Several new phenomena in the formation of ring-banded spherulites of poly(epsilon-caprolactone) and poly(styrene-random-acrylonitrile) blends

Ring-banded spherulites in crystallization of poly(epsilon-caprolactone) and poly (styrene-random-acrylonitrile) blends were observed with polarizing optical microscopy and digital image analysis technique was applied directly to the image obtained by polarizing microscope, Several new interesting phenomena were found. One is that the ring-banded structure is still clearly seen after the analyzer was removed and this astonished phenomenon couldn't result from the general concept about formation mechanism of ring-banded spherulite - lamellae twisting, Another one is that there is a slight, dark line in the bright band when cross polars were added, which may be related to the formation process and mechanism of ring-banded spherulites in the blends of poly (epsilon-caprolactone) and poly (styrene-random-acrylonitrile).

The miscibility of homopolymer random copolymer blends .3. Blends of SAA with polymethacrylates and polyesters

The miscibility of blends of poly(styrene-co-allyl alcohol) (SAA) with poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), poly(n-butyl methacrylate) (PnBMA), poly-epsilon-caprolactone (PCL) or polycarbonate (PC) has been studied by means of NMR, FT-IR and DSC techniques. It was found that SAA and PMMA, PEMA or PCL form miscible blends and SAA is only partially miscible with PC or PnBMA. Both phenyl groups and hydroxyl groups in SAA are involved in the intermolecular interactions between SAA and PMMA, PEMA or PCL. Also the hydroxyl-carbonyl hydrogen bonds existing in all the miscible blends studied are formed partially at the expense of the disruption of self-association of hydroxyl groups in pure SAA. (C) 1997 Elsevier Science Ltd. All rights reserved.

The miscibility of homopolymer random copolymer blends .1. Poly(styrene-co-acrylonitrile) poly(ethyl methacrylate) and poly(styrene-co-acrylonitrile) poly(methyl methacrylate) blends

The miscibility of blends of poly(styrene-co-acrylonitrile) (SAN) with poly(methyl methacrylate) (PMMA) or poly(ethyl methacrylate) (PEMA) has been investigated by means of NMR and DSC techniques. It is found that there are intermolecular interactions between the phenyl groups in SAN and carbonyl groups in PMMA or PEMA, and the strength of this intermolecular interaction strongly depends on the properties of ester side groups in PEMA or PMMA, composition of the blends and a certain composition of the copolymer. It is this specific interaction instead of the intramolecular repulsion force within the copolymer that plays a key role for the miscibility of SAN/PMMA and SAN/PEMA blends.

The miscibility of homopolymer random copolymer blends .4. Poly(vinylidene chloride-co-acrylonitrile) poly(methyl methacrylate) blends

The miscibility of blends of poly(vinylidene chloride-co-acrylonitrile) (VDC-AN) and poly(methyl methacrylate) (PMMA) has been studied with DSC, FT-IR, and NMR methods. The results indicate that the VDC-AN/PMMA blends are miscibile on a molecular level, and the dipole-dipole interactions between C=O and C-Cl-2 and/or interpolymer hydrogen bondings between COOCH3 and CN and CCl groups play the role on the miscibility of the blends. It is found that the -CCl2- groups have two different chemical environments in the pure VDC-AN copolymer, which may result from the different configurations of the copolymer, such as -CCl2- groups in the ''alternating'' segments and -CCl2- groups in the ''blocky'' segments as proposed. It is the -CCl2- group in the ''alternating'' segment that takes part in the dipole-dipole interaction with C=O group in PMMA.

Miscibility and phase behavior in blends containing random copolymers of poly(ether ether ketone) and phenolphthalein poly(ether ether ketone)

The miscibility and phase behavior of polysulfone (PSF) and poly(hydroxyether of bisphenol A) (phenoxy) with a series of copoly(ether ether ketone) (COPEEK), a random copolymer of poly(ether ether ketone) (PEEK), and phenolphthalein poly(ether ether ketone) (PEK-C) was studied using differential scanning calorimetry. A COPEEK copolymer containing 6 mol % ether ether ketone (EEK) repeat units is miscible with PSF, whereas copolymers containing 12 mol % EEK and more are not. COPEEK copolymers containing 6 and 12 mol % EEK are completely miscible with phenoxy, but those containing 24 mol % EEK and more are immiscible with phenoxy. Moreover, a copolymer containing 17 mol % EEK is partially miscible with phenoxy; the blends show two transitions in the midcomposition region and single transitions at either extreme. Two T(g)s were observed for the 50/50 blend of phenoxy with the copolymer containing 17 mol % EEK, whereas a single composition-dependent T-g appeared for all the other compositions. An FTIR study revealed that there exist hydrogen-bonding interactions between phenoxy and the copolymers. The strengths of the hydrogen-bonding interactions in the blends of the COPEEK copolymers containing 6 and 12 mol % EEK are the same as that in the phenoxy/PEK-C blend. However, for the blends of copolymers containing 17, 24, and 28 mol % EEK, the hydrogen-bonding interactions become increasingly unfavorable and the self-association of the hydroxyl groups of phenoxy is preferable as the content of EEK units in the copolymer increases. The observed miscibility was interpreted qualitatively in terms of the mean-field approach. (C) 1996 John Wiley & Sons, Inc.

STUDIES ON STRUCTURE OF EO/THF RANDOM COPOLYETHER(I) - NMR-STUDIES ON SOLUTION ACTION AND COMPLEX

The special action of TEO solution was investigated by 1D, 2D-NMR in CDCl3. For the present measurements, when the concentration of TEO was higher in CDCl3, the chemical shift difference (Delta delta) and the peak number of C-13 NMR spectrum were changed with increasing the solution concentration, At lower concentration(< 3% V/V ), the peaks will be closed together for -CH2O- resonance carbon and it is not the appearance of the narrowed, When temperature was changed, the Delta delta value was contrary to the solvent effect, So, the shifts of the resonance carbon in the NMR spectra indicated clearly that the complex formation for the system of CDCl3, and TEO molecular interaction were affected by the experiment temperature and the solution concentration.

MISCIBILITY OF HOMOPOLYMER RANDOM COPOLYMER BLENDS .2. SMA/PMMA BLENDS

The miscibility of blends of PMMA with SMA (50 wt% MA) has been investigated by means of NMR, FTIR and DSC techniques. The results indicate that the SMA/PMMA blends are miscible on a molecular level, and there are strong intermolecular interactions between the phenyl groups in SMA and carbonyl groups in PMMA. It is the intermolecular interactions instead of the intramolecular repulsion forces within the SMA copolymer that make the SMA/PMMA blends miscible. It is also found that the strength of the intermolecular interactions to some degree depends on the compositions of the blends.

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42,134-149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313-351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313-351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971-5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift. (C) 2008 Elsevier Ltd. All rights reserved.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.