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1.
The dimensions of both cyclic and linear poly(dimethyl siloxanes) in dilute solution in benzene-d6 have been measured by small-angle neutron scattering. The mean-square radii of gyration of the linear polymers are consistent with values predicted from published data, including experimental molar cyclization equilibrium constants. The average dimensions of the cyclic poly(dimethyl siloxanes) in fractions containing z-average numbers of bonds n?z in the range 130 < n?z < 550, were found to be considerably smaller than those of the corresponding linear polymers. The neutron scattering results give a value for the ratio of the z-average radii of gyration for linear and ring poly(dimethyl siloxanes) (containing the same number of monomer units) 〈s2z,l<s2z,r = 1.9 ± 0.2. This ratio may be compared with the value of 2.0 predicted theoretically for ‘flexible’ high molecular weight linear and cyclic polymers, unperturbed by excluded volume effects.  相似文献   

2.
A Monte Carlo method has been devised for calculating the conformation-dependent properties of cyclic poly(dimethyl siloxanes) (PDMS), using Flory, Crescenzi and Mark's rotational isomeric state model. Calculated values of the mean-square radii of gyration 〈s2r〉 of ring molecules unperturbed by excluded volume effects and containing 8–100 skeletal atoms are compared with the 〈s2l〉 values for the corresponding unperturbed chain molecules. Exact enumeration methods were also employed for rings [(CH3)2SiO]w2 with w ? 24 and the results found to be in close agreement with those obtained by the Monte Carlo method. The ratio 〈s2l〈s2r was found to attain limiting values close to 2.0 for w > 30, in agreement with theoretical predictions.  相似文献   

3.
K. Dodgson  J.A. Semlyen 《Polymer》1977,18(12):1265-1268
The limiting viscosity numbers of ten cyclic and ten linear poly(dimethyl siloxane) fractions have been measured in a π-solvent (butanone at 293K) and in two ‘good’ solvents (toluene and cyclohexane at 298K). The dimethyl siloxane fractions studied were in the molecular weight range 800 < M?w < 17 000. The data obtained are compared with related studies published in the literature. The ratio of the limiting viscosity numbers [η]r and [η]l of the cyclic and linear poly(dimethyl siloxanes) with M?w > 2500 was found to be 0.67 in butanone at 293K. This value is identical (within experimental error) to the theoretical ratio [η]r[η]l = 0.66 predicted by Bloomfield and Zimm and others for ring and chain polymers in π-solvents. The ratio [η]r[η]l was found to be somewhat smaller for the higher molecular weight polymers in the ‘good’ solvents.  相似文献   

4.
The diffusion coefficients (D) of cyclic and linear poly(dimethylsiloxanes) (PDMS) have been measured in bromocyclohexane at 288 K and 301 K. Bromocyclohexane has previously been reported to be a θ-solvent for high molar mass linear PDMS at 301 K, but the hydrodynamic radii reported here apparently show the effects of molecular expansion at both temperatures. In addition, the hydrodynamic radii of both linear and cyclic PDMS are found to be insensitive to whether the solvent is toluene or bromocyclohexane. The ratio of friction coefficients frfl for the ring (r) and linear (l) molecules of the same number of segments (x) is in good agreement with the theoretical value of 8 in the impermeable limit and with the experimental value found previously in toluene solution. As x decreases the ratio frfl tends to unity, illustrating the increasing importance of free-draining at low molar mass.  相似文献   

5.
K. Dodgson  D. Sympson  J.A. Semlyen 《Polymer》1978,19(11):1285-1289
A preparative gel permeation chromatographic (g.p.c.) instrument has been constructed and used to separate broad fractions of cyclic poly(dimethyl siloxanes) into sharp fractions with heterogeneity indices M?wM?n = 1.05 ± 0.02. The number-average molecular weights M?n of the cyclic polymer fractions obtained were as high as 50 000, corresponding to number-average numbers of skeletal bonds n?n up to 1300. The concentrations of linear poly(dimethyl siloxanes) in all but the highest molecular weight cyclic polymer fractions prepared are believed to be negligible. The preparative g.p.c. instrument was also used to obtain some sharp fractions of linear poly(dimethyl siloxanes).  相似文献   

6.
High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients (D) and hydrodynamic radii (RH) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration (Rg) obtained by small-angle neutron scattering. While the ratio DringDchain is close to the predicted value of 0.85, the ratio RgRH falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.  相似文献   

7.
The static dielectric permittivities, refractive indices and densities of undiluted oligomeric cyclic and linear dimethyl siloxanes and narrow fractions of cyclic and linear poly(dimethyl siloxanes) have been measured for number-average molar masses M?n in the range 160 < M?n < 7700 at temperatures from 298 to 313 K. Measured total dielectric polarizations have been resolved into their electronic, atomic and orientation components and dipole moments have been derived. The dipole moments of cyclic oligomers ((CH3)2SiO)x (for example, with x = 4, 5) are markedly lower than the dipole moments of the corresponding linear oligomers containing the same number of siloxane bonds. However, for x ? 10, the dipole moments of cyclic dimethyl siloxanes are identical, within experimental error, to those of the corresponding linear dimethyl siloxanes. Measured static dielectric permittivities of the dimethyl siloxanes and poly(dimethyl siloxanes) in solution in cyclohexane are markedly different from the corresponding values for the undiluted siloxanes. These differences are interpreted as resulting from the specific solvent effects.  相似文献   

8.
The equilibrium shapes of cyclic and linear poly(dimethyl siloxane) (PDMS) molecules have been investigated using Flory, Crescenzi and Mark's rotational isomeric state model, together with a Monte Carlo method described previously. The principal axes of the equivalent ellipsoids have been computed and the major change on ring formation was found to be a reduction in the longest axis of the ellipsoid. This result is in agreement with previous studies of other ring molecules. The shapes of the cyclics [(CH3)2SiO]w2 in the region w=20 are disc-like and this observation is related to the different bond angles at silicon and oxygen atoms. Bulk densities and refractive indices of PDMS rings are discussed in relation to the calculated molecular shapes. Histograms are used to illustrate the proportional frequency functions of the radii of gyration and their components sx, sy and sz.  相似文献   

9.
The oxidation process in irradiated polyethylene was investigated by means of the e.s.r. method, and diffusion of oxygen molecules into the crystalline region of polyethylene was studied in detail. Computer simulation was carried out in order to determine various parameters of the process including diffusion constant. In the course of the simulation, the crystallite was assumed to have a plate-shaped form and the diffusion constant was considered to be larger at the region near the surface of the crystallite, Df, and to be smaller at the inner region of the crystallite, Ds. Making these assumptions in the simulation gave a much better result than the assumption based on a sphere-shaped crystallite. DfDs was found to be about 2 for thicker crystallite and it was 4 ~ 5 for thinner crystallite. Diffusion constants at various temperatures were determined, and the order of magnitude of diffusion constants in the crystalline region was found to be 10?16 cm2/sec at about 320K both for thicker and thinner crystallites. The activation energy of diffusion of oxygen in the crystallites was found to be 32 kcal/mol.  相似文献   

10.
The bulk viscosities η of over fifty sharp fractions of cyclic and linear poly(dimethyl siloxanes) in the weight-average molecular weight range 500 < M?2 < 25 000 have been measured at 298 K using a cone- and-plate microviscometer. In the Iow molecular weight region M?W < 1000) the η values for the cyclics were found to be at least three times as large as the values for the corresponding chain molecules. By contrast, in the highest molecular weight region (M?W > 16 000), the η values for the cyclics were approximately one-half those for the corresponding linears. Cyclics and linears containing about one hundred skeletal bonds were found to have similar bulk viscosities. The temperature dependence of the bulk viscosities of eighteen of the cyclic and linear fractions were investigated, and the relationship η = A exp(EviscRT) was used to deduce values for the energies of activation for viscous flow Evisc and the constants A.  相似文献   

11.
Walter Burchard 《Polymer》1979,20(5):577-581
The influence of a size distribution on the angular dependence of the quasielastically scattered light is studied for (i) large hard spherical particles and (ii) large flexible chain molecules. For the spherical particles the angular dependence is shown to depend solely on the size distribution and the particle scattering factor. Combination of conventional elastic light scattering with quasielastic light scattering allows the determination of the z-average radii moments rn?z (n = ?1, 1, 2, …) which define the size distribution. Flexible chains — linear and branched ones — show in any case a linear dependence of the apparent diffusion constant Dapp = Гq2 on q = (λ) sin θ2, when q becomes large. This behaviour represents the flexibility of the spring-bead model with strong hydrodynamic interaction. The initial part on the other hand form a straight line when Dapp is plotted against q2. The intercept of this straight line is the z-average diffusion constant while the slope is proportional to the z-average mean square radius of gyration. Thus, the polydispersity can be estimated from Dz and 〈S2z while the asymptote at large q-values is determined by the internal flexibility of the molecule.  相似文献   

12.
Emulsion polymerization of vinylacetate leads to branched polymers which at high monomer conversions form microgels of the shape and size of the latex particles. Quasielastic light scattering measurements from samples in the pre-gel state give at small q2 a linear angular dependence of Dapp = Гq2 which resembles that of randomly branched chain molecules, where Г is the decay constant of the time correlation function. Extrapolation of Dapp towards zero scattering angle yields the translational diffusion constant Dz. The diffusion constant follows the molecular weight dependence Dz = 9.78 10?5Mw?0.478. The diffusion constant of the microgels, i.e. at molecular weights Mw > 14 106, remains constant because of the finite and constant size of the latex particles. The coefficients kf and kD in the concentration dependence of the frictional and diffusion coefficients are related according to the equation kD = kf ? 2A2Mw ? v? where A2 is the second virial coefficient and v? the partial specific volume of the particle. The coefficient kf is calculated from the experimentally determined quantities kD, A2 and Mw, and the result is compared with the theory by Pyun and Fixman. Accordingly the branched coils in the pre-gel state resemble soft spheres, but the microgels behave more like spheres of some rigidity.  相似文献   

13.
Particle scattering functions P(Q) (where Q represents the wave vector), have been calculated using a Monte Carlo method for cyclic and linear poly(dimethyl siloxanes) (PDMS) containing up to 100 skeletal bonds. A maximum is found in the Kratky plot at u (=Q〈s212)≈2.0 for cyclic PDMS (with root-mean-square radii of gyration 〈s212) and this is in satisfactory agreement with the analytical calculations of Casassa and of Burchard and Schmidt. In addition, other clearly-defined maxima are found at u≈5.0 for PDMS ring molecules with less than ≈40 skeletal atoms. These maxima are believed to be characteristic of small cyclic molecules as they are also predicted for small polymethylene rings. Comparisons are made with experimental small-angle neutron scattering (SANS) data for cyclic and linear PDMS. A single maximum in the experimental Kratky plot at u≈2.0 is found for PDMS ring molecules with an average of 550 skeletal atoms. The experimental data for cyclic PDMS are in better agreement with the Monte Carlo calculations of P(u) than with analytical predictions up to u≈2.0.  相似文献   

14.
F.P Wolf  Geoffrey Allen 《Polymer》1975,16(3):209-217
The relative energetic contribution to the retractive force of a deformed rubber sample, fef, has been evaluated from thermoelastic measurements at constant pressure. Extension ratios λ have been studied in the range 0.88 ? λ ? 1.70 at 20° and 40°C. The results are given for a reference temperature, 30°C. Since data in the transition region from uniaxial elongation to compression were to be evaluated, a new set of equations was derived on the basis of the Gaussian force law, because the usual equation for measurements at constant pressure tends towards infinity when approaching the undeformed state λ = 1.Considerable difference between the results obtained by different, though apparently equivalent, equations have their origins in the deviation of the experimental data from ideal Gaussian behaviour. The influence of this inaccuracy on the terms of the equations is discussed and the most reliable functions for small deformations 0.88 ? λ ? 1.15 and for moderate elongation λ > 1.10 have been identified. With these precautions the Gaussian force law is a satisfactory approximation for the determination of reliable values of fef.The evaluation of data at small deformations is extremely sensitive to experimental error. Even smoothed polynomials L (f) were not sufficient to eliminate an apparent maximum in the fef vs. λ curve. Therefore the linear thermal expansion coefficient βlin(λ), which is a major term in all the fef equations at small deformations, had to be scrutinized critically. Although experimental data in this range showed that βlin(λ) is a slightly S-shaped function, a linear approximation is adequate at moderate elongations.Using one of the new equations together with the linear approximation for βlin(λ) in the region of small deformations, and two equivalent equations at moderate elongation, the energetic contribution to the total stress was found to be fef = 0.18 ± 0.02 for lightly crosslinked natural rubber. Little variation in fef was observed over the full range of measurements: 0.88 ? λ ? 1.70.  相似文献   

15.
Static and dynamic Kerr effect studies on poly(n-butyl isocyanate) (PBIC) and poly(n-octyl isocynate) (POIC) in CCl4 solution are reported and are compared with dielectric studies. The variation of dipole moment μ and Kerr constant factors θ1 and θ2 with temperature suggest the chains for MW ~ 105 depart from a rod-like conformation, and this is also indicated by a detailed analysis of the dynamic Kerr effect and dielectric data. It is shown that the ratio of areas for the rise and decay transients for the Kerr effect are inconsistent with the simple model for rotational diffusion. In addition the averaging process involved in the apparent dielectric relaxation time 〈τD〉 and the Kerr effect decay average relaxation time 〈τK,d〉 is examined and it is shown that for rigid-rod, coil and Kratky-Porod behaviour that 〈τD〈τK,d ? 〈ADAK a factor which would be 3 for rotational diffusion, and is found to be ~1 for PBIC and POIC again indicating the departure from simple rotational diffusion for the present samples.  相似文献   

16.
Small-angle neutron scattering studies have been made of molten and crystalline polypropylene using samples containing small amounts of deuterated polypropylene in a protonated polypropylene matrix. The specimens were characterized by small- and wide-angle X-ray scattering to determine the d-spacing and the degree of crystallinity χ and by gel permeation chromatography to determine molecular weight, Mw, and molecular weight distribution. The degree of crystallinity was varied from 0.5 to 0.7, the d-spacing from 120 to 250 Å and the molecular weight from 34 000 to 1 540 000. Clustering was not observed. The radius of gyration 〈s2w12 of the tagged molecules was approximately proportional to Mw12 and almost independent of d and χ. In the melt similar values were obtained which are, within experimental uncertainties, the same as in a θ-solution. For 〈s2wk2? 1 the scattering law approaches a k?2 dependence. The results are discussed with reference to the chain-folded model but a fit cannot be obtained over all molecular weights. A simple random coil model fits the neutron scattering data partly but this does not explain the origin of the d-spacing.  相似文献   

17.
C Price  G Allen  N Yoshimura 《Polymer》1975,16(4):261-264
Thermomechanical heat of torsional deformation measurements have been made on crosslinked cis-polybutadiene by means of a Calvet microcalorimeter operated at 30°C. When corrected for volume changes utilizing the Gaussian statistical theory of elasticity, the data gave a value for the relative energy contribution to the torsional couple, MeM, of 0.14 ± 0.02. Measurements were also made on a sample subjected to simple tensile deformations. The relative energy contribution to the tensile force (fef) was found to agree within experimental error with the value obtained for MeM, and the two results gave an average value for din 〈r20dT of 4.1 × 10?4 K?1.  相似文献   

18.
Extremely high molecular weight polystyrenes with a M?w in the range 10.8 × 106 to 2.2 × 107 were prepared by emulsion polymerization initiated with a heterogeneous initiator at 30°C, which has a ‘living character’. Samples of polystyrene were characterized by light scattering and viscometry in toluene and benzene at 25°C, and in θ-solvent cyclohexane at 34.8°C. Also determined were the relationships of mean-square radius of gyration 〈s2〉 (m2) and the second virial coefficient A2 (m3 mol kg?2) on the molecular weight, which for toluene and benzene are described in equations: Toluene (25°C) 〈s2〉=1.59 × 10?23M?w1.23; A2=4.79 × 10?3M?w?0.63; Benzene (25°C) 〈s2〉=1.23 × 10?22M?w1.20; A2=2.59 × 10?3M?w?0.59. The parameters in the Mark-Houwink-Sakurada equation were established, for extremely high molecular weight polystyrene in toluene and in benzene, at 25°C into the form giving for [η] (m3kg?1): [η] = 8.52 × 10?5M?w0.61; [η] = 1.47 × 10?4M?w0.56. The mentioned relations, as well as the obtained values of Flory parameter ?0 and of ratio [η]M?w0.5 were compared with solution properties of high molecular weight polystyrene with narrow molecular weight distribution prepared by anionic polymerization by Fukuda et al.  相似文献   

19.
Samples of poly(ethylene terephthalate) (PET) modified with small amounts of trimesic acid groups and hence containing long chain branching have been prepared. From the content of trifunctional modifier and from the experimental value of the extent of reaction, the weight-average molecular weight M?w and branching density B?w have been calculated, assuming that all the end-groups are equally reactive and intramolecular reactions are absent. The values of M?w and B?w have been correlated with the experimental values of intrinsic viscosity [η] and the Newtonian melt viscosity η0. General relations of the following type have been obtained:
f1([η], Mw, Bw) = 0; f20, Mw, Bw) =0; f30, [η], Bw) = 0; f40, [η], Mw) = 0;
In particular, [η] and η0 increase on increasing M?w and decrease on increasing B?w, but, at equal [η] values, η0 increases with B?w. Through the last relation, the reliability limits of which should be experimentally checked, and from measurements of [η] and η0, it is possible to calculate M?w of a branched PET.  相似文献   

20.
J.E.L. Roovers 《Polymer》1975,16(11):827-832
A new method for the synthesis of comb shaped polystyrenes of predetermined structure is described. Silicon-chlorine bonds are introduced into the backbone polystyrene by reaction of SiMe2Cl2 with hydrolysed styrene/vinyl acetate copolymers and coupled with polystyryl-lithium in benzene. From a common backbone polymer a series of comb polymers are prepared that have a constant number of branches but vary in branch length. The MwMn of the whole comb polymers is about 1.3. The comb polymers with high branch density show θ (A2) temperatures lower than that for linear polystyrene. The radius of gyration at θ (A2) [〈S2θ (A2)] is always larger than calculated from random flight statistics. For comb polymers with 20–30 branches 〈S2θ (A2)〈S20,bb increases with λ?0.46 where λ is the fraction of polymer in the backbone. The intrinsic viscosities of the comb polystyrenes at θ (A2) are equal to that of the parent backbone polymer when λ > 0.25 and increase only little when λ becomes equal to 0.1. Similar behaviour is found in toluene. Intrinsic viscosities in cyclohexane at 35°C show a complex pattern because of the θ-temperature variation.  相似文献   

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