEC of the star polystyrenes S1, S2, and S3 at 500 pL/min CHPCI,. The numbered features (1-6) are explained In the text and Tables 111 and IV.
Prediction of Star Polystyrene RIG Signals Inferred by Size-Exclusion Chromatography Data. The linear polystyrenes were used for calibration in SEC. A silica-based SEC column was used with CHzClz as eluent followed by conventional UV-vis absorbance detection. Retention volume data, V,, were measured from the peak of each linear polystyrene, since each was relatively monodisperse with M,/M, I1.08 (Table I). Generally, one plots log M , vs V , in SEC for calibration, but more correctly the retention mechanism depends upon effective molecular size, and thus Rh is the operative physical parameter. One notes by considering eq 3 and 7 that in theory Rh
0:
MW3l5
(16)
for linear polystyrenes in a good solvent. Thus, plotting log M , vs is, more precisely, plotting log R h vs v,, where the slope of each calibration is corrected by the exponentialfactor. For the linear polystyrenes the following calibration was obtained:
v,
where (P), is the square of the radius of gyration of the star polymer and (S2)1 is the square of the radius of gyration of the linear polymer. Furthermore, g is related to the degree of branching by (20, 22) 3f - 2 g=-
f
where f equals 2 for a linear polymer, and thus g equals 1. It is valuable to note that (s2)3/6 is approximately equal to R h in experimentalwork, although this is not theoretically precise. Thus, eq 8 may be modified by considering eq 3,7,9,13, and 14 for a good solvent to yield
VC = ag3/sMw3/5 +b
(15)
where the shrinkage factor has been incorporated into the calibration. Equation 15 is essentially rewriting eq 9 in general form as a function of M,. The adjusted star polystyrene V C data, according to eq 15 and their respective degree of branching (Table I), are also plotted in Figure 2 (m). After correction through the g factor, a notable similarity between the star polymers (m) and linear polymers ( 0 )is evident in Figure 2. This gives one good confidence in the RIG detection as a polymer analysis tool, yet a cross-check of the results in Figure 2 with SEC studies is critical. Essentially, by use of the SEC data of the star polystyrenes in the context of the linear polystyrenes, can the information be applied to predict the V C signals of the star polystyrenes obtained previously by the flow-through RIG detection system?
log M , = -1.609Ve
+ 8.277
(17)
where M , is taken as the molecular weight at the solute peak and V, is the solute retention volume, in milliliters. For this work, no correlations were made to eq 17 outside the total exclusion and total permeation limits of 1.60 and 3.40 mL, respectively. After the SEC calibration with linear polystyrenes was established (eq 17), the star polystyrenes were analyzed on the system and me shown in Figure 5 for S1, S2, and S3. Retention volume data were measured for each feature numbered for S1, S2, and S3 in Figure 5 for subsequent comparison to the linear polystyrenes. By applying the star polystyrenes V, data to eq 17, one calculates the effective, or inferred, linear polystyrene molecular weight. For nearly monodisperse polymers the molecular weight of the peak approximately equals both M , and M,. The results for these measurements and calculations are given in Table 111, listed according to the feature number labeled on the SEC chromatograms in Figure 5. It is interesting to note, that within experimental error, many of the numbered features are present for more than one star polystyrene. Interesting comparisons can be made between the SEC inferred molecular weight of some of the numbered features and the M , of the branches reported by the manufacturer (Table I). For S1 the reported arm M, is 7000 g mol-' (Table I), while feature number 5 (Figure 5) has an inferred molecular weight of 6000 g mol-'.
ANALYTICAL CHEMISTRY, VOL. BO, NO. 24, DECEMBER 15, 1988
Table 1V. Summary of Size-Exclusion Chromatography for Star Polystyrenes by Feature Number (Table 111)and Relative Mass Fractions, hi
Table 111. Summary of Size-Exclusion Chromatography Data: Major Features Observed for Star Polystyrenes SEC feature n0.O 1 2 3 4 5 6
retention volume, V,,mL Wb
M (inferred):
1.71 (0.01) 1.97 (0.02) 2.14 (0.00) 2.25 (0.02) 2.80 (0.01) 3.24 (0.02)
335 000 128 OOO 68 200 45 400 5 910 1160
g mol-l
Major peaks or features are labeled accordingly in Figure 3 for the star polystyrenes S1,S2, and S3. bStandarddeviation of retention volume measurement for three trials of each star polystyrene. ‘Inferred or effective molecular weight of each feature with respect to the linear polystyrenes by eq 17. The approximation is that M = M , = M , for the SEC peaks, and “inferred” indicates the equivalent linear polystyrene M.
star polystyrenea
SEC feature no.b
relative mass fraction, hi, of each feature‘
s1
4 5 6
0.593 0.257 0.150
52
1 3 6
0.500 0.439 0.061
s3
1 2 6
0.864 0.084 0.052
a
Likewise, for S2 the reported arm M,, is 59 200 g mor1, while feature number 3 (Figure 5) has an inferred molecular weight of 68 200 g mol-’, and also, S3 has a reported arm M,, of 116700 g mol-’, while feature number 2 (Figure 5) has an inferred molecular weight of 128000 g mol-’. It appears that the features numbered 1 and 4 are unique for S1,S2, and 53, although S2 and 53 both show feature 1 (Figure 5). Furthermore, each star polystyrene contains feature 6, which may be the same chemical species or nearly so. The correlation between SEC features and M, of the branches is indeed quite strong, suggesting decomposition of the “parent” star polystyrenes producing free linear arms. One might suggest that the star polystyrenes were degraded, or sheared, at the center of the star via mechanical or hydrodynamic forces during the SEC measurements (18,41).Another possibility is that the star polystyrenes contained the variety of species present (Figure 5) prior to SEC analysis. The star polystyrenes studied did not require special storage. Since the SEC conditions were quite mild, i.e., room temperature and low linear flow velocity, the latter possibility seems to be more likely. The complexity of the SEC data of the star polystyrenesjust leads to a better test of the flow method with RIG detection. Our studies have shown that, within experimental uncertainty, each polystyrene has the equivalent absorbance extinction coefficient when taken in units of liters per gram per centimeter. Thus, integration of the major peaks for each star polystyrene, and subsequent normalization within a given chromatogram, provides the relative mass fraction, hi, of each major peak (numbered features). The relative mass fractions for a given star polystyrene chromatogram are defined such that
Chi = 1.000 (18) summing contributions from all peaks. The relative mass fractions of the major peaks, according to feature number, for each star polystyrene are summarized in Table IV. The overall reproducibility in the hi data was slightly better than 5%,which was adequate for this study. The data in Table IV were applied to predict the star polystyrene responses observed with the flow-through RIG detection system. Since the molecular weights of the star polystyrenes in Table I11 are the inferred “equivalent” linear polystyrene molecular weights, it seems reasonable to calculate the s u m of all contributions to the VC signal one would expect to obtain for the star polystyrenes. This is facilitated by employing eq 8 using calibration constants as discussed earlier VCi = O.O84(pV mol3l5 g-3/6)Mw3/6+ 178.7 pV (19) and using
VC, = ChiVCi
2817
(20)
where VCi is calculated by eq 19 using the equivalent linear
Star polystyrenes labeled according to Table I. SEC feature number according to Table 111. ‘Relative Mass Fraction of each SEC feature for a given star polystyrene, such that Chi 5 1.OOO for each uolvmer. Table V. Summary of Star Polystyrene Signals by the Flow Method with RIG Detection, Listed as Coordinate Pairs measurement of prediction methoda uncorrected g-factor corrected SEC predicted
MWo.@, VC coordinate pairs Slb s2b S3b 940,192 396, 192 472, 215
2183, 285 1343, 285 1507, 295
3618, 328 2225, 328 1933,341
Methods as explained in text for data plotted in Figure 2: uncorrected (+), g-factor corrected (m), and SEC predicted (X). bStar polystyrenes labeled as in Table I. polystyrene M , (Table 111) for each star polystyrene peak contribution and each is inserted into eq 20, where VCi contributions are weighted by the corresponding relative mass fraction, hi (Table IV). This provides a predicted star polystyrene response VC, that one might anticipate with the flow-through RIG detection system. The results of applying eq 19 and 20 via Tables I11 and IV are also plotted in Figure 2 (X). It is interesting to note the similarity between the “predicted” VC, responses (XI, from SEC data, and the experimental VC, responses after subsequent correction by the g factor (@. In contrast, the uncorrected star polystyrene RIG detection data in Figure 2 (+) are clearly unique relative to the linear polystyrenes ( O ) , the g-factor corrected star polystyrene data @), or the SEC inferred star polystyrenes responses (X). In order to eliminate any uncertainty in associating star polystyrene data points in Figure 2, the results have been summarized in Table V. From a statistical point of view, both g-factor correction and SEC data prediction of the star polystyrene RIG responses with this flow method are consistent. Considering the complexity of the SEC data for the star polystyrene “standards”, with concomitantuncertainty about their physical properties, i.e., extent of branching, etc., it is remarkable that both approaches yield similar interpretations. Yet, this is anticipated since the polydispersity study with the linear polystyrenes (Table 11, eq 12) was accomplished by using polymer mixtures.
CONCLUSION A flow method that employs RIG detection and provides molecular size information has been proposed and examined. Construction of suitable molecular size calibration curves requires about 1min, without chromatography. The ability of the flow method to measure changes in solute molecular weight was found to be similar to the capability of SEC. This implies that the flow method may be well suited to process
2818
Anal. Chem. 1988, 60, 2818-2821
control applications, by providing a valuable piece of information that may be monitored; effective molecular size of polymers in mixtures. The flow method was linear with injected polymer mass for over 2 orders of magnitude, making qualitative analysis attractive. As a tool for theoretical studies, the flow method offers a viable alternative to either light scattering or ultracentrifugation for providing molecular size information,as correlated to translational diffusion properties of macromolecules. The capability of the device to study very dilute solutions, a 5 X to about 1 X lo4 g mL-' injected solution concentration range, allows one to assume "infinite" dilution conditions for many applications. Recent improvements in the RIG detector design, employing a position sensitive detector, have reduced the required injected concentration by about a factor of 5 (37). The RIG detector may also prove useful if interfaced with field-flow fractionation (FFF) (13-15). Process analysis application of the RIG flow method includes the ability to accurately measure changing polymer polydispersity (2-4). The RIG flow method appears to be an exciting analytical technique that should find wide interest and applicability.
ACKNOWLEDGMENT Valuable discussions with B. E. Eichinger were appreciated.
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(13) Giddlngs, J. C. J . Chem. phvs. 1988, 49, 81-85. (14) Klrkland, J. J.; Yau, W. W. Sclence 1982. 218. 121-127. (15) Caldwell, K. D. I n Chemical Analysk: Modem Methods of fartlcle Slze Analysis; Barth, H. G., Ed.; Wlley: New York, 1984; Vol. 73, Chapter 7. (16) Roovers, J. E. L.; Bywater, S. Macromolecules 1972, 5 . 384-388. (17) Roovers, J. E. L.; Bywater, S. M a c m k u l e s 1974, 7 , 443-449. (18) Bywater, S. In Advances In Pdymer Sclence; Cantow, H. J., et al., Eds.; Springer-Verlag: New York, 1979; Vol. 30, pp 89-116. (19) Bauer, 8. J.; Hadjlchristidls, N.; Fetters, L. J.; Roovers, J. E. L. J . Am. Chem. SOC. 1980, 102, 2410-2413. (20) Roovers, J.; Hadjlchrlstidls, N.; Fetters, L. J. Macromolecules 1983, 16. 214-220. (21) Klein, J.; Fletcher, D.; Fetters, L. J. Faraday Symp. Chem. Soc. 1983, 18, 159-171. (22) Huber, K.; Burchard, W.; Fetters, L. J. Macromolecules 1984, 17, 541-548. (23) Edwards, C. J. C.; Kaye, A.; Stepto, R. F. T. Macmmolecules 1984, 17, 773-782. (24) Zlmm, 8. H. Mecromo/ecules 1984, 17, 795-798. (25) Renn, C. N.; Synovec, R. E. Anal. Chem. 1988, 60, 200-204. (26) Tljssen, R.; Bos, J.; VanKreveld, M. E. Anel. Chem. 1988. 58, 3036-3044. (27) Hancock, D. 0.;Synovec, R. E. Anal. Chem. 1988, 6 0 , 1915-1920. (28) Pawllszyn, J. Anal. Chem. 1986, 5 6 , 243-246. (29) Pawllszyn, J. Anal. Chem. 1988, 58, 3207-3215. (30) Pawllszyn, J. Anal. Chem. 1988, 80, 766-773. (31) Golay, M. J. E.; AtWood. J. G. J . ChrOmtOgr. 1979, 186, 353-370. (32) Atwood, J. G.; Golay, M. J. E. J . Chromatogr. 1981, 218, 97-122. (33) Hupe, K.-P.; Jonker, R. J.; Rozing, G. J . Chromatogr. 1984, 285, 253-265. (34) Garell, P.; Rosset. R. J . Chromatogr. Sci. 1985. 2 0 , 367-371. (35) Rocca, J. L.; Hlgglns, J. W.; Brownlee. R. G. J . Chromatogr. Sci. 1985, 23, 106-113. (36) Flow Cytometry and Sorting, Hydrodynamlc Roperties of Flow Cytometric Instruments; Kachel, V., et ai., Eds.; Wlley: New York, 1979; Chapter 3. (37) Hancock, D. 0.; Synovec, R. E., unpubllshed results. (38) &oh, R.; Hallsz, I. Anal. Chem. 1981, 53, 1325-1335. (39) Cantor, C. R.; Schimmel, P. R. Biophysical CheMtry: Technkpes for the Study of Blobgical Structure and Function; W. H. Freeman: New York, 1980; Part 11. Chapter 10. (40) Merck Index, loth ed.; Merck and Co.: Rahway, NJ, 1983; no. 8732. (41) Barth, H. G.; Carlln, F. J., Jr. J . Liq. Chromatogr. 1984, 7 , 1717-1738.
RECEIVED for review May 9, 1988. Accepted July 18, 1988.
D.O.H.and R.E.S. thank the NSF Center for Process Analytical Chemistry for support of this work (Project Number 86-2).
CORRESPONDENCE Microwave Induced Plasma Atomic Absorption Spectrometry with Solution Nebulization Sir: In the earlier inductively coupled plasma (ICP) dev loping research, the ICP had been investigated for atomic a sorption spectrometry (AAS) by Wendt and Fassel (11,by Greenfield et al. (2),by Veillon and Margoshes (3), by Morrison and Talma ( 4 ) , by Mermet and Trassy (5), and by Bordonali and Biancifiori (6). A multiple pass system (I), a T-shaped plasma cell (2),and a long-path torch (5)have been used to increase the absorption path length. Bordonali and Biancifiori (7) also received a patent in 1972 covering the analysis of trace elements by ICP-AAS. However, researchers of the ICP field supported and verified that the energetic plasma was more suitable for atomic emission spectrometry (AES). In an attempt to reduce spectrum complexity, researchers such as Winefordner et al. (8) have performed atomic fluorescence spectromery (AFS) on the ICP. In light of the spectral interference in ICP-AES, Greenfield (9) has recently
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recalled attention to ICP-AFS and ICP-AAS. The ICP-AAS technique has been performed by Magyar and Aeschbach (lo), by Downey and Nogar ( I I ) , and by Gillson and Horlick (12). Like flame AAS, ICP-AAS exhibits high selectivity, and because of the energetic argon plasma, sample atomization is complete and proceeds without chemical interferences (10). The ICP-AAS system is suggested for use with complex samples, in which high selectivity is desired without the concern for sensitivity (10). These researchers have found the ICPAAS to give high detection limits and low sensitivity (10-12), and they have attributed these disadvantages to the very short absorption path length, which is several times shorter in the plasma than in an AA flame. Mermet and Trassy (5) have addressed this difficulty in their design and construction of an ICP torch for AAS. The ICP-AAS also is useful in some physical measurements for the plasma. These ICP-AAS and ICP-AFS investigations have indicated that there is an
0003-2700/88/0360-2818$01.50/00 1988 American Chemical Society
