Thermal, purity, and solubility properties of cholesteryl esters and their thermal behavior in lipid-water systems.

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1 University f Massachusetts Amherst SchlarWrks@UMass Amherst Dctral Dissertatins February 2014 Dissertatins and Theses Thermal, purity, and slubility prperties f chlesteryl esters and their thermal behavir in lipid-water systems. Gershn Jerry Davis University f Massachusetts Amherst Fllw this and additinal wrks at: Recmmended Citatin Davis, Gershn Jerry, "Thermal, purity, and slubility prperties f chlesteryl esters and their thermal behavir in lipid-water systems." (1969). Dctral Dissertatins February This pen Access Dissertatin is brught t yu fr free and pen access by the Dissertatins and Theses at SchlarWrks@UMass Amherst. It has been accepted fr inclusin in Dctral Dissertatins February 2014 by an authrized administratr f SchlarWrks@UMass Amherst. Fr mre infrmatin, please cntact schlarwrks@library.umass.edu.

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3 TERMAL, PURITY, AND SLUBILITY PRPERTIES F CLESTERYL ESTERS AND TEIR TERMAL BEAVIR IN LIPID-WATER SYSTEMS A Dissertatin Presented by Gershn Jerry Davis Submitted t the Graduate Schl f the University f Massachusetts in partial fulfillment f the requirements fr the degree DCTR F PILSPY December 1969 Majr Subject: Plymer Science and Engineering

4 TERMAL, PURITY, AND SLUBILITY PRPERTIES F CLESTERYL ESTERS AND TEIR TERMAL BEAVIR IN LIPID-WATER SYSTEMS A Dissertatin Presented By Gershn Jerry Davis Apprved as t style and cntent by: {) C -J" (Chairman f Cmmittee) (ead f Department) (Member) (Member) December 1969

5 iii (c) Gershn Jerry Davis 1970 All Rights Reserved

6 T My Family iv

7 ACKNWLEDGEMENT The authr wishes t thank Prfessr Rger S. Prter fr his encuragement and assistance thrughut the perid f this investigatin. Grateful acknwledgement is als due Prfessrs Frank Karasz and Sidney Siggia as members f the Thesis Cmmittee. Acknwledgement fr financial assistance is made t the Natinal Institutes f ealth. A special nte f appreciatin is made t Sphia Kinney wh in typing this thesis had the burden f reading the authr's handwriting

8 TABLE F NTENTS CAPTER I INTRDUCTIN Interest f Spnsr Characterizatin f Chlesteryl Esters Ternary Systems Cntaining Chlesteryl Esters Temperature Calibratin f the DSC CAPTER II References fr Chapter I APPLICATIN F TE DIFFERENTIAL SCANNING CALRIMETER T PURITY MEASUREMENTS Intrductin Functin f the Electrical Lps in the DSC Analysis f the DSC Recrder Trace New Purity Methd Prcedure Discussin f Results frm the New Purity Methd References fr Chapter II CAPTER III EVALUATIN F TERMAL TRANSITINS IN SME CLESTERYL ESTERS F SATURATED ALIPATIC ACIDS Intrductin Experimental Results A. Chlesteryl Esters B. Instrumentatin

9 A. Chlesterl B. Chlesteryl Frmate C. Chlesteryl Acetate D. Chlesteryl Prpinate E. Chlesteryl Nnanate F. Chlesteryl Undecanate G. Chlesteryl Laurate. Chlesteryl Tridecanate I. Chlesteryl Myristate J. Chlesteryl Pentadecanate K. Chlesteryl Palmitate L. Chlesteryl eptadecanate M. Chlesteryl Stearate N. Chlesteryl Nnadecanate 0. Chlesteryl Eicsanate Discussin f Results Cnclusins References fr Chapter III CAPTER IV SME SLUBILITY CARACTERISTICS F CLESTERYL ESTERS Intrductin Develpment f Recrys tallizatin Prcedure A. Thery B. Experiment Purificatin Prcedure

10 Purificatin Results A. Chlesteryl Laurate B. Chlesteryl Benzate C. ther Chlesteryl Esters f Aliphatic Acids 74 Cnclusins References fr Chapter IV 75 CAPTER V TERMAL STUDIES N LIPID-WATER SYSTEMS BY DIFFERENTIAL SCANNING CALRIMETRY WIT REFERENCE T ATERSCLERSIS 84 Intrductin g^ Experimental Prcedure 87 Results gg A. Dipalmityl-L-ct-Lecithin in Aqueus Systems 89 B. Bvine Phsphlipids in Aqueus Systems 91 Discussin f Results 93 A. Significance t Membrane Frmatin 93 B. Significance t Athersclersis 97 References fr Chapter V 98 CAPTER VI TERMAL TRANSITINS F CLESTERYL ESTERS F C R ALIPATIC 1B ACIDS 108 Intrductin 108 Experimental 108 Results 109 References fr Chapter VI 110

11 ix CAPTER VII FUTURE WRK Thermal Studies n ther Lipid-Water Systems 113 Binary Systems f Chlesteryl Esters 113 Surface Prperties f Lipid Drplets and Bilayers 114 Chlesteryl Esters f Saturated Aliphatic Acid Series 115 "C-Crystallizatin" in Binary Systems f Chlesteryl Esters n6 References fr Chapter VII I17

12 TABLE INDEX CAPTER II 1. Naphthalene - Thinaphthene eats f Melting Summary f Benzic Acid and Naphthalene Purity Results by New Methd Purity Prcedure Summary f Naphthalene and p-nitrtluene Purity Results by New Methd Purity Prcedure Summary f Benzic Acid and Naphthalene Purity Results by Perkin-Elmer Purity Prcedure 27 CAPTER III 1. Transitin Temperatures fr Chlesteryl Myristate Chlesteryl Ester Transitin Values Transitin Temperatures fr Chlesteryl Laurate 57 CAPTER IV 1. A Cmparisn f Chlesteryl Ester Transitin Values 78 CAPTER V 1. Thermal Transitins f Dipalmityl-L-a-Lecithin Water Systems Cntaining Chlesteric Cmpunds Thermal Transitins f Sphingmyelin (Bvine) - Water Systems Cntaining Chlesteric Cmpunds 103 CAPTER VI 1. Chlesteryl Esters f C^s Aliphatic Acids Temperatures and eats f Transitin 111

13 xi FIGURE INDEX CAPTER I 1. Temperature Calibratin Curve fr DSC 2- r s:rs ' crrectin Factr f r :t": g av^ 8 CAPTER II 1. Naphthalene Melting Pint Depressin 2. Chlesteryl Myristate Melting Pint Depressin 3. Chlesteryl Prpinate, Crystal-Mesphase Transitin 4. Chlesteryl Prpinate Purity Determinatin - 5. Benzic Acid Melting Curve 6. Benzic Acid Purity Determinatin CAPTER III 1. Aliphatic Esters f Chlesterl, Ttal Transitin Entrpies 2. Aliphatic Esters f Chlesterl, Smectic-Chlesteric Transitin, Transitin Entrpies Aliphatic Esters f Chlesterl, Chlesteric- Istrpic Liquid Transitin, Transitin Entrpies Aliphatic Esters f Chlesterl, Temperatures fr Majr Transitin 5. Aliphatic Esters f Chlesterl, Temperatures f Smectic-Chlesteric Transitin Aliphatic Esters f Chlesterl, Temperatures fr Chlesteric-Istrpic Liquid Transitin 63 CAPTER IV 1. Chlesteryl leate DSC Traces Chlesteryl Laurate DSC Traces 82

14 xii 3. Chlesteryl Benzate DSC Traces CAPTER V Dipalmityl-L-a-Lecithin, Chlesteric Cmpund, Transitin Entrpies (In Water) 2. DSC Cling Curves f Dipalmityl-L-a-Lecithin- Water Systems Cntaining Chlesteric Cmpunds 3. Sphingmyelin (Bvine)-Chlesteric Cmpund, Transitin Entrpies (In Water) CAPTER VI 1. Chlesteryl Esters f C 18 Aliphatic Acid s, Temperatures f Transitin vs. Unsaturatin 112

15 SUMMARY xlii PREFACE This investigatin cnsisted f s thermdynamic evaluatin f Phase behavir and structure in systems Invlving chlesterl and its esters. The gal was t develp thermdynamic data and structural infrmatin n bilgical systems related t membrane rganizatin and specifically t the nature f athersclertic plaques which lead t henrt disease. The experimentatin was divided int fur majr areas f research: quantitative determinatin f ester purity, measurement f ester heats and temperatures f transitin, characterizatin f slubility prperties fr chlestery] esters, and studies n ternary phsphlipid-chlesteryl ester-water systems. Each subject wilt be summarized under its wn heading. PURITY PRCEDURE A new methd is presented fr the calculatin f the purity f rganic, nn-plymeric samples frm Differential Scanning Calrimeter (DSC-1B) recrder melting traces. It is based upn a prbable DSC mechanism f pwer transfer and measurement. Ambiguities in the ne previus methd ffered by Perkin-Elmer, the DSC manufacturer, are reduced. The entire DSC recrder trace is emplyed rather than nly the initial prtin f the curve. By applicatin f this infrmatin, a rapid and meaningful purity determinatin has been develped frm infrmatin n a single DSC trace fr samples which range frm 95 t 99.9% purity. An accuracy within 15% f the actual impurity value can b anticipated.

16 1 XIV CLESTERYL ESTERS F SATURATED ALIPATIC ACIDS The heats and temperatures f transitin fr furteen chlesteryl esters f saturated aliphatic acids have been evaluated using a Differential Scanning Calrimeter, DSC-1B. The transitin data btained in this study indicated that the lwest mlecular weight saturated aliphatic esters f chlesterl t shw mesphase behavir was the prpinate, nt the frmate r acetate. Less pure samples may be supercled in the melt s that mesphases may be bserved fr the tw lwest mlecular weight esters. New transitin data fr the dd esters f chlesterl frm undecanate t nnadecanate have als been btained. Chlesteryl eicsanate was examined and fund t have nly ne transitin, bth n heating and cling, which may indicate that the highest members f this series, when relatively pure, d nt display mesphase behavir. SME SLUBILITY CARACTERISTICS F CLESTERYL ESTERS In this study f sme slubility characteristics f chlesteryl esters, n-pentanl is shwn t be a mre effective slvent than ethanl in which t remve impurities and/r crystalline structural defects frm chlesteryl esters. These impurities can cause additinal transitins n initial heating. n-pentanl is shwn t be a regular slvent fr chlesteryl esters whereas ethanl is nt. This culd be a majr reasn why n-pentanl is better able t discriminate between cmpund and impurity than ethanl. Cntrary t previus reprts, after crystallizatin frm n-pentanl, in cntrast t ethanl, chlesteryl acetate and chlesteryl laurate have nly ne transitin n first heating. A

17 XV detailed study f chlesteryl benzate recrystalli 2e d frm n - pentanl has cnfined that there are tw transitins, ne at C, the secnd at C. The heats f transitin are fund t be 14.7 cal/gm and 0.26 cal/gm, respectively. TERMAL STUDIES N LIP ID-WATER SYSTEMS Lecithin and sphingmyelin rganize in the presence f water int bimlecular layers separated by water. This membrane-like rganizatin can be fllwed thermally with a Differential Scanning Calrimeter. T these binary systems were added either chlesterl r a C lg fatty acid ester f chlesterl - stearate, leate, r linleate. The unsaturated esters are abundantly present in athersclertic plaques. The additin f chlesteryl esters reduces the entrpy f transitin in the rder linleate > leate > stearate. This effectiveness in reducing the entrpy f transitin is surmized t be directly prprtinal t the participatin f the chlesteryl ester in the membrane structure. All transitin temperatures n cling were within C, quite clse t human envirnmental temperatures

18 f the crnary arteries, with r withut cmplicatins 1. CAPTER I INTRDUCTIN Interest f Spnsr This wrk was supprted by the U.S. Natinal Institutes f ealth. In the United States, disrders f the heart caused apprximately ne- third f all deaths in Crnary heart disease accunts fr 80% f all cardiac deaths 1. The term crnary disease is a general designatin fr all frms f mycardial (heart muscle) disrders resulting frm insufficient crnary bld flw. In 99% f the cases, such insufficiency is due t athersclertic narrwing Athersclertic narrwing is prduced by athermatus plaques cnsisting f fatty-fibrus depsits within the intima f the arterial wall which prjects int the lumen f the vessel 1. Chlesterl, bth free and esterified, is the majr lipid cmpnent f plaques in the human arta intima in all stages f the develpment f athersclersis. The surce f this chlesterl is ne f the utstanding prblems in 2 athersclersis research. Characterizatin f the physical prperties f chlesteryl esters and related systems may prvide infrmatin imprtant t the reslutin f this prblem. Characterizatin f Chlesteryl Esters The first f tw majr areas f research pursued in this wrk was the measurement f thermal transitins f individual chlesteryl esters n a Differential Scanning Calrimeter, Perkin-Elmer Crpratin

19 2 Mdel DSC-1B. wever, heats and temperatures f transitin increase as sample purity increases. As a result f this fact, suitable recrys tallizatin techniques were required t purify the chlesteryl esters and a reliable methd f purity evaluatin had t be devised. This led t experimentatin n the fllwing three prblems: 1. Develpment f an imprved prcedure fr determining the amunt f impurity in simple, nn-plymeric, rganic cmpunds. 2. Measurement f the transitin temperatures and heats exhibited by chlesteryl esters f saturated aliphatic acids frm frmate thrugh eicsanate. 3. Determinatin f sme slubility characteristics f chlesteryl esters. There are three chapters in the thesis which describe the results and cnclusins derived frm experiments in each f these three prblem areas. The fllwing technical articles have been written frm this infrmatin: Chapter II: G. J. Davis and R. S. Prter, "Applicatin f the Differential Scanning Calrimeter t Purity Measurements," accepted fr publicatin in the Jurnal f Thermal Analysis. Chapter III: G. J. Davis, R. S. Prter and E. M. Barrall II, "Evaluatin f Thermal Transitins in Sme Chlesteryl Esters f Saturated Aliphatic Acids," accepted fr publicatin in Mlecular Crystals and Liquid Crystals. Chapter IV: G. J. Davis and R. S. Prter, "Sme Slubility Characteristics f Chlesteryl Esters," accepted fr publicatin in Mlecular Crystals and Liquid Crystals.

20 Ternary Systems Cntaining Chlesteryl Esters The applicatin f Differential Scanning Calrimetry t prblems in athersclersis is a relatively unexplred field f research. The basic idea here was t study the thermal prperties f phsphlipid-water systems cntaining chlesteryl esters. The cmpunds chsen fr this study (lecithin, sphingmyelin, and saturated and unsaturated C 18 fatty acid esters f chlesterl) are the majr cmpnents in the abnrmal human plasma lipid assciated with athersclersis 3. Previus DSC studies have been made n lipid-water systems in which ne f the cmpnents was chlesterl in rder t shed light n the pssible rle f chlesterl in bilgical membranes 4 ther experimenters have studied the transitin temperature (41 C) fr dipalmityl lecithin, a majr lipid in the lung membrane, in water by differential thermal analysis and discussed the implicatin f the transitin being clse t bdy temperature 5. The furth chapter fllwing the Intrductin presents the results and cnclusins frm DSC studies f lipid-water systems cntaining chlesteryl esters. In this chapter, the relatinship between athersclersis and the frmatin f bilgical membranes is suggested A technical article has been written frm Chapter V by G. J. Davis and R. S. Prter entitled "Thermal Studies n Lipid-Water Systems by Differential Scanning Calrimetry with Reference t Athersclersis." A revised manuscript has been prepared n this subject fr jurnal submissin.

21 In Chapter VI is presented the heats and temperatures f transitin f the individual chlesteryl esters f aliphatic acids. The bilgical imprtance f these esters has been emphasized in Chapter V. Temperature Calibratin f the DSC The DSC, in cmmn with ther thermmetric devices, requires calibratin t determine the crrespndence f prgram temperature t true temperature 6. This crrespndence is btained by setting a ten-turn ptentimeter called the Average Temperature Calibratin Dial. The mst cnvenient methd is t leave this dial in a fixed psitin and t measure the prgram temperature fr a number f highly pure cmpunds whse temperature is knwn accurately thrugh anther methd. This temperature determinatin requires an adjustment prcedure, described by the Perkin-Elmer Crpratin 6 fr a % pure indium sample. The difference between the true melt temperature and the prgram temperature is the crrectin t the prgram temperature. A plt f crrectin t the prgram temperature 6 versus prgram temperature gives a parablic curve which can be applied t crrect the prgram temperature fr samples whse true melt temperature is nt knwn. This crrectin curve shuld be applied t nly thse heating rates fr which it was devised. A majr disadvantage f the Perkin-Elmer prcedure is that by fixing the Average Temperature Calibratin Dial at ne setting, temperature crrectins as large as 5 C are nt uncmmn. An alternate

22 Prcedure utilized by this experimenter was prepare a plt f sample temperature versus Average Temperature Dial setting, sh wn in Figure 1-1, by determining the accurate setting t give the t rue -Iting pint f a number f relatively pure cmpunds f knwn mel ".t temperature. These cmpunds were fur Fisher triple pint standards, adipic acid, benzic acid, naphthalene, and p-nitrtluene. Ind lum frm Perkin-Elmer and stearic acid and ctadecane frm Applied Sci ence Labratries were als used. In Figure 1-1, the lwer scale ref ers t a secnd range n the DSC, especially useful fr lwer temperature determinatins, which subtracts 100 C frm the prgram temperature reading. The values pltted in Figure 1-1 are applicable fr bth the 1.25 and 2.5 C/min. heating rate. A secnd plt, Figure 1-2, f temperature change per 100 average temperature dial units versus specific prgram temperature (infrmatin prvided frm the Perkin- Elmer instructin manual) allws fr the fllwing crrectin prcedures when the Average Temperature Dial setting des nt match the prgram temperature in Figure 1-1: 1. Find in Figure 1-1 the prper Average Temperature Dial setting fr the particular prgram temperature under cnsideratin. 2. Subtract the Average Temperature Dial Setting used in the experiment frm that determined in (1) 3. Multiply this difference by the temperature change/100 Average Temperature Dial Units fr this prgram temperature fund in Figure 1-2.

23 4. Add this value t the prgram temperature t btain the true temperature Fr this smewhat mre cmplex methd, the temperature crrectin is generally less than 1 C. References fr Chapter I 1. S. L. Rbbins, Eathlfly, Third Editin, W. B. Saunders Cmpany Chapter 15, E. B. Smith, Cardivasc. Res., 1, 111 (1967). 3. E. B. Smith, R. S. Slater and P. K. Chu, J. Atherscler. Res., 8, 399 (1968). 4. B. D. Ladbrlce, R. M. Williams and D. Chapman, Bichem. Biphy Acta, 150, 333 (1968). 5. D. Chapman, R. M. Williams and B. D. Ladbrke, Chem. Phys Lipids, 1, 445 (1967). 6. Perkin-Elmer Crpratin, Thermal Analysis Newsletter, 5, Nrwalk, Cnnecticut.

24 '. 7 FIGURE TEMPERATURE CALIBRATIN CURVE FR DSC fr^heating and cling rales f 1.25 & 2.5 C/min. STANDARD UPPER SCALE INDIUM B AD I PIC ACID BENZIC ACID X NAPTALENE STEARIC ACID p-nitr0t0luene + CTADECANE <D 110 L. D r L Q). Cl E 0) CL E r l LWER SCALE t \ \ \ \ \ \ \ \ Average Temperature Dial Setting 6

25 FIGURE 1-2 TEMPERATURE RRECTIN FACTR FR * AVERAGE TEMPERATURE DIAL. SETTING +- c ID r Temperature ( C)

26 9 CAPTER II APPLICATIN F TE DIFFERENTIAL SCANNING CALRIMETER T PURITY MEASUREMENTS Intrductin Several hundred papers have been published which invlve the use f the Differential Scanning Calrimeter (DSC). ver frty papers invlving the DSC were given at a single meeting in Several f the authrs at this meeting, G. T. Driscll, et al., and R. D. Ennulat, and scientists publishing elsewhere 2 ' 3 have utilized the DSC t determine sample purity by a methd published by Perkin-Elmer the DSC manufacturer 4-6. G. T. Driscll, et al., 1 have demnstrated that this methd can give ptentially misleading results. The purpse f this chapter is t detail the ambiguities f the Perkin-Elmer methd and t ffer an alternative prcedure fr estimatin f the purity f rganic, nn-plymeric samples by DSC. 4 Perkin-Elmer, in its purity methd, recmmends that measurements be made n the initial prtin f the DSC recrder melting trace nly, preferably in the range frm 10 t 50% f the area enclsed by the trace and the baseline. Driscll, et al., give an example f a purity determinatin by this methd in which the mle per cent impurity calculated can be changed by mre than a factr f ten by varying the lwer and upper limits f this range. What is therefre needed is an imprved methd fr purity calculatin by DSC which emplys the entire recrder melting trace and which des nt invlve an arbitrary chice

27 f nly a part f the frward sectin f the DSC trace. Such a prcedure is utlined in this paper. As stated by the manufacturer 5, except fr samples f very high purity, a significant amunt f melting ccurs befre the melting curve rises detectably abve the baseline. In this purity methd, Perkin-Elmer 4 ' 5 implies that this ttally unrecrded energy is a value which can be adjusted until the plt f sample temperature vs. reciprcal f the mle fractin f sample melted fit alng a straight line. wever, with relatively pure samples, the additin f this unrecrded energy t the energy measured by the DSC trace results in heat f melting values which are t high. Althugh the estimatin f hw much f the actual sample transitin heat has nt been recrded by the DSC is a principle prblem, the value f this lst heat can be quite definite. Cnsider the cmpund, naphthalene, whse heat f melting is well established at 35.0 calries per gram 7 fr a theretically 100% pure, crystallizing cmpund. Mastrangel, et al., 7 have determined the heat f melting f naphthalene cntaining varius mle fractins f thinaphthene by adiabatic calrimetry. Their data are presented in the first tw clumns f Table II-l. As a simple mathematical mdel, the energy required t melt the sample can be attributed ttally t the naphthalene present and the thinaphthene can be assumed t be dispersed in the naphthalene s as nt t frm crystals. At mle fractin naphthalene, this mdel can be shwn t be applicable since a A f 35.0 calries per

28 11 gram, as shwn in clumn three f Table II-l, fr naphthalene permits an accurate calculatin f the transitin heat. Thence frm t mle, fractin naphthalene, the sample heat f fusin in cal/gm, A, can be treated as the fllwing linear functin f the mle fractin naphthalene, N : a A = 35.0 N a (tt-l) In this labratry, a Fisher triple pint naphthalene sample was diluted with 0.05 mle fractin f 1,2 diphenyl ethane with which it 8 frms an ideal slutin in the melt. The resultant sample was melted at a heating rate f 2.5 C per minute in the DSC which gave a recrder trace crrespnding t 21.0 calries per gram. Frm the mathematical mdel, 1.8 calries per gram wuld be the lss frm the reductin in mle fractin f naphthalene and 12.2 calries per gram the energy unrecrded by the instrument. The unrecrded energy was 87% f the difference between the energy f the highly pure naphthalene and the energy f the impure sample, as determined by DSC. Similar results were btained with Fisher triple pint benzic acid samples cntaining frm 0.01 t 0.04 mle fractin naphthalene when run n the DSC at a heating rate f 2.5 C per minute. Their unrecrded energy varied frm 85 t 89% f this difference when the sample heat was treated as a linear functin f the mle fractin f benzic acid present. A third system cnsisting f Fisher triple pint naphthalene samples cntaining 0.01 t 0.04 mle fractin p-nitrtluene melted

29 12 at a rate f 2.5 C/min. had unrecrded energy f fr, 83 t 88% f this difference when the sample heat was treated as a linear functin f the mle fractin f naphthalene present. In the purity methd t fllw, fr samples melted at a heating rate f 2.5 C per minute, 87% f the difference between the heat f melting f a highly pure sample and that f an impure sample, as determined by DSC, was estimated t be unrecrded heat. This estimate f per cent heat lss may eventually be shwn t decrease a per cent r tw as the sample size is increased frm 3 t 6 mg. The imprtant prperty f a DSC trace, which is nt knwn with reasnable certainty, is the lcatin n the trace fr the temperature where the sample can be cnsidered t have just finished melting. A clue t its lcatin cmes frm studies f melting pint depressin by impurity. Experiments have been made in this labratry n systems f naphthalene diluted with 1,2 diphenyl ethane and chlesteryl myristate diluted with tluene. Tremendus bradening f the temperature range fr the DSC melting peak trace is bserved with increasing sample impurity. wever, an excellent straight line relatinship was achieved between the reciprcal f the melt temperature, when designated as ccurring at the curve peak, and the lg f the mle fractin f the majr cmpnent, as shxm in Figures II-l and II-2. This means cnfrmance with the Van't ff equatin. The heat f transitin calculated frm the Van't ff equatin fr these systems is cmpared t the knwn value fr naphthalene and chlesteryl myristate in Figures II-l and 11-2 and fund t be in errr by -12.3% and -2.7%

30 respectively. This new prcedure fr the determinatin f sample purity by DSC is based n a trial and errr methd t estimate the lcatin, near the curve peak, f where the sample has just finished melting. Functin f the Electrical Lps in the DSC Any valid methd fr determinatins f sample purity requires an understanding f instrument peratin. Transitin temperatures and heats are determined frm the DSC by measuring the differential pwer required t maintain the same temperature prgram n tw nminally identical and symmetrically placed cups 9. ne cup hlds the weighed samples in a sealed planchet; the secnd cup is the differential reference. Electrical pwer is supplied t the reference and sample hlders thrugh the peratin f tw essentially separate electrical cntrl lps. An average temperature lp maintains the cups at a preset heating rate. The pwer fr this lp is supplied equally t bth cups and is nt recrded. This lp perates by cmparing the average temperature f the tw cups t that demanded by the prgrammer, and the pwer required always is prvided equally t bth cups as needed. The temperature prgram is marked ut n the abscissa f the DSC recrder. A separate electrical lp is used t handle temperature differences between the cups. This secnd lp senses the temperature difference between the sample and reference cups and supplies the differential pwer needed t cmpensate fr the difference; this is the pwer input indicated n the DSC recrder rdinate. Befre and

31 14 after a sample transitin (fr cnditins where the temperature f the sample eup des nt ehange relative t the reference cup temperature), i.e., n transitin r heat capacity difference, the differential pwer supplied t bth cups is the same. During an endthermic transitin, hwever, differential pwer is subtracted frm the reference cup circuit and added t the sample circuit 9. The DSC chart rdinate changes by an amunt prprtinal t the temperature difference between sample and reference cups cnverted t units f pwer, dq/dt r q f as the average temperature f the cups T is P' prgrammed n the abscissa at a rate dt p /dt r T. An exthermic transitin merely reverses the electrical prcess. Imprtantly, each change in the differential temperature lp, as during the melting f the sample, causes the average temperature lp t add cmpensating pwer, divided equally between cups, t maintain the preset heating rate. Nte that the pwer supply fr the average temperature lp is an rder f magnitude larger than that f the differential temperature lp. The functins f the electrical lps described abve culd prvide a simple theretical basis fr a purity methd. Unfrtunately, there appears t be a threshld temperature difference, recgnized t be several thusandths f a degree by the manufacturer, belw which differential heat is nt transferred and q is nt recrded. There are at least tw cnclusins cncerning the peratin f the electrical lps which influence ptential methds fr sample purity. In melting a highly pure sample, fr example, the pwer put in at the start f

32 15 the transitin, t bring sample and reference cup temperatures tgether, is prvided presumably by the average temperature lp. This energy additin and the energy required belw the threshld respnse f the differential lp mentined in the previus paragraph are bth made by the average temperature lp and neither are recrded. The energy put in during the initial prtin f a transitin by the average temperature lp must eventually be transferred t the part f the recrded q curve that ccurs after the sample has undergne the maximum melting rate, which is the regin where the temperature f the sample cup must catch up t the temperature f the reference cup. Fr relatively impure samples, a large fractin f the sample can he. melted ver a wide temperature range befre the threshld temperature difference is reached and the differential temperature lp respnds. The average temperature lp prvides whatever extra pwer is required t maintain T J this pwer is nt recrded and little, If any, f it appears in the latter prtin f the transitin curve. Immediately after the sample is cmpletely melted, the average temperature lp returns t its perating level prir t the transitin; hwever, the sample and reference cups are still at different temperatures. The differential temperature lp must cntinue t transfer energy until these temperatures are equalized. Thus, the recrded energy transferred by the differential temperature lp after melting is energy that had been added by the average temperature lp during melting.

33 Analysis f the DSC Recrder Trace Figure II-3 presents a trace, exactly as it ccurred n the recrder graph f a mdel DSC-IB, fr the crystal-mesphase transitin f chlesteryl prpinate, sample btained frm Applied Science Labratries, Incrprated, State Cllege, Pennsylvania. The area between the curve and the baseline, AGC in Figure II-3, is a measure f the transitin heat. The abscissa f Figure II-3 represents time and/r temperature. Fr example, at a T p f 2.5 C/min., each mark n the abscissa means 1.0 C r 0.4 minutes. The level f impurity in a sample can be calculated frm DSC data and the Van't ff equatin which relates sample temperature, T t sample mle fractin, F, melted at T : s' T s = T " (RT 0 2 N/ A ) (1/F) (II-2) where A B heat f fusin f the pure majr cmpnent R = gas cnstant N = mle fractin f impurity T = melting pint f the pure majr cmpnent A plt f T vs. 1/F will be a line f slpe -RT N/A. A s knwledge f A btained frm the area under the DSC curve r frm the 2 literature permits a calculatin f N, the mle fractin f impurity. ie abve equatin was develped frm Rault's Law and in mst cases

34 17 it can be expected t hld nly fr high purity samples> ^ ^ illicit in the equatin is the assumptin that the i mpurity must be insluble in the slid yet cmpletely sluble in the melt. A sample temperature, f,. can be derived frqm any ^ ^ ^ DSC trace AGC. Take pint E as an example. Drp a line frm E perpendicular t the abscissa intersecting the baseline at. The line E is prprtinal t the temperature difference between the reference, V and the sample, T^ The relatinship between the prgrammed temperature T p, T g, and T r is presented in the fllwing equatin: T s = T p - 1/2 C T r - T s ) (II _ 3) The prprtinality cnstant t determine the actual temperature represented by Ell is derived frm the shape f the DSC trace fr an extremely high purity sample, e.g., % pure indium 4, at the same heating rate f 2.5 C/min. If line E is prprtinal t T. - T then: r s' V = T r - T s where R G " the prprtinality cnstant in C-sec/millical q = the actual value f E in millical/sec t

35 18 During the melting f the extremely pure indium sample, A the actual sample temperature des nt change. Frm the differentiatin f Equatins (II-3) and (II-4), R q can be evaluated fr the indium sample since d 2 q/dt 2 r q is cnstant. R q is the valid prprtinality cnstant fr all distances between trace and baseline at a particular X p r heating rate. Frm Equatin (II-4), the T r - T s value f line E can then be determined and substituted in Equatin (II-3) t give T g. All ther pints n trace AGC can be similarly cnverted t T g values. Each f these T values then shuld s be adjusted by reference t a temperature calibratin crrectin curve similar t that presented by the manufacturer 4. This calibratin curve is a plt f crrectin t the dial reading vs. dial reading, in degrees. Generally samples change temperature thrughut the tracing f the sample melting curve, AGC. Differentiatin f Equatin (II-4) wuld give: R q = T - T n (II-5) v r J s At the curve peak, G, q must equal zer and T equals T. r s This fact suggests that the sample must have cmpleted melting befre the curve peak is reached. Essentially all cmpunds analyzed in this labratry appeared t have their melting pint near but befre the peak f the DSC trace.

36 19 New Purity Methd Prcedure The methd t be described fr the calculatin f 1/F, the reciprcal f the mle fractin f sample melted, is entirely different frm that f Perkin-Elmer 4 ' 5. The fllwing prcedure is ffered fr estimating 1/F at each T : s Arbitrarily chse a likely lcale fr the final sample melting pint which will be prir t but near the peak, B, n tbe DSC trace; fr example, chse pint B in Figure II-3. The chice f this pint is nt critical because the plt f T vs. 1/F must be s a straight line with an intercept at 1/F equals 1.00 at the T crs respnding t pint B (see previus temperature crrectin methd). This pint where 1/F equals 1.00 crrespnds t the melting f the last crystals, and, therefre, the theretical melting pint. Divide the curve int tw sectins with a line frm B perpendicular t the abscissa which intersects the baseline AC at D in Figure II-3. Area ABD f Figure II-3 can subsequently be divided int arbitrarily chsen segments, such as area AE, which can be cnsidered as prprtinal t an uncrrected F value. The sample temperature, T s > a t crrespnding pint E is determined as described previusly. The uncrrected 1/F value fr an area AE is: (1/F) uncrrect = Area AGC Area AE (-6)

37 Area ABD represents energy added by the average pwer l p during the melting f sample, half t the sample hlder and half t the reference hlder. Therefre, energy f size 1/2 ABD is recrded by the differential temperature lp during the energy transfer represented by area BCD. Subtract 1/2 area ABD frm area BCD t btain an area P. This area P represents energy that was added by the average pwer lp befre the differential pwer lp began t recrd and shuld be added t each chsen segment, such as area AE. The value P implies that pwer transfer lags pwer input. Calculate the trace area that a highly pure sample f equivalent weight wuld have and, frm this value, subtract area AGC. Multiply the difference by This is the area crrespnding t the energy that was supplied by the average temperature lp, but nt recrded by trace AGC. Call this value Q. Area AE shuld be further crrected by the additin f its share f the 1/2 ABD recrded by the differential temperature lp during the energy transfer represented by area BCD r 1/2 AE. The crrected 1/F value fr an area AE wuld then be the fllwing: (Area AGC) + Q (1/F) crrect = (II-7) 3/2 (Area AE) + P + Q The calculatin f a cmplete, series f 1/F values wuld be handled similarly.

38 Discussin f Results frm the New Purity Methd Figure II-4 presents plts f T g vs. 1/ F fr bth uncrrected and crrected 1/F values. Nte that the curvature is entirely remved with the crrected 1/F values and the line intersects the 1/F equals 1.00 line within 0.1 degree f its value at B frm Figure II-3. This permits a direct calculatin f N, the sample impurity thrugh the Van't Kff relatinship. The Perkin-Elmer methd als linearizes the T g vs. (1/F) uncrrected plt. Estimates f the accuracy f the purity evaluatins are presented in Table II-2 and II-3. Knwn amunts f naphthalene were added t benzic acid (Table II-2) and p-nitrtluene t naphthalene (Table II-3), all Fisher triple pint samples. The samples were melted, recrystallized frm the melt, and then remelted. The curves frm the remelted samples were analyzed by this new methd fr purity. The data frm bth tables indicate that an accuracy within 15% f the actual impurity value can be anticipated in the 95 t 99.9% purity range. This purity methd is applicable t heating rates ther than 2.5 C per minute by replacement f the 0.87 factr in determining Q with the ne prper fr that heating rate. Fr heating rates f and 1.25 C per minute the factr is larger, that is, the rati f the unrecrded energy t the actual energy lss due t impurities is even greater. Generally, these lw heating rates are reserved fr samples f high purity where Q is apprximately equal t zer. The actual trace f a triple pint benzic acid sample frm Fisher melted at a

39 apparent melting pint is marked by the letter "B.» The plts f' 22 heating rate f C per minute is shwn in Figure II-5. I ts T g vs. 1/F f bth uncrrected and crrected 1/F values fr this b«l»0ic acid sample are presented in Figure II-6. Curvature in the Plt f sample temperature, Tg> vs. 1/F is remved by the prcedure described befre and a melt temperature, T, is determined. j A change in sensitivity r rdinate scale factr des nt seem t effect the 0.87 Q factr significantly. Sample heats f transitin measured at different sensitivities give equivalent results, within experimental errr. The threshld temperature difference des nt seem t be dependent n sensitivity. A cmparisn can be made between the purity values estimated by the new methd and the Perkin-Elmer methd. The Perkin-Elmer methd has been applied t the same benzic acid-naphthalene system presented in Table II-2. The results are shwn in Table Nte that the relative errr by the Perkin-Elmer methd is always negative, that is, the amunt f impurity is always understated. The relative errr can be as large as 30%. The Perkin-Elmer methd appears t give impurity values 15 t 25% lwer than the new methd. References fr Chapter II 1. Cited in Analytical Calrimetry, R. S. Prter and J. F. Jhnsn, Eds., Plenum Press, New Yrk, ]968, en tt. 2. W. L. G. Gent, J. Phys. E., 2, 69 (1969). 3. D. E. Martire, P. A. Blasc, P. F. Carne, L. C. Chw and. Vince, J. Phys. Chcm., 72, 3489 (1968).

40 23 4. Perkin-Elmer Crpratin, Thermal Analysis Newsletter, 5, Nrwalk, Cnnecticut 5. Perkin-Elmer Crpratin, Thermal Analysis Newsletter, 6, Nrwalk, Cnnecticut 6. M. J. 'Neill, Anal. Chem., 36, 1238 (1964). 7. S. V. R. Mastrangel and R. W. Drnte, Anal. Chem., 29, 794 (1957). 8. J. K. Shillingtn, W. J. Watt, and R. D. Whitaker, J. Chem. Ed., 41, 96 (1964). 9. E. S. Watsn, M. J. 'Neill, J. Justin and N. Brenner, Anal. Chem., 36, 1233 (1964). 10. A. Gray, persnal cmmunicatin.

41 TABLE II- Naphthalene - Thinaphthene eats f Melting ^^Jrf 1011 A> Cal/8m A > cal/gtn Naphthalene LSample fjiaphthale^ * a - Purity f riginal sample f naphthalene.

42 TABLE I I- Summary f Benzic Acid and Naphthalene Purity Result By New Methd Purity Prcedure Majr Cmpnent - Benzic Acid (Fisher Triple Pint) Impurity - Naphthalene (Fisher Triple Pint) Mle % Added I inp ur i 1 y Ttal % Impurity % Experimental Impurity Abslute Errr % Relative Errr % Experimentally determined frm the recrystallized melt

43 TABLE I I- Summary f Naphthalene and p-nitrtluene Purity Results By New Methd Purity Prcedure Majr Cmpnent - Naphthalene (Fisher Triple Pint) Impurity - p-nitrtluene (Fisher Triple Pint) Mle % Added Impurity Ttal % Impurity % Experimental Impurity Abslute Errr % Relative Errr % Experimentally determined frm the recrystallized melt.

44 TABLE II-4 Summary f Benzic Acid and Naphthalene Purity Res by Perkin-Elmer Purity Prcedure^ Majr Cmpnent - Benzic Acid (Fisher Triple Pint) Impurity - Naphthalene (Fisher Triple Pint) Mle % Added Imp_urity_ Ttal % Impurity % Experimental Ijnpj rrjity_ : Abslute Errr % Relative Errr % ' Experimentally determined frm the recrystallized melt

45 FIGURE II-l NAPTALENE MELTING PINT DEPRESSIN majr cmpnent naphthalene : diluent : 1,2 diphenyl ethane slpe = 5.06 x A van't hff = 3>93 cal./mle ACTUAL 4,480 cal./mle errr = -12.3% lg e (mle fractin f majr cmpnent )

46 29 FIGURE II-2 CLESTERYL MYRISTATE MELTING PINT DEPRESSIN majr cmpnent : diluent : chlesterl myristate tluene AI ~Wt hff~ 1 0>900 cal./mle A ACTUA L zrll >200 cal./mle errr = -2 7% slpe = 1.82 x lg e (mle fractin f majr cmpnent

47 FIGURE II-3 CLESTERYL PRPINATE CRYSTAL- MESPASE TRANSITIN Tp=2.5 C./rnin., scale = 4x sample wt.=5306mg T D - PRGRAM TEMPERATURE, K

48 31 I ( M W M fa

49 FIGURE II-5 BENZIC ACID MELTING CURVE Tp= C./min., scale = 8x sample wt. = mg T p - PRGRAM TEMPERATURE, K

50 33 c :> r UJ Q >- CC Z) Q_ Q < z UJ 0) E m > 75 II UJ Ql ^' l" X _l <] V CD S II UJ >- h- r E u CL u <D (D +- L U 0 <D u L L L 0 <D U c +- <+- D r u_ CD 00 c CD 0 L u r L Ll I M W M c r J

51 CAPTER III EVALUATIN F TERMAL TRANSITINS IN SME CLESTERYL ESTERS F SATURATED ALIPATIC ACIDS Intrductin Esters f chlesterl differ frm many ther cmpunds whse transitin frm crystalline slid t istrpic liquid is a simple, single-step phase transfrmatin. Chlesteryl esters have at least tw "liquid crystal" mesphases, the smectic and the chlesteric, between the true slid and istrpic liquid. Multiple heat and temperatures f transitin fr eight chlesteryl esters f the saturated aliphatic acid series measured by Differential Scanning Calrimctry (DSC) have been reprted previusly 1. wever, thermdynamic evaluatin f this data shwed that this chlesteryl ester series exhibited quite anmalus behavir. The purpse f the wrk will be t measure the heats and temperatures f transitin fr furteen chlesteryl esters f saturated aliphatic acids by DSC, t analyze this data thermdynamically, and t attempt t explain the reasn fr sme f this anmalus behavir. Experimental A. Chlesteryl Est ers. The ester samples came frm five surces - Applied Science Labratries, State Cllege, Pennsylvania; Analabs, ampden, Cnnecticut; Eastman Chemicals, Kingsprt, Tennessee Aldrich, Cedar Knlls, New Jersey; and Mathesn, Cleman, and Bell, East Rutherfrd, New Jersey. With the exceptin f sme esters frm Applied Science Labratries, all were recrystallized frm n-pentyl

52 35 alchl, washed after the remval f the.ther l iqur in an ethanl _ water slutin, and vacuum dried at 50 C. The purity that each sample attained is recrded in the table presenting the thecal transitins. The purity analysis technique applied is based n the shape f the differential scan 2. The individual samples varied widely m mle per cent purity with all in the range f 96.0 t 99.6% pure. The best chlesterl available fr esterif icatin is btained frm animal surces and is nly abut 98% pure. This is thus a majr limitatin n the quality f available ester samples. In a previus paper by E. M. Barrall, et al., 1 chlesteryl esters were thught t have less than 0.1% impurity, as indicated by spectrmetry analyses. Tw ther analytical techniques fr chlesteryl ester purity applied by Arnld 3 gave values frm 98.1 t 99.6% purity by ne methd 4 and 91.9 t 99.5% by a secnd methd 5. The values by Arnld are mre cnsistent with the purities reprted in this chapter. B - Instrumentatin. The samples were analyzed n a Differential Scanning Calrimeter, Mdel DSC-1B, manufactured by the Perkin-Elmer Crpratin, Nrwalk, Cnnecticut. The calrimeter had previusly been calibrated fr temperature at the applied heating rates f 1.25 and 2.50 C/min. in a temperature range f 50 t 156 C with p-nitrtluene, naphthalene, benzic acid, indium, stearic acid, and adipic acid. eats f fusin were calculated by cmparisn with the area under the melting curve f an exceptinally pure sample f indium supplied by the Perkin-Elmer Crpratin and stated as being % pure. The heat f elemental melting is well established at 6.80 cal/gm.^ As a check n the curve area, the heat

53 f transitin f the indium was als cmputed frm instrument parameters, as the chart rdinate represents cal/sec. and the abscissa, secnds; this methd gave a heat f transitin f 6.89 cal/gm fr indium. Tw t five mg samples were weighed n a Mettler balance t mg and enclsed in an aluminum planchet. All samples were heated t cmplete melting, cled t crystallizatin, and reheated t istrpic liquid. Duplicate runs were made n fresh samples. All values reprted are frm first heating r cling, but, except fr chlesteryl tridecanate, all samples cnsistently repeated the same transitins and heats n reheating. The accuracy f transitin heat presented can be estimated frm multiple runs n Fisher triple pint benzic acid that ranged frm 35.0 t 35.6 cal/gm. A previus investigatin by adiabatic calrimetry gave a value fr benzic acid f 35.2 cal/gm. 7 Accepting this figure fr the mean permitted the calculatin f a standard deviatin f 0.23 cal/gm. A 95% reliability requires tw standard deviatins f cal/gm. Cnversin f this figure t per cent f sample heat gives an expected accuracy f + 1.3%. This estimate is satisfactry fr the sizable calrie change n heating the crystalline material thrugh its initial transitin because the rdinate scale can always be adjusted t give a large full curve n the chart. wever, all mesphase-istrpic transitins had t be run n the scal( f maximum sensitivity smaller than in nrmal melting. (Attenuatin at different sensitivities were. checked fr errr.) In additin, the specific heat befre and after each mesphase transitin is abnrmally

54 37 high which alters the baseline slpe. Frm a cmparisn f the mes- Phase data reprted here fr chlesteryl myristate with that f ther investigatins, such as Barrall, et al., 8 and M. Leclerq, et al., 9 a gd accuracy f ± 0.02 cal/gm can be anticipated. Cnversin f this value t per cent wuld suggest accuracy ranging anywhere frm +3.3% fr nnadecanate t +11.8% fr the smallest heat reprted which is fr the chlesteric-istrpic liquid transitin f chlesteryl prpinate The precisin f transitin temperatures presented here can be estimated frm multiple tests made ver a perid f weeks n the three transitins f a 98.1% purity chlesteryl myristate. The transitin ranges fr each were frm 70.0 t 71.0 C, 77.3 t 78.2 C, and 82.8 t 83.7 C. The expected precisin then is apprximately C. These transitin temperatures n chlesteryl myristate are cmpared with thse f Martire 10, Fridel 11, Gray 12, Arnld 3, and Barrall 2 in Table III-l. The chlesteryl myristate sample f Martire, et al., 10 had a 98.8% purity, as determined by the Perkin-Elmer Crpratin methd f analyzing the shape f the differential scan 13,14. This sample and that f these investigatins are likely cmparable in purity, since the purity analysis technique develped fr this wrk generally gives smewhat lwer purity values n the same sample than 2 the Perkin-Elmer methd. The transitin temperatures reprted by Barrall, et al., are higher than thse reprted here, as are all ther chlesteryl ester melting temperatures reprted in this same

55 38 study 1. The methds f calibratin and peratin f the DSC are likely the determining factrs, rather than purity, fr the higher transitin temperatures reprted previusly by Barrall, et al. Results The temperatures and heats f transitin f furteen chlesteryl esters derived frm saturated aliphatic acids f varying chain length are presented in Table III-2, clumns ne and tw. Values fr unesterified chlesterl are listed first, fllwed by the esters frm the shrtest, frmate, f carbn tail length ne, t eicsanate, f carbn tail length twenty. Eight f these esters have been measured previusly by E. M. Barrall, et al., 1 ' 15 Their results are shwn fr cmparisn in clumns three and fur. The percent difference in A between these new and the published values is presented in clumn five. The purity as estimated by the analysis f the DSC curve shape is presented in clumn six. The final tw clumns shw the calculated entrpies f transitin and the sum f all transitin entrpies fr each cmpund. The thermdynamics f each cmpund studied will be discussed separately. A. Chlesterl. The series, in thery, can be cnsidered t begin with an ester having a carbn tail length f zer, r the parent cmpund, an alchl. wever, the transitin temperature clumn in Table III-2 clearly shws the significant difference f chlesterl frm the remainder f the true ester series. That is, there is a melting temperature decline f 50 C between chlesterl and the first ester, the frmate. The high melt temperature f chlesterl e

56 39 debates a structural stability t thecal energy that is lst n esteriticatin. The chlesterl, received frm Analabs, has ne transitin and exhibited n esphases n either heating r cling which is cnsistent with the literature 16. B. Cfaleeteryl Frmate. This ester exhibited nly simple melting and melt recrystallizatin. It did nt appear t frm mes- Phases. Neither the riginal cmpund frm Aldrich nr a sample recrystallized frm n-pentyl alchl shwed an additinal transitin as suggested by E. M. Barrall, et al. 1 ne f these authrs (EMB) has recently fund that with smewhat less pure samples, the frmate ester can be supercled sufficiently t give a mesphase transitin f 0.08 cal/gm at 57.1 C. C Chlesteryl Acetate. The riginal cmpund frm Mathesn, Cleman, and Bell exhibited the multiple transitin behavir suggested by Barrall, et al. 1 wever, after n-pentyl alchl recrystallizatin, nly ne transitin appeared n melting, n melt recrystallizatin, and n remelting. This cmpund, like the frmate, demnstrated n mesphase character. D. Chlesteryl Prpinate. In this wrk, this ester had the minimum carbn length fr the bservatin f the chlesteric mesphase. The heat absrbed at the chlesteric-istrpic liquid transitin is small but reprducible bth n heating, cling, and n reheating. The high purity f this sample riginally btained frm Eastman Chemicals was achieved by tw recrystallizatins frm n-pentyl alchl. Despite its 99.6% purity, the transitin temperature remains belw that stated

57 by E. M. Barrall, et al. 1 All data in the table are frm melting curves f riginal crystals unless therwise stated. Barrall, et al., 1 detected an additinal transitin n first heating the crystalline material, i.e., tw mesphases, ne f which was a slid-slid transitin, but this transitin did nt appear upn reheating.. Arnld 3 reprts nly tw transitins at 99.6 and 114 C f 11.8 and 0.43 cal/gm respectively (ne mesphase). This cmpund appears t frm nly a single mesphase which can be frmed reversibly n either heating r cling. E * Chj^e^tejrjiJ^ In this investigatin, three transitins were bserved. As with ther experimenters, viz. M. Leclerq, 9 2 et al., and E. M. Barrall, a small third transitin n cling frm the melt, in this case f 0.14 cal/gm at 74.6 C, ccurred. The sample studied here was btained frm Eastman Chemicals. It was recrystallized twice frm n-pentyl alchl. F - Chlesteryl Undecanate. This ester exhibits three transitins n heating, cling, and reheating. This means the reversible frmatin f tw mesphases likely t be identified as smectic and chlesteric. A quite pure sample f 99.6 mle % was received frm Applied Science Labratries. The DSC traces were unusually clear and sharp n the sample as received. There are n knwn previus studies f either the heats r transitin temperatures fr this cmpund. This is the case fr all the higher dd carbn length esterified acids.

The estimator, X, is unbiased and, if one assumes that the variance of X7 is constant from week to week, then the variance of X7 is given by

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