computer ~ e r i e ~1.05
edited by JAMES P. BIRK Arwona State University. Tempe, AZ 85281
Bits and Pieces, 41 Polymer Tacticity in Simulated NMR Spectra Christopher K. Ober Cameii University Ithaca. NY 14850
Molecular composition is an extremely important factor in determining the vhvsical characteristics of a volvmer. Just as significant the manner in which its atoms are arranged. In the classic example of three compositional isomers-poly(viny1 alcohol), poly(ethy1ene oxide) and poly(acetaldehyde)-the properties of each of these polymers is quite different even though their repeat structures all have the formula (CzH40). Another aspect of the architecture of ~ o l v m e r sdenends on their stereochemical nature. Just as there are d- and l-isomers in small molecules that are otherwise identical.. .oolvmers exist with identical comoositions . and with structures that differ only in their stere~chemical arrangement. T h e tacticity of a polymeric material, which is a function of its stereochemical placement, is therefore an important conrept in considering a polymeric chemical structure. Tacticity can determine surh properties as the degree of crystallinity of a polymer, its melting temperature, or even its glass transition temperature. These srereochemical differences can he illustrated hv use of the Fisher oroiertion diaerams " shown in Figure 1.In the polymerization of vinyl monomers, the suhstituent or substituents of the addine monomer oroduce a prochiral center that can he attachei to the chain in one of two ways with respect to the suhstituent(s) on the ultimate unit of the growing polymer chain. Figure 1 shows the meso and racemic diads that mav in . he vresent . such a polymer chain. Note that the meso diad is caused hy two consecutive monomer units added to the growing chain with the orientation of the substituents in the same fashion, whereas the racemic diad consists of two monomer units with substituents added in opposing fashion. A suhstituent, represented hy a circle, might be the methyl ester group of the methyl methacrylate repeat unit. A polymer consisting
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GuMeiines for AuMors of BitsandPiecesappesredin Juiy 1986: the number of BitsandPieces manuscripts is expected to decrease in the hRUm-see the Juiy 1988 and March 1989 issues. BitsandPiecesauthorswho describe programs will make available lialings andlor machine-readable versions of their programs. Please read each description carefully to determine c o m p i b i l i wilh your own comDutina environment before reouestina materials from anv of . , the aumors. Several programs described in thls article and marked as such are available from Project SERAPHIM at 55 per 5x4". disk, $10 per 3'bln. disk: program listings and other written materials are available for $2 each: 52 domestic or 510 foreign postage and handling is required fw each shipment. Make checks payable to Project SERAPHIM. To order, or get a Project SERAPHIM Catalog. write to: John W. Moore, Director. Project SERAPHIM, Department of Chemisby. University ol Wisconsin-Madison, 1101 University Avenue, Madison. WI 53706. (Project SERAPHIM is supported by NSF: Diremrate for Science and Engineering Education.)
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0 racemic dyad
meso dyad
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p ,
Isotactic
Syndiotactic
Heterotactic
mm triad Pm2
rr triad
mr triad
2P,(1-P,)
(l-P,F'
Figure 1. Schematic of diad and triad tacticity of vinyl polymers
of essentially meso diads is said to he isotactic. Similarly, a oolvmer comoosed orimarilv of racemic diads is called svnbioitactic, and one made of arandom mixture of racemic and meso diads in aooroximatelv caual concentrations is described as hecero&ctic.~heminimum number of units needed to define the svndiotactic, isotactir, and heterotactic nequences is three, as shown in the lower portion of Figure 1. The probability of each of these triad sequences can be expressed in terms of P,, the probability of meso diad as shown in the figure. This relationship assumes Bernouillian statistics, discussed later. Probably themost direct method of determining the tacticitv of a oolvmer is to studv i t usine NMR soectroscoov ( I , > ) . cha;lglsin the chemick shift ofthe different mole& lar constituents of the oolvmer. . . . caused bv differences in the stereochemical environment of the polymer chain, can be used to determine polymer tacticity. Modem NMR instrumentation uses computers both to acquire data in the time domain and to transform the data to the frequency domain by means of the Fourier transform technique. The free induction decay or FID, a time relaxation response of a sample t o a pulse of radiation in a magnetic field, is the response that is actually measured. The spectral summation techniaues develooed around hieh-soeed comouters enable the ac&ition of'very high resdiutiln spertra by adding many d is then converted to a individual FID's. The n ~ ~ m m eFID frequency domain spectrum using Fourier transform techniques. A growing amount of literature is available that discusses the measurement of polymer tacticity via NMR and the fundamental principles of the FT-NMR method (34). One maior obstacle for the educator trvine , .. to exolaiu both tacticity and the basic principles of NMR to students is the lackof tools in thearea. With the advent of readilv available computers, i t is now possible simulate the FID &polymer Volume 66
Number 6 August 1969
645
NMR spectra and to use plotting routines to manipulate, transform. and integrate such data. This aooroach has the advantages of expo2ng the student to boti'the concept of tacticitv measurement using NMR s~ectrosco~v. and to the data manipulation aspectsof NMR-instrume&tion without the oroblems of actuallv acauiring- a spectrum. I t also . gives the student the opportunity to explore the data-handlinr and computational capabilities found in most universities.-~escribed here is a subroutine that has been used to simulate the 'H-NMR spectra of poly(methylmethacrylate) with different tacticities. Relative contributions bv each spectral component in the simulation are determined by specifvine the meso diad tacticitv of the nolvmer. Summations bf iamped cosine functions simul&the individual components of the FID and its subsequent Fourier transform results in the NMR spectrum. This subroutine is intended for use with any available plotting program that has Fourier transform capability, and the approach can be used for a variety of polymers for which the chemical shifts of the different tetrad or pentad sequences, for example, are known. Simulations These simulations were performed on a Prime 4000 computer using a Fortran-based plotting routine called "LTPLOT"'. Simulations have also been performed on an IBM PC-AT using another Fortran-based plotting program called "GENPLOT"2, and will be suitable for use with anv plotting routine that has both Fourier transform and intimation capability. Some assumptions were made in develooing the subroutine for the spec&a, even though the simuiations were meant to mimic real spectra as closely as possible. For example, chemical shift of the pentad and tetrad sequences used in the simulations were assumed not to change as degree of tacticity changed. Furthermore, Bemouillian statistics, which requires an assumption about how the hypothetical oolvmerization was nerformed. were assumed to . " be operational in these polymers. Bernouillian statistics were used to relate diad probabilities to higher tetrad and pentad probabilities and therefore to determine the relative peak heights of each component of the spectrum. The use of the subroutine for the simulation of different tacticities of PMMA assumes an understanding of the concepts of diad, tetrad, and pentad tacticities not fully discussed in this paper. If any of these terms are unfamiliar, the reader is referred to ref 1. The fraction of meso diads are set by the value p , which represents the fraction of meso diads in the polymer, P,. For example, a polymer that has 10% meso diads, or is 10% isotactic will have D set a t 0.10. Triad. tetrad. and pentad information can b i obtained from high-resolution- NMR spectra and can be expressed in terms of the diad orobabilities ( 1 ) . A particular'triad (composed of three monomers) can be described by two diads and will have the probability of the product of the diad probabilities. As an example, the heterotactic triad shown in Figure 1 would be the mr triad because it is composed of an rn diad connected co an r diad. This method of specifying the higher order tacticity was used in thesimulationdescribed here. Ina tvnical Dart ofthe algorithm given below for one part of the mmm quartet of poly(methy1 methacrylate): " A
.
rnrnrnab) = 0.25*(p**3)*exp ( - d 5 ) * cos (2M)*2.34*x)
'
LTPLOT is a plotting program used on the Material Science Center Prime 4000 computer. Information about this program can be obtained by writing: Mike Heisier, MSC Computing Center, Corneil University. Thurston Haii. ithaca. NY 14853. Genpiot is a plotting program written for the %AT and compatible computers by Mike Thompson. More information about this program can be obtained by writing to him at Materials Science & Engineering, Corneii University, Bard Haii, ithaca, NY 14853. 646
Journal of Chemical Education
I 0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
Time (seconds) Figure 2. Simulated free induction decay (FID) specrmm.
Poly(methy1 methacrylate), PMMA
i
Heterotactic
)I
kotactic PMMA
Chemical Shift, s
Figure 3. Simulated 'H-NMR spectra of poly(memylmehcrylate~syndiotaP tic, heterotactic. ard isotactic. where mmma specifies this as the component of the spectrum for the a peak of the mmm tetrad,p**3 determines the contribution of the tetrad a t a given meso diad tacticity, the term exp (-xI5) determines the damping, 0.25 indicates the fraction of the multiplet represented by this curve, and cos (200a2.34*x) defines the cosine function for the individual component where x is the time, 2.34 is the chemical shift from TMS, and 200 is a prefactor that determines the resolution of the simulation by spreading out the peaks. The subroutines for simulating the PMMA spectra are available from the author.
A typical FID generated by a simulation using these equations is shown in Figure 2. The general resolution of the FID can he altered in one of three wavs. More severe dampine can be introduced into the spectrum by increasing the i r e f k t o r exoonential term. exo ( - ~ 1 5 )which . will lead to a decrease in the resolution. he apparentresolution of the spectrum can he reduced by decreasing the acquisition time to values less than one, and by taking data in bigger steps than 0.001. Poly(methylmethac~late)Spectra In the simulation of PMMA, the ester methyl was assumed to he unaffected hy changes in tacticity. The methylene group dinplaya tetrad tacticity, while the a-methyl protons show oentad tacticitv. Such differences are actuallv observed in the 220-MHZ-NMR spectrum of PMMA that was used as a model. In this case. the peaks raneina from 6 2.4 to 1.6 are due to the methylene protons, whili tKe peaks at lower 6 are to the a-methvl arouo. Shown in Figure 3 are spectra of varying degrees of taiticiiy. Note that aspectrum with as little as 10%meso diad shows peaks not present in the 100%syndiotactic PMMA spectrum with 0% meso diad. As an example of a possihle student exercise, two FID's of PMMA with different different tacticities were generated. The data was then stored in read-only files accessible to the students. I t was possible for the students to Fourier transform the files, and to then integrate the resulting spectra. After integration, the students could determine the tacticities of the simulated spectra using the Bernouillian relationships for oentad and tetrad chain seements. fn conclusion, such simulations permit teaching of the measurement of tacticitv bv NMR spectroscoov and expose the students to concep~as&iated with NMR spectroscopy itself. In principle, this approach can also he used to simulate '3C-NMR spectra. The described simulation was modelled using the chemical shifts observed in a spectrum of PMMA made with a 220-MHz instrument, hut this approach can he modified in terms of chemical shift and coupling constants with the operator ahle to specify the instrument frequency. In terms of educational excercises, it is also possihle to chanee orohlems annuallv without sacrificine anv of the concepts to he communic&ed by simply supphinithe student withanew FID. As a final note. this method of simulating NMR spectra has heen used in exercises to study changes in copolymer composition as a function of both comonomer composition and reactivity ratios. Acknowledgment The author would like to thank Mike Thompson for help in writing the subroutines used for the simulations and for reading this manuscript. The use of the Materials Science Center Computer Facility is also acknowledged.
Teaching Magnetic Resonance Imaging Using Computer Animation Davld S. Browne, Presley E. Ellsworth IV,9 and Joseph P. Hornak4 Rochesler lnstihm of Technol~gy Rocheater, NY 14623
Magnetic renonnnre imnging (MRI) is n relatively new tomographic imaging technique that is finding use in the medical settinesand thescientific research laboratorv. .17.8). . , The technique"is based on the principles of nuclear magnetic resonance (NMR) soectroscoDv and as a result much of the basic and applied iesearch in this field is conducted by chemists. Involving undergraduate students in magnetic resonance research requires a carefully planned education program in the principles of magnetic resonance. Such a program often requires the student to learn the principles inde-
pendently, as there are usually no appropriate courses at the sophomore and junior level. Modern-day NMR spectroscopy and imaging is performed in the pulsed model (9). The conventional energylevel diagrams used to describe the continuous wave NMR experiment are inadequate for giving the full picture of the pulsed methods. Pulsed methods require an understanding of the behavior of angular momentum in a force field. The student must he ahle to picture not only the macroscopic three-dimensional behavior of magnetization from the nuclear spins hut also the complex pulse and data processing schemes. Several dynamic aspects of magnetic resonance spectroscoov and imaeine are difficult for a student to understand w i i n texthooL i i t h static diagrams are used. Some of these dynamic concepts are precession of the net magnetization in a static magnetic field, the rotating frame of reference, rotation of maenetization by the radio frequency photons, dephasing ofltransverse magnetization, G i n relaxation, slice selection, and two-dimensional Fourier transform imaging. Other aspects of the technique such as the timing diagrams for pulse sequences and two-dimensional Fourier transform data processing are easy to understand once the student has been walked through each and every one of the steps. Unfortunately most textbooks do not have the space to devote to such an endeavor. Consequently, significant amounts of time are snent hv the research advisor ex~laininathese concepts,whichcouid hetter he taught by other means. A logical solution to this problem is to utilize dynamic diagrams of these concepts. The prohlem then becomes how best to create the dynamic material and to make it availahle to the student. Today this material is best generated by computer animation. Three video display modes are then possible. TV video presentations utilize material recorded on videotape for playback using a VCR and TV comhination. The advantage of this technique is the availability of the playback equipment. The disadvantages are that random access of the recorded material is difficult, and picture quality varies from VCR to VCR. Interactive video combines prerecorded video and real-time computer sequences in one display (10).The presentations are of superior quality; however. the s~ecializeddisolav- eauipment is expensive and not . . readily available. ~ e a i - t i m ecomputer animation on a computer maphics monitor is the third option (11).Programs h a y he designed to operate on readiiy availahle pe&onal computers or on a mainframe computer. The advantages of chis&hnique are the ahility to access the material randomly and customize the presentation to a particular viewer. The presentation is limited by the capabilities of the computer on which it is running. We have developed a comouter-based teachine ~ a c k a e e readiy for the pr~nciplesi f NMR lm&ing that operates available IBM PC with color monitor and sinele flooov d ~ s k drive. The IBM PC was chosen because it is readily &ilahle in our department for use by students. The package was written in Turbo Pascal, Borland Associates, because of its graphics capabilities and speed. The approximately 15,000 lines of software code were written by two RIT students on their co-op blocks in a total of 1200 h. The parkage is composed of 15 sequences that are equivalent to chapters in a book. l'he sequences are further divided into screens, which are a series of images and text describing a given ropic. Hoth the sequences and screens are selrctal~lt. from menus. The screens contain text and accom~anvine . . .. animated diagrams that appear simultaneously, thus allow. ine" the reader to oicture the process beine described. l'he 15 sequences available from the main menu are listed next.
on
Present address: FONAR Corporation. Melville. NY. 'Corresponding author. Volume 66 Number 8 August 1989
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