ON-LINE MEASUREMENT OF THE RMS RADIUS OF GYRATIONAND MOLECULAR WEIGHT OF PO_L_'I_M'tD'EPRECURSOR FRACTIONSELUTING FROM A SIZE EXCLUSION CHROMATOGRAPH*

Seong KimPatricia M. CottsWilli Volksen

IBM Research DivisionAlmaden Research CenterSan Jose, California 95120

ABSTRACT: The recent introduction of multi-angle light scattering de-

tectors for size exclusion chromatography has made possible the measure-

ment of the root mean square radius of gyration (R_) and molecular weight

(M) of polymer fractions eluting from a size exclusion chromatography

column. The characterization of the dimensions of a polymer may be ac-

complished with only a few milligrams. The dimensions of a polyimide

precursor prepared by the condensation of the meta-diethyl ester of

pyromellitic dianhydride with para-phenylene diamine have been meas-

ured with this technique. The dependence of Rz on M across the distrib-

ution is compared with that predicted for a freely rotating chain, and with

other similar polymers measured with hydrodynamic techniques.

* this manuscript has been accepted for publication: J. Polym. Sci., Polym.

Phys. Ed., 30, XXX (1992)

• .. A

INTRODUCTION

A primary method of understanding the physical properties of polymers

in solution involves determination of the dimensions of the polymer mole-

cules in solution as a function of molecular weight, M. Theories of the

expected dimensions usually assume a monodisperse distribution of mo-

lecular weights. Fractionation of synthetic polymers to produce narrow 1

molecular weight distributions is very tedious, requires large amounts of iI

sample, and in some cases is not possible due to crystallization, degrada-

tion, or other effects. Fractionation of a synthetic polymer by size-

exclusion chromatography (SEC) requires only small amounts of sample,

and is now routine. However, the vast majority of SEC results are still

reported in terms of a different polymer which is used to calibrate the col-

umn; most commonly polystyrene. Low-angle light scattering detectors

permit direct measurement of the molecular weight of the sample eluting

from the column without reference to a calibration curve, l_ The recent

introduction of multi-angle light scattering detectors developed for use on-

line with SEC permits the measurement of the scattered intensity at as

many as 15 angles as the sample elutes, thus the root mean square radius

of gyration (Rz) as well as M may be measured. 3

The class of materials containing the imide moiety in the polymer back-

bone are known collectively as "polyimides". These materials exhibit an

exceptional thermal stability and solvent resistance making them attractive

for aerospace use and as insulating layers for electronic packaging. In

many cases, a precursor polymer, an amic acid or amic ester, is formed in

the initial polycondensation, which, although already of high M, is still

84

soluble in amide-type solvents such as dimethylformamide,

dimethylacetamide, and N-methylpyrrolidone (NMP). These precursor

polymers may be coated or spun into films from solution, and then cyclo-

dehydrated into the final imide thermally or chemically. These steps are

shown in Figure 1. Since the polyimide is usually insoluble in any organic

solvent, characterization of the molecular properties is usually done with

the precursor material. 4"6

Previously, we reported SEC on a group of similar polyimide precursors in

NMP using a multi-angle light scattering detector. 7 The exceptionally high

values measured for M initially were found to be due to imidization of the

polymer in dilute solution due to methylamine present in the NMP.

Neutralization of the NMP with phosphorous anhydride (P2Os) prior to

use was sufficient to minimize the imidization to the extent that values of

M measured with SEC/LS were in agreement with those obtained from

classical light scattering techniques at higher concentration. Values of Rs

for these polymers were too small to be measured by light scattering with

a 632.8 nm source.

The polyimide precursor studied here, m-PMDA/p-PDA Et2, is formed

from the condensation of meta-diethyl pyromellitate diacyl chloride and

para-phenylene diamine. This repeat unit of the polymer contains a long

rigid segment as may be seen from the structure in Figure 1. In the

imidized form, the meta catenation is removed, and the polymer backbone

is completely 180" catenated, forming a "rigid rod" polymer. In the diester

precursor form, the meta links contribute substantial flexibility, and nearly

free rotation is expected about these bonds. 8'9 The long rigid segment be-!

85

L .... .... •

tween meta links, and the exceptionally high molecular weight attained

permitted the measurement of Rg by light scattering with a 632.8 nm

source.

EXPERIMENTAL METHODS

Synthesi_ The m-PMDA/p-PDA diethyl ester was synthesized as de-

scribed previously for similar polyamic esters. 1°']1 The stoichiometry was

chosen to produce a polymer with a number average degree of

polymerization, (DP)n, of approximately 100. The polyamic esters have a

number of advantages in comparison to the polyamic acids with regard to

solution characterization: 1) the esters may be precipitated as a powder

whereas the amic acids undergo hydrolysis when precipitated, 2) the two

isomeric diesters may be separated, so that a pure meta or para polymer

may be obtained, and 3) the absence of carboxylic acid groups in the esters

minimizes the possibility of ionization of the polymer, which complicates12

the solution properties for the polyamic acids.

Light scattering: Light scattering measurements were made using a

Chromatix KMX-6 photometer (LDC Milton Roy) equipped with a

refectance accessory for measurements at high scattering angle. The low

angle (approximately 4° scattering angle) and high angle (approximately

176") may be used to estimate Rg as has been shown for a series of

polystyrene and poly(ct-methylstyrene). I3 This technique is limited to

moderate molecular weights, such as the condensation polymers studied

86

here. The weight average molecular weight M,,, second virial coefficient

A2, and Rx are then determined from the Equations:

K'c _ 1 (la)Ro - M_,P(O) + 2A2c + 3A3c2 + "'"

or

I K'c1112 I +_.12Mw C= _ •,,1/2 (lb)

"_ Mwll2p(o)ll2

withK' theusualopticalconstantand

p(q)-1/2 = l + qRg/6 .... (2)

where q = (4nn/,_)sin(0/2), n denoting the refractive index, and 2 the vac-

uum wavelength of light. The "square-root" expressions (Equations l b

and 2) have been suggested several times in the literature as graphical aids

to extend the range of q and/or c within which linearity of the concen:

tration or angular dependences is observed. 1416 Equation lb is obtained

from Equation la by setting A3= (I/3)A2 2, and truncating after the c2

term. An advantage of the polydisperse samples is that the upward cur-

vature in the P(O) function expected at higher q is balanced by a down-

ward curvature due to the polydispersity. For polymers with a

Zimm-Schulz most-probable distribution in a O-solvent, Zimm has shown17

that P(q) is linear in q.

The differential refractive index increment (dn/dc) was measured using a

Chromatix KMX-16 laser light scattering photometer (LDC Milton Roy)

with incident light of 623.8 nm and a temperature of 25"C. Five concen-

trations 2 mg/mL < c < 10 mg/mL of m-PMDA/PDA in NMP treated

with P205 were measured, yielding dn/dc = 0.144 mL/g.

SEC/LS: Size exclusion chromatography was carried out using a Waters

GPC-1, consisting of a 5'9:0"pump, a W_I,S'_I_sample injector, an Pe4®ll,dif-

ferential refractometer, and a set of four columns housed in an oven

maintained at 60"C. The columns used were 30 cm in length, of nominal

porosity of 106A, 105A, 104A and 103A of cross-linked polystyrene beads

(Polymer Laboratories, 10pm particle size). The mobile phase used was

NMP, stirred over approximately 0.02M P205 for 1-2 hours, and then fil-

tered through a 3 pm Fluoropore filter (Millipore Corporation) before use. ,_.,..'%

The flow rate was 0.6 mL/minute. 250 _L of a 3.44 mg/mL solution was :?..

injected, resulting in the injection of 0.86 mg of polymer. The columns

were calibrated with a series of 15 narrow distribution polystyrene stand- .:_

ards for calculation of molecular weight averages "relative to polystyrene",PS PS ,

indicated as M_,, M_, , etc. The eluent from the column was directed

through a DAWN Model F multi-angle light scattering detector (Wyatt

Technology) and then back through the differential refractometer to avoid _.

subjecting the fragile refractometer cell to high back pressure. The signals

from the LS detector and from the refractometer were monitored by two

separate data systems: 1) a PC-XT with SEC software from Nelson Ana-

lytical, and 2) a PC-AT with SEC/LS software from Wyatt Technology.

The values of M_at each elution volume i were calculated from Equations

l b and 2 above, using the measured dn/dc. The concentration, c: at each

88

elution volume i was calculated from the integrated area under the RI

peak and the known injected mass. Comparison of the results from SEC

and SEC/LS is discussed below.

Viscometry: The intrinsic viscosity, [_?]of the m-PMDA/p-PDA Et2 sam-

ple was measured in NMP treated with P205 at 25°C. The data was fit

using the Huggins' and Kraemer's relations:

?/spc = [r/] + kn,[_/]2c + ... (3a)

and

_'rl rlrelc = [r/] - (I/2 - kH)[q]2c + ... (3b)

yielding [q] -- 123 mL/g and kn = 0.24.

RESULTS AND DISCUSSION

Molecular Parameters: A summary of the results from the light scattering

and SEC/LS measurements is listed in Table 1. The light scattering re-

sults, [Kc/l_] _t2 versus c for the low and high angles, ® = 4 ° and

® = 176°, are shown in Figure 2. The measured (DP), was nearly 400.

While this is an exceptionally high molecular weight for a polyimide pre-

cursors, we have previously attained molecular weights of this magnitude

for similar polymerizations. 5'12'18

The refractive index (RI) and 90° light scattering chromatograms (LS) for

the m-PMDA/p-PDA Et2 in NMP are shown in Figure 3. The scattering

89

intensity, proportional to the product cM, increases more rapidly at the

high M side of the distribution and is far less sensitive at the low end. A

low M peak clearly visible in the RI chromatogram is not detected at all

in the light scattering. The insensitivity of light scattering to the low M

portion of the distribution can lead to erroneously low values of M,, so that

comparison of M,,/M, from SEC/LS with that obtained from SEC with a

calibration curve should always be considered. The value of M,,]M,, listed

in Table 1 for SEC/LS is significantly smaller than that obtained by SEC,

while the values of Mz/M., are quite similar for both techniques. The

M.,/M,, from SEC, 2.24, is also more consistent with step-growth kinetics

for a condensation polymerization. Thus, the smaller value obtained by

SEC/LS is likely due to the insensitivity of LS to low M species, and the

value from SEC is used in the calculations that follow. Chromatograms

obtained at the other scattering angles were quite similar, becoming more

noisy at lower scattering angles. The molecular weight, M;, and root mean

square radius of gyration, R_.,, at each elution volume i were calculated i

using Equations l b and 2 above, and are plotted for all the fractions in

Figure 4. The points for the M < l0 s are systematically too high, and are

also scattered, and are not considered in the following analysis. In thisI

region, the values of Rz,i are less than 20 nm, so that the angular depend- i

ence is within the uncertainty of the intensity measurement. For

M; > 105, Rz._> 20 rim, so that in this region reasonably precise values of

Rz.i may be obtained. Fitting the data in this region with a least squares

linear regression yields:

90

Rg,i= 0.02 x M0"59 (4)

The exponent 0t of 0.59 is consistent with a flexible polymer chain ex-

panded in a good solvent. However, previous measurements on similar

polymers have indicated that the long rigid backbone "bonds" comprised

of the aromatic ring and the planar trans amide bond introduce sufficient

stiffness to the chain so that non-Gaussian chain statistics can be observed

at the moderate molecular weights usually attained, is The possibility of

these stiffness effects and excluded volume interactions is discussed below.

The Rz., measured by light scattering on the unfractionated polymer may

be compared with the Rz.; measured on the fractions separated by

chromatography. For flexible polymers in a O-solvent, where the exponent

0cis 1/2:

= KM; (5,,)

with K and = identical to those determined on narrow distribution frac-

tions. Using this simple relation, and substituting M, -- M,,(M,/ Mw),with

K and 0tfrom Equation 4 above, we obtain Rs., of 33.7 rim, in comparison

to a measured value of 37.3 nm from light scattering on the unfractionated

polymer (see Table I). A more precise calculation of R_., which is valid for

flexible polymers even in good solvents, requires an analytical expression

for the molecular weight distribution. 19 The distribution of a condensation

polymer may be described by the Zimm-Schulz (or most-probable) dis-

tribution, so that:

_g,a2 2 1= r + co (sb)

where t = 2_ - 1 and co = F(3 + h + e)l(h + 2)'F(3 + h), with

h-I= (Mw/M,)-l, and F denoting the Gamma function. This more

complicated expression yields Rz,zof 34.2 rim, only slightly larger than the

33.7 nm obtained with Equation 5a. Both values are in reasonable agree-

ment with the measured value from light scattering, as may be seen in

Table 1.

Substitution of M, into Equation 4 above yields Rz.wof 23.7 rim, in excel-

lent agreement with the R_,wof 24.4 nm obtained by averaging the SEC/LS

results.

Comparison with Model: Previous work on similar aromatic semi-flexible

polymers has indicated that the long rigid backbone "bonds" connected

by flexible joints about which nearly free rotation can occur results in these

polymers being well approximated by a very simple model, the freely ro-

tating chain. 2° At sufficiently high degrees of polymerization, the polymers

are expected to display Gaussian statistics, and have an exponent of 1/2

in the Ravs M relation in an ideal or O-solvent. However, because of the

long rigid segment between flexible joints, and the moderate degree of

polymerization usually attained for condensation polymers, the exponent

may be greater than 1/2 at lower M. This transition from a stiff or nearly

rodlike molecule at low M to a more flexible one at higher M may be de-

scribed in terms of the Kratky-Porod wormlike chain. El In this model,

chain flexibility is introduced continuously along the chain rather than in

discrete flexible joints, however, the overall molecular dimensions may still

be described by this model. In this model, the stiffness is described in

terms of the persistence length, p, or length along the chain contour for

which an intial vector direction persists. In the low M or rod-like limit,

p = oo, while in the high M or coil-like limit, p = t'j2, where _'_ is the

Kuhn statistical segment length.

To assess whether the exponent of 0.59 is primarily due to stiffness or ex-

cluded volume interactions, _'k is calculated for the freely rotating model

and values of Rg and [r/] calculated for a wormlike chain with this _'_are

compared with those measured experimentally. The Benoit-Doty equation

for Rs of a wormlike chain was used: 22

The length L of a fully stretched out chain was calculated as L = M[ML

with ML estimated from the projection of the monomer unit onto the chain-1

axis, 350 nm Using the model of the freely rotating chain, the equivalent

Kuhn statistical segment length may be estimated from the Eyring for-

mula: 23

where < r2> is the mean square end-to-end distance. At high M or for

Gaussian chains: R__= < r2>/6, when no excluded volume effects are24

present. The length of the fully stretched out chain is then given by:

g3

L = ne sin(_/2)= n,ek (8)

where n and _' are the number and length of the rigid repeat unit, _bis the

effective bond angle from the meta catenation, and n_ and g'_ are the

number and length of the Kuhn segments. The length L is generally less

than n v: due to valence angle restrictions. This leads to an estimate of the

Kuhn length of 4.4 rim, or a persistence length of 2.2 nm. The line of short

dashes in Figure 4 is Rx as a function of M calculated from the Benoit-

Doty equation (Equation 6) with _'kequal to 4.4 nm. Although Rz versus

M is expected to have some curvature for a wormlike chain, in the limited

range of M accessible a linear fit is appropriate, and yields:

Rg,r R = 0.037 x M °'52. (9)

The exponent of 0.52 is less than the experimental value of 0.59, but larger

than the Gaussian chain value of 1/2 expected at higher M. An increase

in _'kto 8 nm has a negligible effect on the exponent, and simply shifts the

curve upward to the line of long dashes as shown in Figure 4. Thus the

exponent a of 0.59 must be at least parrtially due to excluded volume

interactions at M>,-,50,000. At lower molecular weights the experimental

line (the solid line in Figure 4) approaches the wormlike chain calculation,

indicating that excluded volume effects are minimal. This is consistent

with previous work in which similar values for [r/] were measured in good18

and poor solvents for a PMDA/ODA polymer. This lower molecular

, weight range, 10,000 < M, < 50,000, is typical for condensation

polymerizations. Thus it appears that both excluded volume interactions

and stiffness are significant contributions to the exponent a > 1/2 in the

high molecular weight range studied.

The free-rotation estimate for t'k can also be used to calculate an intrinsic

viscosity for comparison with the measured [r/] of 123 mL/g. The analyt-

ical expressions of Yamakawa and Fujii were used, 25 with an estimated

diameter of 0.7 rim. The diameter was assumed to be equal to those of

similar ethyl ester derivatives. Is The calculated [r/] = 124 mL/g, in excel-

lent agreement with the measured value. The calculated [r/] is based on

the measured Mw, and does not include correction for polydispersity. The

viscosity average molecular weight, M,, may be defined as the average for

which the Mark-Houwink-Sakurada constants, K and a in:

[r/] = KM a (I0)

for narrow distribution samples, are also valid for a broad distribution

with the measured It/]. For polymers with the most probable distribution,

it has been shown that 26

M_ 2= (ll)

g. [(l + a)r(l + a)] lla

so that Mw is within 10% of M, for many polymers.

The estimated persistence length of 2.2 nm for m-PMDA/p-PDA Et2 may

be compared with those obtained from intrinsic viscosities of similar

polymers. 6'is These include PMDA/ODA, BPDA/p-PDA and meta and

para isomers of the esters, where ODA is oxydianiline, and BPDA is

95

_______ __.:-_.,. ,_, _.-_'..._,._ _.'_-.._-._.. __ ,_,-_. .._ • -- _

3,3',4,4"-biphenyltetracarboxylic acid dianhydride. The experimental per-

sistence lengths range from 1.8 nm for m-PMDA/ODA Et2 to 4.5 nm for

p-PMDA/ODA Et2. Thus in the precursor form, m-PMDA/p-PDA Et2

is similar in molecular flexibility to these materials. However, in the

imidized form, the source of the flexibility, the meta catenation, is lost.

Measurement of Rx versus M using SEC with a multiangle light scattering

detector with less than 1 mg of polymer has been demonstrated. This

technique circumvents several problems with fractionation. The results are

consistent with measurements on the whole polymer, and with expecta-

tions based on theoretical work of Birshtein. As has been found for several

other polyimide derivatives, the dimensions of m-PMDA/p-PDA Et 2 are

similar to those calculated with a very simple model, the freely rotating

chain. Although the barrier to rotation about the meta linked aromatic

ring is minimal, some effects of stiffness are apparent at moderate molec-

ular weights due to the long rigid repeat unit in the backbone.

96

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on Recent Advances in Polyimides and other High Performance

Polymers, San Diego, California, January 22-25 1990.

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26. reference 15, p.313

1tI!

t

TABLE I

Summary of Results from LS and SEC/LS for m-PMDA/p-PDA Et 2

LS SEC/LS SEC

M,_ (g/mole) 166,000 160,000 ---

Me,s (g/mole) ...... 202,000

104A_ (mL mole / g2) 8.8 ......

R_., (nm) 37.3 34.2 a ---

R_.,, (nm) --- 24.4 ---

Mw/M, --- 1.72 2.24

M,/Mw --- 1.73 1.77

a calculated using Equation 5b in the text.

99

0 0II II

cl/c'y_c _Cl

EfO_c_ c/OEt + H2N--_H2II II

0 0 / -HCl

0 0II II

Et o/C_-_C _OEt

II II Ik Jl -,

o o ,_--_oH

m-PMDA-Et2/PDA _ -2 EtOH

0 0II II

N !

II II0 0

Figure 1. Condensation of pyromellitic diacid diester and p-phenylenediamine to form m-PMDA/PDA diethyl ester, and subsequent imidizationto a "rodlike" polyimide.

_oo _ i ._

i 2 I I I I I I I I I_. 0 1 2 3 4 5

c(g/L)

Figure 2. [KclRo] _t2versus the concentration c for ® = 4* and ® = 176°for m-PMDA/PDA diethyl ester In NMP.

I I I

f\/III

tO

.__ LS RI -

..Q

'- ICO4-,

_ _ -i \I \

_'-"- ' _j/_I I I

10 20 30 40

Elution Volume (mL)

Figure 3. Refractive index and 90 ° light scattering chromatograms form-PMDA/PDA diethyl ester in NMP at 60°C.

60

5

3 I I I t t I I ,I

104 105 1u6

Mw

Figure 4 Rs, versus M, for each fraction (slice) across the distributionssht_wn in Figur_ 3. The. solid hne through the data is the linear regressionfit for Mr > 10, Equatton 4 in the text. The hne. of short clashes is theBenoit-Doty calculation of R_ for a wormlike chain with d'_ equal to 4.4nm, calculated with the freely rotating model. The line of long dashes isthe Benoit-Doty calculation with _'kincreased to 8 nm, showing no changein slope.