摘要:

Rayleigh Scattering From Polystyrene SolutionsBY N. C. FORD, JR., * F. E. KARASZ t AND J. E. M. OWENDepartment of Physics and Astronomy and Polymer Science and EngineeringProgram, University of Massachusetts, Amherst, Massachusetts, 01002, U.S.A.Received 8th January, 1970A laser homodyne spectrometer has been used to study the power spectrum of light scattered fromdilute polystyrene+2-butanone solutions. From the measurements the translational diffusionconstants for the macromolecules were determined as a function of molecular weight and soluteconcentration. The analysis of the data included an estimation of the unperturbed dimensions of thepolymer.In recent years laser homodyne spectroscopy has been applied to studies of thespectral distribution in Rayleigh light scattering from polymers in dilute ~olution.l-~The principal quantity that can be obtained from such investigations is the transla-tional diffusion constant, though in special cases the rotational diffusion constant ofanisometric polymers may be determined also.2* Compared to conventionaltechniques, the measurement of diffusion constants from light scattering studies offerscertain inherent advantages : a relatively high precision, rapid measurement times,minimal data analysis and small sample requirement.Furthermore, because thesystem is in macroscopic equilibrium, the differential binary diffusion constant D(c)for the system (as distinct from an integral diffusion constant) is obtained directly.The significance of translational diffusion constants, in common with parametersobtained from other hydrodynamic measurements of macromolecules in dilutesolution, lies in their application to the characterization of such molecules in terms ofmolecular weight or size, and of shape.Homodyne spectroscopy studies have beenlargely confined to studies of the latter parameter, particularly with respect to thechanges in shape concomitant with conformational transitions in biological polymers.The present study, in contrast, was intended to determine the utility of the techniquefor molecular weight and size studies of random coil polymers, using in the firstinstance a system previously well characterized by conventional means. As a straight-forward method of measuring, for example, mean square end-to-end distances, it isimportant to determine whether the liability of clearly more complex instrumentationcompared to that required for an intrinsic viscosity measurement is outweighed bythe above-mentioned or other advantages.The power spectrumdiffusing macromoleculesMEASUREMENT THEORYI(m) of light scattered from a solution containing freelyis given byCIOACO(u, - 0 0 ) ~ + (Aco)~I(CO) =if terms other than those arising from translational modes may be neglected.Thishas been shown to be so for all cases considered here.' In eqn (l), I, is the intensity* Department of Physics and Astronomyt Polymer Science and Engineering Program22N. C. FORD, JR., F . E . KARASZ AND J . E . M. OWEN 229of the incident light of frequency coo, and C is a constant dependent upon the natureof the solute and solvent.Eqn (1) describes a Lorentzian line with a half width AmwhereAO = D ( c ) ~ (2)in which D(c) is the binary translational diffusion constant of the polymer moleculesin solution at a concentration c, and K = kin-kout represents the change in wavevector of the scattered light. Thus, since I kout [ E! I kin 1,+ + - b+ --*AO = 4D(c) I kin I sin2 812 (3)(4) = [ l6n2D(c) sin2 8/2]/n2Ag,where 8 is the angle at which scattered light is observed, n is the refractive index of thesolution, and ;Lo is the incident light wavelength. A laser homodyne spectrometercan be used to resolve the line width (which is typically of the order of 103-104 Hz) bya self-beating technique and hence yield D(c).The spectral analysis of the audiocfrequency signal produced by the spectrometer can be carried out by means of aconventional wave-analyzer or, as in the apparatus used in this study, the signal canbe processed in a signal correlator in which the auto-correlation function G(z) iscornp~ted.~ The latter is defined byand the Wiener-Khinchine equation shows that G(z) is the Fourier transform of thepower spectrum. As the Fourier transform of a Lorentzian line shape is an expo-nential,where r = 2D(c)K2. The diffusion constant D(c) is thus obtained directly from thetime-constant of the exponential signal. The signal correlator approach to powerspectrum analysis of this kind has many advantages in terms of precision, speed anddirectness.G(z) = const.exp (-Tz), (6) +EXPERIMENTALINSTRUMENTATIONAn apparatus developed here based on the above considerations has been used in thepresent measurements.' It is an improved version of the instrument described previou~ly,~differing in detail but not in essential features. The principal difference resides in the read-out procedure in which an internally generated exponential of variable but known time-constant is subtracted from the experimentally observed correlation function in a mannerarranged to produce a null-signal for all values of z. The desired time constant l7 is thendirectly obtained from the calibrated time-constant of the internal wave-form generator.MATERIALSFor this study six samples of atactic polystyrene prepared by anionic initiation were used.Five of these polymers were obtained from Pressure Chemicals, Incorporated ; the sixthwas the narrow molecular weight distribution polystyrene sample available from the NationalBureau of Standards (NBS 705).The weight-average molecular weights according to infor-mation given by the respective sources were 2.08 x lo4, 5.05 x lo4, 1.6 x lo5, 1.79 x los (NBSsample), 6 . 7 ~ lo5 and 1 . 7 ~ lo6. The M,/M, ratios were 1.10 or less. The solvent usedwas reagent-grade 2-butanone. All materials were used as received230 RAYLEIGH SCATTERINGPROCEDUREPolymer solutions of approximately the chosen concentrations were prepared in thenormal manner. Particulate matter had been previously removed from the solvent by pas-sing the latter twice through ultra-fine sintered-glass filters and the solution was furthercleaned by several additional passes through the filter before final transfer into the samplecell.Precise solute concentrations were established after the measurements gravimetrically.The power spectrum half-width r was measured at a number of angles in the range 15"<6<100" for each solution ; D(c) was then calculated from plots of against sin20/2 accordingto eqn (4).RESULTSAccording to the theory summarized above, a plot of r against sin 26/2 should berectilinear and pass through the origin. Fig. 1, representative of all the solutionsstudied, shows that this was found to be the case. In solutions with stronger scatter-ing power r was measured at fewer angles.The diffusion constants calculated fromthe slopes of this and similar plots were estimated to have an accuracy of k 3 %. Theprecision of the experiment is a function of the solution scattering power and thusfor the lowest solute concentrations, particularly those involving the lower molecularweight polymers, the standard error increased somewhat. For the analysis under-taken below the diffusion constant Do at infinite dilution was required. This wasobtained by extrapolation from measurements of as dilute a solution as possible-lower than 0.05 % for the higher molecular weights and somewhat greater for thelower. The concentration dependence of D(c) introduced some additional error inthis extrapolation, hence the final accuracy of the computed Do in the present study isestimated to be + 5 %.DISCUSSIONMOLECULAR WEIGHT DEPENDENCE OF DoThe molecular weight dependence of Do is shown in double logarithmic form infig.2. As expected from hydrodynamic theory, the results over the molecular weightrange investigated are well represented by the equationwhere, in this study, K' = (3.1 k0.2) x cm2 s-l and b = 0.53k0.02, at 298 K.Weight-average molecular weights were employed uniformly in this calculation.The parameter b is related to the corresponding exponent in the Mark-Houwinkintrinsic viscosity ([q]) equation,Do = KDM-b, (7)[q] = KM"3b = a+1.The intrinsic viscosity of the polystyrene+ 2-butanone system at 298 K has beenstudied several times with results for a ranging from 0.58 to 0.635.The observedvalue, b = 0.53, is thus in excellent agreement with the value calculated from eqn (9).CONCENTRATION DEPENDENCE OF D(C)Previous studies of diffusion and of sedimentation constants as a function ofsolute concentration have indicated that a complex, molecular-weight-dependent,relation exists. For example, Tsvetkov and Klenin l3 in a study of polystyrene in anumber of different solvents observed that D(c) was approximately independent of N. C. FORD, JR., F. E . KARASZ AND J . E . M. OWEN 23 1at concentrations above 5 x g cm-3 (for samples with M , 2: lo6 or greater) ; for5 x 10-4<c< 5 x there was an approximately linear decrease in D(c) with de-creasing concentration ; while a second concentration-independent regime was foundfor solution concentrations less than 5 x g CM-~.Recently Paul and Kemp l4/ I I I 1 I0.2 0'4sin2 812FIG. 1 .-Line width of power spectrum as function of scattering angle for polystyrene (Mw = 1.7 xlo6) in 2-butanone. c = 4.2 x g ~ r n - ~ .L tMvFIG. 2.-Diffusion constant at infinite dilution for polystyrene in 2-butanone as function of molecularweight232 RAYLEIGH SCATTERINGstudied the polystyrene-cyclohexanone system at relatively high concentrations andobserved a qualitatively similar linear decrease in D(c) from an approximately con-centration-independent plateau for high molecular weight fractions, but the soluteconcentration at which the change in regime occurred appeared to be an order ofmagnitude greater. Additionally, they found that for lower molecular weights (lessthan - lo5), D(c) increased with decreasing solute concentration.In the present study we found that D(c) is approximately constant above a soluteconcentration of -3 xThe constant kD is molecular-weight-dependent ; kD was positive for the polymermolecular weights above - lo5 and negative for the lower molecular weight fractions,e.g., kD = 190 cm3 g-l for M, = 6.7 x lo5 and kD 21 - 10 cm3 g-l for M, = 2.08 xlo4.Fig. 3 shows the results for the sample which received the most detailed study,The most important features found are that there exist two different D(c) against cregimes (our measurements were not detailed enough in the c<5 x cm3 g-1region to form any conclusion concerning a possible second concentration-independ-ent regime) ; that there is a linear dependence of D(c) upon c for lower solute con-centrations, and that kD is a function of molecular weight and changes sign at M, - lo5.These observations are at least in qualitative accord with the experimental resultscited above (see also ref.(14) for a more extensive list of results). Furthermore, it ispossible to account for certain of these features in terms of the presently understoodnature of the concentration dependence of D(c). The latter involves contributionsfrom both thermodynamic and hydrodynamic polymer-solvent interactions. ThusD(c) may be expandedwherefis the frictional coeficient for the polymer in solution at concentration c, andA2 and A3 are the second and third osmotic virial coefficients, respectively.Thefrictional coefficient is also concentration dependent and is invariably expanded in apower series form,where fo( E kT/Do) representsf at infinite dilution, and k j and k; etc., are molecular-weight dependent constants. Thusg ~ m - ~ . Below this, D(c) can be expressed in the formD(c) = Do(l +kDC). (10)M, = 6.7 x 105.D(c) = (kT/f)(l+2AzMc+3A3Mc2+ ...), (11)f = fo(l+k>c+k[;c2+ ...), (12)D(c) = DOC1 + (2AZM - k>)c + . . .]. (13)As has been noted, eqn (1 3) can at best be used to explain the observed behaviou rof kD( 3 2A2M- kj) ; because of the uncertainty in the values of the higher coefficientsin the power series, particularly that of klj, little can be stated concerning the concen-tration-independent portion of the D(c) against c curve.In examining the origin of the sign change in kD we note first that the thermo-dynamic contribution to this parameter increases with molecular weight more slowlythan the first power, inasmuch as A , = const.44-7, where y is a constant of the orderof 0.2.' For the polystyrene + 2-butanone system, a number of determinations ofA , have been reported. 9 *which span approximately the same molecular weight range as the present study. ForFor the purposes of the present discussion, it is adequate to express these data in theform A , = 1.7 x M-Oa2 cm3 g-2 in spite of the apparent break in the plot of A ,against M noted by Kurata and Stockmayer, and the arguments presented by theseauthors in favour of a lower value of y.We have used the results of Outer, Carr and ZimN.C . FORD, J R . , F . E . KARASZ AND J . E . M. OWEN 233The molecular weight dependence of k), the hydrodynamic contribution to kD,has been difficult to evaluate theoretically because of the long-range character of theinteractions involved. Pyun and Fixman l7 have derived the expressionwhere t, is the polymer partial specific volume in a solvent of density po and viscosityqo ; so is the infinite dilution sedimentation constant. The factor ky (correspondingto k> in terms of solute volume fraction) varies from 7.16 for hard-sphere interactionsto 2.23 for zero excluded volume, i.e., at the theta temperature, in the Pyun-Fixmantreatment. In the present study it is appropriate to rewrite eqn (14) in terms of diffus-ion constants, thuswhere eqn (7) has been used in deriving (1 6).This gives a molecular weight depend-ence in k ) of M0.59, if we can ignore the very slow variation contained in k?. Fromfig. 1 of ref. (17) we estimate 3 (which cannot be in error by more than a factor of2) and thus findk; = 4.1 x M0*59 (17)using q0 (at 298 K) = 4 . 0 ~ P8 (k: is in units of cm3 g-l).Finally, therefore,kD = 3.4 x 10-3 ~ 0 . 8 -4.1 x 10-2 ~ 0 . 5 9 . (18)Eqn (18) clearly can explain the trends observed ; it predicts a small negative value forkD at low molecular weights and an increasing positive value at higher M. Themolecular weight corresponding to kD = 0 is 1.4 x lo5 which is in good accord withour observations.From eqn (18) we can calculate k, at Mw = 6.7 x lo5 and 2.1 x lo4.These are 45 cm3 g-1 and - 1 cm3 g-I, respectively. The experimental values are 190and about - 10 cm3 g-l. We can also compare the prediction of eqn (18) with theresult of Tsvetkov and Klenin l3 for polystyrene in butanone, (Mw = 3.5 x lo6) :k,(calc.) = 280 cm3 g-l, kD (expt.) = 160 cm3 g-l. In view of the drastic assump-tions made, of the uncertainties in the numerical values used in arriving at eqn (18)and of the experimental error, the comparison between calculated and experimentalresults is encouraging.Finally we consider a recent alternative theory for the behaviour of k ) by Imai.lgThis differs from the treatment of Pyun and Fixman in several respects by predicting,e.g., that k ) = 0 at the theta temperature, and a lower molecular weight dependence invery good solvent.In the latter situation, according to this treatmentk> = CIM3a,, (19)where C, is a constant dependent on the unperturbed molecular dimensions, and a, isthe linear expansion factor determined from viscosity measurements. The corres-ponding expression in the Pyun-Fixman theory isk; = CpFMfa?, (20)where af, the linear expansion factor determined from frictional coefficient analysis234 RAYLEIGH SCATTERINGis nearly identical to the ratio of the actual to the unperturbed r.m.s. molecular end-to-end distance, (r2/r,2)f (= u).15 The difference between eqn (19) and (20) is furtheraccentuated by the fact that a,,<af.l5 For very large extensions, it would thus bepredicted that the molecular weight dependence of k; would differ by a factor offrom M0s2 to M0-33 according to the model chosen.--UNPERTURBED DIMENSIONSUnperturbed dimensions can be calculated from translational diffusion constantsin a manner analogous to that used in intrinsic viscosities analysis for this purpose.15Thus, the desired solvent-independent ratio ($/M)* is given by -Kef = P ( r 3 W (21)where K , f is a constant defined byIn the Kirkwood-Riseman theory, P is a universal constant whose value is 5.1.20 Inmeasurements of Do carried out under other than theta conditions it is necessary todevelop a method of obtaining Kef by using a relation between ccf and M.Two suchrelations that have been widely employed in viscosity analyses are the Flory equationfo = (kTID0) = rlOKtlfM'cr,.(22)o$-E? = CFM', (23)where C, is a constant for a polymer-solvent system at a given temperature, and theKurata, Stockmayer and Roig equation 15* 21(24)(25)3 a f - uf = CKSRg(a flM',where CKsR is a constant analogous to CF and g(af) is a function defined byg(a f) = 8$/(3u; + l)*.[In eqn (23)-(25) we have assumed that a f is identical to a.] We are concerned hereprimarily with the determination of unperturbed dimensions, as distinct from polymer-solvent interaction parameters, and therefore it will not be required to define furtherCF or CICSR.By substituting eqn (22) into (23) and (24) we obtain, respectively,andThese expressions are the analogies of eqn (9) and (58) in ref.(15). By plotting(D,2M)-' against D:M2 or g(af)MDo we can obtain Kef. Fig. 4 illustrates such aplot for the data obtained in the present study. The function g(a,) was evaluated in aone-cycle-iteration procedure by first calculating an approximate KO, and then esti-mating a, from eqn (22). Fig. 4 shows that the experimental scatter is such as topreclude a positive selection of either eqn (26) or (27) as more adequately representingthe data. It is expected, in any case, that differences would tend to be revealed onlywith thermodynamically much better solvents. An alternative possibility of treatingthe data, offering also some further insight into the behaviour of the system, is to usFIG.IN. C. FORD, JR., F. E . KARASZ AND J .E . M. OWEN 23 51 I I Ic x lo3, g ~ r n - ~3.Diffusion constant of polystyrene (Mw = 6.7 x lo5) in 2-butanone3- 2 Ntv)E" 2E!0M(5-XNTrlIY 2Iconcentrat ion.as function of soluteKSR0 4.0 8.0 12.0M2Dix lo9, g2 cm6 s - ~ mol-2FIG. 4.Evaluation of Kef. Circles (lower scale) : individual data points plotted according to eqn(26). Triangles (upper scale) : data plotted according to eqn (27). Solid lines labelled F (lowerscale) and KSR (upper scale) represent smoothed data calculation (Do = 3.1 x M-OpS3 cm2 s-l)plotted according to eqn (26) and (29, respectively236 RAYLEIGH SCATTERINGthe smoothing process implicit in fitting the data to an equation of the form Do =KDM-b (eqn (7)) to calculate Key. The solid curves in fig.4 are calculated thereforeusing KD = 3.1 x and b = 0.53 as found previously. The marked curvaturein these plots is a manifestation of the basic incompatibility of eqn (7) with either (23)or (24) (except for very large molecular extensions or the trivial case where CF =C,,, = 0, i.e., theta conditions), in that eqn (7) predicts a simple power law relationbetween af and M. The lower ends of the curves shown in fig. 4 terminate at pointscorresponding to M = lo4. The essential inability to differentiate between eqn (26)and (27) in this system was confirmed when it was noted that by appropriately changingthe scale of the abscissae it was possible to superimpose the two curves almost com-pletely in the molecular weight range M = lo4 to 5 x lo6.The best value of Kef that can be obtained from fig.4 yields the result, Kef =(4.1 k0.2) x lo-* 8-3 cm mo14, which with eqn (21) gives ( 2 / M ) * = (800+40) x 10-l1cm at 298 K. This value is higher than most results based on viscosity measurements.Usually the latter were carried out in theta solvents, and average around 670 x 10-1crn.l5 However, there is considerable spread in this result especially when dataobtained from other than viscosity measurements or not under theta conditions istaken into account. For example, an analysis based on second virial coefficient resultshas yielded values as high as 775 x lo-" cm (at essentially the same temperature 2 2 ) .The origin of the difference is not clear ; as pointed out above the possibility of signi-ficant errors in the calculation of Kef because of an incorrect (af,M) relation would beexpected only with much better solvents.Neither can the difference be attributed to aheterogeneity correction of P, which would be quite small in this study, althoughcertainly in the right direction.23 It is expected that further measurements of D(c) ina variety of solvents will yield more information on this point.CONCLUSIONThis study has shown that diffusion constants of polymers can now be obtainedreasonably easily and as such form a practical complement to intrinsic viscosities andother dilute solution data in the estimation of molecular weights and size parameters.The homodyne spectrometer used in this investigation can be substantially improvedand therefore it is reasonable to assume that a precision of 1 % or better in D(c) maybe attainable in the near future.This will then yield results for molecular size, etc.,comparable in precision to those obtained by any other technique. There are alsoperhaps some special advantages in diffusion constant measurements (or frictioncoefficient measurements generally) which originate in the virtual equality of theparameters af and a. Finally, in comparing sedimentation and diffusion constantmeasurements, Gouinlock, Flory and Scheraga2 pointed out the complication arisingin the analysis of the former when carried out in mixed solvent because of the possi-bility of specific effects in the polymer partial specific volume. This would not be arelevant problem in diffusion measurements.This research was supported in part by NSF Grant GP-9409 (NCF) and AFOSRGrant 68-1434 (FEK).S.B. Dubin, J. H. Lunacek and G. B. Benedek, Proc. Nat. A c d . Sci., 1967,57, 1164.H. Z . Cummins, F. D. Carlson, T. J. Herbert and G. Woods, Biophys. J., 1969, 9, 518.N. C. Ford Jr. , W. Lee and F. E. Karasz, J. Chem. Phys., 1969, So, 3098.A. Wada, N. Suda, T. Tsuda and K. Sada, J. Chem. Phys., 1969,50,31.S . B. Dubin, G. Feher and G. Benedek, Biophys. J., 1969,9, A 213.ti R. Pecora, J. Chem. Phys., 1968,49, 1032, and earlier references cited thereinN. C. FORD, J R . , F. E . KARASZ A N D J . E . M . OWEN 237’ R. Pecora, J. Chem. Phys., 1969,51,3298.8 W. Lee, Ph.D. Thesis (University of Massachusetts, 1970).P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York,1953), chap., 14.l o C. E. H. Bawn, R. F. J. Freeman and A. R. Kamaliddin, Tram. Farday Soc., 1950,46,1107.l i P. Outer, C. I. Carr and B. H. Zimm, J. Chem. Phys., 1950, 18, 830.l2 J. 0th and V. Desreux, Bull. SOC. Chim. Belges, 1954, 63, 285.l 3 V. N. Tsvetkov and S. I. Klenin, J. Polymer Sci., 1958, 30, 187.l4 D. R. Paul and D. R. Kemp, paper presented at 65th National Meeting of the A.I.Ch.E.,l5 M. Kurata and W. H. Stockmayer, Fortsch. Hochpo1ym.-Forsch., 1963, 3, 196.l6 F. W. Billmeyer, Jr. and C. B. DeThan, J. Amer. Chem. SOC., 1955, 77,4763.l7 C. W. Pyun and M. Fixman, J. Chem. Phys., 1964,41,937.l9 Int. Crit. Tables.l9 S. Imai, J. Chem. Phys., 1969, 50,2116.2o J. G. Kirkwood and J. Riseman, J. Chem. Phys., 1948,16, 565.21 M. Kurata, W. H. Stockmayer and A. Roig, J. Chem. Phys., 1960, 33, 151.22 T. A. Orofino and J. W. Mickey, Jr., J. Chem. Phys., 1963,38,2513.23 E. V. Gouinlock, Jr., P. J. Flory and H. A. Scheraga, J. Polymer Sci., 1955, 16, 383.Cleveland, Ohio, May, 1969

ISSN:0366-9033    

DOI:10.1039/DF9704900228

出版商:RSC    

年代:1970

数据来源: RSC

摘要:

Ultrasonic Relaxation of Rotational-Isomeric Equilibriain Polymer SolutionsBY €3.4. BAUER, H. HASSLER AND M. IMMENDORFERI. Physikalisches Institut der Universitat Stuttgart, GermanyReceived 1 8th February, I970The sound absorption per wavelength p in solutions of polystyrene in benzene and carbontetrachloride deviates from proportionality with frequency in the low MHz range. This could beaccounted for with good agreement by an additional, Debye-shaped excess absorption. Variousmodels for the relevant relaxation process are discussed; the most probable one is the thermalrelaxation of a rotational-isomeric equilibrium within the polymer chain, consisting of a rotationof a single monomer unit. Under that assumption, from the temperature dependence of positionand amount of the absorption maximum the following data of the rotational potential were calculated :separation of the equilibrium energies AH = 0.9 kcal/mol, activation energy AHlz = 7.5 kcal/mol,frequency factor v = 1 .4 ~ 1OI2 s-l.Sound absorption in liquids is caused by several different mechanisms : (i) Theshear part of the longitudinal wave gives rise to viscous absorption. (ii) Both thetemperature and the pressure part of the wave may force internal equilibria to altertheir position periodically ; relaxation phemonena cause a phase lag with subsequentrelaxational sound absorption. When the equilibria are sensitive to a temperaturechange only due to AH # 0 (i.e.? the volume effect AV of the reaction is negligible)one speaks of thermal relaxation. The reserve case (the heat of reaction AH beingneglected) is coinpressional relaxation.The absorption per wavelength, p = a& of the viscous part (assuming frequency-independent viscosity) as well as of any relaxational part much below the relaxationrate (271fmax = l/z) is proportional to the frequency f.Hence, any deviation of pfrom that proportionality indicates a relaxation process, the absorption of which isaccounted for in the most simple case by an additive Debye absorption maximum :The relaxation rate contains kinetic information, and the absorption maximumthermodynamic information about the processes considered (see, e.g., Lamb,Bauer 2).Sound absorption measurements of various authors in polymer solutions (e.g.,PST, PMMA in benzene, carbon tetrachloride, toluene) 3-7 show a deviation fromp - f in the low MHz region.While the results of Cerf and co-workers 3-5 couldnot be accounted for by any relaxation process (their p exhibits one or two suddensteps instead of a Debye behaviour), our own measurements could be fitted by anequation of the form (1). do not contradict theseresults.Pexcess = 2 l U I n a x ~ z / ( l + m2z2>. (1)Recent studies of NomuraEXPERIMENTALWe used a parallel-path pulse apparatus with broad band transducers of the Sell type.At low frequencies (1-5 MHz) diffraction effects counterfeit additional absorption. Wecorrected for that by the method of B a s 8 The validity of this procedure was verified by23H . - J . BAUER, H. HASSLER AND M.IMMENDORFER 239measurements in the pure solvents. The non-resonant transducers enabled us to determinethe absorption values for a large number of adjacent frequencies, and hence a better and moreaccurate least-squares approximation could be calculated.RESULTSFig. 1 shows a typical result, separated into a single Debye absorption part and acontribution p -f due to viscothermal and vibrational relaxational absorption. Theuse of CC14 as solvent enhances the Debye part relative to the other (fig. 2). The twosets of points correspond to two samples with broad (PST IIIc, 0, technical grade,Mz2200 000) and narrow (PST 430 000, 0, 2 = 430 000) distribution of molecularweight. Apparently there is only a small influence of the chain length on the processbeing observed.-1050 50.20.1f [MHzIFIG.1 .-Absorption per wavelength and excess absorption.To associate the excess absorption with an internal mechanism the concentrationand temperature dependence has been investigated (fig. 3). The mean Debye curvesresulting from the least-squares separation method, exhibit a proportionality betweenexcess absorption and concentration. An increase in the temperature shifts theabsorption maxima to higher frequencies and decreases the maximum absorptionslightly.DISCUSSIONThe excess absorption could also be a viscous one, if the additional viscosityinduced in the solution by the polymer molecules relaxed in the frequency regio24d) ULTRASONIC RELAXATIONAFIG. 2.-Dependence onmolecular weight.10 2 0 I 2 5f [MHzl1052m40FIG. 3.-Dependence on X Iconcentration and temperature. H0.50.20.I I II 2 5 10 20f [MHzH.-J. BAUER, H . HASSLER AND M. IMMENDORFER 241observed. Applying Rouse's theory on the experimental static viscosity of thesolution, one obtains a much smaller relaxation rate l/z = 2nfmax ; in addition onewould not expect a single but a multiple relaxation.Other possible processes within the solvent may be excluded from the discussionas well: non-associated solvents do not show any structural relaxation; and theconcentration dependence locates the process on the chain molecule itself.The most simple equilibria on the chain molecule which could relax, in thefrequency region considered, are of the rotational-isomeric type (as in low-molecularweight substances).Transitions between only two different conformations wouldgive rise to a single relaxation process as observed experimentally. The independenceof the results from the chain length demonstrates that the process responsible occurson a small section of the molecule.MAXIMUM ABSORPTIONThe maximum absorption per wavelength of a single equilibrium (for not toolarge relaxation strengths) is~ ( y - 1 ) AH aexp(-AHIRT) AV Cpp " a x E ? ~ R ( ~ ) (l+aexp(-AH/RT))2(1-T m) '(y = ratio of specific heats, Cp = molar heat capacity, 8 = thermal expansioncoefficient, a = degeneracy).Since it contains the thermal (AH) as well as the compressional (AV) part of therelaxation, no simple statement can be made about either of those quantities. Asis common in the instance of rotational-isomeric relaxation (but questioned recentlyby Crook and Wyn-Jones lo) we neglect the volume effect AV and obtain(3)a exp (-AH/RT) - SC,(l+aexp(-AH/RT))'-R'' T IspFIG.4.Rotational potential.The temperature dependence of p,,, is mainly determined by that of the relaxing heatcapacity SC,, which possesses a maximum, beyond which SC, decreases with increasingT as is found experimentally. The experimental prnax-values and their temperaturegradient are in agreement with eqn (3) if we assume (a) a = 2, i.e., the upper state istwofold degenerate as in the rotational potential of fig. 4 ; (b) the process occursonce in every monomer unit; and take (c) AH = (0.940.1) kcal/mol monomer ;remembering (d) that we neglected the volume effect.An estimation shows that amere compressional relaxation (AH = 0) with a AV/V of only 2 % would yield thesame ,urnax. For the final distinction between the assumed thermal and compressiona242 ULTRASONIC RELAXATIONrelaxation very accurate measurements in solvents with strongly differing heatcapacities are necessary.RELAXATION RATEIf for thermal relaxation and small relaxation strengths, the transition rate fromthe upper to the lower state was calculated from the positions of the maxima by(4)Fig. 5 shows the Arrhenius plot of the results with a frequency factor of 1.4 x 10l2 s-,and an activation energy, AHz1 = 6.6 kcal/mol monomer. The total potentialdifference is AHlz = AH,, +AH = 7.5 kcal/mol monomer.Tz 1 = 2?tfmax/( 1 + cc exp ( - AH/RT)).I oa5 - IIrn u 42.5I o 7530 333 280 O K66 kcal /MOI \ 1.1 x I O ” ~ e R ’0 10 percent PST Ill in C C i 45 percent PST 630 000 in CCI2.5 3 3 51031~FIG.5.-Arrhenius plot of the transition rate rzl.TWO-STATE MODELThere is a difference between rotational isomeric transitions in low-molecular-weight substances and polymers; a rotation about a single bond in the latter forcesone part of the molecule to have a large movement through the solvent that is in-compatible with the high transition rate. Therefore a second rotation about anadjacent bond in the opposite sense is very probable since it then affects only a smalllocal part of the molecule.The regular conformation of isotactic polystyrene is a3-1 helix with the potential sequence gtgtgtgtgt. A change of one gauche position ginto a trans t or minus gauche 3 with an opposite rotation of the next but one bondcould give the twofold upper level :g t g t g t g t g t g tg t g t g t t t g t g tg t g t g t g t t t g tThe effect of the rotations about these two bonds is the rotation of a whole monomerunit, cf. fig. 6 FIG. 6.-Regular (1) and rotated (2) conformation.[To face page 242HA. BAUER, H . HASSLER AND M. IMMENDORFER 243J. Lamb in PhysicaZ Acoustics, W. P. Mason ed., (Academic Press, New York 1965), vol. IIA,chap. 4.H.-J. Bauer in PhysicaZ Acoustics, W. P. Mason ed. (Academic Press, New York, 1965), vol.IIA, chap. 2.R. Cerf, R. Zana and S. Candau, Compt. rend., 1961,252,681 ; 1961,252,2229 ; 1962,254,1061.C. Tondre and R. Cerf, J. Chim. Phys., 1968,65,1105..I. Lang, J. Chim. Phys., 1969, 66,88.H. Nomura, S. Kato and Y. Miyahara, Nippon Kagaku Zasshi, 1967,88,502 ; 1968, 89, 149 ;1969, 90, 250. ' H.-J. Bauer and H. Hassler, Proc. 6th Int. Congr. Acoustics, (Tokyo), paper J-5-11, and KoZloid-Z.,1969,230,194.R. Bass, J. Acoust. SOC. Amer., 1958,30,602.P. E. Rouse, J. Chem. Phys., 1952,21,1272.K. R. Crook and E. Wyn-Jones, J. Chem. Phys., 1969,50.3445

ISSN:0366-9033    

DOI:10.1039/DF9704900238

出版商:RSC    

年代:1970

数据来源: RSC

摘要:

Dielectric and Viscoelastic Relaxation in Dilute Solutions ofSome Non-Gaussian ChainsBY S . B. DEV, R. Y. LOCHHEAD AND A. M. NORTHDept. of Pure and Applied Chemistry, University of Strathclyde, Glasgow, C. 1.Received 30th December, 1969Dielectric and viscoelastic measurements have been made on dilute solutions of poly(buty1isocyanate). The measurements confirm that the molecules are predominantly rod-like in hydro-dynamic behaviour. The end-over-end rotation times obtained from both sets of observations havebeen analyzed by three methods. The monomer projection length along the major axis cannot beevaluated independently of the value chosen for the length-to-thickness ratio, but it is probably lessthan 1.1 A and greater than 0.6 A. Application of the Kratky-Porod model to molecules for whichthe chain length is less than the persistence length must be treated with caution.For poly(buty1isocyanate) the persistence length obtained from dilute solutions is 230 monomer units, althoughextrapolation of a wider concentration range to infinite dilution yields a value of 400 monomerunits. Concentration has a marked effect on chain stiffness parameters (increasing apparent cylinderradii or decreasing persistence lengths) which is explained in terms of side-by-side dipole association.The dielectric measurements of Phillips made on a variety of samples of poly(N-vinyl carbazole)have been analyzed using equations suitable for rod-like or stiff-coil polymers. For molecularweights above 50,000 the molecules are coil-like with a Kratky-Porod persistence length of 250monomer units.Shorter chains are rod-like in which the projection length of each monomer unitalong the rod is roughly 3 the monomer length. This suggests that the short chains (8-20 monomerunits) adopt a semicircular arc outline. Both polymers show increasing departures (in both thedielectric and the viscoelastic parameters) from rod-like behaviour as the temperature is raised. Thechange is continuous through room temperature so that there is no reason for assigning a perfectstructure (helical or otherwise) to solutions at these temperatures. The experimental data do not,generally, allow sensible treatment using number average molecular weights, so that weight (or per-haps even higher) averages must be used for heterodisperse samples.For all polymer molecules composed of real monomer units (as opposed to infinites-imal freely rotating links) there must be a chain length below which the behaviour of themolecule is essentially rod-like, and another chain length above which possiblemolecular curvature permits the adoption of a random-coil conformation.Atintermediate chain lengths, vector properties of the molecule obey neither idealrandom coil (Gaussian or random-walk) statistics, nor ideal linear statistics. Indeed,the molecule behaves as a " bent rod " or highly prolate ellipsoid." Rigidity " can be conferred on a polymer chain by the adoption of a helicalstructure, as evidenced by many polypeptides and biopolymers. A synthetic polymerfor which such a structure has been postulated 1v to explain dynamic behaviour ispoly(buty1 isocyanate).It has been suggested that at molecular weights below 70,000the polymer is rod-like in dilute solution, existing as a helix with monomer projectionlength Lo along the principal axis 1.1 A, and helix radius B about 11 A. However,the effects of concentration, temperature and molecular weight distribution on thisinterpretation are not clear. Most of the experimental work here reported dealswith dielectric and viscoelastic relaxation studies on two samples of this polymer.However, " rigidity " can be conferred on a polymer chain by the presence ofbulky side groups and an associated large barrier to intramolecular backbone rotation.An example of this seems to be poly(N-vinyl ~arbazole).~ In this paper some di-24S.B . DEV, R . Y . LOCHHEAD A N D A . M. NORTH 245are analyzed in terms of models of this inter- electric measurements of Phillipsmediate non-rod non-gaussian state.MOLECULAR ROTATIONAL RELAXATION TIMEFor large molecules the rotational relaxation time depends on the cube of lineardimensions, so that when monomer units build regularly into a rod the end-over-endrotational time is proportional to the cube of the degree of polymerization (neglectingend effects). However, if the rod can sag or bend, the hydrodynamic behaviourpasses through that of a highly prolate ellipsoid of revolution to that of a random coil,when the rotational time varies as approximately the 9 power of the degree of poly-merization. For a " rigid " polar molecule in which end-over-end rotation is fasterthan intramolecular conformational change, both dielectric and viscoelastic relaxationmeasurements yield the gross rotational time.This introduces a new definition of" flexibility " based on the comparison of intramolecular segmental rotation ratewith the overall whole molecule rotation rate.It is usual to discuss the end-over-end rotational time of molecules approximatingto rod-like form using one of three equations: that of Perrin for highly prolateellipsoids, that of Kirkwood and Auer for perfect rods with no end corrections, andthat of Broersma for perfect rods but accounting for end corrections. All equationshave similar form :- WoL36kT[ln (LIB) - y ] ' *e-o-t? -y = 0.702 (Perrin),y = o (Kirkwood-Auer),y = 1.57-7(1/ln (L/B)-0.28)2 (Broersma),L = nLo.Here Lo is the projection length of each monomer unit down the rod length (majoraxis), B is the radius of the rod (semi-minor axis), and n is the degree of polymeriza-tion.qo is solvent viscosity. One uncertainty in the use of such an equation iswhether, for polymer heterodisperse in molecular weight, n should be a weight ornumber average (nw or nn), or a mean (nwn,)*. This point is discussed later.The equation also carries certain restrictions as to its use. Thus, for a rod (orprolate ellipsoid) one dimension must be larger than the other two, so nLo/B>2.The Broersma equation includes this in the form nLo/B>e2.Also, chemical know-ledge indicates that for addition polymers across a substituted double bond Lo < 3 Aand B > 3 A so that nL,/B<n. Thus 2/n<Lo/B<l.The end-over-end rotational relaxation time can be evaluated as the conventionaldielectric relaxation time observed in the frequency dependence of dielectric per-mittivity and loss. It can also be observed in the frequency dependence of the complexshear modulus of the solution. Thus, the contribution to this from the polymersolute shows a curve towards frequency independence in G' and a point of inflexionin G" at the relaxation frequency (see fig. 2, 3). These are incorporated in theexpressions for perfect rods (Kirkwood and Auer 6), and for prolate ellipsoids(Cerf and Sheraga 8).G'M/RT = Bo2k2/(1 + 02k2) Kirkwood-Auer, (2)G'MIRT = Bo28/( 1 + 0202) Cerf-Scheraga, (3)G"M/RT = Auk + Bok/(l+ w2k2) Kirkwood-Auer, (4)G"M/RT = A o + Bo/( 1 + w2tI2) Cerf- Scheraga.(5246 DIELECTRIC AND VISCOELASTIC RELAXATIONHere G', G" are the real and imaginary components of the shear rigidity modulusof a solution, viscosity q, in solvent viscosity qo ; co is angular frequency ; A = 3,B = 3, k = 4 for the Kirkwood-Auer expression, and A = 1.6+p2/15(log2p-$),B = p2/5(log2p-q), and 8 = $0, where D is the rotational diffusion coefficient,p = ratio of major-to-minor axis of ellipsoid ( p > 10 for Cerf-Scheraga expression).VECTOR PERSISTENCE LENGTHThe above analysis is most properly valid for those molecules whose contourdeparts only slightly from rod-like form.At the other extreme, for the " worm-like "chain which almost approaches coil-like form it is usual to apply a treatment suchas that of Kratky and P ~ r o d . ~ In this model, vector properties of the chain arediscussed in terms of a " persistence length " i.e., a measure of the distance in onedirection over which the property of interest extends essentially unchanged. In thepresent study the vector dipole moment along the chain is involved, and so themolecular dipole moment p and the " persistence dipole moment " pq are related bywhere po is the monomer dipole component along the chain and n is the degree ofpolymerization. Measurements of p and p o can be used to calculate pq, and hencethe " persistence number of monomer units ", nq = pq/po.( ) represents averagequantities. Both the region of molecular weight for which this equation is applicableand po can be found from a measurement of <p2) for polymers covering a range of0/---.(>(>3 02 0I 00 10 20 3 0 4 0n+FIG. 1 .-Dependence of dipole moment on chain length : 0, poly(N-vinyl carbazole) 25°C ; , poly-(butyl isocyanate) after Bur and Roberts ; c) , poly(buty1 isocyanate) this work (0.064 g dl-1 25°C).molecular weights. For very short chains ((p2)/n)* is proportional to n3, whereas forvery long chains ((p2)/n)* is independent of n3 (see fig. 1). The region of curvaturein a plot of ((p2)/n)f against n+ delineates the molecular weight region where departuresfrom rod-form occur, and at the higher molecular weight end of the curvature eqn(6) might apply.Since the Kratky-Porod persistence length is formally a limit asn+w, it will not be correctly calculated at the low molecular weight end of thecurvatureS . B. DEV, R . Y . LOCHHEAD AND A . M. NORTH 247EXPERIMENTALMATERIALSTwo samples of poly(buty1 isocyanate) were prepared by the method of Shashoua.'OThese were found to have osmotic number average molecular weights of 2 . 8 9 ~ lo4 and2.29 x lo4. The weight average molecular weights determined by light scattering at 4358 8,were 6 . 0 ~ lo4 and 4 . 0 ~ lo4 respectively.The measurements of Phillips4 were made on two samples of poly(N-vinyl carbazole)prepared by charge-transfer polymerization using auric chloride as initiator.These hadnumber average molecular weights (measured in a vapour-pressure osmometer) of 1.66 x lo3and 4.72 x lo3. Unfortunately, no reliable measurement of weight average molecularweight was obtained and so the molecular weight distribution is unknown. However,since the polymerization was carried to high conversion it would be expected that Mw 2 2Mn.Further measurements were made on polymers of number average molecular weight 4.57 xlo4, 8.6 x lo4, 9.17 x lo4 and 11.2 x lo4. These were prepared l1 by radical polymerizationto low conversion, and Mw-2Mn. Toluene was used as solvent throughout.TECHNIQUESThe dielectric measurements were made at frequencies between lo2 and lo6 Hz usingapparatus described previously. l2 Viscoelastic measurements were made using torsionallyoscillating quartz crystals resonant at 20, 40, 130 KHz also using equipment describedpreviousIy.12 Various concentrations ranging from 0.05 to 1.0 g dl-l were studied.Computations of chain characteristics were carried out on an I.C.L.1905 digital computer.Lo and B were calculated from frequencies of maximum dielectric loss using eqn (1). Cal-culations were made according to the Broersma equation unless necessary conditions wereinvalidated when they were made with the Perrin form or, if that too was inapplicable, theKirkwood-Auer form. Polymer dipole moments were obtained using the equationwhere N is Avogadro's number, c is concentration, E~ and E , (the limiting low- and high-frequency permittivities) were obtained from Cole-Cole diagrams of the measured per-mittivities.These values of (p2) were used in eqn (6) along with p o obtained from thelimiting low molecular weight value of ((,u2)/n2)*. The equation was solved numericallyby applying the bisection technique, the iteration procedure being continued to a quadraticconvergence of lo-'. In the numerical calculation no assumption was made as to therelative magnitudes of po and ,uq, i.e., it did not involve expansion of the exponential followedby truncation of high order terms. Strictly, eqn (6) is valid only for very large values of n.RESULTSEVIDENCE FOR ROD-LIKE BEHAVIOURPOLY(N-VINYL CARBAZOLE)From the curvature of ((,u2)/n)3 against n* the behaviour is rod-like at molecularweights below 4 x lo3 (fig. 1).A plot of (,u2)* against n, including iso-propylcarbazole for n = I, is linear up to n = 200. Also attempts to calculate pg, nq forthe two lowest molecular weight polymers do not yield sensible answers, confirmingthe inapplicability of the coil-like treatment to these two chains.POLY(BUTYL ISOCYANATE)For this polymer a region of linear dependence of ((p2)/n)* on n i is evident(fig. 1). Furthermore, when a wide range of molecular weights are studied,2 thedielectric relaxation time varies as the 2.7 power of the molecular weight for value248 DIELECTRIC A N D VISCOELASTIC RELAXATIONI 1lo3urf, HzFIG. 2.-Poly(buty1 isocyanate) Mw 65,000 in toluene-reduced values of the real shear modulusagainst reduced frequency. The full curve represents the Kirkwood-Auer predictions for rigid10'r4 10'Lu"d%1n rAIlo5v10"rods of same Mw.P10' 104 10' lo6urf, HzFIG.3.-Poly(buty1 isocyanate) M, 65,000 in toluene-reduced values of the imaginary shearagainst reduced frequency. The full curve represents the Kirkwood-Auer predictions for rigidrods of same MwS . B. DEV, R . Y . LOCIIHEAD AND A . M . NORTH 249less than 7 x lo4. The contributions to the real and imaginary shear moduli ofsolutions (0.0644-1.0367 g dl-l) of polymer (M, = 6.5 x lo4) are illustrated in fig.2 and 3. Also shown are theoretical Kirkwood-Auer curves for rigid rods calculatedusing the weight average molecular weight. Temperature has been used as a time-variable to extend the three crystal frequencies in the usual way.12 Theoreticalcurves calculated from number average quantities lie above the curve presented, andthe theoretical curve (Zimm) for flexible coils neither passes through nor resemblesthe outline of the experimental points.ANALYSIS OF DIELECTRIC RELAXATION TIMES AS Te-0-ePOLY ( N-VINYL CARBAZOLE)in terms of the end-over-endrotational time is here reported for the two polymers, M, 1.66 x lo3 and 4.72 x lo3.Since the polymers are of broad (unknown) distribution, values of Lo and B arereported for various average molecular weights (reported as multiples of M,) intable 1.Calculations which yield impossibly large Lo, or impossibly small B,values are not included.An analysis of the dielectric relaxation timesNo sensible values were obtained from M, or 2Mn.TABLE 1Lo AND B (A) FOR TWO LOW MOLECULAR WEIGHT SAMPLES OF POLY(N-VINYL CARBAZOLE) INTOLUENE.calc. fromM , = xM,X(a) M n 1,660444888(b) Mn 4,720444888temp. "C- 82- 69- 51- 82- 69- 51- 73- 49- 31- 73- 49-310.02-0.97148.30.77/38.40.59/29.51.93 196.51 MI530.861430.97 /480.531260.431210.10LolB0.04 0.301.93148 - -1.54138 1.82118 -0.76119 1.20112 -0.58/14.6 0.92/9.2 -1.18 129 1.40114 1.6815.60.96124 1.51115 1.61 /5.41.92148 - -0.85121 0.9419.4 -1.02 125 1.24112.4 -0.56/14 0.68 16.8 -0.45/11.3 0.55/5.5 -1.06126 1.16p1.6 1.48 149The following observations can be made.(i) The value obtained for Lo is notindependent of the value chosen for Lo/B for these short chains.(ii) For any selectedvalues of Lo/B, Lo decreases with increasing temperature. We interpret this asevidence for a " bent-rod " form. Increasing temperature results in greater segmentalfreedom, increased molecular curvature, and so in a less prolate ellipsoid of revolution(fig. 4a). (iii) For any selected value of Lo/B and temperature, (constant curvature),Lo decreases with increasing molecular weight. Again, this indicates a " bent-rod "chape to the chain (fig. 4b).PO LY(BUTYL ISOCYANATE)tures are analyzed in table 2.The dielectric relaxation times for various concentrations over a range of tempera250 DIELECTRIC AND VISCOELASTIC RELAXATIONb.a.\FIG. 4.-Apparent projection lengths for (a) two chains of equal length butchains of equal curvature but different length.different curvature (b) twoWe note that (i) values of Lo and B are not independent of Lo/B; (ii) for givenLo/B the value of Lo decreases with increasing temperature ; and (iii) also with chainlength; (iv) for any given value of Lo, B always increases with concentration.ForLo = 1.1 A, B rises from 5 A at 0.05 g dl-1 to 60 A for 1.12 g dl-l. This could bedue to side-by-side aggregation or to qo failing to represent the medium viscosity.However, a similar trend is observed when the solution viscosity is used instead ofqo. This evidence for aggregation becomes apparent at 0.3 gdl-1 in polymer ofM, 4.0 x lo4 and at 0.1 g dl-l in polymer of M, 6.0 x lo4.TABLE 2g dl-10.2520.2570.1290.1290.0640.0640.5180.5180.2590.2590.1280.128L~ AND B(A) FOR TWO SAMPLES OF POLY(BUTYL ISOCYANATE) IN TOLUENEconcentration fmax calc.LOBHz from 0.005 0.01 0.04 0.10 0.30x 10-41.7 Mn1.7 Mw2.0 M*2.0 Mw2.0 Mn2.0 M w2.0 Mn2.0 M w2.0 M n2.0 Mw2.9 M n2.9 Mw(a) M n 28,900 ; Mw 65,000 ; at 25°C1.26/252 1.25/125 1.75143.60.61 1122 0.82/82 0.93/23.21.20/239 1.19/119 1.65/41.30.58/116 0.78/78 0.88/21.91.201239 1.19/119 1.65/41.30.58/115 0.78/78 0.88/21.9(b) Mn 23,100; Mw 40,000; at 20°C1.10/220.4 1.08/108.0 1.96/48.90.13/25.2 1.05/105.1 1.28/32.01.08/215.3 1.06/105.6 1.91 /47.80.12/24.6 1.03 /lo3 1.25 /3 1.30.961192.7 0.94194.5 1.71 142.70.1 1 /22.0 0.92/91.9 1.12/28.0-1.07/10.71.01 /lo.11.01 po.1---1.53/15.31.49/14.91.33/13.3---1.21/4.0 -----1.76p.91.72/5.21.5415.1-temp. "C17.830.537.446.766.5S. R. D E V , R. Y . LOCHHEAD AND A . M. NORTH(c) Mn 28,900; Mw 65,000 at different temp. ; conc. 0.0644 g dl-l0.0051.07/2150.52/103.71.07 /2 14.60.52/103.71.01 I2010.48/97.20.97/1930.47/93.40.61 /1220.30/59.20.0 11.0611060.70/69.71.06/1060.70 /69.71.00/99.70.65 165.30.96/95.20.63/62.30.61 /60.70.40/39.7LodE41.48 13 1.110.79/19.71.48/37.10.79/19.71.39134.80.74/18.51.34/33.40.71 /17.70.85 /2 1.20.45/11.20.11.81 /18.10.91 /9.11.81 /I 8.10.91 /9.11.69/16.90.85 18.51.63/16.30.82 /8.21.03 /10.30.52p.225 10.3----1.99/6.61.91 /6.41.21 /4.04---ANALYSIS IN TERMS OF THE KRATKY-POROD CHAINPOLY(N-VINYL CARBAZOLE)of four coil-like polymers of different molecular weight(but similar molecular weight distribution) have been analyzed in terms of the Kratky-Porod worm-like chain model.The value of ,uo at 25°C is obtained from the dataof fig. 1, and is 0.10 D. The persistence lengths are listed in table 3. No values canbe obtained for the polymer, Mn 45,700, indicating that the chain length is still tooshort to show true coil-like behaviour. The persistence length should be less thanthe chain length for a real coil, and so only those values calculated from the weightaverage molecular weight can have any significance. These show that (n,), is about250 at 25°C.The dipole momentsTABLE 3 .-KRATKY-POROD PERSISTENCE LENGTHS FOR FOUR SAMPLES OF POLY(N-VINYLCARBAZOLE) AT 25°C ; ,uo = 0.10 D.237 1.20 no value no value445 1 S O 491 223475 1.81 670 259580 2.49 5.91 282mean value of (n4), 255nn <p:> x lO-3DZ ns from M, n4 from M,POLY( BUTYL ISOCYANATE)The Kratky-Porod persistence lengths of the most dilute solutions of the twopolymers studied are reported in table 4.The value p0 = 1.13 D was obtainedfrom the data of fig. 1. Again, values calculated from M, indicate either that thechains are too short for the treatment to be applicable, or that weight average quantitiesmust be used. The weight average values of n, (mean value 232, value at infinitedilution 400) are realistic, and indicate that the chains do depart from rod-likebehaviour, but that the extent of coiling cannot be great.The effect of temperatureon the persistence length of the larger polymer (0.0644 g dl-l) is illustrated in fig. 5.A regular decrease with increasing temperature is apparent.DISCUSSIONAPPLICABILITY OF THE VARIOUS MODELSIt is not possible to use these results to determine which equation for rod-likepolymers (Broersma, Perrin or Kirkwood-Auer) is most valid. The reason is tha252 D I EL E C TR I C A N D V I S C 0 E LA STI C RE I, A X A 1 1 0 Nvariations in length and thickness parameters derived from the end-over-end rotationalrelaxation time differ less with y than with the value selected for the length-to-thickness ratio. Indeed, the results suggest that this difficulty may be insuperablefor real chains, since the equations only apply to molecules which do not departmarkedly from rod-like form, and this small extent of curvature is only achievedTABLE 4.-KRATKY-POROD PERSISTENCE LENGTHS FOR TWO SAMPLES OF POLY(BUTYLISOCYANATE) IN TOLUENE.p o = 1.13 D(a) M n 28,900 ; Mw 65,000 ; 25°Cconc. n4 from M, n4 from M,g dl-1 25°C 25°C0.351 1770 2350.257 1692 1930.129 no sensible 305value0.064 5980 180(b) M, 23,100 ; Mw 40,000 ; 20°Cconc. n4 from Mn n4 from M,g dl-1 20°C 20°C0.546 895 1760.518 3362 2000.259 1809 1920.128 no value 378Mean value ( r ~ , ) ~ 232Values from all solutions extrapolated to infinite dilution, 400.20 40 60temp. "Ctoluene, Mn 28,900; Mw 65,000; 0.0644 g dl-'.FIG.5.-Kratky-Porod persistence length as a function of temperature. Poly(buty1 isocyanate) inin chains so short that ln(nL,/B) cannot be approximated by InnL,. Previousworkers who have evaluated Lo and B for such chains have not investigated sufficientlylow (but still theoretically valid) values of Lo/B.The applicability of the Kratky-Porod treatment is more difficult to assess. Itvields a satisfactory treatment of those chains sufficiently long to be coil-likeS . B . DEV, R . Y. LOCHHEAD AND A. M . NORTH 253However, the treatment has been applied l 3 to chains where the chain length is lessthan the persistence length. This is done by expanding the exponential containingthe ratio of chain-to-persistence lengths and then truncating the series. The usefulnessof this approach for rod-like chains seems doubtful on two grounds.The first isthat the Kratky-Porod treatment starts from the idea of a freely rotating chain, andintroduces the persistence length as the sum to infinity of the projections of successivebonds. The use of this concept in molecules where the chain length is less than thelength of a single equivalent freely rotating link gives cause for concern. The secondis that the persistence length is essentially a measure of curvature and describes thedistance along the direction of the first monomer unit before the chain has twistedto 90" (has no further correlation with) this direction. An attempt to measurethis curvature by observing the orientational or hydrodynamic properties of a rodwith only limited (and transient) departures from linearity seems unduly optimistic.In support of this, those polymers which can be described by the rod-like modelsyield either no or unreasonably large persistence dipole moments when investigatedusing eqn (6).Consequently, the treatment is not reliable when applied to shortstiff chains of markedly rod-like behaviour.PO LY ( N - v I N Y L c ARB A z o LE)The dipole moment data indicate that the polymers of number average molecularweight greater than 50,000 are coil-like in solution at room temperature. Underthese circumstances the Kratky-Porod model can be applied and should yield apersistence length shorter than the chain length. This is so only when weight averagequantities are considered in the calculation.The treatment should not be applicableto polymers for which the chain length is less than the persistence length, and, inaccord with this, we can obtain no realistic solution to eqn (6) for polymer n, 237.The mean value of <n,), is 255, confirming earlier suggestions that this chain isabnormally rigid.The two shortest chains studied are much shorter than the persistence length, andso should be amenable to treatment as rod-like entities. When this is attempted,no solutions of eqn (1) are possible if based upon M, or 2 M,. This is further evidencethat weight average quantities must be used in the calculations. Unfortunately,M, values were not available for these polymers. Consequently, the values obtainedfor Lo depend upon the value chosen for M,/M,, as well as for Lo/B.With theseshort chains the conditions imposed on possible values of Lo/B are restrictive, andonly values between 0.02 and 0.20 yield realistic solutions. The variation in Lowith L,/B or M,/M, is greater than with y (use of Broersma, Perrin or Kirkwood-Auerequations).Generally, the Lo values at the low temperatures and M,/Mn of four are rangedaround 5 of the monomer unit length. The large B values are not in accord with atight helical conformation, and so the most plausible picture is of an irregular structureapproximating in shape to a semicircular arc.POLY( BUTYL ISOCYANATE)Our results are not entirely in agreement with those of other workers.2 Thefirst point concerns the use of the dielectric loss frequency-half-width as a criterion ofmolecular weight distribution.Both of these polymers were heterodisperse inmolecular weight, but in dilute solution studied above 20°C the loss peak had ahalf-width of 2.1 decades. A value of 2 decades had been suggested as a criterionfor a sufficiently narrow distribution that any type of molecular weight average coul254 DIELECTRIC AND VISCOELASTIC RELAXATIONbe used in calculation. This point is particularly important for the short rod-likechains, where characterization of M, is difficult, and for which we found the reportedfractionation procedures most unsatisfactory.For these molecules there is agreement that when the degrees of polymerizationare a few hundred, the molecules are intermediate in shape between rods and coils.The wiscoelastic data suggest that the overall behaviour is more prolate ellipsoidor rod-like than random coil-like.This raises the question as to the significance of a persistence length obtained fromthe Kratky-Porod treatment. The value of 900 reported previously was obtainedby visual curve fitting. We have re-examined the same data using a numericalsolution of eqn (6) and display the results in fig.6. In this figure, theoretical Kratky-Porod predictions of ((p2)/n)* against M;l are plotted for various values of p4,and the experimental points are added. While the best fit of aZZ points is probablywith nq 664 (pa 750) this value is heavily weighted by those chains of Mw less than2 x lo5 which are presumed to be rod-like.At the highest molecular weights (mostI __II I -r I071 1.43 2.15 286 357 4 2 9 51 0 5 1 ~FIG. 6.--Kratky-Porod predictions for the dipole moment against molecular weight relationship.Full curves, theory for various pq ; 0, this work (infinite dilution) ; a, data of Bur and Roberts.2coil-like polymers) the data of Bur and Koberts tend to a persistence length of 400monomer units. In this study the dilute solutions yield a mean persistence lengthof 230 monomer units, although consideration of all concentrations up to 1 g dl-lgives an extrapolated infinite dilution value of 400. Since there is evidence for someside by side association in these solutions which would lower p 2 , we favour the infinitedilution value as being the most meaningful solution to eqn (6) for these chains.However, since they are rod-like in character, the true value for the isolated coiS .B . DEV, R . Y . LOCHHEAD AND A . M . NORTH 255may be less than this. The treatment cannot be applied to these polymzrs usinnumber average molecular weights.Analysis of the relaxation behaviour yields similar conclusions whichever of thethree forms of eqn (1) are applied. For these two polymers, chemical considerationslimit possible upper values of Lo/& and theoretical rod-like considerations limitlower values. We find that, within the whole of the permitted range, evaluation ofLo and B is not independent of the value chosen for Lo/B. This point has beenoverlooked by previous workers, and is important because the rod-like treatmentsare strictly applicable only to such short chains.Although we can present only a range of Lo and B values, certain conclusions doemerge.The first is that the calculated thickness is concentration dependent, fig. 7.Consequently, values extrapolated to infinite dilution are probably most meaningful.When this is done taking Lo as 1.1 A using either the Perrin or Broersma relation-ships, the infinite dilution cylinder radius is about 5A ; this is small for a regular helixand more closely resembles the chain thickness. However, higher B values can beobtained assuming only slightly lower values of Lo, e.g., an infinite dilution value of11 A is associated with Lo taken as 0.9 A. When weight average molecular weightsare used in the calculation, most possible Lo values are close to 1 A, so it is unlikelythat the chain exists as a regular planar zig zag or as the tight helix described l4(Lo 1.9A) for the crystalline state.In this respect these results agree with the con-clusions of Bur and Roberts,2 but suggest that the helix is less perfect than describedby them. This conclusion is reinforced by the observation that temperature hasan effect (reducing Lo) both above and below room temperature.CONCLUSIONSWhile the Kratky-Porod model can be applied to coil-like chains, its applicationto chain lengths less than the persistence length must be regarded with caution.Incautious use results in the evaluation of incorrectly large persistence lengths256 DIELECTRIC A N D VISCOELASTIC RELAXATIONFor heterodisperse polymers, number average molecular weights are unsuitable forthe evaluation of chain stiffness parameters, the most realistic values being obtainedfrom weight average quantities.Poly(N-vinyl carbazole) is confirmed to be a remarkably rigid chain for a vinylpolymer.Long chain coils have a persistence length of about 250 monomer unitsat room temperature, and short chains (8-20 monomer units) have a “bent-rod”outline approximating to a semicircular arc. (Monomer projection length about 3monomer unit length). Poly(buty1 isocyanate) of 200-500 monomer units is pre-dominately rod-like in character. The Kratky-Porod persistence length is calculatedat infinite dilution as 400, but the true value for longer chains could be somewhat less.The calculated monomer projection length of poly(buty1 isocyanate) is not necessarilyindependent of the value chosen for the chain length to thickness ratio. Previous calcu-Iations of the projection length have not been carried to permissible low values of theratio. The monomer projection length is probably less than 1.1 for which value thecylinder radius at infinite dilution approaches the molecular chain thickness. Smallerprojection lengths and larger radii (indicating a looser helix or some rod curvature)cannot be ruled out. Cylinder radii (or prolate ellipsoid minor axes) are increasedwith concentration, indicative of side-by-side aggregation, as might be expected forsuch large dipole moments. For both types of polymer, persistence and monomerprojection lengths are decreased by increasing temperature, confirming that a certainflexibility does exist within the rod-like form.The authors acknowledge the support of the Science Research Council for thiswork.H. Yu., A. J. Bur and L. J. Fetters, J. Chem. Phys., 1966, 44,2568.A. J. Bur and D. E. Roberts, J. Chem. Phys., 1969,51,406.A. M. North and P. J. Phillips, Chem. Comm., 1968, 1340.P. J. Phillips, Ph. D. Thesis (Liverpool University, 1968).F. Perrin, J. Phys. Radium., 1934, 5,497.J. G. Kirkwood and P. L. Auer, J. Chem. Phys., 1951, 19,281.R. Cerf, Compt. Rend., 1952,234,1549.0. Kratky and G. Porod, Rec. Truu. Chim., 1949,68,1106.’ S. Broersma, J. Chem. Phys., 1960,32,1626.lo V. E. Shashoua, W. Sweeny and R. F. Tietz, J. Amer. Chem. SOC., 1960,82,866.l 1 J. Hughes and A. M. North, Trans. Faruduy Soc., 1966,62,1866.l2 A. M. North and P. J. Phillips, Trans. Furaday SOC., 1967, 63,1537.l3 P. J. Flory, Statistical Mechanics of Chain MoZecuZes, (Interscience, New York, London,l4 U. Shonueli, W. Traub and K. Rosenheck, J. PoZymer Sci., 1969, A-2,7, 515.Toronto, 1969)

ISSN:0366-9033    

DOI:10.1039/DF9704900244

出版商:RSC    

年代:1970

数据来源: RSC

ISSN:0366-9033    

DOI:10.1039/DF9704900257

出版商:RSC    

年代:1970

数据来源: RSC

ISSN:0366-9033    

DOI:10.1039/DF9704900268

出版商:RSC    

年代:1970

数据来源: RSC

摘要:

GENERAL DISCUSSIONDr. H. C. Booij (Geleen) said: In their paper, Stockmayer et al. state that accordingto the bead-and-spring models the deformation of a molecule in a flow field ispredicted to be without limit, in contradiction to experimental evidence. However,these models are not meant for studying large deformations, because the spring forceused is closely correlated with the Gaussian approximation of the distribution of theend-to-end distances of the segments at equilibrium. This inapplicability can also beconvincingly demonstrated in the following way. For every normal mode of motionof the necklace model, the increase of free energy is equal to+aAF(z) = kT/ f ( z ) In fo dR,where fo(z) and f(z) denote the equilibrium distribution and the flow-disturbeddistribution of a mode of relaxation time z, respectively.For simple shear flow witha rate of shear equal to q this increase in free energy is-0l) fo(z)AF(z) = RT[z2q2-0.5 In (1 +z2q2)]iffo(z) is taken to be a Gaussian distribution. This energy difference is already aslarge as 70 kcal/mol at z, values of about 10. Hence, according to this model thestored free energy would, even at these moderate shear rates, be large enough toproduce chain rupture, which is not observed experimentally. However, at theseshear rates the end-to-end distance of the segments becomes so large that the linearapproximation of the Langevin formula can no longer be used. Application of theLangevin distribution function affects the expression for&) and yields much smallervalues for the deformation and the increase of free energy of the normal modes insteady shear flow.Prof.W. H. Stockmayer (Dartmouth College, U.S.A.) said: The calculationdescribed by Booij is a graphic way to demonstrate the physical unreality of Gaussiansprings at high deformations. I hope that our text does not give the impression thatwe were surprised at these limitations, which have long been well known and arephysically obvious. The analytical advantage of a quadratic potential energy is sogreat that tricks may be acceptable to salvage at least some of the benefits. Thus,for example, Reinhold and Peterlin limit the deformability of a Rouse chain bymaking the effective spring force constant a function of the shear rate.Dr.A. J. Hyde (Strathclyde University) (communicated): If EgelstafYs remark,about the intermolecular distance having to be considerably greater than the moleculardiameter for the theory to apply, is correct, then this might also provide a reason forthe plateau in the (D, c) curve, since the critical concentration does seem to lie inthe region where the molecular diameter is about half the intermolecular distance.If this argument is correct, one would expect the “ critical concentration ” to varyas M-3.H. C. Booij and P. H. van Wiechen, J . Chem. Phys., 1970,52,5056.H. C. Booij, Ph.D. thesis (Leiden, 1970).C. Reinhold and A. Peterlin, J. Chem. Phys. 1966, 44,4333.27278 GENERAL DISCUSSIONDr. R. Ullmann (Ford Motor Co., Michigan) said: The frequency range in whichEgelstaff’s experiments are conducted is high enough so that the characteristic time mayrepresent only a few molecular jumps.Does he find, consequently, that the apparentdiffusion constant is frequency dependent ?Dr. P. A. Egelstaff (A.E.R.E., Harwell) said: Yes, if you call the function z(m) afrequency dependent diffusion coefficient. However, there are other functionswhich one might choose for this purpose and which reduce to the diffusion constantas m-0. Consequently this is not a useful concept and I prefer to use phrases like“ the spectral density of the velocity correlation function ”.Prof. W. H. Stockmayer (Dartmouth College, U.S.A.) said: The hyperbolicdependence of mobility on concentration in the system polystyrene + chlorobenzene(fig. 4 in the paper of Rehage et al.) is reminiscent of that observed by Fujita inother polymer + solvent systems and correlated by him with the expression,in which the free volume vy is taken to be a linear function of volume fraction. HaveRehage et al.tried an equation of the above type on their results?u = A exp (-B/u,)Prof. G. Rehage (Unioersity of Clausthal) said : The data, which we found in thesystem polystyrene + chlorobenzene show no good agreement with the equationsgiven by Fujita, but we did no further investigations to prove equations based onsuitable assumptions about free volume.Prof. F. H. Home (Michigan State University) said: I would make two commentson the paper of Rehage, Ernst, and Fuhrmann. First, although it is not customaryto utilize activity coefficients in discussing polymer solutions, they can be useful indescribing various aspects of non-ideality.In their paper, one would haveP l ( w m = m 1 +(a In yr/a In PrI1, i = 192,where yl is an activity coefficient. It would appear to be particularly important totake careful account of non-ideality in any detailed analysis of the concentrationdependence of D near the critical region.Secondly, although a precise definition of non-Fickian diffusion is not offered byRehage, Ernst, and Fuhrman, I infer from their $ 3 that they mean by this term anyprocess in which the calculated diffusion coefficient depends on time. Of course, adiffusion coefficient is a well-defined property of the mixture and cannot depend ontime.An apparent time dependence therefore indicates an error in the choice ofworking equations : viz., ‘‘ Fick’s Laws ” were used when they should not have been.“ Non-Fickian ” diffusion below the glass transition temperature has been attributedto “ relaxation phenomena,” or chemical reactions, by Fuhrmann and Rehageand, more mathematically, by F r i ~ c h . ~There are other possible sources of “ non-Fickian ” diffusion which do not appearto have been investigated thoroughly enough (if at all) to reject them. Fick’s secondlaw, even in the form of eqn. (14) of their paper, is incomplete whenever bulk flowReport Prog. Phys., 1966, 29, 333.H. Fujita, Adv. Polymer Sci., 1961, 3, 1.ref. (31) of their paper.H. L. Frisch, in Non-Equilibrium Thermodynamics, Variational Techniques, and Stability,R.J. Donnelly, R. Herman and I. Prigogine, ed., (University of Chicago Press, 1966), p. 277GENERAL DISCUSSION 219(convection) persists. This difficulty can be avoided if the partial specific volumes donot depend on c0ncentration.l Although they claim, at the end of Q 2(a), that thevolume change on mixing is very small, I should prefer to see a more thorough analysis.Less well-known sources of “ non-Fickian ” diffusion are the “ inertial andviscous terms” which appear in a generalized form of Fick‘s first Forisothermal, isobaric binary diffusion in the absence of viscous stresses, Fick’s first lawbecomes(in their notation). To my knowledge, the second term, the “ inertial term ”, hasnot been considered in analyses of diffusion systems which exhibit “ non-Fickian ”behaviour .J1 = - D(aP,laz>-(U1/P~~>(aJl/at)Prof. G.Rehage and Dr. J. Fuhrmann (University of Clausthal) said : The firstpart of Horne’s remark about the non-ideality of the polystyrene + cyclohexane systemnear the critical point has been studied in our laboratory by means of osmotic measure-m e n t ~ . ~ ~ The data given in fig. 11 show a pronounced dependence of the thermo-dynamic factor on both temperature and concentration. The minima shift towardsincreasing polystyrene concentration with decreasing temperature. Because osmoticmeasurements cannot be performed near the critical point an extrapolation to thevalue l/RT(aApl/i?x*l)T,P = 0 is uncertain.So the dashed line in fig. 1 reaches the\\\\\\\\\0 0.05 o h 0.1 5x:FIG. 11 .-Concentration dependence of 1 /RT(aApl/axy)~,p in the system polystyrene+ chloro-benzene. x: = segment mol fraction of the solvent.S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam,1962), p. 256.S. R. deGroot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam,1962), p. 29.D. D. Fitts, Nonequilibrium Thermodynamics (McGraw-Hill, New York, 1962), p. 162280 GENERAL DISCUSSIONcritical point within the limits of error of this graphical extrapo1ation.l In thehomogeneous region a detailed analysis of the concentration dependence of thediffusion coefficient can be performed by interpreting the data of osmotic measure-ments.Horne also mentioned the problems of thoroughly investigating possible sourcesof “ non-Fickian ” diffusion. We found that bulk flow due to volume change onmixing can be caused by either a diffusion-controlled volume change (Fickiandiffusion, which can be evaluated by the method given by Sauer and Freise 33-evenif the partial specific volume depends on concentration) or by a relaxation-controlledvolume change induced by diffusion, i.e., a superposition of diffusion and relaxationphenomena. The first example leads to a time-independent diffusion coefficienti.e., the diffusion coefficient is defined exactly because the concentration-profile isthe only independent variable defining the non-equilibrium state of the system.Thesecond example (superposition of diffusion and relaxation) leads to an evaluation ofa time-dependent “ apparent ” diffusion coefficient because a concentration profileand a profile of a second independent variable are needed to describe the non-equilibrium state of the system. Thus, the change of two independent variablescauses coupled fluxes, which have to be considered in the working equation thatHorne mentioned. Fick’s second law then reads in the paper under discussionwhere ;is the centre of mass (“ barycentric ”) velocity and Ti the rate of the relaxationprocess. The generalized form of the phenomenological law for the flux ;is givenby Frisch,2 that of the production term Ti is given in ref. (29). To our knowledgethe “inertial term” has not been considered in analyses of experimental data of“ non-Fickian ” diffusion systems.The reason for that may be the-&experimentaleiror in determining reference velocities.Dr. P. A. Egelstaff (A.E.R.E., HarweZZ) said: I would ask a question of Karaszet aZ. and Pecora et al. I assume that the polymer solution is dilute, which means thatthe distance d2 between molecules is much greater than the size of a molecule d l , i.e.,I assume also that the solvent is invisible? and for simplicity will consider opticallyisotropic molecules. Then we have at least three possible regimes for light scatteringexperiments. The first iswhere A is the wavelength of light and 8 the scattering angle. In this case one takesa sum over all pairs of molecules and the spectral width is related to the binarydiffusion coefficient (i.e., to concentration fluctuations).d2 B di- (1)47c sin (8/2)/A427c/d2 427c/dl, (2)The second case is24d2 -g 47c sin (8/2)/A 4 27c/d, (3)and here one neglects terms for which i # j in the sum over pairs, and the spectralwidth is related to the self-diffusion coefficient (in the absence of molecular interactionsthis is, presumably, the same as the binary diffusion coefficient).This extrapolation is strictly valid if the polymer component is monodisperse.(G. Rehage andD. Moller, J . Polymer Sci. C, 1967,16, 1787.H. L. Frisch, J. Chem. Phys., 1964, 41, 3679GENERAL DISCUSSION 28 1The third possibility is2n Id2 < 24dl < 4n sin (0/2)/A (4)in which case one measures the internal structure of the molecule.Karasz et al.dismiss case (3), but do not discuss the difference between the cases(1) and (2). Would they explain where they fit into their theory and also discuss thesituations arising when d , - d2 ?Would you give examples of the magnitude of dl, d2 and ( 2 sin (0/2)/A]-l intheir work, and also comment on how well they satisfy the condition d2%d1. Sincethey find a concentration dependence I suppose that dl -d2 and their solutions areby definition nut dilute?Prof. R. Pecora (Stanford University) said: In reply to Egelstaff, I have brieflydiscussed his cases two and three in my paper. A detailed discussion is given inref. (2), (3) and (1 1)-(13) of the paper.I agree with his comments about the difference between cases one and two.Inthe case where dl -A2, the analogues of cases one and three, i.e.,4n sin (612) 2n - 2n <-----a d2 4’and2n - 2n 4n sin (812)d , - p A ’seem to yield the same conclusions as before, and case two does not apply. Acomplicated case which I have not treated arises when2n 2n 4n sin (012)-N--N dl d2 A ’In this case neither the hydrodynamic nor the molecular theory is fully valid.Prof. F. E. Karasz and Prof. N. C. Ford (University of Massachusetts) said: Inreply to Egelstaff, for the solution with molecular weights M = 6.7 x lo5 we makethe following estimate : dl = 1600 A ; 570 < dz < 1770 A (dependent on concentration) ;4 2 sin (0/2) = 4500 so that the solution is indeed concentrated. However, thetime-scale over which a macromolecule forgets its velocity due to the solvent viscosityis z = MD/kT - 4.4 x 10-l2 s for this molecular weight.During this time the mole-cule moves about 0.1 A. We conclude that any effects due to hard-core interactionof macromolecules are negligible in determining the concentration dependence of ourmeasured D. Furthermore, in the absence of long-range forces between molecules, theassumption that intermolecular correlation functions vanish is valid even in highconcentrations. Thus, it must be only the difference between solvent-solute and solute-solute interactions that leads to an apparent concentration dependence of the diffusionconstant.Dr. R. U h a n (Furd Mutor Co., Michigan) said: In the light scattering methodof determining dynamic behaviour of macromolecules, the translational diffusion ofthe single molecule and the relative motion of two chain segments on the samemolecule seem to be difficult to distinguish.Would Pecora and Ford explain howthis would be done? Are they able to obtain any estimates of an intramolecularrelaxation time 282 GENERAL DISCUSSIONProf. R. Pecora (Stanford University) said: In reply to Ullman, there are manysituations in which one may observe intramolecular relaxation times by light scattering.If one observes the polarized spectrum of scattered light as a function of IC( = 4n/;1 sin 8/2), the lineshape at low angles should be a single Lorentzian with linewidthproportional to the translational diffusion coefficient of the molecule.At highangles, additional Lorentzians should appear in the spectrum which have contribu-tions to their widths from intramolecular relaxation times. This method is applicableonly to very large molecules. Experiments of this type have been d0ne.lIntramolecular relaxation times should also contribute to the spectrum if thereare segment polarizability changes associated with the structural change. Observa-tion of the depolarized spectrum should also be a valuable source for obtaining intra-molecular relaxation times. As far as I know, no experiments of this type have asyet been attempted.Prof. F. E. Karasz and Prof. N. C. Ford (University of Massachusetts) said : In replyto Ullman, since the spectral width of light scattered by translational diffusion is depen-dent upon scattering angle whereas that from the relative motion of chain segment orfrom rotational processes is not, the various processes may be separated by a carefulstudy of the angular dependence of the spectrum.In most cases, intramolecular re-laxation times will be too short to be accessible to our present experimental techniques.Prof. F. H. Horne (Michigan State University) said: With respect to the paperof Ford, Karasz, and Owen, I would comment on " osmotic virial coefficients,"A2, A s , . . ., defined bywhere c is concentration in mass per unit volume and M2 is molecular weight ofsolute. Unlike the analogous virial coefficients for a gas, osmotic virial coefficientsare not due entirely to non-ideality, i.e., osmotic virial coefficients defined by (1) donot vanish for ideal mixtures.This is evident when we recall that the thermo-dynamic expression for osmotic pressure is (with neglect of isothermal compressi-bility terms)4where 4 is the osmotic coefficient, v; is the molar volume of pure solvent, and x1 ismol fraction of solvent. Conversion of (2) to a power series in concentration yields,for an ideal mixture (4 = 1)IT = cRT(M,l+A,c+A3c2+ ...) (1)II = -(+RT In x,>/u,O, (2)n = CRT(M,~+A~C+A!$~+ ...), (3)A; = M , 2 ( ~ i - ~ ~ , " ) ,Aid = MT3(vi2 - V ~ V ; +$vY2),where vi is molar volume of solute.Although (1) is satisfactory for expressing data, any attempt at interpretation ofA2, A3, . . . must take account of (3). Some part of each osmotic virial coefficient isdue to the expansion of lnxl in powers of c, and that part has nothing to do withmolecular or intermolecular behaviour.H.Z. Cumins, F. D. Carlson, T. J. Herbert and G. Woods, Biophys. J., 1969, 9, 518;S. Fujime, J. Phys. Soc., Japan, 1970, 28, 267, and ibid., in press.see, e.g., Y. Yeh, J. Chem. Phys., 1970, in press.B. H. Zimm, J . Chem. Phys., 1946,14, 164.I. Prigogine and R. Defay, ChemicaZ Thermodynamics (Longmans, Green, and Co., London,1954), pp. 326-330GENERAL DISCUSSION 283Dr. A. J. Hyde (Strathclyde University) said: I would ask Ford and Karasz towhat they attribute the lack of variation of D after a certain critical concentration.A naive first thought would suggest that the linear variation in D might no longercontinue when the solution becomes ‘‘ packed ” with polymer molecules ; but arough calculation shows that this is certainly not the case for the polymer in theirfig.3 for which “ close packing ” would not occur until ca. 8 x g/ml even if theradius of gyration did not decrease with concentration.Prof. F. E. Karasz (University of Massachusetts) said: In reply to Hyde, calcula-tions show that even for a densely packed solution collisions between macromoleculesand solvent molecules are more important in determining the diffusion constant thanare collisions between macromolecules. The reason for the concentration dependencemust therefore be sought in thermodynamic terms ; e.g., third- and higher-ordervirial coefficients may provide the answers.It is also clear that the concentrationrange examined is relatively very limited ; at higher solute concentrations the binarydiffusion constant must start to increase again.Dr. P. F. Mijnlieff, Mr. W. J. M. Jaspers, Ir. G. Ooms and Dr. Ir. H. L. Beckers(Koninklijkelshell-Laboratorium, Amsterdam) (communicated): In the evaluation ofthe results of sedimentation measurements, the logical procedure is the extrapolationof the sedimentation coefficients to zero concentration, the main object being thedetermination of the characteristics, e.g., the radius of gyration, of the single coil. Thecalculation of the frictional properties of a polymer coil usually involves detailedconsideration of the hydrodynamic interactions between the segments, the frictionalcoefficient of a segment being introduced as a parameter.Another approach to thecalculation of the frictional coefficient is the application of the hydrodynamic lawsto the coil which is treated as a permeable sphere.l This demands the knowledge ofthe permeability from point to point in the coil, i.e., as a function of the concentration ;we obtain this information direct by ultracentrifugation at finite concentrations.Recently we derived the following relation between the sedimentation coefficientS1 of the polymer and the permeability k :where k is defined by Darcy’s law for the flow of solvent through a porous medium,effected by a pressure gradient : Jo = -k(grad P)/qo ; Jo = solvent flow in cm3/sper cm2 of the porous medium, yo = solvent viscosity, c1 = polymer concentrationin g/cm3, El and 5, = partial specific volume of polymer and solvent, respectively.(At not too high concentrations the factor (l-Cl/G0) can be identified with thebuoyancy factor (1 - Ulpo) normally used in velocity sedimentation.) Relation (l),which has been derived using irreversible thermodynamics, is valid at any concentra-tion.It is particularly useful, however, when the concentration is so high that thepolymer segments are homogeneously distributed in the solution, so that the sedi-mentation becomes comparable with the flow of solvent through a porous plug.3In this situation the sedimentation is independent of the polymer molecular weight ;this can be used as an indicator for homogeneous segment distribution.Application of relation (1) to sedimentation measurements on polymer solutionsFor a homogeneous cloud of beads as a model, H.C. Brinkman (Research, 1949,2,190) calcu-lated frictional coefficients for polymer molecules, using an expression he derived for k.P. F. Mijnlieff and W. J. M. Jaspers, Truns. Furaduy Suc., submitted for publication.From the analogy between sedimentation in a concentrated polymer solution and plug flow,J. H. Fessler and A. G. Ogston, Truns. Furuduy Suc., 1951, 47, 667, derived an expression for S1 asa function of concentration.k = slyo/cl(l -~l/vo), (1284 GENERAL DISCUSSIONof various concentrations in the region of homogeneous distribution gives thepermeability as a function of the concentration.For coils of poly-a-methylstyrene(PAMS) of various molecular weights and known radius of gyration we have calcu-lated frictional coefficients in the solvents toluene and cyclohexane, using theBrinkman-Debye equation of motion and assuming a Gaussian segment-distribution.Thelagreement with experimental values is good (see table 1).TABLE 1 .-FRICTIONAL COEFFICZENTS OF POLY-a-METHYLSTYRENE, IN g /Sin cyclohexane in toluenetheory expt theory expt0.30 x M = 1.OX lo6 0.27~ loe6 0.29~ 1W6 0.31 xM = 3.4 x lo6 0.49 x 0 . 5 3 ~ 0.66~ 0 . 6 2 ~M = 6 . 5 ~ lo6 0.77~ 0.75 x 1.02x 1W6 0.94~A comparison of the permeabilities in the two solvents at the same concentration(homogeneous distribution) reveals an anomaly : the permeability in cyclohexane at35°C ( = 8) is about three times as large as in toluene at 25°C.The temperaturedependence of the permeabilities in the two solvents, measured for PAMS, M =6-5 x lo6, at a concentration of 1.64 g/lOO cm3, is shown in fig. la. In cyclohexane1.1 r 8 rPERMEABILITY INSOLUTIONS OFPOLY -&-METHYLSTYRENEc.I.64 g/lOO rnlCYCLOHEXANE~/ /7 LTOLUENE6-SECOND VlRlAL COEFFICIENT OF -\\SOLUTIONS OF \POLY -d- METHY LSTYRENE,3t ::I ; I f l : , : ,25 75 125 25 75 125 I750.3temp., "C temp., "C(4 (4FIG. 1.the permeability strongly decreases with increasing temperature, whereas in tolueneonly a slight increase is observed. We conclude from this behaviour that at the 8temperature the polymer chains tend to aggregate on a micro scale, resulting in acoarser distribution of polymer in the solution and a larger k value.The minimumin k for cyclohexane at 100°C suggests a reversal of the solvent quality. This hasbeen confirmed by measurement of the second virial coefficient (light scattering) as afunction of temperature, pointing ultimately to a lower critical solution temperatureat about 180°C (see fig. lb).Stockmayer has brought to our notice a publication.2 They determined permea-bilities from permeation experiments on polymer gels and by ultracentrifugation ofpolymer solutions using eqn (1). Conclusions about the diameters of polymer chainswere drawn by comparison with the flow behaviour in macroscopic hydro-dynamicmodel-systems.G. Ooms, P. F. Mijnlieff and H. L. Bakers, to be published.R.Signer and H. Egli, Rec. trav. chim., 1950, 69, 45GENERAL DISCUSSION 285Prof. G. Rehage (University of Clausthul) said : Concerning the contribution ofMijnlieff et al. we would draw attention to ref. (S), in which the laws for infinitedilution are investigated in connection with the quality of the solvents. The mobility,the fraction coefficient, the sedimentation coefficient and the mean square end-to-enddistance of the polymer have been evaluated according to equations due to H. Kuhnland W. Kuhn,2 Flory and T~vetkov.~Prof. W. H. Stockmayer (Dartmouth College, U.S.A.) said: The results of Bauerand Immendorfer are particularly welcome because they seem to dispose of a greatpuzzle produced by earlier acoustic experiments on polymer solutions.The processwhich the authors have observed acoustically in polystyrene solutions appears closelyrelated to that seen in dielectric dispersion of solutions of poly-p-chlorostyrene andother polystyrene derivatives (fmax-30 MHz in benzene at 25°C) and also in n.m.r.relaxation of polystyrene solutions (spin-lattice relaxation time TI at 30 MHz forpara ring protons about 0.2 s in tetrachloroethylene at 25"C, corresponding to anorientational correlation time of about 50 ns). The activation energy found in thedielectric experiments is about 5 kcal/mol, in satisfactory accord with the acousticvalue. The molecular model proposed for the process is similar to one of severalsuggested by Monnerie and Geny * in their Monte Carlo studies of the dynamics ofdiamond-lattice chains.Prof.D. Patterson (McGill University, Montreal) said : With reference to thepaper by Bauer and Immendorfer, if compressional relaxation (AV # 0) were apossibility, the process of mixing polymer and solvent-two liquids of widely differentfree volume-could result in a displacement of the rotational isomer equilibrium ofthe polymer. The polymer, being in a " decompressed " molecular environment,would move toward a higher proportion of the bulkier isomer with an attendanteffect on the thermodynamic mixing functions, particularly HE.Dr. R. ullman (Ford Motor Co., Michigan) said: Would North explain why thepartially flexible chain model of Kratky and Porod should not be used for polymerchains shorter than the persistence length? Is it possible that the torques on themolecule cause the polymer chain to flex to a greater degree when the molecularweight is high than it does with lower molecular weight samples? Would this accountfor the apparent decrease in persistence length with increasing molecular weight ?Prof.A. M. North (University of Strathclyde) said: In answer to Ullman's firstquestion, our objection to the use of the Kratky-Porod relationship for these veryshort chains is essentially a practical one. The Kratky-Porod treatment starts fromthe concept of a freely rotating chain and then develops the persistence length as ameasure of chain curvature defined as a limit when the chain is infinitely long. Itseems, to us, dangerous to discuss or attempt to measure this quantity by makingH.Kuhn, Experientia, 1946,2, 64.H. Kuhn, W. Kuhn, J. Chem. Phys., 1948,16,838.P. J. Flory, Principles ofPolymer Chemistry, (Ithaca, New York, 1953).N. V. Tsvetkov and S. J. Klenin, J. Polymer Sci., 1958, 30, 187.W. H. Stockmayer, H. Yu and J. E. Davis, Polymer Preprints (Amer. Chem. SOC.), 1963, 4(2),132.B. Baysal and W. H. Stockmayer, paper presented at I.U.P.A.C. Symp. Macromol. Chem.,(Toronto, 1968).L. Monnerie and F. Geny, J. Chim. Phys., 1969, 66,1691.' D. W. McCall and F. A. Bovey, J. Polymer Sci., 1960,45, 530286 GENERAL DISCUSSIONobservations on chains which are shorter than a single freely rotating unit. Putanother way, in an experiment such as these, one is trying to measure the curvatureof an finitely bent chain by making observations on molecules which are hardlybent at all.The fact that we (and also Eisenberg) report differing calculated per-sistence lengths when measurements are made on polymers of different molecularweights seems to confirm the inadequacy of the procedure.Ullman’s second question is extremely interesting and I am aware of no exactanswer to it. It is known that the infinitely large molecule does not exist in solutionbecause the hydrodynamic shear forces acting on it would cause degradation.Consequently, these same forces which are a function of the chain size must be ableto promote gross bond distortions or curvature on regions of the chain. One is,therefore, led qualitatively to agree with Ullman that there will exist a shear-inducedcurvature in long chains which might very well be absent in short chains.Again,this is in accord with the experimental results presented by ourselves and Eisenberg.Dr. Henryk Eisenberg (The Weizmann Institute of Science, Israel) said : Similarobservations to those of S. B. Dev, R. Y. Lochhead and A. M. North have beenmade in light scattering and hydrodynamic studies of nucleic acid solutions. Doublehelical fragments of DNA in various sizes can be obtained by careful sonic irradiationof DNA solutions. We find that fragments of molecular weight about 5 x lo5,contour length about 2500 A, are stretched to almost 90 % of their full extension, andbehave in almost rod-like fahion. Calculation of an apparent persistent length, bya formal application of the Kratky-Porod theory for the wormlike coil leads to avalue appreciably higher than usually attributed to high molecular weight DNA(cf.also. ref. (3)). This result may well be due to the inapplicability of the simpleKratky-Porod theory to short chains (although formally the theory covers the wholerange from rigid rods to Gaussian chains) rather than to a decreased inherentflexibility of short DNA chains.Prof. A. M. North (University of Strathclyde) said : In reply to Claesson, a problemin polymer molecular dynamics lies in determining how many covalent single bondsmust exist between a ‘‘ probe ” group and a polymer chain so that rotation of thegroup can occur independently of segmental rotation in the chain. When the ‘‘ probe ”is fluorescein thiocarbamate four bonds capable of rotation lie between the fluoresceinresidue and the chain. Consequently I wonder if Claesson would amplify the state-ment in his paper that “the rotational motion of the fluorescein molecule. . . isalmost completely governed by the micro-Brownian motion of the HEC chain.”Prof. S . Claesson (Uppsala Universitet) said: In reply to North, perhaps ourstatement requires some clarification. Of course, the presence of four bonds betweenthe HEC-chain and the fluorescein residue has the consequence that the rotationalmotion of the dye residue is rather independent of that of the chain. The maineffect of the attachment is, that the dye is kept permanently in a region where theconcentration of chain segments is fairly high. Therefore the local viscosity aroundthe dye residue, which governs the degree of polarization, depends strongly on themicro-brownian motion of all the chain segments which are present in that vicinity.G. Cohen and H. Eisenberg, BiopoZymers, 1966,4,429.H. Eisenberg, Biopolymers, 8, 1969, 545.J. B. Hays, M. E. Magar and B. H. Zimm, BiopoZymers, 1969, 8, 531

ISSN:0366-9033    

DOI:10.1039/DF9704900277

出版商:RSC    

年代:1970

数据来源: RSC

摘要:

AUTHOR m E X *Anderson, J. E., 257Baranov, V. G., 137.Bauer, H.-J., 238.Beckers, H. L., 283.Berry, G. C., 121.Booij, H. C., 277.Byers Brown, W., 177.Carpenter, D. K., 182.Chikahisa, Y., 182.Claesson, S., 268,286.Cruickshank, A. J. B., 106,174.Delmas, G., 98.Dev, S. B., 244.Domb, C., 78, 82, 83.Edwards, S. F., 43, 81, 82.Egelstaff, P. A., 193, 278, 280.Eisenberg, H., 176, 286.Ernst, O., 208.Flory, P. J., 7, 81, 164, 173.Ford, N. C., 228,282.Fuhrmann, J., 208,279.Gobush, W., 182.GomCz-Ibhfiez, J. D., 165.Harris, D. H. C., 193.Hassler, H., 238.Hicks, C. P., 106, 163, 170, 175.Horne, F. H., 278, 282.Huggins, M. L., 164, 175.Hyde, A. J., 81, 277, 283.Immendorfer, M., 238.Jaspers, W. J. M., 283.Karasz, F. E., 278,281,282, 283.Kirste, R. G., 51.Koningsveld, R., 144, 179, 180.Konynenburg, P. H. van, 87.Liddell, A. H., 115.Liu, Kang-Jen, 257.Lochhead, R. Y., 244.Malcolm, G. N., 164.Marsh, K. N., 77.Martin, J. L., 80.Mijnlieff, P. J., 283.North, A. M., 244,285, 286.Odani, H., 268.Owen, J. E. M., 228.Ooms, G., 283.Patterson, D., 98, 169, 170, 173, 285.Pecora, R., 222, 281,282.Ptitsyn, 0. B., 70.Rehage, G., 77, 176,208,278,279,285.Rigby, M., 78.Rowlinson, J. S., 30, 168, 180.Scott, R. L., 76,87, 164, 171, 179.Shimanouchi, T., 60,85.Silberberg, A. , 162.Stepto, R. F. T., 81, 164.Stockmayer, W. H., 80, 180, 182, 277, 278, 285.Swinton, F. L., 115.Teja, A. S., 168.Tompa, H., 163.Ullman, R., 82, 167,257,278,281, 285.Young, C. L., 166.* The references in heavy type indicate papers submitted for discussion

ISSN:0366-9033    

DOI:10.1039/DF9704900287

出版商:RSC    

年代:1970

数据来源: RSC