dilute solution properties of asymmetric six-arm star polystyrenes

Dilute Solution Properties of Asymmetric Six-Arm Star Polystyrenes

CHRISTIAN JACKSON,'* DONNA J. FRATER,Z and JIMMY W. MAYS'

'Central Research and Development, E. I. duPont de Nemours and Company, Experimental Station, P.O. Box 80228, Wilrnington, Delaware 19880-0228; *Department of Chemistry, University of Alabama at Birmingham, Birmingham, Alabama 35294-1 240

SYNOPSIS

Six-arm star polystyrenes having varying numbers of short and long arms attached to the same molecule have been synthesized by anionic polymerization. The molecules have been characterized by high resolution size exclusion chromatography using multiangle light scattering and viscosity detectors. This technique has allowed the radii of gyration and intrinsic viscosities to be measured for stars with each possible combination of arms. The branching parameters g and g' are computed and compared with theoretical expectations. It is found that short arms add preferentially to the stars, because of reduced steric effects. The molecule with one long and five short arms exhibits behavior closest to that of a linear chain (largest branching ratios). The effect of arm polydispersity on solution properties of stars is discussed. 0 1995 John Wiley & Sons, Inc. Keywords: asymmetric star polystyrenes solution properties size exclusion chromatography * light scattering - viscometry

I NTRO DUCT1 0 N

The dilute solution properties of branched polymers have been the subject of numerous experimental and theoretical investigation^.'-^ In par- ticular, nearly monodisperse uniform star molecules prepared by anionic polymerization have been extensively studied and their dilute solution properties (for molecules with up to 270 arms!) are relatively well under~tood.'-'~ Unfortunately, many-armed stars are better models for polymeric micelles than for commercial branched polymers, because they exhibit dilute solution behavior typical of hard spheres due to the very high chain segment den~it ies . '~

Relatively few attempts have been made to pro- duce model polymers that simulate some of the het- erogeneity present in a typical branched polymer (e.g., polydispersity in molecular weight, variation in the nature and placement of the branch sites, and

* To whom correspondence should be addressed. Journal of Polymer Science: Part B: Polymer Physics, Vol. 33,2159-2166 (1995) Q 1995 John Wiley & Sons, Inc. CCC 0887-6266/95/152159-08

variation in branch lengths). Some work on synthesis and properties of graft copolymers having uniform backbone length and irregularly placed branches of equal length have appeared.15-'' Regular H-shaped polystyrenes and "star-combs'' have also been synthesized and s t ~ d i e d . ' ~ ~ ~ ~

In this work, we report the synthesis and solution properties of six-arm star polystyrenes having a bi- modal distribution of arm lengths. This work may be viewed as an extension of the work of Pennisi and Fetters,'l who first produced asymmetric three- arm stars comprised of combinations of long and short arms. Size exclusion chromatography (SEC) with on-line viscometry and multiangle laser light scattering (MALLS) is employed to study the impact of the type of branching on the intrinsic viscosity, [s], and radius of gyration, R G . The branching parameters g and g',4-6

g = (%A4

g' = ( E ) M

2159

2160 JACKSON, FRATER, AND MAYS

Table I. Used in the Synthesis of Asymmetric Star Polymers

Mole Fractions of Short and Long Arms

Mole Fraction of Mole Fraction of Sample Short Arms Long Arms

AS-100 100 AS-75 75 AS-50 50 AS-25 25 AS-O 0

0 25 50 75

100

which compare the squared radii of gyration and intrinsic viscosities of linear and branched of equiv- alent molecular weight, M , are computed and compared with results of simulations and theory.

EXPERIMENTAL

A series of six-arm polystyrene stars with different fractions of short ( number-average molecular weight, M,, = 23,000 g/mol) and long ( M , = 105,000 g/mol) arms were prepared using standard high vacuum, break-seal techniques, in all-glass reac- tors." The arms were initiated using purified (dis- tilled) sec-butyllithium in benzene. After completion of polymerization ( 2 days), the active polystyryl- lithium anions were allowed to react with a few units of isoprene to reduce steric hindrances during the linking reaction. Appropriate amounts of the long- and short-arm species were split-down under vacuum, and appropriate amounts of the arms to give

0.014 r 1.1

0.012 - - .= 5 0.010 - e e

91

? B 8 0.004-

c

$ 0.008- - 5 0.006 -

2 0.002 -

OOOO I

42 44 46 48 50 52

Elution volume (rnL)

Figure 1. ( * * .), and light scattering (---) tracings for AS-100.

Differential refractometer (-), viscometer

0.014

0.012 -

36 3 8 4 0 4 2 4 4 4 6 Elution volume (mL)

Figure 2. (

Differential refractometer (-), viscometer * ), and light scattering (---) tracings for AS-0.

the molar ratios shown in Table I were added to the linking agent 1,2-bis (trichlorosilyl) ethane ( Pe- trarch). The excess of arms was 14% for AS-O,21% for AS-25, 27% for AS-50,20% for AS-75, and 20% for AS-100. Linking was conducted for 2 96 h a t 4Ooc. In some instances, the stars were fractionated from toluene /methanol mixtures to remove excess arm components. Polystyrene standards (Polymer Laboratories, Amherst, MA) were used as the linear reference materials.

Details of the SEC /viscometry/MALLS method have been described p r e v i o u ~ l y . ~ ~ Briefly, the SEC unit employed was a Waters 150C ALC/GPC (Wa- ters Associates, Milford, MA). The mobile phase was tetrahydrofuran (THF) (E. M. Science, Gibbs- town, N J ) a t a flow rate of 0.5 mL/min. Six 300 X 7.5 mm id . columns were used; three columns were packed with 10-pm particles (Phenogel linear columns, Phenomenex, Torrance, CA) and three

Table 11. Uniform Stars

Results for Unlinked Arms and

20 K arm 23,300 1.02 0.158 11.4 100 K arm 105,300 1.00 0.437 14.1 AS-100 star 132,700 1.01 0.309 10.9 AS-0 star 424,000 1.02 0.866 21.0 AS-0 star

shoulder 639,000 1.01 0.836 22.5 ~

Results are the averages of three separate injections.

PROPERTIES OF ASYMMETRIC STAR POLYSTYRENES 2161

/

Om7 I 0.006 - - .- s 0.005

b

I

I3

3 0.004

8

- i 0.003 9 8 0.002 5 a

0.000

0.000 36 38 40 42 44 46

Elution volume (mL)

Figure 3. ( . - - ) , and light scattering (---) tracings for AS-75.

Differential refractorneter (-1, viscorneter

columns were packed with 5-mm particles ( PLGel Mixed-C, Polymer Laboratories). Polymer solutions were prepared with concentrations ranging from 1.0 to 2.0 mg/mL. Polymer solution (100-200 pL) was injected onto the columns for each measurement. Polymer concentration was measured using the differential refractometer housed in the ALC /GPC unit. A Viscotek Model 150R viscometer (Viscotek Corporation, Houston, T X ) and a Wyatt Technol- ogy DAWN-F MALLS photometer with a 10-mW argon-ion laser operating a t a wavelength of 488 nm (Wyatt Technology, Santa Barbara, CA) were used as described previously.23 The specific re-

0.007

0.006

F 5 0.005 P L

I

2

- 3 0.004

g 0.003 -

ij 0.002

0" O.Oo0

I ~

I I

36 38 40 42 44 46 Elution volume (mL)

Figure 4. ( - - * ), and light scattering ( - - - ) tracings for AS-50.

Differential refractometer (-1, viscometer

0.007

0.006

F 5 0.005 I3 L 5 0.004 i 0.m B f 0.002 B

- al u)

O.Oo0


Figure 5. (

Differential refractometer (-), viscometer * * ), and light scattering (---) tracings for AS-50.

fractive index of polystyrene in T H F was taken as 0.199 mL/g.24

RESULTS AND DISCUSSION

The refractometer, viscometer, and light scattering tracings for the uniform short-arm and long-arm stars are shown in Figures 1 and 2, respectively. In both cases there are two smaller peaks, a t larger elution volumes, in addition to the stars. These peaks correspond to residual arm, due to the excess

le+6 9e+5 8e+5 7e+5 6e+5

5e+5

4e+5 2 .g 3e+5

- 5 3 2e+5 s"

E

B a

1 e+5 9e+4


Figure 6. Molecular weight from light scattering at each elution volume for AS-50. The refractorneter tracing is also shown for reference.


38 3 8 4 0 4 2 4 4 46 Elutbn volume (mL)

Figure 7. Intrinsic viscosity at each elution volume for AS-50. The refractometer tracing is overlaid on the same volume scale for reference.

used in the reaction, and a small amount of dimer ( the residual linear chains were not terminated under anaerobic conditions). For the long-arm star ( AS-0) there is also a pronounced shoulder on the lower elution volume (higher molecular weight) side of the star peak (Fig. 2 ) . The values of M,, the polydispersity ratios M,/M,, R G , and [ q ] are given in Table 11. The values for the shoulder on the long- arm star are also given.

For uniform arm-length stars the number of arms can be determined from the ratio of the star molecular weight to the arm molecular weight. For AS- 100 this ratio is 5.7, indicating essentially complete linking to form a six-arm star. However, for AS-0 the ratio corresponding to the main peak is 4.0. This indicates that coupling did not go to completion within 2 96 h a t 40°C25; this is also consistent with the large amount of residual arm component ob- served in Figure 2. However, the high molecular weight shoulder on the chromatogram is due to fully coupled stars [ i.e., M , (star)/M, (arm) = 6.11. Thus, this polymer consists of a mixture of four-, five-, and six-arm stars. These differences in the rate of linking of isoprene-capped polystyrenes with 1,2- bis (trichlorosily ) ethane are consistent with the earlier observations of Roovers and Bywater26 re- garding molecular weight effects on kinetics of linking at 30°C.

Figure 3 shows the detector responses for the polymer made from 75% short arms and 25% long arms (AS-75). There are four distinct partially resolved peaks and an additional high molecular weight tail a t the lowest elution volume. Figure 4

shows the detector tracings for AS-50, the polymer made using 50% short and 50% long arms. In this case, there are three distinct peaks and possibly a fourth a t 43.5 mL. In addition, there is a shoulder a t 39.5 mL and a high molecular weight tail a t 37- 39 mL.

Figure 5 shows tracing for AS-25, the polymer with 25% short arms and 75% long arms. There are four partially resolved peaks and two higher molecular weight shoulders a t 38 mL and 39.5 mL. In each of the mixed arm polymers there are clearly a t least five main species.

Figure 6 shows the measured molecular weight a t each elution volume for AS-50. The flat regions in the curve correspond to the individual peaks. The decrease in the slope of the molecular weight versus elution volume curve from the average slope is due to band broadening of the peaks. [q] and R(; as a function of elution volume for the same sample are shown in Figures 7 and 8, respectively. These curves are qualitatively similar to that seen in Figure 6.

Table 111 shows the results for the six identifiable peaks or shoulders in the chromatograms of the mixed-arm stars. There are seven possible ways in which the long and short arms can combine to make six-arm stars, with zero to six long arms per star. If the two arms are assumed to have equal probability of reacting with the linking reagent, the distributions of these species can be calculated. Table IV shows the predicted molecular weights and number fractions of each species, and Table V shows the computed weight fractions for each of the seven species. The values for the fractions are calculated using

30

36 3 8 4 0 4 2 4 4 46

Elution volume (mL)

Figure 8. AS-50. The refractometer tracing is also shown.

Radius of gyration at each elution volume for

PROPERTIES OF ASYMMETRIC STAR POLYSTYRENES 2 163

Table 111. Results for Individual Peaks of the Mixed-Arm Stars

38.5 39 40.5 41.5 42.5 44.5

550,000 0.856 21.6 19.6 0.906 442,000 0.807 20.2 17.8 0.883 368,000 0.784 19.5 16.6 0.851 277,000 0.720 17.9 14.7 0.820 196,000 0.584 15.4 12.2 0.793 114,000 0.451 13.3 9.35 0.703

Table IV. Calculated Molecular Weights and Number Fraction Distributions for the Seven Possible Six-Arm Stars

Zero One Two Three Four Five Six Sample Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms M = 120,000 200,000 280,000 360,000 440,000 520,000 600,000

- - - - - - AS-100 1.000 AS-75 0.178 0.356 0.297 0.132 0.033 0.004 0.000 AS-50 0.016 0.094 0.234 0.312 0.234 0.094 0.016 AS-25 0.000 0.004 0.033 0.132 0.297 0.356 0.178

- 1.000 AS-0 - - - - -

20,000 g/mol and 100,000 g/mol as the molecular weights of the short and long arms.

There is good agreement between the predicted molecular weights for each of the possible stars and the experimental values in Table 111. However, it is apparent from the refractometer chromatograms and the measured weight fractions of each species given in Table VI that the experimental weight fractions are very different from the predicted val-

ues. In all three mixed-arm samples there are more short arms on the stars than expected. This is due to the faster diffusion coefficient and lower steric hindrance to linking for the short arms compared to the long arms. The anion at the end of the polymer chain is "hidden" in a coil, which is larger for higher molecular weight material. Because an excess of arms is used in the reaction and the smaller arms react more quickly, fewer of the long arms become

Table V. Calculated Weight Fraction Distributions of the Seven Possible Six-arm Stars

Zero One Two Three Four Five Six Sample Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms

- - - - - - AS-100 1 .ooo AS-75 0.089 0.297 0.346 0.198 0.060 0.009 0.001 AS-50 0.005 0.052 0.182 0.312 0.286 0.135 0.026 AS-25 0.000 0.002 0.019 0.099 0.272 0.386 0.222

- 1 .ooo AS-0 - - - - -

Table VI. Measured Weight Fractions for the Three Asymmetric Stars

Zero One Two Three Four Five Six Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms Long Arms

AS-75 0.12 0.30 0.38 0.10 0.08 0.01 0.01 AS-50 0.10 0.11 0.42 0.22 0.12 0.02 0.01 AS-25 0.20 0.19 0.34 0.20 0.05 0.01 0.01

2164 JACKSON, FRATER, A N D MAYS

0.8

t? 4 0.7 c a r ._ ,! 0.6 6

0.5

Table VII. and the Different Species in the Mixed Stars

Branching Factor for the Uniform Stars

Star (Probable Short : Long Arm Ratio) g g' e

.

AS- 100

38.5 mL (1 : 5) 39 mL (2 : 4) 40.5 mL (3 : 3) 41.5 mL (4 : 2) 42.5 mL (5 : 1) 44.5 mL (6 : 0)

AS-0 0.674 0.436 0.481 0.547 0.635 0.752 0.843 1 .o

0.607 0.517 0.591 0.654 0.728 0.823 0.862 1.0

0.79 0.79 0.72 0.70 0.70 0.68 0.87 - -

attached to the chlorosilane core. The sharpness of the peaks and their uniform molecular weights sug- gest that there are very few stars with less than six arms present except in the high molecular weight tail. As all the expected species can be identified from the data and the individual peaks can be identified from the data, the individual peaks can be used to study the effect of mixed-arm lengths.

For each identifiable species the branching factors g and g' can be calculated using the relationships between [ q ] , R(;, and M for linear polystyrene in THF. These data have been previously determined in our laboratories.23 The values ofg andg'are listed in Table VII along with values of the empirical E

parameter, defined as

g' = g'. (3)

0.9 -

0.8 - 2 : 8 0.7 - m .

$ 0.6 -

L

c .

5 : m -

0.5 -

0.4 - 1 0.3

0 1 2 3 4 5 6 Number of long arms

Figure 9. tion of the number of long arms per star.

Branching factorsg (0) andg' (0) as a func-

0.9 '." t

0.8 1.0 1.2 1.4 1.6 1.8 2.0 Polydlsperdty of arms

Figure 10. Branching factors g (A) and g' (0) plotted against the polydispersity of the arm molecular weight distribution.

The value of g for the symmetrical six-long-arm star, 0.436, is in good agreement with the theoretical value of 0.444 obtained from the random flight model and with previous measurements for symmetric six- arm tars.^,^ From the friction coefficient calcula- tions of Stockmayer and F i ~ r n a n , ~ a g' value of 0.51 may be estimated that is also in accord with the experimental value of 0.517 found for sample AS- 0, although this value is slightly lower than previous experimental values for polyisoprene stars.26 It should be noted, however, that the theoretical g and g' values are estimates for chains under 0 conditions,

0.78 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Polydisperstly of arms

Figure 11. persity on the ratio R,/R,.

Effect of branch molecular weight polydis-

PROPERTIES OF ASYMMETRIC STAR POLYSTYRENES 2 165

/' /

/

/' - a 0.9 8 0.6 -

- ._

.E 0.6

0.5 - - c -

0.4 -

0.3 le+5 1 e+6

Molecular weight (~mol )

Figure 12. Mark-Houwink plot for AS-50. The dashed straight line shows the relationship for linear polystyrene.

whereas our data are generated in a thermodynam- ically good solvent. For the short-arm symmetrical star (AS-loo), the measured values of g and g' are considerably larger due to the strong impact of en- hanced excluded volume interactions around the core for many-armed low molecular weight stars3 The peak at 44.5 mL appears to be unreacted long arms rather than six-short-arm stars, as both g and g' are about unity. Both the linear 120,000 g/mol arm and the AS-100 star have about the same hydrodynamic volume and could not be resolved. For six-arm stars with random arm lengths, g is predicted4 to be 0.643; this value is very close to the value of 0.635 that is measured experimentally for the star with equal numbers of long and short arms.

The variation of the branching factors with the number of long arms per star is shown in Figure 9. The values of both g and g' increase initially when one long arm replaces a short arm, then they both decrease as the number of long arms increases fur- ther. This is because the long arms dominate the size of the molecules; a six-arm star with one or two long arms has a radius of gyration and hydrodynamic size that is closer to that of a linear molecule of the same molecular weight than that of a uniform six- arm star with the same molecular weight. This effect can be related to the distribution of arm lengths. The Zimm-Stockmayer theory4 prediction, as noted above, for a star with a random distribution of arm lengths is in accord with the findings for the star with three long and three short arms. This is larger than the value for the symmetrical (uniform) star. For stars with fewer than three long arms even

higher g values are measured. We can define a molecular weight polydispersity for the arms as

Arm polydispersity = (4)

This characterizes the molecular weight distribution of the mixture of arms before they are linked to- gether. For uniform stars the arm polydispersity is 1. For the mixed-arm stars the arm polydispersity increases with the number of short arms and achieves a maximum of 1.8 for the star with five short and one long arm. Both branching factors show a steady increase with this measure of the arm molecular weight polydispersity (Fig. 10). The data for the AS-100 star are omitted due to its additional excluded volume effects. It should be noted in this regard that crowding around the star core may also influence the dependence of the branching factors on polydispersity. It is seen that the branch length polydispersity has less effect on the viscometric radius that it does on R G . The relationships between polydispersity and the branching factors, taken from the linear fits to the data on logarithmic axes, are

1 e+5 1 e+6

Molecular weight (g'mol)

Figure 13. Plot of log radius of gyration vs. log molecular weight for AS-50. The dashed straight line shows the relationship for linear polystyrene.


The combined [?I, RG, and M data allow the effect of star architecture on the ratio of viscometric radius to radius of gyration to be explored. The effect of branch length polydispersity on this ratio is shown in Figure 11. As the polydispersity increases the ratio decreases towards the value for linear polystyrene.

Figure 12 shows the Mark-Houwink plot for AS- 50. The data look very similar to those for randomly branched polymers; the slope decreases with increasing molecular weight and approaches zero. However, in the present case this effect is due to the decrease in branch molecular weight polydispersity with increasing molecular weight. The number and functionality of branch points is the same in each molecule. In contrast, for randomly branched polymers this effect is attributed, primarily, to the increased number of branches for higher molecular weight species.27 Figure 13 shows RG as a function of M for the same polymer. The data are similar to those of Figure 12, reaching a slope of zero at the highest molecular weights. This indicates an increase in M without any corresponding increase in size.

In summary, model six-arm star polymers were used to study the effect of branch length polydispersity on the branching parameters g and g'. The polymers were characterized by SEC in THF, using both light scattering and viscosity detectors. Mo- lecular weight, radius of gyration, and intrinsic viscosity distributions were measured. For star polymers made with mixtures of short and long arms it was found that the size was significantly affected by the arm molecular weight polydispersity. Both branching factors increased from the values for uniform arm length stars as the arm length polydispersity increased.

J.W.M. and D.J.F. thank the DuPont Company for sup- porting the work done at UAB.

REFERENCES AND NOTES

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3.

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Received February 22, 1995 Revised May 10, 1995 Accepted June 13, 1995

dilute solution properties of asymmetric six-arm star polystyrenes

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