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br-j03
The relation between osmotic pressure and the Gibbs function may also be developed in an analogous way .
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br-j03
In the above development we have applied the thermodynamics of equilibrium (referred to by some as thermostatics) to the steady state .
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br-j03
This can be justified thermodynamically in this case , and this will be done in a separate paper which is being prepared .
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br-j03
This has an interesting analogy with the assumption stated by Philippoff that `` the deformational mechanics of elastic solids can be applied to flowing solutions '' .
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br-j03
There is one exception to the above statement as has been pointed out , and that is that fluids can relax by flowing into fields of lower rates of shear , so the statement should be modified by stating that the mechanics are similar .
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br-j03
If the mechanics are similar , we can also infer that the thermodynamics will also be similar .
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br-j03
The concept of the strain energy as a Gibbs function difference * * f and exerting a force normal to the shearing face is compatible with the information obtained from optical birefringence studies of fluids undergoing shear .
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br-j03
Essentially these birefringence studies show that at low rates of shear a tension is present at 45 ` to the direction of shear , and as the rate of shear increases , the direction of the maximum tension moves asymptotically toward the direction of shear .
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br-j03
According to Philippoff , the recoverable shear s is given by * * f where |c is the angle of extinction .
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br-j03
From this and the force of deformation it should be possible to calculate the elastic energy of deformation which should be equal to the * * f calculated from the pressure normal to the shearing face .
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br-j03
There is another means which should show the direction and relative value of the stresses in viscoelastic fluids that is not mentioned as such in the literature , and that is the shape of the suspended drops of low viscosity fluids in shear fields .
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br-j03
These droplets are distorted by the normal forces just as a balloon would be pulled or pressed out of shape in one 's hands .
<NONE>
<NONE>
[ "Ces", "gouttelettes", "sont", "déformées", "par", "les", "forces", "normales", "de", "la", "même", "façon", "qu&apos;", "un", "ballon", "serait", "tiré", "ou", "enfoncé", "dans", "les", "mains", "d&apos;", "une", "personne", "." ]
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br-j03
These droplets appear to be ellipsoids , and it is mathematically convenient to assume that they are .
<NONE>
<NONE>
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br-j03
If they are not ellipsoids , the conclusions will be a reasonable approximation .
<NONE>
<NONE>
[ "S&apos;", "il", "ne", "s&apos;", "agit", "pas", "d&apos;", "ellipsoïdes", ",", "les", "conclusions", "seront", "une", "approximation", "raisonnable", "." ]
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br-j03
The direction of the tension of minimum pressure is , of course , given by the direction of the major axis of the ellipsoids .
<NONE>
<NONE>
[ "La", "direction", "de", "la", "tension", "de", "la", "pression", "minimale", "est", ",", "bien", "sûr", ",", "donnée", "par", "la", "direction", "de", "l&apos;", "axe", "principal", "des", "ellipsoïdes", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j03
Mason and Taylor both show that the major axis of the ellipsoids is at 45 ` at low rates of shear and that it approaches the direction of shear with increased rates of shear .
<NONE>
<NONE>
[ "Mason", "et", "Taylor", "montrent", "tous", "deux", "que", "l&apos;", "axe", "principal", "des", "ellipsoïdes", "est", "à", "45", "tours", "à", "faible", "taux", "de", "cisaillement", "et", "qu&apos;", "il", "s&apos;", "approche", "de", "la", "direction", "...
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br-j03
(Some suspensions break up before they are near to the direction of shear , and some become asymptotic to it without breakup .)
<NONE>
<NONE>
[ "Certains", "suspensions", "se", "brisent", "avant", "qu&apos;", "elles", "ne", "soient", "près", "de", "la", "direction", "du", "cisaillement", ",", "et", "d&apos;", "autres", "deviennent", "asymptotiques", "sans", "rupture", ".", ")" ]
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br-j03
This is , of course , a similar type of behavior to that indicated by birefringence studies .
<NONE>
<NONE>
[ "Il", "s&apos;", "agit", ",", "bien", "sûr", ",", "d&apos;", "un", "type", "de", "comportement", "similaire", "à", "celui", "indiqué", "par", "les", "études", "de", "biréfringence", "." ]
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br-j03
The relative forces can be calculated from the various radii of curvature if we assume: (A) The surface tension is uniform on the surface of the drop .
<NONE>
<NONE>
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br-j03
(B) That because of the low viscosity of the fluid , the internal pressure is the same in all directions .
<NONE>
<NONE>
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br-j03
(C) The kinetic effects are negligible .
<NONE>
<NONE>
[ "Les", "effets", "cinétiques", "sont", "négligeables", "." ]
[ "<NONE>", "effect%1:19:00::", "kinetic%3:01:00::", "be%2:42:03::", "negligible%3:00:00:minimal:00", "<NONE>" ]
[ "<NONE>", "effect%1:19:00", "kinetic%3:01:00", "be%2:42:03", "negligible%3:00:00:minimal:00", "<NONE>" ]
[ "<NONE>", "3", "2", "4", "5", "<NONE>" ]
[ "<NONE>", "0.244", "0.306", "0.217", "0.459", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j03
(D) Since the shape of the drop conforms to the force field , it does not appreciably affect the distribution of forces in the fluid .
<NONE>
<NONE>
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br-j03
These are reasonable assumptions with low viscosity fluids suspended in high viscosity fluids which are subjected to low rates of shear .
<NONE>
<NONE>
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br-j03
Just as the pressure exerted by surface tension in a spherical drop is * * f and the pressure exerted by surface tension on a cylindrical shape is * * f , the pressure exerted by any curved surface is * * f , where |g is the interfacial tension and * * f and * * f are the two radii of curvature .
<NONE>
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br-j03
This formula is given by Rumscheidt and Mason .
<NONE>
<NONE>
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br-j03
If a is the major axis of an ellipsoid and b and c are the other two axes , the radius of curvature in the ab plane at the end of the axis is * * f , and the difference in pressure along the a and b axes is * * f .
<NONE>
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br-j03
There are no data published in the literature on the shape of low viscosity drops to confirm the above formulas .
<NONE>
<NONE>
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br-j03
However , there are photographs of suspended drops of cyclohexanol phthalate (viscosity 155 poises) suspended in corn syrup of 71 poises in a paper by Mason and Bartok .
<NONE>
<NONE>
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br-j03
This viscosity of the material in the drops is , of course , not negligible .
<NONE>
<NONE>
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br-j03
Measurements on the photograph in this paper give * * f at the maximum rate of shear of * * f .
<NONE>
<NONE>
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br-j03
If it is assumed that the formula given by Lodge of * * f , cosec 2lc applies , the pressure difference along the major axes can be calculated from the angle of inclination of the major axis , and from this the interfacial tension can be calculated .
<NONE>
<NONE>
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br-j03
Its value was * * f from the above data .
<NONE>
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br-j03
This appears to be high , as would be expected from the appreciable viscosity of the material in the drops .
<NONE>
<NONE>
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br-j03
It is appropriate to call attention to certain thermodynamic properties of an ideal gas that are analogous to rubber-like deformation .
<NONE>
<NONE>
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br-j03
The internal energy of an ideal gas depends on temperature only and is independent of pressure or volume .
<NONE>
<NONE>
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br-j03
In other words , if an ideal gas is compressed and kept at constant temperature , the work done in compressing it is completely converted into heat and transferred to the surrounding heat sink .
<NONE>
<NONE>
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br-j03
This means that work equals q which in turn equals * * f .
<NONE>
<NONE>
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br-j03
There is a well-known relationship between probability and entropy which states that * * f , where \q is the probability that state (i.e. , volume for an ideal gas) could be reached by chance alone .
<NONE>
<NONE>
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br-j03
this is known as conformational entropy .
<NONE>
<NONE>
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br-j03
This conformational entropy is , in this case , equal to the usual entropy , for there are no other changes or other energies involved .
<NONE>
<NONE>
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br-j03
Note that though the ideal gas itself contains no additional energy , the compressed gas does exert an increased pressure .
<NONE>
<NONE>
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br-j03
The energy for any isothermal work done by the perfect gas must come as thermal energy from its surroundings .
<NONE>
<NONE>
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br-j04
A proton magnetic resonance study of polycrystalline **f as a function of magnetic field and temperature is presented .
<NONE>
<NONE>
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br-j04
**f is paramagnetic , and electron paramagnetic dipole as well as nuclear dipole effects lead to line broadening .
<NONE>
<NONE>
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br-j04
The lines are asymmetric and over the range of field **f gauss and temperature **f the asymmetry increases with increasing **f and decreasing T .
<NONE>
<NONE>
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br-j04
An isotropic resonance shift of **f to lower applied fields indicates a weak isotropic hyperfine contact interaction .
<NONE>
<NONE>
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br-j04
The general theory of resonance shifts is used to derive a general expression for the second moment **f of a polycrystalline paramagnetic sample and is specialized to **f .
<NONE>
<NONE>
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br-j04
The theory predicts a linear dependence of **f on **f , where |j is the experimentally determined Curie-Weiss constant .
<NONE>
<NONE>
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br-j04
The experimental second moment **f conforms to the relation **f in agreement with theory .
<NONE>
<NONE>
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br-j04
Hence , the electron paramagnetic effects (slope) can be separated from the nuclear effects (intercept).
<NONE>
<NONE>
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br-j04
The paramagnetic dipole effects provide some information on the particle shapes .
<NONE>
<NONE>
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br-j04
The nuclear dipole effects provide some information on the motions of the hydrogen nuclei , but the symmetry of the **f bond in **f remains in doubt .
<NONE>
<NONE>
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br-j04
The magnetic moment of an unpaired electron associated nearby may have a tremendous influence on the magnetic resonance properties of nuclei .
<NONE>
<NONE>
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br-j04
It is important to consider and experimentally verify this influence since quantitative nuclear resonance is becoming increasingly used in investigations of structure .
<NONE>
<NONE>
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br-j04
**f appeared to be well suited for the study of these matters , since it is a normal paramagnet , with three unpaired electrons on the chromium , its crystal structure is very simple , and the unknown position of the hydrogen in the strong **f bond provides structural interest .
<NONE>
<NONE>
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br-j04
We first discuss the **f bond in **f .
<NONE>
<NONE>
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br-j04
We then outline the theory of the interaction of paramagnetic dipoles with nuclei and show that the theory is in excellent agreement with experiment .
<NONE>
<NONE>
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br-j04
Indeed it is possible to separate electron paramagnetic from nuclear effects .
<NONE>
<NONE>
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br-j04
The information provided by the electron paramagnetic effects is then discussed , and finally the nuclear effects are interpreted in terms of various motional modified models of the **f bond in **f .
<NONE>
<NONE>
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br-j04
Theoretical studies of the hydrogen bond generally agree that the **f bond will be linear in the absence of peculiarities of packing in the solid .
<NONE>
<NONE>
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br-j04
Moreover , it will be asymmetric until a certain critical **f distance is reached , below which it will become symmetric .
<NONE>
<NONE>
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br-j04
There is ample evidence from many sources that the **f bond in **f is symmetric .
<NONE>
<NONE>
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br-j04
The **f distance in **f is 2.26 A .
<NONE>
<NONE>
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br-j04
There is evidence , though less convincing than for **f , that the **f bond in nickel dimethylglyoxime is symmetric .
<NONE>
<NONE>
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br-j04
Here the **f distance is 2.44 A .
<NONE>
<NONE>
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br-j04
A number of semiempirical estimates by various workers lead to the conclusion that the **f bond becomes symmetric when the **f bond length is about 2.4 to 2.5 A , but aside from the possible example of nickel dimethylglyoxime there have been no convincing reports of symmetric **f bonds .
<NONE>
<NONE>
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br-j04
Douglass has studied the crystal structure of **f by x-ray diffraction .
<NONE>
<NONE>
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br-j04
He finds the structure contains an **f bond with the **f distance of **f .
<NONE>
<NONE>
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br-j04
There is , then , the possibility that this **f bond is symmetric , although Douglass was unable to determine its symmetry from his x-ray data .
<NONE>
<NONE>
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br-j04
Douglass found **f to be trigonal , Laue symmetry **f , with **f , **f .
<NONE>
<NONE>
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br-j04
X-ray and experimental density showed one formula unit in the unit cell , corresponding to a paramagnetic ion density of **f .
<NONE>
<NONE>
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br-j04
The x-ray data did not permit Douglass to determine uniquely the space group , but a negative test for piezoelectricity led him to assume a center of symmetry .
<NONE>
<NONE>
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br-j04
Under this assumption the space group must be **f and the following are the positions of the atoms in the unit cell .
<NONE>
<NONE>
[ "En", "vertu", "de", "cette", "hypothèse", ",", "le", "groupe", "d&apos;", "espace", "doit", "être", "le", "satellite", "et", "les", "positions", "des", "atomes", "dans", "la", "cellule", "unitaire", "sont", "les", "suivantes", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j04
**f .
<NONE>
<NONE>
[ "Voir", "aussi", ":" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
br-j04
This space group requires the hydrogen bond to be symmetric .
<NONE>
<NONE>
[ "Ce", "groupe", "d&apos;", "espace", "nécessite", "que", "la", "liaison", "hydrogène", "soit", "symétrique", "." ]
[ "<NONE>", "group%1:03:00::", "<NONE>", "space%1:03:00::", "require%2:42:00::", "<NONE>", "<NONE>", "hydrogen_bond%1:19:00::", "hydrogen_bond%1:19:00::", "<NONE>", "symmetric%3:00:00::", "<NONE>" ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
Douglass found powder intensity calculations and measurements to agree best for **f .
<NONE>
<NONE>
[ "Douglass", "a", "trouvé", "des", "calculs", "et", "des", "mesures", "de", "l&apos;", "intensité", "de", "la", "poudre", "pour", "convenir", "le", "mieux", "avec", "le", "logiciel", "." ]
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br-j04
These data lead to a structure in which sheets of Cr atoms lie between two sheets of O atoms .
<NONE>
<NONE>
[ "Ces", "données", "conduisent", "à", "une", "structure", "dans", "laquelle", "des", "couches", "d&apos;", "atomes", "de", "Cr", "se", "trouvent", "entre", "deux", "couches", "d&apos;", "atomes", "d&apos;", "oxygène", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
The O atoms in each sheet are close packed and each Cr atom is surrounded by a distorted octahedron of O atoms .
<NONE>
<NONE>
[ "Les", "atomes", "d&apos;", "oxygène", "de", "chaque", "nappe", "sont", "serrés", "et", "chaque", "atome", "de", "Cr", "est", "entouré", "d&apos;", "un", "octaèdre", "déformé", "d&apos;", "atomes", "d&apos;", "oxygène", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
The **f layers are stacked normal to the [ 111 ] axis with the lower oxygens of one layer directly above the upper oxygens of the neighboring lower layer , in such a manner that the repeat is every three layers .
<NONE>
<NONE>
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br-j04
The separate layers are joined together by hydrogen bonds .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
A drawing of the structure is to be found in reference 6 .
<NONE>
<NONE>
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[ "<NONE>", "drawing%1:10:00::", "<NONE>", "<NONE>", "structure%1:07:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "reference%1:10:03::", "<NONE>", "<NONE>" ]
[ "<NONE>", "drawing%1:10:00", "<NONE>", "<NONE>", "structure%1:07:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "reference%1:10:03", "<NONE>", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "<NONE>", "4", "<NONE>", "8", "9", "<NONE>", "10", "11", "<NONE>" ]
[ "<NONE>", "0.366", "<NONE>", "<NONE>", "0.378", "<NONE>", "0.302", "0.273", "<NONE>", "0.507", "0.347", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
The gross details of the structure appear reasonable .
<NONE>
<NONE>
[ "Les", "détails", "de", "la", "structure", "semblent", "raisonnables", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
The structure appears to be unique among ROOH compounds , but is the same as that assumed by **f .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
The bond angles and distances are all within the expected limits and the volume per oxygen is about normal .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j04
However , the possible absence of a center of symmetry not only moves the hydrogen atom off **f , but also allows the oxygen atoms to become nonequivalent , with **f at **f and **f at **f (space group **f), where **f represents the oxygens on one side of the **f layers and **f those on the other side .
<NONE>
<NONE>
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br-j04
However , any oxygen nonequivalence would shorten either the already extremely short **f interlayer distance of 2.55 A or the non hydrogen bonded **f interlayer interactions which are already quite short at 2.58 A .
<NONE>
<NONE>
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br-j04
Hence it is difficult to conceive of a packing of the atoms in this material in which the oxygen atoms are far from geometrical equivalence .
<NONE>
<NONE>
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br-j04
The only effect of lack of a center would then be to release the hydrogen atoms to occupy general , rather than special , positions along the [ 111 ] axis .
<NONE>
<NONE>
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br-j04
If the **f bond is linear then there are three reasonable positions for the hydrogen atoms: (1) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets; (2) all hydrogen atoms lie on a sheet , but the sheet is closer to one oxygen sheet than to the other; (3) hydrogen atoms are asymmetrically placed , either randomly or in an ordered way , so that some hydrogen atoms are closer to the upper oxygen atoms while others are closer to the lower oxygen atoms .
<NONE>
<NONE>
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br-j04
Position (2) appears to us to be unlikely in view of the absence of a piezoelectric effect and on general chemical structural grounds .
<NONE>
<NONE>
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br-j04
A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position (3) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another , and also since ordered `` up '' and `` down '' implies a larger unit cell , for which no evidence exists .
<NONE>
<NONE>
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br-j04
Therefore , the only unknown structural feature would appear to be whether the hydrogen atoms are located symmetrically (1) or asymmetrically (3).
<NONE>
<NONE>
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br-j04
Douglass prepared his sample of **f by thermal decomposition of aqueous chromic acid at 300 - 325 ` C .
<NONE>
<NONE>
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br-j04
Dr. Douglass was kind enough to lend us about 5 grams of his material .
<NONE>
<NONE>
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br-j04
This material proved to be unsatisfactory , since we could not obtain reproducible results on various portions of the sample .
<NONE>
<NONE>
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br-j04
Subsequently , we learned from Douglass that his sample contained a few percent **f impurity .
<NONE>
<NONE>
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br-j04
Since **f is ferromagnetic , we felt that any results obtained from the magnetically contaminated **f would be suspect .
<NONE>
<NONE>
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br-j04
Plane suggested another preparation of **f which we used here .
<NONE>
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br-j04
500 ml of 1 M aqueous **f with 1 g **f added are heated in a bomb at 170 ` C for 48 hours .
<NONE>
<NONE>
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br-j04
A very fine , gray solid (about 15 g) is formed , water-washed by centrifugation , and dried at 110 ` C .
<NONE>
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