Configurational Properties of a Stiff-Chain Diaryl-Substituted

23

Downloaded by TUFTS UNIV on June 20, 2017 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch023

Configurational Properties of a Stiff-Chain Diaryl-Substituted Polysilane in Dilute Solution Patricia M. Cotts, Robert D. Miller, and Ratnasbapa Sooriyakumaran Almaden Research Center, IBM, 650 Harry Road, San Jose, CA 95120-6099

The properties in dilute solution of a diaryl-substituted polysilane indicate that the chain exhibits substantial stiffness in solution, with a persistence length of approximately 100 Å. To estimate the persistence length, measurements of the mean-square radius of gyration, intrinsic viscosity, and hydrodynamic radius at infinite dilution for a series of molecular weights were fitted to theoretical expressions for the wormlike chain. The large persistence length is consistent with the long wavelength (395 ±10 nm)for maximum electronic absorption observed for the diaryl-substituted polysilanes. Results are compared with those reported previously for dialkyl-substituted polysilanes.

THE EQUILIBRIUM FLEXIBILITY

of a polymer chain backbone, that is, the ability of the backbone bonds to rotate, has always been of great interest to polymer scientists. Silicon-containing polymers present opportunities for the investigation of configurational properties that are not available with morecommon carbon-backbone polymers. A completely unrestricted chain consisting of η bonds of length I, with all bond angles equally probable, has a mean-square end-to-end distance given by < r 2> = ψ η

(la)

Real polymer chains of fixed bond angles and restricted rotation have 0065-2393/90/0224-0397$06.00/0 © 1990 American Chemical Society

Zeigler and Fearon; Silicon-Based Polymer Science Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

398

SILICON-BASED POLYMER SCIENCE: A COMPREHENSIVE RESOURCE

larger values of , which may be expressed in a similar form

= n l

(lb)

2

k k

in which n and l are no longer the actual number of bonds and bond length, respectively, but are the number and length of larger imaginary bonds that yield the correct value of when the polymer backbone is treated as an unrestricted chain (I). The additional criterion necessary to define the length of the Kuhn statistical segment l and n is that k

k

k

k

L = nl

(2)


k k

in which L is the contour length or the length of the fully extended chain. Adherence to equation lb may be regarded as a definition of flexibility. Thus, chain molecules may be flexible despite considerable energy differ ences among rotational states of adjacent bonds. Larger hindrance to rotation necessitates larger values of l and thus the ratio l ll may be used as a measure of chainflexibility.For example, for typical synthetic organic poly mers with carbon backbones, l ll — 10. On the other hand, larger values of I in the real chain can result in higherflexibility(l /1 is small), as is observed for poly(dimethylsiloxane) (PDMS). The longer bond reduces steric hin drance to rotation. For highly hindered chains, as l becomes very large, the number of statistical segments n becomes too small for equation lb to be valid for molecular weights of interest, and these chains are regarded as stiff. With anyflexibilityin the chain, equation lb is valid at sufficiently high molecular weights, but these molecular weights are often beyond those obtainable for stiff synthetic polymers. Polymers exhibiting substantial stiffness are often treated as a KratkyPorod wormlike chain (2) or a variation thereof. The degree of stiihess is represented by the persistence length q, which may be defined as the pro jection of the end-to-end vector r in the direction of the first bond. The wormlike chain encompasses the limits of the flexible Kuhn chain discussed earlier, with q = l /2, and the completely rigid rodlike polymer, with q = oo. Actual polymer chains with a persistence length equal to or greater than their fully extended end-to-end length (contour length) L will approach the behavior of rodlike chains, but again at sufficiently high molecular weights (M), they may be treated asflexiblechains. The models just discussed apply to chains in an ideal or θ solvent, in which excluded volume interactions are absent. In practice, solution prop erties are more often determined in good solvents in which long-range ex cluded volume interactions lead to an increase in . These long-range interactions increase with M, so that equation lb is no longer valid. Excluded volume interactions and chain stiffness can be difficult to distinguish without measurements in a θ solvent. h

k

k

k

k

k

k


23.

COTTS ET AL.

Configurational

399

Properties of a Polysilane

The long bonds in silicon-containing polymers can result in greater flexibility, relative to carbon-backbone polymers, as observed for PDMS. However, highly substituted all-silicon-backbone polymers (polysilanes) may be stiff despite the long Si-Si bond (2.35 A) because of large steric hindrance caused by two bulky groups on each backbone atom. Previously, we investigated the properties in dilute solution of dialkylsubstituted polysilanes, including poly(di-n-hexylsilane) (PDNHS), in good solvents (3). The global polymer chain dimensions in solution were measured by using both thermodynamic and hydrodynamic techniques. The ratio l /l was —20 for this polymer; this value is twice as large as values obtained for most carbon-backbone polymers. However, because the molecular weights are large, the polymers are still flexible and are expected to obey equation lb in the absence of long-range excluded volume interactions. In this chapter, we report measurements on a diaryl-substituted poly silane, poly[bis(p-n-butyl)phenylsilane] (PBPNBPS), in which the bulky phenyl groups may provide more substantial steric hindrance to rotational freedom than do the dialkyl substituents. Reported values of the wavelength of maximum electronic absorption are large (395 ± 10 nm) and cannot be attributed solely to electronic substituent effects (4).


k

Experimental Procedures Intrinsic Viscosity. Dilute-solution viscometry of samples in toluene was car ried out in a Cannon-Ubbelohde semimicrodilution viscometer (size 25) in a tem perature-controlled bath (25.0 ± 0.2 °C). At least three concentrations were measured, and the results were extrapolated to infinite dilution by using the Huggins and Kramers relations [η] = ^

c

+ kWc

[η] = ^

(3a)

+ ...

+ (*' - ±)[η]% + . . .

(3b)

in which [η] is intrinsic viscosity, k is the Huggins coefficient, η Γβ ι = t \Jt h, and η* Ρ = T]rei - 1. t \ and f soiv are the efflux times of the solution and solvent, respectively. Values of T|rei varied from 1.2 to 1.6, and no correction for kinetic energy was applied for fsoiv > 100 s. r

so

so

m

n

Static Light Scattering. The weight-average molecular weight (Mw), the ther modynamic second virial coefficient (A2), and the s-averaged mean-square radius of gyration (RG,/) were determined with a Chromatix KMX-6 low-angle light-scattering photometer and a Brookhaven BI200SM photogoniometer. Values of M w and A 2 were obtained with the more precise KMX-6 photometer from measurements at a scat tering angle of 4° at several concentrations c K c

1


(4)


400

in which the Rayleigh factor fi9 for a scattering angle of 4° was substituted for R 0 = Re-»o without correction. The constant Κ is given by „ _

4>n n (dnldc) 2

2

2

in which η is the refractive index of the solvent (1.497 for toluene), N is Avogadro's number, λ 0 is the wavelength of the incident light (6328 A), and dn/dc is the dif ferential refractive index increment (0.131 mL/g). No corrections were made for anisotropy (pv), because at a scattering angle of 0°, p v was small (pv[0°] = 0.0044 for sample 4-2). The root-mean-square z-averaged radius of gyration RG,Z was measured with both instruments. The BI200SM photogoniometer was used with software from Brookhaven Instruments to determine KclR% for 11 angles (15° < θ < 150 °), and these values were fitted to the equation Downloaded by TUFTS UNIV on June 20, 2017 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch023

A

«e,c

"e = 0,c \

& /

in which q = (1/λ0)(4ιτη) sin (Θ/2). Measurement of R , with the KMX-6 photometer using the dissymmetry method described previously (3) yielded values within 5% of those determined with the Brookhaven photogoniometer. For all measurements, R was independent of concentration in the range measured. The angular dependence of KC/RQ, of sample 64-2 is shown in Figure 1. G Z

Gz

C

Dynamic Light Scattering. The hydrodynamic radius, Rh, is defined as the Stokes radius from the mutual diffusion coefficient at infinite dilution (DG) Do =

0.0

0.2

^βΓ 6irn 0 R h

0.4

(7)

0.6

0.8

sin20/2 Figure

1. Angular

dependence

of Kc/R e , c for 1.58 mglmh.

sample 64-2,

with c


23.

COTTS ET AL.

401

Configurational Properties of a Polysilane

in which η 0 is the solvent viscosity, fcB is the Boltzmann constant, and Γ is temper ature. The limiting diffusion coefficient was determined by extrapolation of D at four to five concentrations c to infinite dilution. D is defined by c

c

(8)

D = YJq* c

in which T is the first cumulant of the correlation function C(f) at each concentration, c

In Γ ^ - ΐ 1


IB

11/2 1 , β

J

= 1η6ΐ/«-Γβί +

..

^ 2

2

(9)

in which Β is the measured base line, h is an optical factor, t is time, and μ 2 is the second cumulant. Software for cumulant analysis from Brookhaven Instruments was used tofitthe measured correlation function C(t) to equation 9 by using a weighted second-order polynomial nonlinear regression. The measured base line Β of the correlation function C(t) was determined from the average of four delay channels (1029-1032) multiplied by the sample time At. The calculated and measured base lines were within 0.1% for all runs used in the analysis. The sample time At was chosen with the criterion Δ ί = —rr ml

(10)

c

in which m is the number of channels (m = 128). This criterion provides a larger number of points in the initial decay of the correlation function (for the determination of Tc) at the expense of less precision in the second cumulant μ 2 . The normalized second cumulant, μ 2 /Γ«Λ was 0.3 ± 0.1, consistent with the polydispersity of these samples. A representative correlation function is shown in Figure 2. Size Exclusion Chromatography. The molecular weight distribution of each sample was determined by size exclusion chromatography (SEC). A volume of 150 μΙ, of each sample at a concentration of 1-2 mg/mL was injected onto a set of four 30-cm PLgel (cross-linked polystyrene) columns (with porosities of 106, 105, 104, and 103 Â) housed in a Waters 150C liquid chromatograph at 40 °C. The mobile phase was tetrahydrofuran, and the concentration detector was a differential refractometer. The column set was calibrated with a series of 15-20 narrow-distribution pol ystyrene (PS) standards (Polymer Laboratories), and the data were fitted to a thirdorder polynomial log M = A + Bt + Ct + Dt 2

3

(11)

in which t is the peak elution time of a PS standard of molecular weight M. Calculation of molecular weight averages relative to PS was carried out with an IBM PCXT with software from Nelson Analytical. The chromatograms of all samples are shown in Figure 3.

Results Molecular Weight Determination. Results obtained for all samples measured are listed in Table I. No unusual behavior was observed with any


402


-1.111561 Β = 5.294413x10e b = 0.329 Γ =1008.91 rad/s


ι m α

-2.708346 15

JL

2040

Time (μββο)

Figure 2. log of normalized correlation function C(t) as a function sample 64-2, with c = 1.18 mglmh.

of time for

of the measurements, and interpretation of the data was straightforward. All reported results (other than those for SEC) were obtained in toluene, which was a thermodynamically good solvent for the polymer. However, as will be discussed later, the contribution of the excluded volume effect to the experimental parameters is expected to be small. Measurements of M w by light scattering carried out in other solvents (tetrahydrofuran and hexane) were in agreement with results obtained in toluene. This result and the consistency of results from the variety of techniques used suggest that ag gregation is not a problem for these solutions. Aggregation is often a con tributing factor in solutions of stiff-chain polymers, particularly those that can crystallize. The M w values obtained from SEC (M W S E C ) calibrated with PS standards agree quite well with M w values from light scattering (MW L S ). This unexpected result may be explained by Figure 4, which shows the [η]·M relations for PS, PBPNBPS, and PDNHS. At similar molecular weights, PS and PBPNBPS have very similar values of [η], that is, their hydrodynamic vol umes are similar. In comparison, the PDNHS curve (3) lies significantly below that for PS, so that values of M W S E C relative to PS are expected to be much smaller than the true M w determined by light scattering. The increased stiffness of PBPNBPS relative to either PDNHS or PS may be seen in the increased slope of the curve relative to the other two in Figure 4.


23.

COTTS ET AL.

Configurational


403


o

Elution Volume (ml) Figure 3. SEC chromatograms of samples studied.

Estimation of Persistence Length. Correction for Polydispersity Effects. Estimation of the persistence length from the experimental data by using the Kratky-Porod wormlike chain model requires correction for polydispersity effects. The unusual (and sometimes multimodal) distributions obtained for polysilanes are not amenable to an analytical form for the distribution. The samples used in this study were nearly monomodal by SEC, with only sample 4-2 containing a high-molecular-weight tail (Figure 3). For the purpose of this study, correction of the ^-averaged radius of gyration (R J to a weight-averaged value (flG)W), that is, the radius of gyration that would be measured for a monodispersed sample with M = M w , may be approximated by G

(12)



13 49 450 550 1800

(xlO

± ± ± ± ±

1 5 50 80 200

g/mol)

LS W

M

4

g

2.6 ± 0.5

—

2.1 ± 0.5 1.0 ± 0.4 3.3 ± 0.5

z

( X10- mL · mol) c

,(A) a

265 ± 15 70 ± 20 600 ± 20 335 ± 35 600 ± 20 430 ± 30 1235 800 ± 80

—

"Values were calculated from RG,zls as described in text. ^Values are relative to polystyrene. "This sample showed a high-molecular-weight tail (see Figure 3).

4-32 4-2 64-2 75-2 67-2

Sample

3

20 50 292 268 510

± ± ± ± ±

*k(A)

[T\](mL/g)

— 2 3 17.7 ± 0.5 18 169 ± 12 30 — 20 454 ± 20

Table I. Summary of Experimental Data


M

S £ C

9.5 41 506 193 1800

3

(Χΐ0 \ΐπιοψ

M,/M„ 1.2 10c 2.6 1.8 2.0


23.

COTTS ET AL.

10

4

Configurational

10


5

10

6

405

:

10

Figure 4. [η]*M relations for PS (short dashes), PDNHS (long dashes), and PBPNBPS (solid line).

with MJM determined by SEC, because R is approximately proportional to M ° 7 for these polymer samples. Equation 12 is correct for Gaussian coils with an exponent of 0.5 for any distribution. For coils expanded from Gauss ian dimensions because of either or both long- and short-range interactions, the molecular weight distribution must be known to calculate the precise average. For the distributions observed in this study, the ζ average is ex pected to be within 15% of the correct average. The experimental values of [η] and R h were sufficiently close to weightaveraged quantities to be used without correction. The R h value was obtained from the first cumulant of the autocorrelation function, which yields the ζ average of the diffusion coefficient. However, because the diffusion coefficient D is inversely proportional to R h , the actual R h value more closely reflects M w for many synthetic polymers. Although these quantities (and the values of R G w obtained previously) are not exactly equal to those that would be obtained for a monodispersed sample with M = M w , further correction is within the uncertainty of the limited data. W

G

Excluded Volume Interactions.

cluded volume interactions to and R G decreases as the polymer chain becomes stiffer. This tendency may be visualized as arising from the less frequent intramolecular segment-segment interactions in a stiff-chain poly-


The con

406


mer. A more quantitative assessment may be obtained through the interpenetration function ψ

Ψ =

Τ

(13)

3

or, similarly, the parameter Α 2 Μ / [ η ] . Both parameters vanish when ex cluded volume interactions are absent (A2 = 0) and increase to an asymptotic value as the excluded volume parameter α increases, α is defined as


" ' - ^

Configurational Properties of a Stiff-Chain Diaryl-Substituted

Recommend Documents