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Molecular polarizations of some phosphonitrilic compounds Arsenault, Maureen A. 1973

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MOLECULAR POLARIZATIONS OF SOME PHOSPHONITRILIC COMPOUNDS BY MAUREEN A. ARSENAULT B.Sc. (Hon. Chem.) University of New Brunswick A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1973 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada - i i -ABSTRACT A study of the d i e l e c t r i c properties of some phosphonitrilic f l u o r i d e s , chlorides and chloride-fluorides i n cyclohexane solutions was carried out and evidence was found to support the hypothesis that these compounds a l l have a non-negligible atom p o l a r i z a t i o n caused by low frequency vibrations of the molecules. The d i s t o r t i o n p o l a r i z a t i o n of one of the geminally substituted isomers of the compound N.P.F.Cl, was measured and this datum was used as support 4 4 4 4 for assigning the 1,1,3,3-isomer structure to the compound. - i i i -TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i CHAPTER I. GENERAL INTRODUCTION 1 A. Introduction 1 1. Phosphonitrilic Compounds 1 2. Dipole Moments 3 B. Object of Research 6 CHAPTER I I . THEORY 10 A. Derivation of the Debye Equation 10 B. The Solution Equations and Guggenheim's Method .... 23 CHAPTER I I I . EXPERIMENTAL 32 A. Materials and Equipment 32 B. Procedure 34 C. Data and Results 37 CHAPTER IV. DISCUSSION 41 A. The Question of Atom P o l a r i z a t i o n 41 B. Previous Methods of Dealing with Atom Po l a r i z a t i o n . 46 C. Atom Po l a r i z a t i o n and Phosphonitrilic Compounds ... 47 D. Orientation Effects i n Phosphonitrilic Chloride-Fluorides 56 - i v -Page E. Conclusions and Suggestions for Further Work 62 APPENDIX A 63 APPENDIX B 64 REFERENCES 66 - v -LIST OF TABLES Table Page I Data and Results for Phosphonitrilic Halides 38 I I Other Dipole Moment Results for Phosphonitrilic Compounds 49 I I I Far Infrared Results for N_P.C1- and N,P.C10 55 3 3 6 4 4 8 IV P o l a r i z a t i o n per Monomer Unit Calculated for Some Phosphonitrilic Compounds 57 - v i -LIST OF FIGURES Figure Fage 1-1 a. N.P.C1.(NMeV isomers 3 3 4 2 1 b. N 3P 3Cl 3(NMe 2) 3 isomers 7 1-2 N 4 P 4 ( C 6 H 5 ) 6 ( N 3 ) 9 isomers 8 1-3 N.P.F.C1, isomers 8 4 4 4 4 3-1 Schematic diagram of thermostat including connections to dipolemeter ( l e f t ) and heater-pump (right) 35 3-2 Flask for use with v o l a t i l e compounds 36 3-3 a. e vs. weight f r a c t i o n for N^P^F^C^ b. n Q vs. weight f r a c t i o n for N^P^F^C^ 39 3- 4 Po l a r i z a t i o n vs. ring size for (NPF2) n 40 4- 1 Dipole vector diagram f o r N P F 2C1 4 and N ^ F ^ C ^ .. 57 4-2 (NPC^)^ molecular structure 61 4-3 (NPBr^)^ molecular structure 61 - v i i -ACKNOWLEDGEMENTS F i r s t of a l l I would l i k e to thank my supervisor, Professor N.L. Paddock, for his patience and help throughout the course of this work. I would also l i k e to thank Dr. J.B. Farmer for some useful discussions about equipment. A word of thanks must also go to Dr. D.J. Patmore for purifying some of the compounds. The help and encouragement of my friends and family were appreciated during my stay i n B r i t i s h Columbia. These people include the rest of the lab group, especially Mike and Tim, a l l my friends i n Room 457 and my parents and s i s t e r i n New Brunswick. F i n a l l y I wish to thank Miss Diane Johnson who successfully deciphered the manuscript and pati e n t l y typed this thesis. - 1 -CHAPTER I GENERAL INTRODUCTION Phosphonitrilic Compounds Phosphonitrilic compounds are polymers made up of the repeating unit (X(X')PN) where X may or may not be the same as X', and X and X' may be a halogen, a pseudohalogen such as azide or isothiocyanate or any of the following organic functional groups; alkyl, alkoxy, aryl, aryloxy, amino, thioalkyl. A large number of compounds where X = X' have been synthesized as well as a great many where X is not the same as X' for one or more of the monomer units in the polymer. Phosphonitrilic compounds may be either linear or cyclic polymers, of which the cyclic 1-3 polymers have been more thoroughly investigated. A number of reviews are available describing the synthesis, structure and reactions of cyclic phosphonitriles. The first cyclic phosphonitrile was synthesized in 1334 by 4 Liebig who was attempting to make the amides of phosphoric acid by reacting PCl^ and NH^Cl, but instead obtained a small amount of phosphonitrilic chloride trimer (N0P_C1,). Later, Stokes"* carried out J j D work which showed that there existed a homologous series of phospho-n i t r i l i c chloride polymers of the formula (NPC1„) up to at least the I n heptamer (n = 7). It was he who first suggested the cyclic formulae - 2 -31 which have since been confirmed by infrared, Raman, P NMR and X-ray studies. The phosphonitrilic fluorides, however, are more difficult to prepare as an attempted synthesis analogous to that used for the chlorides gives ammonium hexafluorophosphate instead. It was not until 1956 that Seel and Langer^ succeeded in making the fully fluorinated cyclic phosphonitriles by reacting the cyclic chlorides and KSC^F. Al l the cyclic fluorides are comparatively volatile, and a l l but the trimer and tetramer are liquid at room temperature, these last two being solids with melting points of 27.2-27.4°C and 30.4°C, respectively. 7 Cyclic phosphonitrilic fluorides up to (NPF2^17 ^ a v e D e e n reported in g the literature and there appears to be no reason why larger ring compounds of this type cannot be made, as a l l the smaller ring compounds are stable to such reactions as disproportionation at room temperature. Though in some ways these compounds are comparable to benzene and other related conjugated cyclic hydrocarbons, a major difference is that the stability of the cyclic phosphonitriles appears to be independent of ring size, for example (NPF ) is as stable as (NPF ),.. The lack of Information on very large rings is mainly due to the problem of obtaining large enough samples of the pure compounds, which must be separated from any or possibly a l l of the following; mixtures of linear polymers, mixtures of chloride-fluorides, mixtures of cyclic fluorides of ring sizes other than the one of immediate interest. The most often used method of separation and purification is gas-liquid chromatography, though fractional distillation may be used to separate larger quantities of material. - 3 -Dipole Moments The measurement of dipole moments of molecules is a relatively new technique, the earliest papers having been published in 1924. The measurement of dieletric constants, which for many methods of i dipole moment determination is a necessity, has been done since 1892. From 1924 there was an immediate surge of interest in dipole moment measurements which peaked in the period 1930-32. ' The next upsurge started after the Second World War ended and culminated in 1949. This was due to two factors; f i r s t , the end of the war released more money into non-defence oriented research and second, the technique of microwave spectroscopy was developing rapidly and becoming sensitive enough to give accurate data for calculation of dipole moments (from the Stark effect). The microwave method has the advantage that no knowledge of dieletric constants is necessary. A third upsurge of interest in dipole moments occurred in the mid-1950's."^ The bulk of dipole moment studies has always been carried out on organic compounds. This is related to the methods used to obtain the values of the dipole moment, which require data from the pure gas, or the pure liquid or a solution of the compound in a non-polar solvent. Most inorganic compounds of interest are not sufficiently volatile or else not liquid at suitable temperatures or are insoluble in non-polar solvents. It is therefore not surprising that the ratio of the number of organic compounds studied to the number of inorganic Is about 12:1 and has been so for many years. The phosphonitrilic halides are good candidates for dipole moment studies owing to their high solubilities in such non-polar solvents as cyclohexane, and - 4 -therefore i t may be possible to obtain information about ring size effects on the properties of phosphonitriles by studying their dielectric properties. There are several methods available to obtain dipole moments of molecules, though not a l l the possible methods may be applicable to 1 the same compounds. The most important of these methods are as follows. (1) The measurement of the dielectric constant of a known amount of the pure gaseous compound is carried out at a series of known temperatures. The polarization is then calculated and plotted against the reciprocal of the absolute temperature. The slope is directly proportional to the square of the dipole moment. (2) The measurement is carried out of the dielectric constant, density and refractive index of the pure liquid at a known temperature and the Onsager equation or one of its modifications is used to calculate the dipole moment. (3) The dielectric constant and density may be measured for each of a series of solutions of known concentrations of the compound of interest in a non-polar solvent at a known constant temperature. The Halverstadt-Kumler or Hedestrand equations are used to calculate the dipole moment. ( 4 ) The dielectric constant and refractive index of each of a series of solutions of known concentrations of the compound of interest in a non-polar solvent may be measured at a known constant temperature. The dipole moment may then be evaluated by the method of Guggenheim. ( 5 ) The dielectric constant and dielectric absorption of a solution of known concentration of the compound of interest in a non-: - 5 -polar solvent may be measured at a series of known frequencies in the microwave region at a known constant temperature. From such data, a dipole moment of the compound may be calculated. (6) The line separations in the microwave spectrum of a compound caused by the Stark effect may be measured. These line separations are a function of the dipole moment of the molecule. (7) The absolute intensities of infrared absorption bands may be measured. These intensities are functions of the matrix elements of the dipole moment of the molecule. However, i t is very difficult to obtain these integrated intensities and so the method does not find a great deal of practical use at present. (8) Molecular beam methods are used to determine the dipole moments of compounds such as alkali halides, whose moments cannot be measured by more conventional methods. These methods are adaptations of the Stern-Gerlach experiment on magnetic moments. (9) Electrostriction methods measure the decrease in volume of a gas at constant pressure and temperature caused by application of an electric field. This method serves only to give orders of magnitude of dipole moments because the volume changes are very small and difficult to measure accurately. The most commonly used of these methods are the first six mentioned because from these methods i t is possible to obtain fairly accurate values of the dipole moment of a molecule for a reasonable investment in cost and labour. - 6 -Object of Research One important use of dipole moments i n the past has been to study orientation e f f e c t s , such as cis-trans isomerism. Orientation effects may also be studied by dipole moment measurements on substituted 12 phosphonitrilic compounds. Koopman et a l . have used dipole moment results i n assigning structures to the tetrachlorobis(dimethylamino)-phosphonitrile trimer isomers as w e l l as to the isomers of t r i c h l o r o -tris(dimethylamino)phosphonitrile trimer, which are shown i n Figure 1-1. Similar work has been carried out on c i s and trans-tribromotriphenyl-13 phosphonitrile trimers by Nannelli and Moeller, on c i s and trans-i t tetrafluorobisphenylphosphonitrile trimers by Al l e n and Moeller, on c i s , trans and geminal (1,1-bis) isomers of N^P^Cl^(NHMe)^ by Lehr"*"^ and on the 1,5-cis and trans isomers of hexaphenyldiazidophosphonitrile 37 tetramer, N.P.(C,H C) r (N.)„ by Sharts et a l . These l a s t two compounds 4 4 b j fa 3 2 are shown i n Figure 1-2. One object of the work described i n this thesis i s to attempt to decide whether the geminally substituted compound N^P^F^Cl^ i s the 1,1,3,3 or the 1,1,5,5-isomer, both of which are shown i n Figure 1-3. There i s , however, a l i m i t a t i o n on the use of dipole moments for s t r u c t u r a l determinations i n inorganic chemistry. In organic chemistry, where the method has been widely used, the compounds have very small atom polarizations (a f u l l e r explanation w i l l be given i n Chapter IV) and thus the values of dipole moments determined by the usual methods have only a small error due to the neglect of this atom p o l a r i z a t i o n . However, this i s not true of many inorganic compounds and, i t was - 7 -1,3 - trans Figure 1-1a N 3P 3Cl 4(NMe 2) 2 isomers NMe 2 NMe 2 1,3,5-trans Figure M b N3P3Cl-[NM<?2)3 isomers - 8 --N. C6Hs N3 / No L i 1.5 - c i s Figure 1-2 N j P J C ^ y N j ^ isomers N, 15-trans N S S M CI U3.3- tetrachloro 1,155-tetrachloro Figure 1-3 (NPFCl) f t (gem) isomers - 9 -intended to try to determine what effect atom polarization has on phosphonitrilic compounds, whether dipole moments determined for phosphonitrilic compounds are valid and whether i t is necessary to revise theories of structures of these compounds that were based on dipole moment results. - 10 -CHAPTER II THEORY Derivation of the Debye Equation In order to have a better understanding of the factors affecting dipole moments, i t is necessary to carry out the derivation of the equation relating dipole moment to directly measurable or calculable quantities. The derivation given below is almost entirely taken from Smyth.^ The dielectric constant of a material, e_, is an electrical constant characteristic of a medium between two charges. A condenser is an electric conductor, which, is charged with a quantity of electri-city £ at a potential V will have a capacitance For the case of a condenser consisting of two parallel conducting plates each of area A 2 cm , separated by a distance r_, and between which is a medium of dielectric constant _e_, then the capacitance C^  is e A C = electrostatic units (2-1) 4irr To determine the dielectric constant of a medium, the capacitance of the condenser is measured with the medium of interest between the plates and then compared to the capacitance of the same condenser with a standard medium between the plates. The standard chosen is a vacuum, and for a vacuum e = 1, so therefore e_ of the medium of interest is then e = C_ C (2-2) o where C is the capacitance of the condenser with a vacuum between the plates. The dielectric constant of a material is a dimensionless quantity. The next situation to consider is a condenser in a vacuum where r_ 2 is very small compared to the plate dimensions, i.e. _r << A. Let one plate have a charge +Q, and the other a charge and let o_ be the surface density of charge. Inside the condenser, the intensity of the electric field perpendicular to the plates is If the space between the plates is f i l l e d with a homogeneous material of dielectric constant the charges (+Q and -Q) on the plates remain the same but the field strength drops to o E = 4no (2-3) o E = 4iro7e (2-4) Therefore the decrease E = E -E = 4 i r a(l-l/e) = 4 i r a(e-l)/E o (2-5) - 12 -This same AE could also be effected by reducing o to - S ^ z l l = P* (2-6) which can be done by charging the surface of the d i e l e c t r i c opposite each of the plates with a charge of opposite sign to that of the plate. The surface density of t h i s charge would then equal P_, and i s * produced by an induced charge s h i f t through the d i e l e c t r i c . P_ i s usually referred to as the p o l a r i z a t i o n . A quantity c a l l e d the e l e c t r i c displacement, ID, i s defined as D = 4iro (2-7) and i t can be shown that D = eE (2-8) Because D -E = 47T0(l-l/e) = 4 T r a(e-l)/e (2-9) i t follows that D = E + 4irP* (2-10) By eliminating I) and rearranging the following re s u l t may be obtained: e-1 = 4 I T P * / E (2-11) - 13 -* * The charges +P on one surface of the dielectric and -P 0^  on the opposite surface resulting from charge displacement through the * dielectric give an electric moment of _P Ar to the dielectric slab, where _r is its thickness (which also is the distance between the conducting plates). Since Ar = V (2-12) the volume of the slab, the total electric moment must be equal to P V * and therefore _P is the electric moment per unit volume. Thus the polarized slab behaves like an assembly of parallel electric dipoles, with each dipole consisting of a pair of charges equal in magnitude but opposite in sign (+e, -e) separated by a small but finite distance r. The size of the moment is m = er (2-13) Molecular polarizability can now be defined; i t is a parameter related to induced dipole moment. Consider a charge e^  bound elastically to an equilibrium position. Now any displacement from equilibrium will be opposed by a restoring force fr, where f is a proportionality constant. The restoring force can be treated as a Hooke's Law type force; that is the force is proportional to the displacement. An electric field F_ will cause such a displacement by exerting a force Fe on the charge until the displace-ment is such that the two forces are equal, i.e. - 14 -Fe = fr (2-14) An electric moment m = er (2-15) is created by this displacement so by solving for r_ and substituting into equation (2-14) the electric moment becomes m = Fe 2/f (2-16) For a molecule containing several charged particles, each of charge e_ (say electrons) the total induced moment is Em = FIe 2/f " (2-17) Now the molecular polarizability can be defined as the electric moment induced in a molecule by a unit field F = 1 esu = 300 volts/cm The symbol used for molecular polarizability is a o so then a = Ze 2/f (2-18) o and f can be seen to be the force constant for the binding of the charges. - 15 -The next step is to derive the equation relating dipole moment to measurable quantities. This requires the derivation of the Clausius-Mosotti equation. Consider the following situation. Let a constant electric field, F_, be applied to a sphere of a continuous, isotropic dielectric. The electric moment induced in the sphere is m = a F (2-19) s s where a g is the polarizability of the sphere. Now i t has already been shown by rearranging equation (2-11) that P* = (e-l)E/4ir (2-20) and the volume of the sphere is defined as V = 4*3^/3 (2-21) where a is the radius of the sphere,so substituting into equation (2-19) gives 3 m = p* v = . m a F s 4ir 3 s (e-l)Ea^ = a F (2-22) 3 s The total field E produced inside the sphere is E - [3/(e+2)]F (2-23) - 16 -This may be substituted into equation (2-22) to give e-1 _ s e+2 a s f (2-24) A molecular formula may be made by making the following substitution into equation (2-24) a = N a s s o 4ira3/3 = V/N = 4TT33/3N , s s s where a is the molecular polarizability, N is the number of molecules -o r -s in the sphere of radius a g and a. is the approximate molecular radius. The formula obtained from equation (2-24) is e-1 _ a e+2 - | (2-25) a A more useful form of this equation may be obtained by substituting the value of a found in 4ira3/3 = M/Nd (2-26) where N is Avogadro's number, d_ is the density of the substance and M is its molecular weight. The result obtained by substituting equation (2-26) into equation (2-25) is - 17 -or , a 4irNd g"1. = _2 (2-27) e+2 3M K } 1 „ 4 i r N a _ _ 2 _ (2-28) e+2 d By substituting the Maxwell relation e - n 2 (2-29) where ii is the refractive index of the material the following equation, which is the Lorentz-Lorenz equation for molar refraction is found. 2 T M 4irNct • f - v - R <2"30> n +2 The force J_ may be broken down into three components F^, F^ and F^. is the force due to the charges of surface density o_ on the condenser plates so that ¥ ± = 4TTCJ (2-31) F 2 is due to .the polarization of the material outside the sphere under consideration. It consists of the force due to the layers of induced * charge on the material facing the condenser plates (-4irP ) plus the force due to the charge on the "surface" of the sphere being considered, (+4irP /3) so the total force F is - 18 -F 2 = -4TTP* + 4TTP*/3 (2-32) is the force due to the material contained within the sphere of interest and depends on the structure of the material. There is no general expression for F^, but in cubic crystals (due to their symmetry) and in gases, F^ = 0 a n ^ f° r liquids in which the molecules are randomly ordered in the absence of an electric field, F^ = 0 approximately. The lack of a general expression for F^ places a limitation on the types of substances for which the remainder of this discussion will apply. As an approximation, F^ may be set to zero, i.e. F 3 = 0 (2-33) and thus F = 4TTO - 4irP* + 4TTP*/3 ' (2-34) It can be shown (by substituting equation (2-6) into equation (2-4)) that E = 4ua - 4irP* (2-35) so Now F = E + 4TTP*/3 (2-36) P * = Kjm (2-37) where is the number of molecules per cc so that P * - N-m - N.a F = N.o (E + 4TTP*/3) (2-38) 1 l o l o • - 19 -If equation (2-20) is substituted into equation (2-38) the result is = N.a (E + —r • < ^ ) (2-39) 4i; 1 o 3 4TT This can be rearranged to give . 4irN.a £ - (2-40) Now in a pure substance, Nx = Nd/M (2-41) so therefore , 4irNda ET-1 _ O E+2 3M or e-1 M _ o_ e+2 * d 3 (2-42) = P (2-43) which is identical to the Lorentz-Lorenz equation (equation (2-30)) derived previously for optical wavelengths. The quantity P_, calculated from this equation (2-43), is the molar polarization and both P_ and a have the dimensions of volume. Therefore when a is constant, then -o -o P_ is constant and the expression is complete, but this is only true i f the material under consideration does not have a permanent dipole. Also P_ is approximately independent of temperature for substances for which i t and the molar refraction, R are almost equal numerically. - 20 -Equation (2-43) is the Clausius-Mosotti equation. It was Debye who first developed the theory to explain the effect that a permanent dipole has on the molar polarization, and a brief outline of his treatment follows. Ignoring for the present the electric moment induced by the field J_, consider the effect only of the permanent moment. For any arbitrary orientation 0_ of the polar molecule with respect to the direction of the field F_, the potential energy is According to Boltzmann's Law, the number of molecules distributed with the axes of their dipoles pointing in the directions within a solid angle d& is where A is a constant dependent on the number of molecules considered, k_ is the Boltzmann constant and T_ is the temperature in degrees Kelvin. By substituting equation (2-44) into (2-45) and integrating to find the total number of molecules in a l l possible directions, this total is found to be U = -yFcose (2-44) A exp(-U/kT)dn (2-45) Number = SA exp((uFcos6)/kT)dH (2-46) The total moment is - 21 -Moment = fk exp (yFcos9/kT)cos9dQ (2-47) Dividing equation (2-47) by equation (2-46) gives the average moment per molecule or - _ fk exp((yFcos9)/kT)ycos9dfl ,„ m fk exp((yFcos9)/kT)dft ^ } In order to integrate equation (2-47) more easily, the following substitutions should be made: x - yF/kT z = ,-cos9 dfi = 2irsined9 Integration and simplification of equation (2-47) gives m exp(x) + exp(-x) 1 , N 1 T / % ; o v — = — f~\ f—r - — = coth(x) = L(x) (2-48) p exp(x) - exp(-x) x x the Langevin function. The series expansion of the function is 3 L(x) = | - | j • + ... (2-49) The values of x measured in dipole moment studies are sufficiently small that i t is enough to consider only the fir s t term of the series expansion, so therefore 2- = x/3 (2-50) ° r 2 m - u F/3kT (2-51) - 22 -This effect is added to the effect of the induced moment so that the total mean moment is 2 M = a F + u2F/3kT = (a + H _ ) F (2-52) o o 3kT The total polarizability a_ is thus a - a o + H _ ( 2 _ 5 3 ) and therefore the general expression relating dipole moment to polarizability is p = £ZdL . M = ^EN« = , + ilL ) (2-54) * e+2 d 3 3 (ao 3kT ; U This above derivation is of course a classical treatment of the subject. An equation relating dipole moment to polarizability can be obtained by using quantum mechanical postulates, and when this is done, a correction term f(T) appears so that the quantum mechanical equation Is . „ 4irNa . XT 2 1 + 2 d 3 ^ + ~T~ " 3kf ( 1 _ f ( T ) ) ( 2 _ 5 5 ) where f.(T) is a non-linear function of the dipole moment and is inversely proportional to temperature. This correction is experimentally indistinguishable from zero in a l l cases except for a few low molecular weight hydrides and so is not used in ordinary experimental work with solutions. - 23 -The Solution Equations and the Guggenheim Method The Debye equation as originally given applied only to the case of pure gases, however, many compounds are difficult or impossible to vaporize at reasonably low temperatures. Therefore i t becomes necessary to obtain dipole moments of compounds dissolved in non-polar solvents and to find an equation relating the measured properties of these solutions to the dipole moment of the pure solute. Consider the situation of a polar solute, whose physical properties will be distinguished by a subscript 2, and a non-polar solvent, whose properties will be denoted by a subscript 1 (properties of the solution will be denoted by the subscript 12). It was shown by equation (2-43) that P = (4ITN/3)CX (2-56) and i t is known from experimental work that P_ is closely additive for dilute solutions so for a two-component solution £12 1 _ 4ir , 4TT C,,. 7~f2 ~ "3 V l + "3 n2 a2 ( 2 " 5 7 ) where ot_ is the polarizability and ri the number of molecules per cc (for each component respectively). The mole fractions of each component are 2^  - nj/O^ + n 2) (2-58a) * 2 = n 2/( n ; L + n 2) (2-58b) - 24 -and the molar polarizations are V± = 47TNa1/3 (2-59a) P 2 = 4uNa2/3 (2-59b) The density of the solution is d12 = ( t l l H l + n 2 M 2 ) / N (2-60) where M is the molecular weight. By solving for n^ in equation (2-58a) and n 2 in equation (2-58b) , and substituting equation (2-57) becomes 7^2 - T V W + 3 ( 2- 6 1 ) and equation (2-60) becomes d12 = ( x 1 ( n 1 + n 2 ) M l + V W V / N ( 2 _ 6 2 ) If both sides of equation (2-61) are divided by d_ and rearranged, the result is 12 . 11 2 2 _ 4TT 4ir Zo A ~~T X a N + — X a0N c 1 2 + 2 d i 2 3 11 3 2 2 X1 P1 + X2 P2 = P 12 (2-63) - 25 -or, since for a two component system = i-x; '2 then P12 = P l + ( P2 ~ P 1 ) X 2 (2-64) The p o l a r i z a t i o n of the solution, P ^ J i s calculated from the values of the d i e l e c t r i c constant and density of the solution so i f P^ i s known, then can be calculated. For a solution of a polar solute i n a non-polar solvent, the assumption i s made that P^ i s independent of concentration and i s a constant, though this i s only approximately true; so that any deviation from l i n e a r i t y i n a plot of P ^  v s > x 2 w i l l be attributed to a v a r i a t i o n of P^ due to dipole-dipole interactions which change with changing concentration, may then be plotted against and the re s u l t i n g curve extrapolated to i n f i n i t e d i l u t i o n (X„ = 0). The value of P„ thus obtained i s referred to as P. ,.from -2 ' -2 -2«> « which interaction effects and any solvent effects have been approximately eliminated. The value of the dipole moment, u_, calculated by use of P „ for the polar molecule i s usually f a i r l y close to the value of y —2°° (vapour). Alternatively,instead of cal c u l a t i n g and extrapolating the pol a r i z a t i o n to i n f i n i t e d i l u t i o n , the d i e l e c t r i c constant and density data can be extrapolated. There are two procedures that can be followed here; either e_ and cl can be extrapolated d i r e c t l y (the Halverstadt-18 Kumler method) or the Debye equation can be modified and e_ and ti (the r e f r a c t i v e index) can be used for extrapolation (the Guggenheim 19 method). For the HalverstadfKumler method the procedure i s as follows. - 26 -Consider the equations: e12 = e l + a' X2 <2-65a) V12 = V l + B' X2 (2-65b) where V = 1/d. A plot of v s- x 2 a n c* o n e °^ -12 V S ' -2 § i v e slopes of c£* and g_' respectively, and intercepts of e^ and respectively. To determine these values should be substituted into 3a*VM (e,-l) P, = + (M V + M g') 1 . (2-66) 2~. ( ^ + 2 ) 2 2 1 1 (£;L+2) which i s of the same form as an equation proposed by Hedestrand. 18 The Guggenheim method, and especially Smith's modification of i t , i s an easier method to use, and with the a v a i l a b i l i t y of highly accurate dipping refractometers i s ju s t as accurate. The derivation 20 , given here closely follows that of Smith. Just as P12 = P 1 X 1 + P 2 X 2 ( 2 " 6 7 ) so the molar r e f r a c t i o n i s = + R 2X 2 (2-68) The molar volume, V, may be approximated by V12 = V 1 X 1 + V 2 X 2 ( 2 _ 6 9 ) Equations ( 2 - 6 7 ) and ( 2 - 6 8 ) may be rewritten as follows: < ^ 2 L T 2 - ) V 1 2 = ^ > V 1 X 1 . + ( P e + ? a + P o ) X 2 ( 2 " 7 0 ) 2 2 n - 1 n - 1 ( ^ - T ) V 1 2 * ( - | — > V 1 X 1 + P e X 2 ( 2 " 7 1 ) n 1 2 + 2 n x +2 where P i s the electronic p o l a r i z a t i o n , P i s the atom pol a r i z a t i o n and -e -a P i s the p o l a r i z a t i o n due to the permanent dipole moment and P + P + -o f t- -a -e P Q = P 2 - These terms w i l l be explained i n more d e t a i l i n Chapter IV. Subtracting equation ( 2 - 7 1 ) from equation ( 2 - 7 0 ) gives < 7 ^ f 9 " - f - ) v i , = (T^TT " ~ f - > v i X i + < P * + P J X 9 ( 2 - 7 2 ) . e , 0 + 2 2 12 e ,+2 2 1 1 a o 2 12 12 n^+2 Equation ( 2 - 6 9 ) may be rearranged and substituted into equation ( 2 - 7 2 ) to give 2 2 ( 7 ^ 2 " - T T 7 ) V 1 2 = (e7+2 - - T - W l l - W + ( P a + P o ) X 2 12 n i •> 2 1 n .+2 ( 2 - 7 3 ) Now ( ( — — p—)V.. ) i s the atom p o l a r i z a t i o n of the solvent. E l n^+2 Then a quantity P ' can be defined as e l ~ 1 n l - 1  3 e l + 2 n 2 +2 2 and thought of as a sort of atom p o l a r i z a t i o n for the solute, and - 28 -substituted into equation (2-73) to give £ 1 2 _ 1 n l 2 _ 1 e l - 1 n l _ 1 fcr^Zo - ) V 1 9 = ( - ^TT " - 5 — ) V 1 9 + (P.-Pa'+P )X E..+2 2 12 E-,+2 2 12 a a o 2 12 n, ,+2 1 n.,+2 i Z 1 (2-75) I f equation (2-75) i s divided on both sides by V a n <^ Xi2^-12 r e P ^ a c e c i by C_, which i s the concentration of solute i n moles per unit volume, the equation then becomes ~ -5Tr) • ^ • ^  + ( W + V C <2"76) 12 n i 2 n^+2 and t h i s may be s i m p l i f i e d s l i g h t l y by defining n +2 and substituting to give D 1 0 = D, + (P -P '+P )C (2-78) 12 1 a a o 2 A plot of D 1 0 vs. C_ gives a slope of (P -P ' + (4TTNU /9kT)) and an intercept equal to D^ . Guggenheim made the assumption that atom polarizations are proportional to molecular volumes and furthermore suggested that P and P ' could be equated, thus eliminating atom polarizations. Equation (2-78) then becomes 11m 3D = 4TTNU2 ( 2 _ I Q . C-X) 3C o 9kT v ' 20 Smith then suggests that i t would be better to use weight fractions for the concentration units and thus eliminate any need to know the densities of the solutions. The weight f r a c t i o n , u^j i s related to £ by C = m^/K^V which when substituted into equation (2-78) gives D., = D.. ( P -P »+P )CO_/M,V (2-80) 12 1 a a o 2 2. or assuming again that P = P 1 —3. 3. 2 _ ATTNU _ l i m 8D_ o $m P o " -9kF" " V l w2-*0 B u y ( 2 _ 8 1 ) 3D 3 £ 3 n The slope (-—) i s related to the quantities (- ) and (-—) by a(x>2 2 2 3D = 3 H_ 6 9n (2-82) 9 A )2 ~ ( E l+2) 2 9 a )2 (n x 2+2) 2 8 a i2 By using the notation that ) i s a and'C-^—) i s 6, equation (2-81) ou) 2 — da) 2 becomes P o = [3M 2V i a/( e i+2) 2] - [ 6 * ^ 3 / ( n ^ + 2 ) 2 ] (2-83) and also y = [ (9kTP Q) / (4TTN) ] ' ^ (2-84) This method of calculating dipole moments has the advantage that the data for e^ 2 a n t* n^ 2 are separately extrapolated, so that any errors i n e^ 2 and n^ 2 w i l l be e a s i l y detected. Also for a p a r t i c u l a r solvent at a known constant temperature, the factors 3 M 2 V 1 / ( e l + 2 ) 2 a n d 6 M 2 V i 7 C11!*4-2)2 - 30 -are constants, therefore the c a l c u l a t i o n of the o r i e n t a t i o n p o l a r i z a t i o n of the dipole moment i s very much s i m p l i f i e d . For a laboratory equipped with a dipping refTactometer, the Guggenheim method i s by far the easiest way to obtain data for dipole moments. The refTactometer i s easy to c a l i b r a t e , measurements are rapidly obtainable, and a solution from which a questionable datum was obtained can e a s i l y be remeasured. A very important thing to keep i n mind about dipole moments i n general, and the Guggenheim method i n p a r t i c u l a r i s that the absolute values of data such as temperature, d i e l e c t r i c constants and r e f r a c t i v e indices need only be accurate to 0.5% to give accurate values of the dipole moment of a molecule but, the values of d i e l e c t r i c constants and r e f r a c t i v e indices amongst themselves must be much more accurate. To explain more concretely, i t i s necessary f o r example to have the temperature i n the thermostat controlled to + 0.02°C because both d i e l e c t r i c constants and re f r a c t i v e indices are strongly temperature dependent, but as long as any variations i n temperature can be controlled to + 0.02°C i t i s of much less importance whether the mean temperature i s 298.0°K or 298.1°K. 2 To obtain the dipole moment y, i t i s necessary to f i r s t calculate y and then take the po s i t i v e square root of th i s number. This process 2 cuts the error by h a l f , i . e . a 1% error i n y i s a 0.5% error i n y. In any event, with the equipment and techniques presently available, one cannot expect accuracy i n y greater than +0.05 D and most investigators quote t h e i r results with an error of the order of + 0.10 D. The only method of obtaining dipole moments that can give more accurate re s u l t s than those quoted i s the microwave method, and - 31 -microwave work to obtain dipole moments of phosphonitrilic compounds i s not feasible due to the large number of atoms i n these compounds and due to the f l e x i b i l i t y of the molecules. Though the Guggenheim method of determining dipole moments i s much easier to use, there are circumstances i n which i t i s not applicable. I t i s not possible to measure the r e f r a c t i v e index of a substance or solution accurately near an absorption band. For example, using the Na l i n e s as the sources of i l l u m i n a t i o n , i t would not be possible to measure the r e f r a c t i v e index of a l i q u i d that absorbed an appreciable amount of yellow l i g h t . I f i n dipole moment measurements the solutions used are coloured, i t may become necessary to calculate dipole moments by the Halverstadt-Kumler method and to measure the densities of the solutions as accurately as possible. - 32 -CHAPTER I I I EXPERIMENTAL Materials and Equipment Cyclohexane (Fisher, c e r t i f i e d ACS Spectranalyzed) was stored over molecular sieves (BDH Type 13X) overnight before use. Carbon t e t r a -chloride (Fisher, c e r t i f i e d ACS Spectranalyzed) was also stored over molecular sieves overnight before use. Trimeric and tetrameric phosphonitrilic chlorides (N^P^Cl^ and N^P^Clg) were p u r i f i e d by r e c r y s t a l l i z a t i o n from petroleum ether to constant melting points of 112.5°C for the trimer ( l i t . 112.8°C) 2 1 and 122°C for the tetramer 21 ( l i t . 122.8°C). Phosphonitrilic f l u o r i d e trimer (N_P_F.) was J J b 7 8 -.prepared by reacting KSO„F and N_P_C1, i n p a r a f f i n o i l at 140°C. ' / j o b I t was p u r i f i e d by successive trap-to-trap d i s t i l l a t i o n s on a vacuum l i n e . Tetrameric phosphonitrilic f l u o r i d e (N P.F ) was p u r i f i e d by a 4 4 o series of trap-to-trap d i s t i l l a t i o n s on a vacuum l i n e . The higher phosphonitrilic f l u o r i d e s , (NPF„) , n = 5 to 12, and also the mixed 2. n chloride-fluorides, ( N ^ ^ C l ^ , ( N ^ F ^ X l ^ ) , ( N ^ P ^ C l ^ , ( N ^ ^ C l ^ , (N^P^FgCl^) and (N^P^FgCl^) were p u r i f i e d by gas-liquid chromatography using a 10' x 3/8" column packed with 20% SE-30 on Chromosorb W and a helium flow rate of 55 ml per minute. The p u r i f i e d compounds were collected i n glass c o l l e c t i o n tubes cooled i n an acetone-C02 bath. - 33 -A graded series of four or f i v e solutions of each compound were prepared using cyclohexane as the solvent. The concentrations of each of the solutions were determined by weighing the empty container, the container with added compound and the container plus compound with added solvent i n order to determine the weight of solute and weight of solvent for each solution. The concentrations were then calculated as weight f r a c t i o n s . A WTW Dipolemeter, Type DM01, with a DFL-1 c e l l , was used to measure the capacitance of each solution. The capacitances of a i r and of CCl^ were measured as standards. Because the capacitance of the Dipolemeter c e l l plus contents i s d i r e c t l y proportional to the d i e l e c t r i c constant of the contents, one then can use the known values of the d i e l e c t r i c constants of a i r and CCl^ together with t h e i r measured capacitances to determine the conversion factor from capacitance to d i e l e c t r i c constant for the Dipolemeter. This conversion i s best expressed i n the form = a* (capacitance reading) + b where a and b were redetermined before each set of data f o r a compound was collected. A capacitance reading was arrived at by taking nine separate readings for each substance or solution i n the c e l l and using the arithmetic mean of these readings as the capacitance reading. A dipping refractometer (Carl Zeiss) was used to measure r e f r a c t i v e indices of the solutions. The refractometer was calibrated at the beginning of each data run using the c a l i b r a t i n g prism supplied by the manufacturer. The refractometer has a scale engraved on the eye-piece and a reading i s obtained by determining the boundary l i n e separating the bright portion of the scale from the dimly l i t portion. - 34 -A vernier scale i s b u i l t into the instrument which allows scale readings to be made to four s i g n i f i c a n t figures. These scale readings may be converted into r e f r a c t i v e indices by using the tables supplied by the manufacturer. A metal-walled c e l l with a bayonet lock i s also supplied and this c e l l i s f i l l e d with the solution of interest and locked onto the refractometer. After allowing 15 minutes for e q u i l i b r a -t i o n i n a thermostat bath, nine scale readings were obtained and the arithmetic mean of these was used to determine the r e f r a c t i v e index of the solution. In order to ensure constant temperature of the solutions when measuring t h e i r r e f r a c t i v e indices and d i e l e c t r i c constants,a thermostat bath was set up and regulated to provide a constant temperature of 298°K (25°C) with maximum fluctuations of + 0.02°. A schematic diagram of the thermostat bath i s shown i n Figure 3-1. I t was found necessary to use a cooling c o i l i n order to obtain constancy of tempera-ture i n the bath. D i s t i l l e d water was used as the bath l i q u i d . Procedure The standard procedure for obtaining a set of data from a compound was as follows. A graded series of four or f i v e solutions of the compound i n cyclohexane were prepared by weighing the components into a glass container. Figure 3-2 shows the container used for N P F £ and J 3 o N.P.F0, for the other compounds a 50 ml volumetric f l a s k was used. An 4 4 o a n a l y t i c a l balance was used fo r weighings, with an accuracy of +0.0001 g -3 The concentrations of the solutions ranged from 4.00 x 10 to 2.50 x 10 i n terms of weight f r a c t i o n . The Dipolemeter was calibrated using a i r - 35 -Figure 3-1 Schematic diagram of Thermostat including connections to Dipolemeter (left) and heater-pump (right) - 36 -Figure 3-2 Flask for use with volatile compounds and carbon tetrachloride as standards. The refTactometer was calibrated with the c a l i b r a t i n g prism supplied by the .manufacturer. The Dipolemeter c e l l was then f i l l e d with cyclohexane and was stoppered and allowed to reach the temperature of the thermostat bath. This e q u i l i b r a t i o n took ten to f i f t e e n minutes. Then nine readings of the capacitance of the c e l l and contents were recorded. The cyclohexane was then withdrawn from the Dipolemeter and the metal c e l l for the refTactometer was f i l l e d and attached to the refTactometer, which was then placed on a holder so that the c e l l was immersed i n the thermostat bath. Ten to f i f t e e n minutes were allowed f o r e q u i l i b r a t i o n and nine scale readings were then recorded. The same procedure was then repeated with the most d i l u t e solution of compound i n solvent. This procedure was repeated as many times as necessary, each time using the least concentrated of the solutions remaining to be measured. In - 37 -thi s manner, data were collected for a l l the solutions prepared. After a l l data were collected, the mean capacitance readings were converted to d i e l e c t r i c constants and the mean refractometer scale readings were converted to r e f r a c t i v e indices. Concentrations i n terms of weight f r a c t i o n were calculated for each solution and graphs of d i e l e c t r i c constant vs. weight f r a c t i o n and r e f r a c t i v e index vs. weight f r a c t i o n were plotted. The slopes of these graphs were determined and substituted into the equation p 3 M2 v _ 6 i< 2v d ( £ ; L+2) 2 (n^+2) 2 derived i n Chapter I I (equation (2-83)). Data and Results The data and re s u l t s are a l l presented i n Table I. The graphical results for a t y p i c a l compound, N^P^F^C^ are shown i n Figure 3-3. A graph of p o l a r i z a t i o n vs. rin g size for the phosphonitrilic fluorides i s given i n Figure 3-4. - 38 -Table I. Data and Results for Phosphonitrilic Halides. Compound 2 10 x Maximum Maximum Minimum Dis t o r t i o n concentration d i e l e c t r i c r e f r a c t i v e p o l a r i z a t i o n (weight fractions) constant index i n cc. (F^  ) (NPF 2) 3 1.88 2.0152 1.42228 4.4 (NPF.2)4 2.25 2.0171 1.42222 13.4 (NPF 2) 5 2.60 2.0178 1.42192 17.2 (NPF 2) 6 2.37 2.0170 1.42228 21.9 (NPF 2) ? 1.50 2.0170 1.42273 29.4 (NPF 2)g 2.75 2.0186 1.42228 37.5 (NPF 2) 9 2.07 2.0182 1.42252 45.7 (N P F 2 ) 1 Q 1.76 2.0189 1.42259 66.4 (NPF 2) 1 ] L 2.23 2.0195 1.42247 55.3 ( N P F 2 ) 1 2 2.56 2.0195 1.42225 54.2 (NPC1 2) 3 2.65 2.0239 1.42465+ 17.6 (NPC1 2) 4 2.55 2.0254 1.42520T 31.3 N 3 P 3 F 4 C 1 2 2.35 2.0229 1.42296 4. 26.6 N 3P 3F 2C1 A 3.41 2.0297 • 1.42412T 30.1 N 4 ? 4 F 6 C 1 2 2.36 2.0223 1.42290 4- 33.2 ' N 4 P 4 F 4 C 1 4 2.52 2.0272 1.42377 43.5 N 5P 5F 8C1 2 2.23 2.0224 1.42293 1.42360+ 42.9 N 5 P 5 F 6 C 1 4 2.24 2.0271 61.4 * Minimum d i e l e c t r i c constant was that of cyclohexane which i s 2.0150 at 25°C. ** Refractive index of cyclohexane i s 1. 42356 at 25°C. ^ In these compounds, re f r a c t i v e index rose with solution concentration - 39 -Figure3-3a € vs. weight fraction for N 3 P 3 F A 50 40 30 20 10' 200 190 x I vt Iran. ,3 ^ y v c i - r i ^ A 70 60 50< 2.0160 05 , • UO 15 10 x weight fraction 20 25 too Figure3-3b. DQ VS we'ght fraction for N3P3F,Cl2 1.0 15 107 x weight fraction 25 - 40 -- 41 -CHAPTER IV DISCUSSION The Question of Atom P o l a r i z a t i o n The t o t a l p o l a r i z a t i o n , P, may be broken down into three components; electronic p o l a r i z a t i o n , d i s t o r t i o n p o l a r i z a t i o n and atom p o l a r i z a t i o n , a l l of which are the result of applying an e l e c t r i c f i e l d to a c o l l e c t i o n of molecules. The t o t a l p o l a r i z a t i o n i s the p o l a r i z a t i o n obtained from d i e l e c t r i c constant data. The electronic p o l a r i z a t i o n , which i s due to the movement of electrons i n the molecule, i s obtained by o p t i c a l methods, for example measurements of r e f r a c t i v e indices. The d i s t o r t i o n p o l a r i z a t i o n i s due to the orientation of the permanent dipoles, while atom p o l a r i z a t i o n i s the name given to the portion of the t o t a l p o l a r i z a t i o n caused by the movement of atomic nuclei r e l a t i v e to one another i n a molecule. There are a number of ways of causing such movement; by stretching of bonds j o i n i n g the n u c l e i , by changes i n bond angles and by torsional movements of nu c l e i with respect to one another. These movements are classed as v i b r a t i o n a l and so evidence for them should be found i n the infrared spectra of the molecules concerned. Because of i t s nature, atom p o l a r i z a t i o n i s not l i k e l y to bear any numerical r e l a t i o n -ship, to the electronic p o l a r i z a t i o n or to the orientation p o l a r i z a t i o n , but should instead be accessible to cal c u l a t i o n either by means of a knowledge of the force constants of bending and stretching that may be obtained v i a infrared spectroscopy or by means of a knowledge of the r e f r a c t i v e index - U7 of the compound i n the i n f r a r e d p o r t i o n of the spectrum. I f the r e f r a c t i v e index data are a v a i l a b l e , then a S e l l m e i e r type of r e l a t i o n -ship can be used to c a l c u l a t e the r e f r a c t i v e index at zero frequency ( i n f i n i t e wavelength). Using t h i s value of the r e f r a c t i v e index to c a l c u l a t e the molar r e f r a c t i o n gives a r e f r a c t i o n equal to the sum of the e l e c t r o n i c and a t o n i c p o l a r i z a t i o n s , i n s t e a d of just being equal to the e l e c t r o n i c p o l a r i z a t i o n , which i t i s i f no account i s taken of the infrared r e f r a c t i v e index data. Such data are, however, not readily available, and so the most common method of d e a l i n g w i t h atom p o l a r i z a t i o n i s to make an a r b i t r a r y correction f o r i t s . Smith"*""*" 22 23 quotes Van Vleck and Cartwright and Errera, who showed that low frequency modes of v i b r a t i o n such as bending make the greatest contribu-t i o n to atom p o l a r i z a t i o n because they have small enough force constants to give atom polarizations of the expected.magnitude. Such vibrations ; w i l l absorb i n the f a r - i n f r a r e d i n the range of about 50-200 cm "*". Therefore, i f there ex i s t absorptions i n the infrared i n t h i s range, these absorptions can be used as evidence that the molecule i n question may have a considerable, non-negligible atom p o l a r i z a t i o n . This sort of 24 1 3 argument was used by Coop and Sutton when explaining the unexpectedly . high "dipole moments" of some symmetric diketones. For benzoquinone, 25 " 1 Hammick, Hampson and Jenkins carried out calculations assuming the \ atom p o l a r i z a t i o n could be ascribed to the two carbonyl groups. I t 24 was Coop and Sutton, however, who showed mathematically that the high apparent orientation p o l a r i z a t i o n of benzoquinone was due to atom • . p o l a r i z a t i o n . They showed that i f benzoquinone were treated as an 5^  e n t i t y consisting of two independent one-dimensional o s c i l l a t o r s , that^_~ the frequency of the v i b r a t i o n calculated from the p o l a r i z a t i o n was very - 43 -close to that of a vibrati o n observed i n the far infrared by Cartwrigh 23 26 ™1 and Errera ' at 120 cm . Coop and Sutton assumed that the two carbonyl groups vibrate i n the plane of the benzene ring and perpendicular to the carbon-oxygen double, bond. The atom polarization caused by two independent one-dimensional o s c i l l a t o r s i s P = 8TTNU 2/9V a o where y_ i s the moment of the vib r a t i n g group and i s the force constant of the vi b r a t i o n . For benzoquinone, P ^ 9 cc. and u_ = a —18 2.5 x 10 esu-cm for a carbonyl group, which gives a value of V q of —12 2 1.17 x 10 erg/radian /molecule. This force constant corresponds to a frequency of about 111 cm 1 which i s very close to the observed value of 120 cm"1. Because of the nature of atom p o l a r i z a t i o n , i t may be expected to be a roughly additive quantity for molecules of s i m i l a r structure. 27 To quote Smith "Atomic p o l a r i z a t i o n values seem to depend p r i n c i p a l l y on the nature of the dipole groups which are i n opposition, and not upon the size of the groups l y i n g between them. I t must be infe r r e d , therefore, that the effe c t l i e s i n the v i b r a t i o n a l c h a r a c t e r i s t i c s of the polar groups". Extending t h i s statement, then one might expect that a series of compounds made up of a repeated polar group could be expected to have atom polarizations that increased roughly proportionally to the number of repeating units. As an example, consider the n-alkanes, CH^CCI^)jjCHg* a s the series of compounds and the -CIL,- group as the 28 repeated polar group. Smyth has tabulated the atom polarizations of - 44 -the n-alkanes ( h i s data were obtained by measuring p o l a r i z a t i o n s at different temperatures) up to n-dodecane and has c a l c u l a t e d the increase of atom p o l a r i z a t i o n per added -CH^- group as 0.07 c c , which, considering the low p o l a r i t y of carbon-hydrogen bonds appears to be a reasonable increment. For the case of the m e t a l l i c acetylacetonates a s i m i l a r a d d i t i v i t y was found and i t was n o t i c e d that the r a t i o of the atom polarizations for a series of acetylacetonates was the same 24 2 as the r a t i o of the number of acetylacetonate groups per metal atom. The high residual polarizations of these compounds were not at f i r s t thought to be due to atom p o l a r i z a t i o n but instead were thought to be explained by one of the following reasons: (1) the chelate rings were not f u l l y symmetric, (2) the compounds were not f u l l y chelated, (3) the molecules are e a s i l y bent by thermal c o l l i s i o n s and remain t h i s way long enough to orient i n the e l e c t r i c f i e l d used to measure p o l a r i z a t i o n s , (4) there i s some sort of solvent e f f e c t . 29 Finn, Hampson and Sutton, however, disposed of a l l four of these explanations and concluded that the high residua l polarizations were r e a l l y atom pola r i z a t i o n s . Application of resonance concepts eliminated the f i r s t explanation, and the second was shown to be most improbable because there was no v a r i a t i o n of t o t a l p o l a r i z a t i o n with temperature as would be expected i f the second p o s s i b i l i t y were true. As f a r as the p o s s i b i l i t y of thermal bending i s concerned, Finn, Hampson and Sutton carried out a rough c a l c u l a t i o n to show that the frequency of such bending would be too high to permit the molecule to orient i t s e l f - 45 -i n the f i e l d . The f o u r t h e x p l a n a t i o n was e l i m i n a t e d b e c a u s e t h e v a r i a t i o n i n t o t a l p o l a r i z a t i o n w i t h solvent was o n l y s l i g h t and a l s o was n o t i n the manner p r e d i c t e d by the a c c e p t e d s o l v e n t e f f e c t t h e o r i e s . Further evidence f o r t h e i r c o n c l u s i o n t h a t t h e anomalous p o l a r i z a t i o n of the compounds was due to atom p o l a r i z a t i o n was found b y Coop and 24 Sutton who measured p o l a r i z a t i o n s i n the vapour phase f o r these and other compounds and found the p o l a r i z a t i o n s constant w i t h i n e x p e r i m e n t a l error over temperature ranges up to 150° depending upon w h i c h compound was considered. They encountered considerable d i f f i c u l t y w i t h some o f the compounds due to t h e i r decomposition but were able to conclude that the m e t a l l i c acetylacetonates, the symmetric diketones and most of the other compounds which they examined did have high but r e a l atom polarizations. A more recent discussion of atom polarizations and t h e i r e f f e c t s i n a series of c y c l i c dimethylsiloxane oligomers has been contributed 30 by A l v i k and Dale who were trying to obtain information on molecular conformations of the d i f f e r e n t oligomers by measuring t h e i r dipole moments. They found however that such information could not be obtained for the siloxanes because they had no way to accurately measure the atom po l a r i z a t i o n s . From microwave absorption work carried out by 31 Dasgupta, Garg and Smyth i t was already known that the atom p o l a r i z a -t i o n was of the order of 15% and 22% of the t o t a l p o l a r i z a t i o n for the trimeric and tetrameric c y c l i c dimethylsiloxane oligomers, therefore, a very considerable error i n the dipole moments of the compounds due to t h i s atom p o l a r i z a t i o n was not e a s i l y correctable. The conclusion ;/ of A l v i k and Dale that the high apparent dipole moments of the c y c l i c - 46 -diiuethylsiloxane o l i g o m e r s were due to atom p o l a r i z a t i o n was s u p p o r t e d by t h e i r determination o f the e n t r o p i e s and e n t h a l p i e s of f u s i o n and 32 the i n f r a r e d spectra of the compounds. The i n f r a r e d s p e c t r a were very complicated, as would be e x p e c t e d f o r f l e x i b l e m o l e c u l e s , and, molecules of high f l e x i b i l i t y a r e exactly those t h a t have h i g h atom polarizations. When m o l e c u l e s a r e as f l e x i b l e as t h e s e a r e , then inversion into conformations h a v i n g a net d i p o l e moment w i l l o c c u r due to low frequency vibrations and i t i s i n t h i s a r e a o f consideration that "we enter a doubtful t e r r i t o r y i n which i t may be d i f f i c u l t or a r b i t r a r y to distinguish between dipole orientation and atom 31 p o l a r i z a t i o n . " This same t e r r i t o r y must also be entered when a d i e l e c t r i c study of phosphonitrilic compounds i s carried out. Previous Methods of Dealing with Atom P o l a r i z a t i o n A s has been stated previously, i t is-very d i f f i c u l t to measure the atom p o l a r i z a t i o n of a molecule. Refractive index data from the infrared portion of the spectrum, used i n conjunction with a Sellmeier type relationship w i l l enable the ca l c u l a t i o n of the atom p o l a r i z a t i o n or else an estimate of atom p o l a r i z a t i o n can be made from force-constant data obtained i n the f a r infrared. Usually, though, such data are not a v a i l a b l e , and the procedure then has been to estimate a value of P^. There are three main approaches for such an arb i t r a r y estimation. One can assume P = 0, i . e . that P i s so small compared to P that i t may be neglected. Another way i s to assume that P & i s a certain percentage of P , because i t has been found for many small organic molecules that P i s about 5% to 15% of P . Evidence for this comes -a -e - 47 -from microwave studies where dipole moments can be c a l c u l a t e d w i t h o u t any knowledge of P . A t h i r d , s l i g h t l y d i f f e r e n t approach, i s sometimes used when ref r a c t i v e i n d e x d a t a are c o l l e c t e d ( f o r example when using the Guggenheim method). R e f r a c t i v e i n d i c e s a r e u s u a l l y measured with respect to the Na^ l i n e , and the values so measured a r e normally a few percent higher than the r e f r a c t i v e i n d i c e s calculated for zero frequency. I t i s then assumed that the value of the re f r a c t i v e index f o r the Na^ l i n e used i n the calculations i s s u f f i c i e n t l y high enough to account for the effects of atom p o l a r i z a -t i o n . I t has been found, however, that there are a number of compounds for which these approximations are inadequate. Atom P o l a r i z a t i o n and Phos p h o n i t r i l i c Compounds A number of dipole moment determinations have been carried out on 12—16 33—37 phosphonitrilic compounds ' i n order to obtain information on t h e i r structures and, i n the case of mixed substituent derivatives, distinguish d i f f e r e n t isomers from one another. An example of this 12 i s the work of Koopman et a l . on the isomers of N^P^Cl^NMe^^ and the isomers of N^P^Cl^NMe^-j (see also Figure 1-1). In doing this work, no allowance was made for atom p o l a r i z a t i o n effects but since such effects would be s i m i l a r for a l l of the isomers of a p a r t i c u l a r molecular formula, t h i s neglect probably does not inva l i d a t e t h e i r r e s u l t s . As an example of a d i f f e r e n t sort of problem for which dipole moment data was used i n an attempt to determine a structure, the case of (NPC^)^ may be considered. Several determinations of i t s dipole - 48 -33-36 moment have been made by d i f f e r e n t workers w i t h c o n f l i c t i n g r e s u l t s . 33 Krause whose determintion was the e a r l i e s t , found y = O.ul D from d i e l e c t r i c constant and s p e c i f i c volume measurements at v a r y i n g 34 temperatures. Corfield's estimate of u < 0.14 D was c a r r i e d out by measurement of the d i e l e c t r i c constant and d i e l e c t r i c a b s o r p t i o n of a solution of (NPCl^)^ ± n benzene at d i f f e r e n t frequencies i n the microwave region of the electromagnetic spectrum, a l l at a constant temperature. She then estimated the relaxation tine of the dipole p o l a r i z a t i o n and from t h i s datum estimated a maximum d i p o l e moment. Her method has the advantage of not being affected by atom p o l a r i z a t i o n . 35 The work of Allcock and Best was done by two methods, f i r s t a direct determination of the dipole moment of the pure l i q u i d using the Onsager equation f o r calculations, and second a determination of d i e l e c t r i c constants and r e f r a c t i v e indices of benzene solutions of known concentrations of the trimer to enable calculations of the dipole moment 36 by means of the Guggenheim equation. The result, of Kokoreva et a l . was calculated with the Eedestrand equation using measured d i e l e c t r i c constants and r e f r a c t i v e indices. As can be seen i n Table I I , variations i n temperature notwithstanding,, the agreement among the various workers i s not good. None made any allowance for possible atom p o l a r i z a t i o n 34 (except f o r C o r f i e l d whose method eliminates the need for such an allowance) and none appeared to consider t h i s necessary. At the same time, a l l but the Russian workers used t h e i r results to "prove" that (NPC^)^ i s almost planar i n s o l u t i o n , a r e s u l t j u s t i f i e d by the 38 infrared and Raman spectra but very questionable according to the dipole moment data alone. - 4 9 Table I I . Other Dipole Moment Results for Phosphonitrilic Compounds. Compound y(D) Method" References (NPC1 2) 3 0.51 a at -20°->95°C 33 (NPC1 2) 3 0.14 b 34 (NPC1-). 0.98 c at 120° 35 Z J 0.92 d at 70° 35 0.83 d at 30° 35 (NPC1 2) 3 0.93 e 36 (NPC1 2) 4 0.39 a at -20°+95°C 33 (NPC1 2) 4 0.20 b 34 (NPC1 2) 5 ' 0.47 a at -20°->95°C 33 (NPC1 2) 6 0.48 a at -20°->95°C 33 (NPC1 2) 7 0.54 a at -20°->95°C 33 N 7 P 6 C 1 9 0.72 a at -20°+95°C 33 (NPF 2) 3 0.10 b 34 (NPCOC.H,.),), 3.00 c at 120° 35 O J Z J 3.28 d at 70° 35 2.84 d at 30° 35 N 3P 3Cl 5(NC 4H g) 3.74 e 36 1,3-trans-N 3P 3C1 4(NC 4H 8) 2 3.28 e 36 1,3-cis-N 3P 3C1 4(NC 4H 8) 2 5.02 e 36 l,l,3-N 3P 3Cl 3(NC 4Hg) 3 4.36 e 36 1,3,5-trans-N 3P 3C1 3(NC 4H 8) 3 2.44 e 36 1,3,5-cis-N 3P 3C1 3(NC 4H 8) 3 5.64 e 36 1,1,3,5-cis N 3P 3CI 2(NC 4H 8) 4 ; 4.19 e 36 N 3P 3(NC 4H 8) 6 1.75 e 36 N 3P 3C1 5(NC 5H 1 0) 3.67 e 36 - 50 -Table I I (continued) Compound •(D) Method References 1,3-trans-N 3P 3C1 4(NC 5H 1 0) 2 1, 3-cis-N 3P 3C1 4(NC 5H 1 0) 2 1,1,3,5-cis-N 3 P 3 C 1 2 ( N C 5 H 1 0 ) 4 N 3P 3(NC 5H 1 0) 6 N 3P 3Cl 5(NC 4H gO) 1,3-trans-N 3P 3C1 A(NC AH 80) 2 1,3-cis-N 3P 3C1 4(NC 4H 80) 2 N 3P 3C1 5(NC 2H 4) N 3P 3C1 5(NMe 2) 1,3-trans-N 3P 3C1 4(NME 2) 2 1,3-cis-N 3P 3Cl 4(NMe 2) 2 1,3,5-trans-N 3P 3Cl 3(NMe 2) 3 N3P3C15(NHMe) l,l-N 3P 3Cl 4(NHMe) 2 1,3-cis-N 3P 3Cl 4(NHMe) 2 1,3-trans-N 3P 3Cl 4(NHMe) 2 1,3,5-cis-N 3 P 3 ( C 6 H 5 ) 3 B r 3 3.02 4.61 3.99 1.16 1.91 1.85 2.70 3.07 3.12 2.61 4.3 2.01 3.41 2.94 4.33 4.03 2.88 2.70 4.12 3.80 5.27 e e e e e f a i n benzene a i n C 6H 1 2 a i n benzene a i n C 6H 1 2 a i n benzene a i n C 6H 1 2 a i n benzene a i n C 6H 1 2 36 36 36 36 36 36 36 36 12 12 12 12 15 15 15 15 15 15 15 15 13 o - 51 -Table I I (continued) Compound p(D). Methods References 1,3,5-trans-N 3 P 3 ( C 6 H 5 ) 3 B r 3 N P (o-phenylenedioxy), 3 3 1,5-cis-V 4 ( C 6 H 5 W 2 1,5-trans-W C 6 H 5 W 2 1,3-cis-V 3 V W 2 1,3-trans-N3 P3 F4 ( C6 H5>2 1,3-cis-2.36 1.9 3.7 0.2 4.3 2.5 4.4 g d at 70° not stated not stated 13 16 37 37 14 14 14 Methodsused were as follows: a) Smith modification of Guggenheim method b) d i e l e c t r i c constant and d i e l e c t r i c absorption c) Onsager equation, using pure melt d) Guggenheim method e) Hedestrand method f) Onsager and Bottcher method g) Halverstadt and Kumler method. - 52 -Some dipole moment work has a l s o been done on other phosphonitrilic compounds as outlined i n Table I I . As f a r as assignment of s t r u c t u r a l isomers to d i f f e r e n t compounds of the same molecular formula, such as N^P^X^Y^, i s concerned, the non-allowance f o r atom p o l a r i z a t i o n i s probably not too s e r i o u s a problem, at l e a s t not s u f f i c i e n t l y s e r i o u s so as to invalidate any conclusions drawn. For the three isomers of the formula N„P„X,Y„, the 3 J> 4 2 atom polarizations w i l l be s i m i l a r and may be treated as a constant factor as long as only the three such compounds are considered together. When, however, a series of compounds such as N„P»X Y. , m = 0-6 or 3 3m 6-m (NPX„) , n = 3,4... must be considered, then some decision must be Z n made about the best way to deal with atom p o l a r i z a t i o n . Phosphonitrilic halides are known to be f l e x i b l e molecules; evidence for t h i s coming from infrared and Raman spectra."^ I t i s therefore reasonable that these molecules should have high atom polarizations and that atom p o l a r i z a t i o n should be roughly proportional to the number of repeating groups i n the polymer. The l i n e a r i t y of the graph of p o l a r i z a t i o n vs. ring size for the phosphonitrilic fluorides (Figure 3-4) i s another piece of evidence that suggest the existence of a high atom p o l a r i z a t i o n . However, before t h i s explanation i s accepted, other possible explanations for the high d i s t o r t i o n p o l a r i z a -t i o n of these compounds must be shown to be unacceptable. A high d i s t o r t i o n p o l a r i z a t i o n for a compound or group of compounds might be explained i n one of the three following ways. The f i r s t i s that the compounds might be e a s i l y bent by thermal c o l l i s i o n s and might remain bent long enough to orient i n the e l e c t r i c f i e l d , producing a dipole - 53 -moment. This does not explain the proportionality c f the p o l a r i z a t i o : to ring s i z e . Also i f a ca l c u l a t i o n of the period of v i b r a t i o n of this thermal bending were carried out, for example i n the manner of 29 Finn, Hampson and Sutton, the period of o s c i l l a t i o n i s found to be much too small. The trimeric ring i s treated as a s e t of t h r e e one-dimensional o s c i l l a t o r s . The group moment for the PClj group i s of —18 the order of 2 x 10 esu-cm and for the trimeric chloride the 'polarization i s 17.6 cc. Using equation V = 127rNy2/9Pn o -13 2 the result obtained i s 5.7 x 10 ergs/radian . This would lead to -12' -13 vibrations with a period of o s c i l l a t i o n of the order of 10 -10 seconds whereas for orientation effects to be s i g n i f i c a n t , a period of o s c i l l a t i o n of the order of 10 ^-10 1 1 seconds i s required. This means that thermal bending of the molecules i s not an adequate explana-t i o n of the high d i s t o r t i o n p o l a r i z a t i o n of phosphonitrilic halides. A second possible explanation i s a lack of symmetry of the r i n g , but this can be very e a s i l y eliminated. From X-ray d i f f r a c t i o n studies of some homogeneously substituted phosphonitrilic derivatives, i t i s found that a l l the P-N bond lengths i n a p a r t i c u l a r compound are the same. This i s also true of a l l the P-X bond lengths i n any one 42-49 compound. Although a variety of configurations, many with non-zero dipole moments, are i n p r i n c i p l e available to the phosphonitrilic derivatives of the larger r i n g s i z e s , i n practice X-ray studies show that the configuration of highest symmetry, which usually has a zero dipole moment, i s the one normally adopted. This explanation also has - 54 -the disadvantage that i t does not explain the l i n e a r i t y of the po l a r i z a -tion vs. ring size relationship. A t h i r d possible explanation i s some sort of solvent e f f e c t but th i s can be eliminated for two reasons. F i r s t there are data available for phosphonitrilic chlorides for the pure l i q u i d , f o r benzene as solvent"^ for d e c a l i n 3 3 and for cyclohexane, and the results obtained show greater discrepancies among diffe r e n t workers using the same solvent than the discrepancies among different workers using d i f f e r e n t solvents. Preliminary work i n connection with t h i s thesis was also carried out on phospho n i t r i l i c chloride trimer using carbon tetrachloride as the solvent and the results obtained were su b s t a n t i a l l y the same as those obtained using cyclohexane as solvent. The i n a b i l i t y of a l l the other proposed explanations to account for the d i s t o r t i o n p olarizations of the phosphonitrilic halides therefore leaves only one source f o r t h i s p o l a r i z a t i o n and that i s atom p o l a r i z a t i o n . Now i f atom p o l a r i z a t i o n i s the cause of the d i s t o r t i o n p o l a r i z a t i o n of the f l u o r i d e s , then i t i s l i k e l y also to be the cause of the high p o l a r i z a t i o n of the phosphonitrilic chlorides and again should be roughly proportional to the number of monomer units. This conclusion i s supported by the data obtained i n t h i s work. For the phosphonitrilic chloride trimer and tetramer there are published data for the fa r infrared region of the spectrum 3^'^ part of which are shown i n Table III. The existence of vibrations i n the far infrared i s evidence to support the existence of high atom po l a r i z a t i o n s , as i s the general f l e x i b i l i t y of the molecules, but some mathematical backing of thi s hypothesis i s desirable. The basic equation used by Coop and Sutton 24 - 55 -Table I I I . Far Infrared Results for N.P.C1, and N.P.C1 0? 8' 4 1 3 3 6 4 4 8 Nujol mull c c ± ^ solution (NPC1 ) 140 w 140w . 6 162 vw 179 w 189 w 188 brd,w 208 vw Nujol mull CCl^ solution C r y s t a l l i n e f i l m (NPC1_). 56 vw 2 4 141 vw 141 w 140 w 150 w 158 w 156 w 167 w 176 m 172 vw 189 w 187 m 197 vw Pa = 4TTNU2/9V (4-1) o may be used as a s t a r t i n g point. This equation applies to the case of one one-dimensional o s c i l l a t o r . For the phosphonitrilic halides there are n o s c i l l a t o r s each of which i s a PX 2 group. The assumption that the PX 2 groups are the o s c i l l a t o r s i s made because the low frequency v i b r a t i o n a l modes of•phosphonitrilic chlorides have been assigned as PC1 2 wagging and tor s i o n a l m o d e s . F o r example, f o r (NPC1 2) 3 with three o s c i l l a t i n g groups, equation (4-1) must be modified to P\ = 36TTNy 2/9V (4-2) 3L O - 56 -This equation s t i l l contains two unknowns (N i s Avogadro's number). u and V . The procedure here i s to estimate y, the moment of the — -o . — PCI., group, and calculate V from the measured value of P . The moment of the PC1 2 group i s expected to be of the order of 1-2 Debye units. Using the value for y_ of 2.0 Debye u n i t s , a value for V , the -12 2 force constant, i s 1.7 x 10 erg/radian . A force constant of this magnitude can be attributed to one or more vibrations i n the region of 150-200 cm ^. Infrared active vibrations i n t h i s region have been recorded (see Table I I I ) and t h i s evidence strengthens the hypothesis of the existence of high atom p o l a r i z a t i o n f o r phosphonitrilic compounds. Orientation Effects i n Phosphonitrilic Chloride-Fluorides The acceptance of the above explanation of atom p o l a r i z a t i o n and i t s effect on phosphonitrilic compounds implies two things, f i r s t that i t i s possible to calculate a p o l a r i z a t i o n per PX^ group for the chlorides and the fluorides and second, that such data could be used to help distinguish between geminally substituted isomers, for example those shown i n Figure 1-3. In Table IV are shown the polarizations per PX 2 group calculated from some of the p h o s p h o n i t r i l i c halide results given i n Chapter I I I . I f a vector analysis of the geminal compounds N_P_F.C1. and N-P„F.Cln 3 3 2 4 3 3 4 2 i s carried out, i t can be shown that they should have the same dipole moments. The r i n g skeleton i s almost planar so that the NPN i n t e r n a l angles are 120°. The PX 2 group moments may be treated as vectors bisecting the NPN external angles i n the plane of the r i n g , and can be thought of as shown i n Figure 4-1. - 57 -Table IV. Polarization per Monomer Unit Calculated for Some Phospho-n i t r i l i c Compounds. Compound n Distortion polarization (cc) Polarization per PX0 group (cc) (NPC12)3 3 17.6 5.9 (NPC12)4 4 31.3 7.8 (NPF2) 3 3 4.4 1.5 (NPF2)4 4 13.4 3.4 (NPF2) 5 5 17.2 3.4 (NPF2)6 6 21.9 3.6 Figure 4-1 Dipole vector diagram for NJPJ F A and N 3P 3F 4Cl z - 58 -Now for N 3P 3F 2C1 4, y V e r t ( P C l 2 ) = 2u(PCl 2)cos60 c = 2y(PCl 2) • 1/2 = U(PCI2) y ( N 3 P 3 F 2 C l 4 ) = |u(PF 2) - y ( P C l 2 ) | For the other compound, N 3P 3F 4C1 2 > u V e r t ( P F 2 ) = 2y(PF2)cos60° = 2y(PF 2) • 1/2 = y(PF 2) y ( N 3 P 3 F 4 C l 2 ) = |y(PCl 2) - y(PF 2) However the two compounds have d i f f e r e n t measured d i s t o r t i o n p o l a r i z a t i o n s , for the d i f l u o r i d e the value i s 30.1 cc. and for the te t r a f l u o r i d e the value i s 26.6 cc. I f the atom p o l a r i z a t i o n i s eliminated from each compound, then the residual p o l a r i z a t i o n w i l l be due to the dipole moment of the compound. Using the symbol P for orientation -o po l a r i z a t i o n as before, then P (N_P_F,C1.) = P(N_P.F„C1.) - P (PF ) - 2P ( P C I , ) o 3 3 2 4 3 3 2 4 a I a I = 30.1 cc - 1.5 cc - 2(5.9 cc) = 16.8 cc . - 59 -F (N P F CI.) = P(N„P_F.C19) - 2P (PF.) - P (PC1„) o 3 3 4 z 3 3 4 2 a I a 2 = 26.6 cc - 2(1.5 cc) - 5.9 cc = 17.7 cc The dipole moments for the molecules may be calculated from the equation -18 z^ — y = 0.01281 x 10 /PT (4-3) For the d i f l u o r i d e , y_ = 0.91 D and for the tet r a f l u o r i d e _y_ = 0.93 D. Within the usual experimental error of + 0.05 D these numbers are the same. For the tetrameric mixed chloride-fluorides studied, a s l i g h t l y d i f f e r e n t problem must be discussed. I t i s known that substitution of chlorine by fluorine i n pho s p h o n i t r i l i c chlorides proceeds i n a geminal manner,^ that i s after the f i r s t chlorine atom i s replaced by a f l u o r i n e , the second chlorine replaced w i l l be attached to the same phosphorus atom, i n other words the replacement sequence i s PC1 2 -s- PC1F -> PF 2 Therefore, when f l u o r i n a t i n g a phosphonitrilic chloride i t i s known that a l l the compounds with an even number of fluorines are geminal. For the compounds N.P.F.Cl, there are two p o s s i b i l i t i e s as shown i n 4 4 4 4 Figure 1-3 i n Chapter I; the compound may be either the 1,1,3,3-isomer 19 or the 1,1,5,5-isomer. The F NMR spectra for compounds of this type - 60 -are very complex and are not amenable to a f i r s t order treatment, therefore NMR cannot be used as a way of distinguishing one isomer from the other. By examining the NMR spectra of the compounds, N^P^F^Cl^ and N^P^F^Cl,. prepared i n the same reaction, Emsley and Paddock reached the conclusion that N.P.F.Cl, was the 1,1,3,3-isomer. From 4 4 4 4 dipole moment data i t should be possible to d i f f e r e n t i a t e the two p o s s i b i l i t i e s . The atom p o l a r i z a t i o n for the N^P^F^Cl^ molecule may be determined i n the same way as was done above for the trimeric compounds and then compared to the measured d i s t o r t i o n p o l a r i z a t i o n . I f they are equal, then the orientation p o l a r i z a t i o n of the compound i s zero, the compound has a zero dipole moment and therefore must be the 1,1,5,5-isomer. I f on the other hand the calculated and measured po l a r i z a t i o n values are unequal, then the compound has a dipole moment and i s the 1,1,3,3-isOmer. The cal c u l a t i o n i s as follows. Po(N.P.F.Cl.) = PCN.P.F.Cl.) - 2Pa(PF„) - 2Pa(PCl 0) 4 4 4 4 4 4 4 4 2. 2 = 43.5 - 2(3.4) - 2(7.8) = 43.5 - (6.8 + 15.6) = 21.1 cc The values of Pa (PF 2) and Pa(PCl 2) were chosen as the ones calculated from the tetrameric flu o r i d e and chloride respectively i n order to eliminate any possible ring size e f f e c t . The result of the above cal c u l a t i o n supports strongly the conclusion that the N^P^F^Cl^ compound whose po l a r i z a t i o n was measured i s the 1,1,3,3-isomer. - 61 -A s i m i l a r analysis f o r the pentameric compound N-P.F.Cl. cannot 5 _> o 4 be completed because changes i n the configuration of the pentameric ring could mask changes i n orientation of substituents. For the two pentameric phosphonitrilic halides for which X-ray d i f f r a c t i o n studies have been r e p o r t e d , 4 7 ' 4 8 a c a l c u l a t i o n by Hartsuiker and Wagner 4 8 shows that N,.P5C110 can t h e o r e t i c a l l y adopt the "heart-shaped" configuration adopted by N.P' Br,„ and that N_P_Br.„ could t h e o r e t i c a l l y j j 1(J 5 J 10 take the shape adopted by N P C I ^ Q , which i s shown i n Figure 4-2. The structure for N^P^Br^Q i s shown i n Figure 4-3. The Figure 4-2. .. (NPClg^ molecular structure Figure 4-3 (NPBr^ molecular structure X-ray studies showed that each molecule only adopted i t s own configura-t i o n i n c r y s t a l s . Without a knowledge of the configuration of the ring for N P F and for N.P-F^Cl., an analysis to determine which of two _> -> -LU D i) O 4 possible isomers of the N P F CI. was measured i s impossible. - 62 -Conclusions and Suggestions for Further Work In conclusion, two results have been obtained from t h i s work. F i r s t i t has been shown that Guggenheim's approximation that atom p o l a r i z a t i o n i s proportional to molecular volume does not apply to the phos p h o n i t r i l i c halides. For the phosphonitrilic chlorides and fl u o r i d e s , atom p o l a r i z a t i o n i s a s i g n i f i c a n t factor i n the t o t a l d i s t o r t i o n p o l a r i z a t i o n and proper allowance must be made for i t . Second, evidence has been given to strongly support the hypothesis that the compound N.P.F.Cl. made by the reaction of N.P.C10 and KSO„F under heat and 4 4 4 4 4 4 8 2 reduced pressure"*"*" i s the 1,1,3,3-isomer. For further work, a l i n e of approach that could prove il l u m i n a t i n g i s to obtain the far infrared spectra of the phosphonitrilic fluorides and the higher phosphonitrilic chlorides. Force constants obtained from an analysis of such spectra could be used to v e r i f y and predict . atom polarizations of these and related compounds. - 63 -Appendix A There are a number of d i f f e r e n t systems of nomenclature for the compounds referred to i n th i s thesis as c y c l i c phosphonitriles. The names "phosphonitrilic" or "phosphcmitrile" are the oldest, and for the more simply substituted compounds have the advantages of being short and readily comprehensible. Two other nomenclature systems e x i s t , 52 the IUPAC system and the system used by such authors as Allcock. The IUPAC system would name N„P„F, as 2,2,4,4,6,6-hexafluoro-2,2,4,4,6,6-3 3 o hexahydro-1,3,5,2,4,6-triazatriphosphorine. This system has gained l i t t l e popularity among workers i n the f i e l d . The other system denotes compounds containing the s t r u c t u r a l unit as phosphazenes, where the phosphonitrilics are'considered to be polymers and derivatives of the hypothetical compound phosphazene, H3P=NH. A rin g system i s given the p r e f i x "cyclo" and the number of monomer units i n the ring i s referred to by one of the prefixes " t r i " , " t e t r a " and so on as appropriate. The convention used for numbering the ring atoms i s to s t a r t the numbering at phosphorus, which then gives the substituents the lowest possible numbers. By this convention, N„P„F^ i s c a l l e d 1,1,3,3,5,5-hexafluorocyclotriphosphazene. The older 3 3 o naming system was used i n t h i s thesis because of i t s wide use i n the l i t e r a t u r e and because of i t s s i m p l i c i t y . (-P=N) - 64 -Appendix B At t h i s time, i n s c i e n t i f i c l i t e r a t u r e there are s t i l l several systems of units used to l a b e l physical quantities. Though journals i n physics and chemistry no longer use the B r i t i s h Imperial system of u n i t s , there are other systems s t i l l i n use based on metric measurements. For dipole moments and other properties that may be classed under the general heading of e l e c t r i c a l , the system used i n the past was the non-rationalized three-quantity centimeter-gram-second system. I t i s now recommended that a l l physical and chemical data be expressed i n the r a t i o n a l i z e d four-quantity meter-kilogram-second-ampere system, which i s referred to as Systeme Internationale or SI for short. To be thorough, t h i s requires rederivingmost equations, but i f such derivations are carried out the old and new equations can be compared and conversion factors for derived quantities can be calculated. This has been done 53 for dipole moments by Hoppe. For the p o l a r i z a t i o n , Hoppe obtains P = (£-1) M = % , N u 2 (e+2) ' d 3e 9 e kT o o where e i s the p e r m i t t i v i t y of a vacuum and e i s the r e l a t i v e -o -p e r m i t t i v i t y of the d i e l e c t r i c . The SI units for some quantities important i n dipole moment calculations are: u = dipole moment: coulomb-meter 3 -1 P = p o l a r i z a t i o n : m -mole £ q = p e r m i t t i v i t y of a vacuum: farad-meter 1 e = r e l a t i v e p e r m i t t i v i t y of d i e l e c t r i c : dimensionless 2 a = p o l a r i z a b i l i t y : farad-meter - 65 -The conversion factor for the dipole moment i s -30 1 Debye = 3.335640 x 10 coulomb-meter. No attempt has been made i n t h i s thesis to work, i n SI units, i n order to f a c i l i t a t e comparison with the older l i t e r a t u r e . - 66 -REFERENCES 1. N.L. Paddock and H.T. Searle, Adv. Inorg. Chem. Radiochem. , 1_, 347 (1959). 2. N.L. Paddock, Quart. Rev. (London), 18, 168 (1964). 3. H.R. Allcock, Chem. 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Vos, Acta Crystallogr., 15, 539 (1962). 47. A.W. Schlueter and R.A. Jacobson, J. Chem. Soc A, 2317 (1968). 48. J.G. Hartsuiker and A.J. Wagner, J.C.S. Dalton, 1069 (1972). 49. A.J. Wagner and A. Vos, Acta Crystal l o g r . , B24, 1423 (1968). 50. J . Emsley, J. Chem. Soc A, 5005 (1970). 51. J. Emsley and N.L. Paddock, J. Chem. Soc. A., 2590 (1968). 52. H.R. Allcock, Phosphorus-Nitrogen Compounds, Academic Press, New York 1972. 53. J.L. Hoppe, Educ. Chem., % 138 (1972). 

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