Light Scattering by Polymers Two Experiments for Advanced Undergraduates

G. P. Matthews University of Oxford Physical Chemistry Laboratory, South Parks Road. Oxford OX1 302, Great Britain

In a recent issue of THIS JOURNAL, which included the proceedings of the State of the Art Symposium on polymer science, Mattice ( I ) expressed the conrern that chemist,^ who have spent their entire career in academia may never have worked with macromdecules. either in the classroom or in the lahoratory." This article describes two light-scattering ex- periments that h a w recently been introduced into the phys- ical chemistry teaching lahoratory a t Oxford and that give students the chanre not. onlv to studv macromolecules but also to gain much mnre information about structure t,han can he derived from the more usual osmometq, viscometry, and elasticity experiments.

The first exwriment involves the measurement of the mass-average molar mass and degree of coiling of polystyrene and is interpreted hy the full mathematical theory of light scattering. The second experiment concerns the study of transitions in gelatin. The solutions are rather more diffirult to handle than the polystyrene solutions, hut little theory is involved and the experiment could he performed with a sim- pler, lahoratnry-huilt instrument. Either experiment may be performed in a half-day period. The analysis of the resultr; of the first experiment takes a further session, with length de- pendent on whether or not a computer program is available, as is disrussed helow. The primary structure of a polymer is determined by the type and numher of atoms in a polymer chain, the secondary st,ructnm hy the mode and degree of chain coiling, and the quaternary structure by the way in which neighboring chains interact. The two experiments to- gether illustrate the elucidation of these three levels of structure. The tertiarv structure of nolvstvrene would he the . " . degree to which the coil was kinked in various places; no in- formation is ohtained about this hecause to derive the sec- ondary structr~re in this experiment one has to assume that the coil is not kinked. Apparatus (2)

In a light-scattering photometer, a collimated light heam of known wavelength is generated, typically by passing the emission from a water-cooled, mercury-vapor lamp through a green Wrat ten- ty~e filter which ahsorhs all but the 546 nm line. The sample &contained in a round glass cell, which is immersed in a vat of dust-free toluene. The toluene has a re- fractive index similar to that of the sample cell and, therefore, almost entirely eliminates reflections and refractions from the cell fare. For the light-scattering experiment, the entire de- tector assembly is rotated around the sample cell and accu- rately set to preselected angles, while in the gelatin experi- ment it is fixed a t 90" to the incident heam. The photomul- tiplier signal is output to a chart recorder. In the first experi- ment this helps compensate for noise in the signal caused by dust in the sample. The true signal is the haseline on the re- corder, although excessive noise may shift this. The chart recorder also allows the study of the time-dependent changes in the gelatin experiment. Light-Scattering Experiment with Polystyrene

Theory The theory of light srattering is h a s 4 on the work of Ray-

leigh (.?), Dehyr, and Zimm ( 4 ) , as outlined in a previous ar-

tirlr in .JO~'RN.%I. (5). Onlv the rmrepts and equations rsrrntial for the experiments will be mentumed here.

Rayleigh's theor; assumes a scattering volume in a sample molecule. which is small compared to the wavelength of the incident light and filled with a homogeneous continuum. In- cident light induces in the continuum an oscillating dipole which becomes a secondary source of low intensity radiation, i.e., it gives rise to light scattering.

Simple considerations of the geometry of the scattering process for unpolarized light lead to an expression for the Rayleigh ratio Re:

where i~ is the intensity of the scattered light a t an angle R between the incident and scattering ravs. and in is the int,en- - . sity of the incident beam.

For small isotropic particles, Re is related to the mass av- erage relative molar mass, M,, of the solute by the Dehye equation

where

M , is the mass-average molar mass, n is the refractive index of the solution. Nn is Avoeadro's constant. X is the waveleneth in the medium ofthe iniident beam, C i$ the concentra&n and [dnldC] is the specific refractive index increment (mea- sured in a differential refractometer). T o a good approxima- tion, dn/dC -- (n -no) /C, where no is the refractive index of the solvent. Axis the second virial coefficient of the scattering equation, which characterizes deviations from an ideal solu- tion due to the interaction between solute and solvent. I t is identical with the corresponding term ohtained from osmotic . pressure measurements. Terms with higher powers of C are ordinarily negligible. . . .

The ~(attering intensities of the polystyrene solutions must he corrected fcnr iolvttnt ttffrcts, the rhanae with anale ot'the volume of solution monitored by the pho6multiplie~, and the angle dependence of the scattering intensity mentioned ear- lier. These may he calculated respectively by: (1) subtracting the solvent intensity io from the solution intensity i at each angle, (2) multiplying the intensities by sin 8 , and (3) dividing them by (1 + cos2R), finally yielding a corrected intensity a.

Expressing eqn. ( 2 ) in terms of experimental variables

c-0 where iO, is the scatterine intensitv a t 90' for the solvent and R& is the solvent ~ay le igh ratio. r he quantity IClalsz8is the intercept of C/a ohtained hy independently extrapolating R and the concentration C to zero. The extrapolations are drawn on a Zimm plot, in which C/a is plotted against ((sin2 8/21 + kc). k is an arbitrary constant chosen to spread the points so that they can he properly extrapolated. Figure I shows a Zimm

552 Journal of Chemical Education

sin2;+kC Figure 1. Zimm plot for polystyrene in benzene.

plot for polystyrene in benzene, based on measurements made in the undereraduate lahoratorv. (The students' own exoeri- ments k e with tnluene,'as explained below.) 1; the example, k = 200. The solid points are the intersections of the extrapolations to zero angle with appropriate values of kC (i.e., (sin2012) + kC a t 0 = 01, and the extrapolation to zero con- centration with sin2 812 (i.e., (sin2 012) + kC at C = 0). These points are then extrapolated in turn t o give the common in- tercept on the C l a axis, in this case 20.5 X 10-6g ~ m - ~ for X = 3.91 X cm-3.

These Zimm plot calculations are an ideal candidate for a computer program either simply to calculate the Cln values (6) or, as a t Oxford, also to output Zimm plots for various trial values of k.

I'olystyrene sol~~tions are susprnsions of linear coiling chain maleculc~s with a distrihurion of degrees of polymeri7ation. It may he shown (4) that for such systems the ratio of the initial slope of the solvent line to the intercept is given hy

m t ~ a l slope R r 2 -- = - zntereept 3XZ L,

L, is the z-average. root-mean-snuare distance between the .. . rnds of the chain, i.e.. it involvcs thez-average term (n')/(n). The t-average is nlso the term associated with i~l~racrntrifi~ge mmsurements and is always largrr than the mass average. I f the dispersivn (n') of the distr ihtion can he found, e.r.. hv . - . "

polymer solution theory or the inco~poration of osmometer measurements, the mass average may he c&ulated from the z-average. The r.m.s. radius of gyration (pi)'!2 may also he obtained, since for a random coil ( ~ 2 ) " ~ = (L,2/6)1!2.

Finallysthe mass of the styrene monomer may he calculated from its chemical formula. From this, and the mass-average molar mass of polystyrene, may be calculated the mass-a;- erage degree of polymerization. The corresponding length L of the polystyrene chain is calculated, assuming that each momomer unit adds 0.155 nm to its length. The degree of coiling is then LIL,.

Experimental

For light-scattering experiments to be successful, the sample and cells must st scrupulously dean. The only way to he sure of removing

all dust from the cells is to soak them in rhrarnir arid. This is achieved by mnking n PTFF lid for s glass vat (such as n pneumatic trough) with holes to support the calls, and filling the trough and the insides of the cells with acid. This has proved effective and, with suitnhle warning notices, quite safe. When required, the cdls are removed, emptied, washed with a high-pressure water jet, and then distilled water, and dried in an oven. Dust is removed fmm samples hy filtering them through a 0.22-u Millinore filter in a lahoratnrv-hnilt (or com- mrrcinl, holder. Ho~vrvrr much cnre is taken, thecomplrtr chmina- tiqm 01 dust rake5 pr:n<tiw;d i* nrwr a~.hieved In. undrrpradt~tl~es Fortunately, however, the Zimm plot extrapolation procedure con- denses so much information down to a single intercept that even if parallel extrapolation curves are "force-fitted" and entire sets of points ignored, a fairly accurate result may still he ohtained.

The traditional solvent for light-scattering experiments is benzene, but its use is now avoided in teaching laboratories. The students therefore use toluene, whirh is a very good solvent for polystyrene (7). The absolute scattering power of toluene may he measured on the photometer hy comparing the intensity nt 90° with that from benzene. for whichRsois 13 X 10-"(8). Alternative1y.a glass standard that has been calibrated relative to hensene may he used. The other parame- ters which are required for toluene are dnldC = 0.11 &kg-' and n = 1.49 (9), which from eqn. (3) give K = 9.91 X lWR cm2 mol g-I for X = 64fi nm at 2S°C.

The polyctvnnr #wed is 1 readily ~vn~lnhl~,rommerrinl prepamtmn s\ i th a mulnr muc-of nppn~r~mntrlg I00 On0 A molar mnssdwrihw tion curve 12 supplied from rhe mnnufnrtor~ra. nnd is usrd hv rhc demonstrators to estimate the z-average molar mass, and for dis- cussions with the students. It has not proved necessary to use the nnrrower fractions whirh are available at extra cost.

Gelatin and Its Properties

Gelatin is a oolvelectrolvte, i.e.. a macromolecular com- pound which contains man); ionizable groups within the same mdecule. The moln:i~lrs iurr caonlh~ nf hc>inr (,ither ~ositivelv or negatively charged according to whether positive ions (in- cluding H+) or negative inns (including OH-) are oredomi- nantl; adsorbed. 'They also possess an isoelectricpoint a t which the net charge on the oarticles is zero: this occurs when p o ~ i t ~ \ , e and negative ions are adsnrhed roan equal extent. In distilled water, larae elecrroitntic effrrts hetwrrn neighhoring polyelectrolyte chBins occur. At the isoelectric which for gelatin occurs a t pH 5.1, the maximum number of charges areavailable for these interactions, which also provide light- scattering centers. The formation of aggregates in gelatin, as discussed below, can only he ohserved in solutions containing salt, which prevents these interactions from masking the more subtle struct,ural effects.

Light-scattering experiments have shown that gelatin molecules are random coils with mean confieurations com- parable to those of typical synthetic polymers. They form gels through bonding hetweens secondary valencies, whirh form non-permanent linkages a t varying locations. Such secondary valence eels undergo thermo-reversihle eel-sol transitions.

I t natkally follows that systems containing gel linkages exhibit an increase in the amount of light they scatter as their concentration is increased. This arises from the increasing size or numher of the densitv fluct,uations in the gel, which form - the scattering centers.

However, an alternative structure for gelatin has heen proposed (10). I t has been suggested that under certain con- ditions eelatin solutions contain aeereeates which are cross- .... .. I~nkcd hy very small rrvstallites. These agprrgntes show the characterist~c of beine increaqinelv ordered at high cmcrn- trations, whereupon the amount hilight scattered-is reduced and may actually decrease with concentration.

Experimental

As before the cells and solutions for the experiment must heahso- lutely clean, and a procedure similar to that deserihed earlier is fol- lowed. Because of the higher viscosity of the gelatin solutions, they filter better if they and the filter holder are warmed, and if a low pressure of compressed air is applied to the filter unit.

Five solutions are made up. Solutions 1,2 and 3 are 0.9,3.0, nnd fi.0 g, respectively, of gelatin in I00 cm" of 0.16 M NaCl solut,ion (sup-

Volume 61 Number 6 June 1984 553

Solution 4'

Solution 5,

L OO 40 80 120 160

Minutes Figure 2. Light-scanering intenstty of gelatin gels and solutions

plied). Solurions 4 and 5 areof 0.9g adatin in 100cm3distilled water. 1\11 i h ~ solutions are stirred and warmed for ahout 1 h. Suluiim 4 is adjuswd to pH 5 and solution h to pH X by adding 1 M HCl ur NaOH dropwise from a fine dropping pipet. The pH's are measured with nariow-range indicator paper (or a pH meter). The five solutions are then solidified by dipping the el ls for at least 10 min into an ice-salt freezing mixture.

The intensity of light scattered at 90°, im, from solutions 1,2, and

3 is monitored on the chart recorder as a function of time for half an hour each or until the trace ceases to change. Meanwhile solutions 4 and 5 are melted, and their light intensity compared with the final readings of solution 1. Once again a glass standard is employed.

The light-scattering properties of gelatin depend critically on the thermal history of the sample. This means that all five solutions must be treated similarly and effectively precludes repetition of the ex- periment-the students must be right the first time!

Results Typical results are shown in Figure 2. I t can be seen that the

scattering intensities pass through a maximum as the solutions melt but that this effect is suppressed a t higher concentrations (solution 3). There is also an overall inversion in light-scat- tering intensity as the concentration is increased from solution 1 to 2w 3. pinally there is a decrese in intensity from solution 4 (pH 5) resolution 5 (pl i 8 ~ , a n d asimilar changecan heseen with solutions made up in svdium chloride sulution. All these effects can be interpreted hs rhesrudents thnmah thoughtful application of the theory described earlier.

Acknowledgment

This experiment was made possible by the gift of a Sofica light-scattering photometer from the Nuffield Department of Clinical Biochemistry in the Radcliffe Infirmary, Oxford, and through the invaluable assistance and encouragement of F. L. Swinton, New University of Ulster, Coleraine, Northern Ireland.

Literature Cited

(3) Lundberg, J. L.. Polymer Reprints, 10.338 (1969). 1 0 Zirnm, 8. H., J. Chem Phys., 14 1093 and 1099 11948). 1.5) Ward.T. C.. J.CHEM.EDUC..S~.W~ 119811.

1971. p. 496. 17) Outer, P., Can, C. I., and Zimm, 8. H.,J Chom. Phys, 18. g10 11950). 18) Ref. 10.p. 1116. 19) B~andrup,J..andImmcwf E.H. 1Editors)."PalymerHandbmk"2nded.,John Wiley

and Sons, New Ymk, 1975. 110) Boedtker. H., and Doty. P., J Phy3 Chrm., 58.968 119.54).

554 Journal of Chemical Education