Determination of Molecular Weight and Size of Ultrahigh Molecular

8 Determination of Molecular Weight and Size of Ultrahigh Molecular Weight Polymers Using Thermal Field-Flow

Downloaded by FUDAN UNIV on January 13, 2017 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0247.ch008

Fractionation and Light Scattering Seungho L e e a n d O h - S e u n g K w o n 3M C o m p a n y , 3M C e n t e r , St. P a u l , MN 55144

Thermalfield-flowfractionation was used to characterize ultrahigh molecular weight poly (methyl methacrylate) (PMMA) with a light-scattering detector. The influence of the differential refractive index increment (dn/dc) and the second virial coefficient (A ) on the measured molecular weight (MW) and the molecular size was investigated using a broad polystyrene standard having the nominal MW of 250,000. No significant change was observed in MW, and size with A -A could be assumed to be zero. Debye plot showed a good linearity for the entire range (0-180°) of the scattering angle. For ultrahigh MW PMMA, Debye plot was not linear, and the multiangle measurement was necessary for the extrapolation of data. Both MW and size increased with A , and thus A could not be assumed to be zero for ultrahigh MW polymers. 2

2

2

2

2

P O L Y ( M E T H Y L METHACRYLATE) ( P M M A ) has remained the most w i d e l y used material for the optic portion of the intraocular lens since it was first implanted into human eyes i n the late 1940s. It is dimensionally and chemically stable and more transparent than most other types o f optical glasses. T h e original type very high molecular weight ( M W ) P M M A . In this form, P M M A is amenable to lathe-cutting, compressioncasting, and cast-molding fabrication techniques. It can also be tumblepolished. Because of P M M A s excellent balance of properties, very little has been done until recently to develop other optic materials. Generally, acrylic polymers are brittle. M o d i f i e d acrylics having properties unattainable b y the basic unmodified compositions are n o w offered (1-3). 0065-2393/95/0247-0093$12.00/0 © 1995 American Chemical Society

Provder et al.; Chromatographic Characterization of Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1995.


94

CHROMATOGRAPHIC CHARACTERIZATION OF POLYMERS

M W determination of these high M W polymers using size-exclusion chromatography (SEC) is sometimes difficult because portions of these materials are beyond the linear calibration range of most S E C columns. Thermal field-flow fractionation ( T h F F F ) has been used for the characterization of a wide range of organic-soluble polymers i n dilute solutions (4). In T h F F F , elution volume of a sample is a function of M W , and thus the molecular weight distribution ( M W D ) of the sample can be determined from its elution profile. T h F F F offers higher resolution than S E C i n its normal range of operation (5). T h F F F is particularly useful for characterizing very high M W polymers that are difficult to analyze using S E C (6-8) and microgel-containing polymers (8). T h F F F elution volume (or time) is a function of D / D , where D is the thermal diffusion coefficient and D is the mass diffusion coefficient (9, JO). T h e mass diffusion coefficient D of a polymer molecule i n a fluid w i t h viscosity η is given by (J J) T

T

0

(1)

where R is the universal gas constant, Τ temperature, N the Avogadro's number, M viscosity-average M W , and [η] intrinsic viscosity. If the value of D is available, the M W of a polymer can be determined directly from its T h F F F elution volume using equation 1. Values of D are not readily available and no theory exists to describe D w i t h k n o w n physicochemical parameters. A calibration is usually r e q u i r e d to determine M W D of polymers using T h F F F . It is noted that T h F F F has been used to study thermal diffusion phenomenon and to determine D (12, 13). MW-sensitive detectors (e.g., differential viscometer, light scattering detector) have been used to eliminate the need for calibration in T h F F F . W i t h a differential viscometer, the intrinsic viscosity distribution (IVD) of a polymer is measured. T h e I V D is then converted to M W D using M a r k - H o u w i n k ( M - H ) constants (14). The use of accurate M - H constant is essential i n this method. Low-angle laser light scattering ( L A L L S ) has also been used for T h F F F (15). U n l i k e viscometry, the light-scattering method measures the absolute M W of polymers directly. In multiangle laser light scattering ( M A L L S ) , the scattered light intensity is measured over a broad range of the scattering angles. Besides the M W , the mo lecular size can be measured from the angular dependence of the scat tered light intensity. A l t h o u g h M A L L S has been used i n S E C for various applications (16-18), it has not yet been used w i t h T h F F F . In this study, M A L L S was combined w i t h T h F F F to investigate the applicability of T h F F F for the characterization of ultrahigh M W polymers. A

T

T

T

T


8.

Ultrahigh Molecular Weight Polymers

L E E & KWON

95

Theory Theories on T h F F F and light scattering have been discussed i n numerous publications. Equations that are needed for the discussion of results are briefly reviewed here. In T h F F F , the retention ratio, R, is given b y (6) V° R = = 6\

(2)

for well-retained solutes. T h e full expression for R is somewhat com plicated (J9) and is not discussed here. V° is the channel volume and V is the elution volume. T h e retention parameter λ is related to D / D by r


T

ΔΤ

(3)

where A T i s the temperature drop across the channel. C o m b i n i n g equa tions 2 and 3, D / D can be calculated from the measured elution volume V . T h e M W is then determined using a calibration curve (log (D/D ) vs. log M) constructed w i t h a series of narrow standards. As M W i n creases, D decreases (eq 1), and λ decreases (eq 3). Thus i n T h F F F , l o w M W species elute earlier than high M W species. W h e n light passes through an inhomogeneous m e d i u m such as a polymer solution, it is scattered i n all directions. T h e light scattering at an angle θ by the solute is measured by the excess Rayleigh ratio Re w h i c h is defined b y T

r

T

TJ Η*

r -

(^fl,solution

J geom

^fl,solvent)

/A \

^

V*)

where i ^ o i u t i o n and I n v e n t are the intensities of the scattered light b y the solution and the solvent, respectively, and l is the intensity of the incident light. T h e geometric factor f = r^/V, where r is the distance between the scattering source and the detector and V is the scattering volume. F o r a dilute polymer solution, the excess Rayleigh ratio R is related to the weight-average molecular weight (M ) and the second virial coefficient (A ) of the polymer by (20) 0

geom

w

2

^

= MM-2A cM P ) 2

w

e

(5)

where K * is a constant defined b y (18)

Ν λ„ Α

4


W

96


for vertically polarized light, dn/dc is the differential refractive index (RI) increment, n is the R I of the solvent at the incident wavelength λ . T h e solute concentration c (g/mL) is calculated by 0

0

Δ

(7)

η

(dn/dc)

where Δη is the difference i n R I between the solution and the pure solvent. ΡΘ is the scattering factor (or form factor) and is expressed as a power series i n s i n (Θ/2) as 2

Ρ = 1 -


β

+ a

a , s i n (|) 2

s i n (|)

-

4

2

a

sin ( f ) +

' ' '

6

3

(8)

w h i c h can be simplified to P,=

l - a ,

s i n (I)

(9)

2

for low scattering angles. T h e coefficient α = ( 4 x n / X ) ( r ) / 3 , where ( r ) is the %-average mean square radius of the polymer. T h e root mean square radius (or R M S radius) V ( r ) is sometimes called "radius of gyration'\ F o r each slice of the fractogram, the intensity of the scattered light is measured at a set of discrete scattering angles, and a D e b y e plot [RQJ K*c vs. s i n (0/2)] is constructed. W h e n θ = 0, ΡΘ = 1, and equation 5 becomes λ

g

2

0

0

2

g

2

z

z

g

2

z

2

M

where (R /K*c) e

tion 10, M

e=0

w

w

(1 -

2A cM ) 2

w

(10)

is the y-intercept of the D e b y e plot. B y solving equa

of the slice is obtained from

2 (intercept) 1 + V I - 8A c (intercept) 2

It is noted that the product, 2 A c M is m u c h smaller than 1 for most T h F F F (or S E C ) experiments, and equation 10 is further simplified to 2

f-^]

w

=M

W

(12)

Thus, M is directly obtained from the t/-intercept of the D e b y e plot. T h e mean square radius is obtained from the slope of the D e b y e plot w

by


8.

L E E àc KWON

97


-3X m 0

2

0

(13)

167r n M (l - 4A cM ) 2

0

2

w

2

w

where m is the slope of the D e b y e plot at zero scattering angle, m 0

0

= d ( i V K * c ) / d ( s i n (fl/2))' 0 = 0 · 2

(


Experimental

Details

T h F F F . T h F F F was carried out with a Polymer Fractionator model T100 (FFFractionation, Inc., Salt Lake City, UT) equipped with a Waters model 590 pump and a 20-mL loop Rheodyne injector (Rheodyne Inc., Cotati, C A ) . Detectors were a M A L L S (Wyatt Technology model D A W N F, Santa Barbara, C A ) and a refractive index (RI; Hewlett Packard model 1037A, Palo Alto, CA) connected in series with the RI following the M A L L S . The light source of the M A L L S is a H e - N e laser (632.8 nm). The T h F F F channel is 0.0127 cm thick, 1.9 cm in breadth, and 45.6 cm long. Lightscattering data were collected and processed using the A S T R A software provided by Wyatt Technology. F o r conventional T h F F F experiments (without a light-scattering detector), a calibration curve (log (D/D ) vs. log M ) was constructed using a series of narrow polystyrene (PS) standards having M W s of up to 9.35 million D a . The calibration curve showed an excellent linearity for the entire M W range. The T h F F F - R I (refractive index) data were collected and processed using the software provided by F F F r a c tionation, Inc. T

dn/dc Measurement. A laser differential refractometer ( L D C / M i l t o n Roy model K M X - 1 6 , Riviera Beach, F L ) was used for dn/dc measurements. S E C . S E C was carried out at room temperature with an H P 1090 Chromatograph (Hewlett Packard, Palo Alto, C A ) equipped with an RI detector (Hewlett Packard model 1037A). Columns were Permagel 500-, 1 0 10 -, and 100-À columns (Column Resolution, Inc., San Jose, C A ) connected in series. A l l S E C experiments were run in tetrahydrofuran (THF) at 1.0 m L / m i n . Samples were dissolved in T H F and filtered through a 0.2-mm poly(tetrafluoroethylene) disposable filter (nonsterile, 25 mm disc). The i n jection volume was 100 m L . The column set was calibrated using a series of narrow PS standards having M W ranging from 2000 to 7.7 Χ 10 . The calibration curve (log M W vs. retention time) was obtained by fitting the data with a third-order linear regression, and the curve started deviating from linearity at the M W of ~ 5 million due to the column exclusion. 3

6

6

Materials. Narrow PS standards were obtained from Pressure C h e m ical Company (Pittsburgh, PA). A broad PS standard ( M W = 250,000) was obtained from American Polymer Standards Corp. (Mentor, O H ) . The P M M A materials were Perspex C Q U V obtained from Imperial Chemical Industries (Wilmington, D E ) and U V 52E obtained from Pharmacia Ophthalmics Inc.(Monrovia, C A ) . High-performance liquid chromatography-grade T H F from JT Baker Inc. (Phillipsburg, Ν J) was used as a carrier for all T h F F F and S E C experiments. The polymer solutions had concentrations of - 0 . 2 % (wt/vol).


98


Results and

Discussion

The determination of polymer M W and R M S radius using light scattering measurement requires the knowledge of dn/dc and A values (see eqs 6, 7, 11, and 13). A broad PS standard having the nominal M W s of M = 100,000, M = 250,000, M = 430,000 was used to review the basics of polymer characterization using T h F F F - M A L L S - R I . F i g u r e 1 shows T h F F F elution curves of the PS standard obtained from light scattering (at 90°) and R I detector. T h F F F conditions were AT = 50 °C, flow rate = 0.3 m L / m i n w i t h the stop-flow time of 1 m i n . T h e values of dn/dc and A are available i n literature for many p o l y mer-solvent systems. F o r the polymer-solvent systems whose dn/dc and A values are not available, separate measurements are required. T h e dn/dc can be measured by differential refractometry and A by the static mode of light scattering. A range of dn/dc and A values are re ported for the P S - T H F system: dn/dc = 0.186 - 0.193 c m / g and A = 8.32 Χ 1 0 " - 2.11 Χ 1 0 " m L m o l / g at the wavelength of 633 nm (21). F o r the PS standard used i n study, the dn/dc value of 0.190 was measured using a laser differential refractometer. T h e A value was not measured separately. Table I shows the M W s and the R M S radii of the PS standard de termined w i t h different dn/dc and A values. Equations 11 and 13 i n dicate that both the M W and the R M S radius increase as A increases. N o significant changes were observed i n M W s and sizes w h e n A was varied at the constant dn/dc value of 0.2. It is noted that A c o u l d be assumed to be zero. As mentioned earlier, the product A c M is usually 2

n

w

z


2

2

2

2

3

4

4

2

2

2

2

2

2

2

2

M A L L S (90°)

I

0.0

Iii

.

.

.

I 5.0

.

•

.

.

I 10.0

.

L

Elution Volume (mL) Figure 1. ThFFF elution curves of a broad PS standard having nominal MWs o / M = 100,000, M = 250,000, and M = 400,000. ThFFF conditions are ΔΤ = 50 °C and flow rate = 0.3 mL/min. n

w

z


8.

99


L E E & KWON

Table I. Molecular Weights and RMS Radii of 250,000 M W PS Standard Determined by T h F F F - M A L L S - R I Using Different dn/dc and A Values 2

dn/dc

A


0.200 0.200 0.200 0.200 0.200 0.200 0.190 0.180

Μ

2

1.48 1.48 1.49 1.49 1.50 1.48 1.56 1.65

0 1 X 10"-4 2 X 10"-4 4 X 10"-4 8 Χ ΙΟ-4 Ι χ ιο-4 ί χ ιο-4 ί Χ 10"-4

w

2.58 2.58 2.58 2.58 2.59 2.58 2.71 2.87

Χ ΙΟ 5 Χ ΙΟ 5 Χ ΙΟ 5

ΙΟ ΙΟ ΙΟ ΙΟ Χ ΙΟ

Χ Χ Χ Χ

Μ

M

η

5 5 5 5 5

3.99 3.99 4.00 4.00 4.01 3.99 4.20 4.44

Χ ΙΟ 5 Χ ΙΟ 5 Χ ΙΟ 5 Χ ΙΟ 5 Χ Χ Χ Χ

ΙΟ ΙΟ ΙΟ ΙΟ

5 5 5 5

*"g»n

ζ

Χ ΙΟ 5 Χ ΙΟ 5 Χ ΙΟ 5 Χ Χ Χ Χ Χ

ΙΟ ΙΟ ΙΟ ΙΟ ΙΟ

5 5 5 5 5

r

g,w

(nm)

(nm)

(nm)

15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2

20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0

25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0

much smaller than 1, and the A terms i n equations 11 and 13 are neg ligible. T h e term A cM becomes increasingly important as the M W or the concentration of the sample increases. T h e effect of A on the M W and size for ultrahigh M W P M M A materials is discussed later. The M W is inversely proportional to the product K * c (see e q 12) and the product K*c is proportional to dn/dc (see eqs 6 and 7). Thus for a given R , the calculated M W is inversely proportional to the dn/dc value used for the calculation. A s dn/dc decreases from 0.2 to 0.18 at the fixed A value of 1 X 1 0 ~ , the M W s increase proportionally as expected. Because the size is determined from the slope of the D e b y e plot, it is independent of dn/dc. Figure 2 shows the D e b y e plot for the slice at the elution volume of 3.7 m L . T h e values of dn/dc and A were taken as 0.19 and zero, 2

2

2

0

4

2

2

xlO

5

5.00 j

1

4.00

-

3.00

h

2.00

J-

1.00

-

* ^

0.00

I

0.0

1

0.25

1

1

0.50

0.75

1.00

Sin (0/2) 2

Figure 2. Debye plot for the PS standard shown in Figure 1 at the elution volume of 3.7 mL.


100


respectively. T h e data were extrapolated using the first-order linear regression, and M W of 2.74 Χ 1 0 and R M S radius o f 20.9 n m were obtained for the slice (see eqs 11 and 13). T h e first-order least square line is shown as a solid line. A c c o r d i n g to equation 9, the D e b y e plot is linear at low scattering angles. F i g u r e 2 shows a good linearity for the entire range ( 0 - 1 8 0 ° ) of the scattering angles. T h e M and R M S radius determined for the whole distribution o f the P S standard are plotted against the elution volume i n Figures 3 and 4, respectively. F i g u r e 3 shows a good linearity between log M W and log V as expected from T h F F F theory (see eqs 1-3). A t the beginning and the end of the elution curve, the detector signal becomes too weak to measure the M W accurately. T h e noise shown at the high end of the elution volume is due to the weak R I response (relative to the lightscattering signal) as it approaches the baseline (see F i g u r e 1). F i g u r e 4 also shows the expected increase i n size w i t h increasing elution volume. T h e plot becomes noisy at the elution volume below about 3 m L . A s the molecular size becomes m u c h smaller than the wavelength o f the light source, the angular dependence of the light scattering disappears (isotropic scattering) and an accurate determination o f molecular size becomes difficult. Figure 5 shows the plot o f R M S radius versus M W on a l o g - l o g scale. T h e data for the elution volume lower than 3 m L were d r o p p e d 5

w


r

î.Oxio F

~

7

—

"

I

1.0x10

S3 ο

1.0x10

1.0x10 10.0

1.0 Elution Volume (mL)

Figure 3. ure 1.

MW versus elution volume for the PS standard shown in Fig


8.

101


L E E & KWON 100.0


*

10.0

1.0 0

2

J

4

u

6

8

Elution Volume (mL)

Figure 4. EMS radius versus elution volume for the PS standard shown in Figure 1.

80.0

10.0 I 2x10

I

I

I

I

1

1

1

1 lxlO

s

6

Molecular Weight

Figure 5.

RMS radius versus MW for the PS standard shown in Figure 1.


102


because of excessive noise i n the R M S radius as shown i n F i g u r e 4. T h e slope of the plot depends on the molecular density (17, 18). As the density of the molecule increases due to branching, cross-linking, or the existence of the microgels, and so on, the slope of the plot decreases, and thus the R M S radius versus M W plot can be used for polymer con formation studies (17). The first-order least-square fit of the data is shown as a dotted line. T h e slope is 0.57, w h i c h agrees w e l l w i t h the result reported elsewhere for P S - T H F system (18). T h e same T h F F F - M A L L S - R I system was used to characterize two ultrahigh M W P M M A materials (Perspex and U V 5 2 E ) . A power p r o gramming (22) was used for T h F F F operations w i t h the programming parameters of initial AT = 40 ° C , predecay time t = 5 m i n , t = —10 m i n , and the h o l d AT = 10 °C. T h e flow rate was fixed at 0.5 m L / m i n . F i g u r e 6 shows the traces from light-scattering (90°) and R I detector for the P M M A materials. F i g u r e 7 shows the D e b y e plot of the Perspex at the elution volume of 11 m L . U n l i k e the plot for the PS standard shown in F i g u r e 2, the plot is not linear: a fourth-order regression was required to fit the data. As M W increases, the A term (A cM) and thus the higher order terms i n equation 8 become increasingly important,


x

2

a

2

Perspex

Figure 6. Elution curves for power programmed ThFFF runs of PMMA materials with parameters tj = 5 min, t = —JO min, initial ΔΤ = 40 °C, and flow rate = 0.5 mL/min. a


8.


LEE&KWON

103

xlO 10.0

6

7.50

5.00

υ

* *

2.50


0.00 0.0

0.25

0.50

0.75

1.00

Sin (0/2) 2

Figure 7.

Debye plot for PERSPEX at the elution volume of 11 mL.

and the D e b y e plot starts deviating from the linearity. Multiangle mea surement is thus necessary for the accurate determination of M W and R M S radius of ultrahigh M W polymers. A range of dn/dc and A values are also reported for the P M M A T H F system: dn/dc = 0 . 0 8 4 - 0 . 0 8 8 c m / g and A = 5.3 Χ 1 0 " to 1.1 X 10~ m L m o l / g at the wavelength of 633 n m (21). Table II shows the M W s and the R M S radii calculated for the Perspex using different d n / dc and A values. U n l i k e for the PS standard discussed earlier, both M W and R M S radius increase w i t h A . T h e A terms i n equations 11 and 13 become increasingly important as the polymer M W increases, and A can no longer be assumed to be zero. T h e calculated M W decreases w i t h increasing dn/dc, whereas the size remains unchanged. M W s and R M S radii of Perspex and U V 5 2 E obtained from T h F F F M A L L S - R I are summarized i n Table III. T h e values of dn/dc and A were taken as 0.083 and 2 Χ 10~ , respectively, for both polymers. Figures 8 and 9 show the plots of M W D and the R M S radius versus 2

3

4

4

2

2

2

2

2

2

2

4

Table II.

Molecular Weights and RMS Radii of P E R S P E X Determined by T h F F F - M A L L S - R I Using Different dn/dc and A Values 2

r

dn/dc 0.083 0.083 0.083 0.083 0.088

A

M

2

0 2 5 2 2

Χ X Χ X

10" 10~ 10~ 10~

4 4 4 4

4.31 4.42 4.61 4.42 4.15

10 10 10 10 Χ 10

Χ Χ Χ Χ

M

Μ„

n

6 6 6 6

6

5.87 6.10 6.55 6.10 5.73

10 10 10 10 Χ 10

Χ Χ Χ Χ

6 6 6 6

6

8.01 8.31 8.90 8.31 7.80

2

Χ 106 Χ Χ Χ Χ

10 10 10 10

6 6 6 6

g,n

r

g,w

r

g,w

(nm)

(nm)

(nm)

91.6 92.8 95.5 92.8 92.7

103.8 106.0 110.7 106.0 105.7

114.0 116.5 122.2 116.5 116.2


104

CHROMATOGRAPHIC CHARACTERIZATION OF POLYMERS Table III. M W and RMS Radii Determined by T h F F F - M A L L S - R I for P M M A Materials g,w

Tg.w

(nm)

(nm)

(nm)

92.8 62.2

106.0 84.5

116.5 113.6

r

M


Perspex U V 52E

M

M

n

w

4.42 Χ 10 1.83 Χ 10

6

6

6.10 Χ 3.77 Χ

10 10

6

6

z

8.31 Χ 10 8.00 Χ 10

6

6

M W , respectively. In F i g u r e 9, no significant difference in the slope was found between two materials: 0.346 for Perspex and 0.354 for U V 5 2 E . Those slopes are lower than that obtained for the PS standard i n F i g u r e 5, w h i c h indicates both P M M A materials have higher molecular density than the PS standard. T h e P M M A materials were also characterized using conventional T h F F F and S E C without the use of light-scattering detector. R I traces from S E C are shown in F i g u r e 10, and the M W s determined by T h F F F and S E C are summarized i n Table I V . F o r the same sample, the M W s obtained from T h F F F are higher than those obtained from S E C . As the polymer size approaches the exclusion limit of the columns, the M W tends to be underestimated i n S E C . There is also a possibility of shear degradation as these ultrahigh M W polymers pass through the S E C columns. 1

2.0,

Molecular Weight Figure 8.

MW distributions of PMMA materials shown in Figure 6.


8.

105


L E E & KWON

300.0 UV52E


Slope = 0.354

40.01 lxlO

I

I

!

•

•

•

• • i

lxlO

6

•

I I I

5xl0

7

7

Molecular Weight

Figure 9.

RMS radius versus MW for PMMA materials shown in Figure 6.

§

UV52E

0.0

5.0

10.0

15.0

20.0

Elution Time (min)

Figure 10.

SEC of PMMA materials in THF at 1 mL/min.



106

Table IV. M W Determined by T h F F F - R I and S E C - R I for P M M A Materials M


ThFFF-RI Perspex U V 52E SEC-RI Perspex U V 52E

2.77 Χ 10 1.37 Χ 10 0.832 Χ 10 0.577 Χ 10

6

6

6

6

7.11 Χ 10 3.99 Χ 10 2.14 Χ 10 1.67 Χ 10

6 6

6

6

z

11.6 Χ 10 7.24 Χ 10 3.58 Χ 10 3.06 Χ 10

6

6

6

6

Conclusions W i t h its multiangle capability, M A L L S can be used to measure the size as w e l l as the absolute M W of polymers. T h e multiangle capability seems to be particularly important for the determination of M W and R M S radius of ultrahigh M W polymers as the D e b y e plot deviates from the linearity. It is also important for the analysis of ultrahigh M W poly mers to use accurate A value as w e l l as dn/dc as the resulting M W and R M S radius tend to vary w i t h those values. E v e n w i t h an absolute M W detector such as light scattering, the accuracy of the polymer M W determined b y a separation technique depends on the resolution of the separator because the M W is calculated based on the assumption that each data slice is monodisperse. Thus, it is important to choose a separation technique that provides higher res olution for the polymers to be analyzed. T h F F F offers higher resolution than S E C for high M W polymers, particularly for polymers w i t h M W near or higher than 1 million D a . 2

Acknowledgments W e acknowledge L e n a Nilsson of W y a t t Technology for helpful discus sions on the light-scattering applications.

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RECEIVED for review January 6, 1994. ACCEPTED revised manuscript June 13, 1994.


Determination of Molecular Weight and Size of Ultrahigh Molecular

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