摘要:

A theoretical and computational investigation has been made of the effect of temperature and of various energetic parameters upon the course of homogeneous nucleation in suspensions of droplets undergoing cooling at a constant rate. The applicable theory involves integrals, unsolvable in closed form, that were evaluated numerically. For a given size distribution of droplets, the plots of number‐fraction crystallized vs time have virtually identical shapes regardless of the cooling rate. The curves can be superposed by translation along the time axis. This superposability obtains regardless of the breadth of the size distribution. Thus, the superposability assumption tacitly invoked by early investigators in this field is justified. Furthermore, it was found that the integrations performed numerically gave, in the range of experimental interest, results within 3% of the analytical solution obtained by Burns and Turnbull by series expansion of the integrand.The pre‐exponential term in the expression for the nucleation rate is calculable for specific values of droplet size and cooling rate and is extremely sensitive to the magnitude of the energetically determined constant term appearing in the exponent. For the specific case of suspensions of polyethylene droplets a change of 10% in the constant term, necessitates a change of three orders of magnitude in the exponential.Finally, values of the interfacial energy product, &sgr;2&sgr;e, of 1.59×104and 1.50×104erg3·cm−6were calculated for polyethylene from the droplet cooling data of two independent groups of investigators.

ISSN:0021-8979    

DOI:10.1063/1.1709102

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

An experimental study and review of the literature on the oriented crystallization of high polymers was made to develop an understanding of how ``row‐nucleated'' or shishkebab microstructures and the fibrillar links between lamellar crystals may be formed. A new mechanism is proposed for the formation of the fiber nuclei in flowing melts, based on the mechanical alignment and extension of molecules that are entangled with, and extend between, two or more rotating clusters in the melt. Similar alignment of molecules can occur when entangled clusters are pulled to different lamellar crystals during crystallization, producing intercrystallic links.

ISSN:0021-8979    

DOI:10.1063/1.1709103

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A transverse resonance acoustic spectrometer was used to investigate the effect of diluents on the dynamic mechanical properties of poly‐2‐hydroxypropyl methacrylate (PHPMA) and poly‐2‐hydroxyethyl methacrylate (PHEMA) down to −196°C. Samples were prepared by polymerizing the monomer‐diluent mixtures through ultraviolet radiation. In the dry sample of PHPMA, below the glass transition temperature, there is an internal friction peak at −90°C (gamma peak). With the introduction of 0.5 vol % water, the gamma peak broadens into a shoulder, with the concomitant appearance of a new ``diluent peak'' at −25°C. Addition of higher water content causes the internal friction curve to exhibit only one single peak, the position of which shifts to lower temperatures while the strengths of the loss peaks increase with increasing diluent concentration. Similar observations were made for other hydrogen‐bonding diluents, i.e., deuterium oxide, methanol, and glycerol. For nonhydrogen‐bonding diluents, chloroform and cyclohexane, the gamma peak was retained while a shoulder appears around −20°C. Isoproponal, on the other hand, produces an internal friction curve that appears to be ``borderline'' between the above two cases. For PHEMA, which has a gamma peak at −100°C in the absence of diluents, the addition of 0.5 vol % water produced an internal friction curve that possesses a doublet near −60°C. Again, at higher water concentration one observes only a single peak. When cyclohexane was used as the diluent, the doublet character persists up to 5% diluent concentration. These observations were examined in the light of the molecular motion hypothesis. A dual mechanism is suggested that attributes the new diluent peak to the composite of displaced beta and gamma processes. It is postulated that beta transition is lowered due to the plasticizing action of the diluents, while the gamma transition is elevated on account of the hindering effect of the immobilized diluent molecules. At sufficiently high diluent concentration, these two peaks merge into the single observed peak.

ISSN:0021-8979    

DOI:10.1063/1.1709104

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The effective barrier to reorientation is calculated for a chain which may occupy two equivalent energy states, 180° apart for the case where the chain is allowed to twist during the reorientation process. Results are obtained for (I) a ``parabola‐antiparabola'' and (II) a cosine form for the intermolecular energy. The results for (I) and (II) are similar, but differ both in form and magnitude from that obtained earlier using a cusplike barrier. Both (I) and (II) lead to the conclusion that a chain will behave as a rigid rod up to a critical chain length, and then exhibit twisting for all lengths exceeding this critical value.

ISSN:0021-8979    

DOI:10.1063/1.1709105

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A study has been made of the mechanical‐relaxation behavior of an ethylene‐methacrylic acid copolymer containing 4.1 mole % acid units and its partially ionized sodium salts. Degrees of ionization, estimated from infrared analysis, ranged from 0% to 78%. The weight‐percent crystallinity of the samples, determined by differential‐scanning calorimetry, varied from about 15 for the acid copolymer to about 7 for the 78% ionized copolymer. Four relaxation regions have been observed. They are labelled &agr;, &bgr;′, &bgr; and &ggr;, and each has been assigned to motions within the amorphous phase of the polymer. In plots of the logarithmic decrement against temperature (at 1 cps), the &agr; peak for the annealed acid copolymer occurs at 50°C and shifts to higher temperatures with increasing degree of ionization. This trend is consistent with the increase in melt flow viscosity with increasing ionization and, on this basis, the &agr; process is attributed to the long‐range diffusional motions of chain segments. The &bgr;′ peak occurs at 23°C for the annealed acid copolymer and decreases in magnitude with increasing ionization. Hence the &bgr;′ mechanism is attributed to the micro‐Brownian motions of chain segments involving the breaking and reforming of intermolecular hydrogen bonds between dimerized carboxylic‐acid groups. The latter assignment is supported by infrared studies of hydrogen bonding as a function of temperature. The &bgr; peak is absent for the acid copolymer but appears at −10°C for the ionized polymers and increases in height with increasing ionization. Thus, the &bgr; process is attributed to motions of branched chain segments including the ionic (carboxylate) side groups. The onset of the &ggr; peak is observed at −120°C and is associated with the local motions of linear methylene sequences. The observation that the &bgr; peak is located at a temperature very close to the &bgr; peak (−20°C) for ordinary branched polyethylene, must cast considerable doubt on the widely held view that the ionic side groups are associated to form strong interchain links. Alternative hypotheses are suggested to explain the increase in ultimate tensile strength and melt flow viscosity with increasing ionization.

ISSN:0021-8979    

DOI:10.1063/1.1709106

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

In this paper the macroscopic elastic properties of heterogeneous bodies are studied in terms of the elastic properties of freely orienting microscopic units. Special attention is given to the differences in predicted macroscopic behavior which result from simplifying assumptions regarding stress or strain within a heterogeneous body. By comparison with experimental data, the possibilities and limitations of the concept of freely orienting microscopic elastic units are shown.

ISSN:0021-8979    

DOI:10.1063/1.1709107

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

If a flexible filament marked at intervals along its length is struck transversely by a flying projectile, high‐speed photography reveals a shifting of the marks caused by passage of a strain wave, and analysis of these shifts provides data on the strain and average strain velocity in the wave. Tests were performed on strips of lightly vulcanized natural rubber at transverse impact velocities up to 65 m/sec, and the resulting strain‐velocity distributions analyzed for viscoelastic effects. The analysis showed that although creep effects were small in the observation time interval of 1–8 msec after impact, significant creep must have occurred at the point of impact within the first millisecond, and additional significant creep occurs at times greater than 8 msec. The strain‐wave‐front velocity calculated from the quasistatic stress‐strain curve was 35.2 m/sec, but a value of approximately 60 m/sec was observed in the tests. The strain at the wave front, however, tended to attenuate as the wave propagated causing a progressive decrease in the observed value of the strain‐wave‐front velocity.

ISSN:0021-8979    

DOI:10.1063/1.1709108

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The polarized‐fluorescence experiment for measurement of preferred orientation is analyzed mathematically. The intensity is dependent uponPandA, unit vectors describing the positions of the polarizer and analyzer, and upon the orientation distributionN(&agr;, &dgr;) of the chromophoric group of the polymer. In the case of biaxial or uniaxial symmetry, the intensityIPAfor any combination ofPandAvectors is expressed as linear combination of nine fundamental intensities characteristic of a given sample. These intensities form a 3×3 matrix, each entryIijbeing the intensity obtained withPandAparallel to theith andjth principal axes of the sample. Of the nine components ofI, only five are independent for a biaxially oriented sample; two for uniaxial orientation. EachIijis proportional to ⟨xi2xj2⟩Av, wherexiandxjare the components of the chromophore vector along the corresponding principal axes. Calculated matrices are shown for several model distributions. Nishijima'sPfunction is related to theIij's, and the problem of measuring biaxial orientation is discussed. TheIij's are also shown to be directly related to the second‐and fourth‐order coefficients in the spherical harmonic expansion of N(&agr;, &dgr;). These coefficients can be measured directly by a few simple experiments involving spinning the sample between crossed or parallel polarizers. Thus, the experimental error in their determination can be minimized.

ISSN:0021-8979    

DOI:10.1063/1.1709109

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Recent considerations by Wada make it appropriate to extend a previous discussion of Gru¨neisen ``numbers'' for polymers and other molecular solids. Wada hypothesized that the proper Gru¨neisen constant for polymers is&ggr;G=&agr;V/&bgr;Cvb, whereCvbis theinterchain contribution to the heat capacity at constant volume; &agr;, &bgr;, andVare the volumetric thermal expansivity, the compressibility, and the volume. To the extent that a polymer can be treated as a vibrational lattice, the hypothesis appears to be consistent with&ggr;G=&Sgr;&ggr;i&egr;(xi)/&Sgr;&egr;(xi), averaged over Einstein oscillator functions &egr;(xi) withxi=hvi/kT. At low temperatures, &egr;(xi) is much larger for the low‐frequency modes, so that they tend to determine &ggr;Gbelow the Debye −&thgr;. Since &ggr;i=−∂ ln&ngr;i/∂ lnVand since low &ngr;iare likely to be more sensitive to changes inV, it is expected that &ggr;Gwill be larger for molecular solids than for metallic, ionic, or covalent crystals. Earlier predictions and Wada's calculations agree that &ggr;G≈4 might be typical for polymers and suggest that ∂&ggr;/∂T>0. The correlation,E&agr;l2≈15 N/m2°K2, between modulusEand linear expansivity &agr;lled to the prediction, now verified, that there should be relations between the harmonic and anharmonic moduli. The anharmonic coefficients in the relation &Dgr;V/V0=a1p+a2p2+a3p3+&cellip;area2=C1a12anda3=C3a13, where for metalsC2=−2.5±0.5, and for polymersC2=−4.0±0.1 andC3=8.8±0.2. A phenomenological theory based on a ``bundle of tubes'' model is developed which is in good agreement with data and according to which &ggr;G=−C2andd&ggr;G/dT∼&agr;C2. The relation of &ggr;Gto intermolecular potential functions also is discussed and some qualtitatively encouraging results are obtained.

ISSN:0021-8979    

DOI:10.1063/1.1709110

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A transverse quadratic electro‐optic effect has been observed in a wide range of niobate transparent glass—ceramic systems. The electro‐optic constant has been determined as a function of composition, temperature, and wavelength. A semiquantitative measurement of the frequency response has also been made. It has been found that the electro‐optic constant correlates reasonably well with the square of the static dielectric constant. Remanent polarization has been induced under the influence of a dc field. The resulting linear electro‐optic effect has been measured in both transverse and longitudinal modes.

ISSN:0021-8979    

DOI:10.1063/1.1709111

出版商:AIP    

年代:1967

数据来源: AIP