Makromol. Chem., Rapid Commun. 8,451 -455 (1987) 45 1

Determination of branching by gel size exclusion chromatography in combination with on-line small angle light scattering

Peter Lang, Walther Burchard *

Institut fur Makromolekulare Chemie der Universitat Freiburg, Stefan-Meier-Str. 3 1 , D-7800 Freiburg i. Br., FRG

(Date of receipt: April 21, 1987)

Branched macromolecules are characterized by the shrinking parameters g, g ', and h defined by Eqs. (1)-(3) ' -3)

g = (SZ)b/(S2)lin ( 1 )

g ' = [Vlb "VIlin (2)

h = q i n = (Rh )b )!in (3)

where quantities for branched (b) and linear (lin) chains are compared at the same molecular weight. In these equations ( S 2 ) is the mean-square radius of gyration, [q] the intrinsic viscosity, D the translational diffusion coefficient and Rh the correspond- ing hydrodynamic radius defined by D through the Stokes-Einstein relationship D = k T/(6x qo R,, ) with solvent viscosity qo .

Here we want to report another technique which yields a branching-sensitive para- meter via on-line low angle light scattering/gel permeation chromatography. In some instances this parameter can be of greater use than the quantities of Eqs. (1) - (3).

Low angle light scattering (LALS) combined in series with gel size exclusion chro- matography (GPC, HPLC) allows an unambigious determination of the molecular weight distributions, whatever chain architecture the macromolecules might have. The technique requires an instrument that allows the recording of light scattering intensity at scattering angles as low as six degrees. If the radius of gyration R, = ( S2 ) is less than or even equal to the wavelength of the light used in the experi- ment, the effect from spatial dimensions can be neglected, and one has

K . c 1 + ( 1 / 3 ) ( R i q 2 ) = - - + 2A,c P l /Mw + 2Azc

R, MW (4)

and the molecular weight of a fraction from on-line GPC is obtained as

Separation of molecules according to the molecular weight distribution into various fractions proceeds in the GPC-column according to the size of the polymer molecules and not according to their molecular weight. This is clearly seen in Fig. 1 for the

0173-2803/87/$01 .OO

452 P. Lang, W. Burchard

examples of molecular weightlelution volume diagrams of linear poly(methy1 meth- acrylate) (PMMA) fractionated in tetrahydrofuran (THF) and for two star-microgels bearing on the average 1 1 and 43 arms per crosslinked nucleus. The average number of arms per nucleus was simply calculated by dividing the over-all molecular weight by the molecular weight of one PMMA-arm.

These star-microgels differ from common regular star-branched macromolecules in that their centre is composed of a densely crosslinked microgel, which has a certain size distribution. Since the arms are narrowly distributed in length, the nucleus distribution produces a corresponding distribution of the number of arms. Fig. 2 shows the weight fraction distribution of the two star-microgels in THF. One notices from Fig. 1 that for the same molecular weight the elution volume V, is shifted to larger values as the average number of branches is increased.

20.0 22.0 26.0 VJml

Fig. 1 . Influence of the degree of branching on the elution volume V, . (0 ) : Linear poly- (methyl methacrylate) (PMMA) chains, (U): PMMA/ethylene dimethacrylate (EGDMA) star- microgelwith an average number of arms f = 11 and weight-average molecular weight of arm length M , = 44000, (A): PMMA/EGDMA star-microgel with an arm length (M, = 20200) and an average number of arms f = 43

Dondos, Rempp and Benoit4s 5, suggested a generalized separation relationship by which the hydrodynamic volume V, of a macromolecule is the essential parameter. According to the Fox-Flory relationship V, is related ot the intrinsic viscosity as

The generalized calibration curve is then given by

In V, = ln([q] M / @ ' ) = V(, - mu,' = V, (7)

where V, is the exclusion volume below which no separation should occur; rn is a con- stant which describes the efficiency of the separation, and @, @' represent the viscos- ity function (Flory constant), referring to the radius of gyration and the hydro-

Determination of branching by gel size exclusion chromatography in combination. . . 453

Fig. 3. Dependence of the factor 1.0 eAve (Eq. 8) on the number of arms f per crosslinked nucleus of poly(methy1 methacrylate) 0.5. (PMMA)/ethylene dimethacrylate star-microgels with average number of PMMA arms f = 1 1 (.land f

0

''?-.-, *. '.

" 0 2.0 L.0 6.0 8.0 10.0 12.0 11.0 106.Mi

Fig. 2. 1 1 , arm length M, = 44000 (A) andf = 43, arm length M, = 20200 ( 0 ) ; tion of species with molecular weight Mi

Molecular weight distribution of two star-microgels with average number of armsf = = weight frac-

-, \

0 8

a .o

I I

dynamic volume, respectively. Assuming the validity of Eq. (7) for branched molecu- les as well, but with a different prefactor %, one obtains for Mb = yi, from Eq. (7)

andf ina l lywi thh '= exp(-m.AV,)

Fig. 3 shows the result of a plot of h' as a function of the number f of arms per microgel. Within the limits of the experimental error both star-microgels exhibit the same dependence on the number of arms. Like the shrinking factors given by Eqs. (1) - (3) h' also depends only on the number of arms and not on their length. This leads to the conclusion that the ratio qin /% is also a function offalone and has no arm-length dependence.

454 P. Lang, W. Burchard

At present, further work is in progress which will show whether a relationship simi- lar to Eq. (9) can also be established for randomly branched materials.

We are aware of the fact that the fractions, which are represented by the points in Fig. 2, are not uniform with respect to molecular weight. Since separation proceeds in the column according to the hydrodynamic volume of the polymers the incomplete separation involves a non-uniformity of the molecular weight as well as a heterogene- ity of structural composition. In the present case the structural composition is uniquely correlated to a special molecular weight, but in the more general case of randomly branched macromolecules both effects have to be considered as not fully correlated to each other and therefore require another type of measurement to be separated.

Experimental part

The linear narrowly distributed poly(methy1 methacrylate) (PMMA) samples, used in this study, are products of R6hm GmbH, Darmstadt. Sample PLlO was polymerized by the present authors using the Group Transfer Polymerization (GTP) technique developed by Webster et al.6), and sample LlO is a linear fraction from the raw product of sample S10.

Samples SlOf and S20f are commercial star-microgels of du Pont de Nemours, Wilmington, USA, in which the fractions of non-attached linear chains were separated by precipitation fractionation. These star-microgels were prepared by first polymerizing methyl methacrylate with the GTP technique followed by adding ethylene dimethacrylate (EGDMA), whereupon EGDMA forms a small microgel with dangling PMMA chains.

All samples have been characterized by static and dynamic light scattering using the ALV 3000 Goniometer system (ALV Langen, Germany) and by the KMX-6 small angle light scatter- ing instrument, distributed by Milton Roy, Germany. Molecular weights and number of armsf for the star-branched samples are given in Tab. 1. Further details will be published elsewhere’).

Tab. 1. Weight-average molecular weights @ of linear poly(methy1 methacrylate) samples, (used for the calibration of the gel permeation chromatography GPC column) and of fraction- ated star-microgels SlOf and S20f and their corresponding arms. The number of armsf results from the ratio of the molecular weights of SlOf and SlOa and of S20f and S20a, respectively

~ ~ ~~

Linear chains Star-microgel

sample code M, . sample code M,. f 3835/81L 2,s fractionated microgels: 3835/92P 6,45 SlOf 90,3 42,6 591 1 /4F 16,6 S20f 45,4 10,7 3835/93S 12,7 591 1/5R 147,O arms of star-microgel: PLlO 2,o SlOa 2,12 L10 2 S S20a 4,25

The scattering intensity was recorded with the KMX-6 instrument and the concentration by a refractive index detector. The two curves as a function of the elution volume were analyzed by a digital correlator accessory allowing to convert the light scattering curve into a molecular weight curve and the refractometer curve into the corresponding concentration curve. The points given in Fig. 1 correspond to the respective volume fraction of the elution volume.

Determination of branching by gel size exclusion chromatography in combination. . . 455

') B. H. Zimm, W. H. Stockmayer, J. Chem. Phys. 17, 1301 (1949) 2, W. H. Stockmayer, M. Fixman, Ann. N. Y. Acud. Sci. 57, 334 (1953) 3, W. Burchard, M. Schmidt, W. H. Stockmayer, Macromolecules 13, 1265 (1980) 4, A. Dondos, P. Rempp, H. Benoit, J. Chim. Phys. 62, 821 (1965)

6) 0. W. Webster, W. R. Herther, D. Y. Sogah, W. B. Farnham, T. V. Raja Baber, J . A m .

'1 L. Lang, W. Burchard, manuscript in preparation

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