MODELLING OF CHEMICAL STRUCTURES ·w iTH EXPAND ED POLYSTYRENE SPHERES

By K. s. TETLOW, M . .A.. , B.SC., F.R.I.C.

Belle Vue Boys' Gmmmar School, Bmd.ford

The modelling of chemic~tl structures with expanded poly­styrene spheres has been a practice in the U .S.A. for some years, and Sanderson1 has devised a teaching method in which his electronegativity scale is reflected in his models.

Expanded polyst,yrene spheres are now manufactured in Britain2 for teaching purposes. These spheres are made from Bextrene-X polystyrene beads, to which is added a propelling agent that inflates the material when it is heated. Dow polystyrene, at present available only in the U.S.A.,3 produces a lighter sphere with a rougher surface. Though aesthetically pleasing and easy to cut, the lighter spheres have less mechanical strength and are not suitable for some of the techniques described in t his article. In addition they soften excessively on glueing and thus sometimes lose shape.

The purpose of this article is to introduce teachers to the theory and practice of the use of polystyrene spheres for modelling. The struct-t:U'es described are not highly accurate scale models, but they wil l help considerably to give students an introduction to shape in depth and states of aggregat.ion.

In general the following broad classification of chemical structures holds :

l. Ionic crystals-assemblages of positive and negative ions (typified by sodium chloride) .

2. Molecular crystals-discrete covalent units, low freezing and boiling points (exemplified by sulphur).

3. J.l1acr01nolecula1· st1·uctures-e.g. ice, diamond.

4. Layer st1·uctuns-e.g. graphite.

5. Close-packed spheres-as in metals.

UNI-UNIV.A.LENT IO::<IC S'fRUCTURES

Inter-nuclear distances have been calculated, mainly from X-ray measurements on crystalline solids. Similarly, data for ionic radii are readily available. These measurements are precise. Some useful values are given below.

TABLE I

IO~IC RADII (A)

Cations

Na+ 0·95 K + 1·33 Cs+ 1·69

Anions

CI- 1-81 Br- 1·95 r- 2·16

Modell. Nylon 66. Colours: Black, White, Grey, Blue

7

8 EDUCATION IN ClmMISTRY

These ions are assumed to be spherically symmetrical. ince the largest sphere avai lable in ecouomic quantity is of 2 in. diameter, an economic sca.le would be 1· in. = l A. To choose a larger scale would make chloride ions rather expensive, and as they are frequently used in modelling their cost determines the scale to be used.

In constructing ionic models it is more important to get the radius ratio (0·95/ l· l for sodium chloride) nearly correct t han to match exactly the ionic radius of each ion on tho SCl~ lo ~ iu. = 1A. For this reason a l-in. sphere will be suit~~ble for Xa+ and a 2-in. ·phere for 01-, ·i. '! . ratio about l : 2.

To assemble a model of t he sodium chloride crystal it will be found sat.isfactory to join l -in. and 2-in. spheres alternately in rows after coloru·i.ng and glueing at the approximate points of contact (Fig. l ).

Row I

Row 2

Row 3

Scale: 0 2 3 4

J:'ig. 1

While the glue is still tacky it is possible to press the rows together i11to the sodium chloride structure. There is sufficient 'gi,e' in the spheres and tacky glue to adjust minor imperfections in positioning in the original row: when the structure is being finally assembled and pressed into hape.

The so-ca.lled body-centred structure of caesium chloride can be modelled from a 1;}-in. sphere for Cs+ and a 2-in. sphere for Cl- . Again assembly by eye is satisfactory, packing eight chloride ions round a central cae ium ion with the aid of glue after colour­in.!. It will be found that after some .~i ion., have been packed minor imper­fec · ~ are ,moothed out, as the structure

is pressed into shape while the glue is still tacky.

lt has not been found necessary to drill or punch the spheres to assemble the e simple 6-to-l or -to-1 structures. However a tem­plate for this purpose is described later if mechanical assistance is required. Dow polystyrene sphere were found to be particu­larly good for these models because their low mechanical strength aids alignment by press­ing, but perfectly good results are obtained with t he harder Elford spheres.

)fQLECULAR CRYSTALS

In molecular crystals the atoms are l inked by covalent bonds into molecules but only weak van cler ·waals attractions or hydrogen bonds hold the molecules together in the crystal. In solid iodine, for example, two different internuclear distances are noted (Fig. 2}, one corresponding to the covalently

Scale: 0 I I I I I I I I I

2 I

Fig. 2

3 I

4 I

I inked iodine atoms giving t he so-called covalent radius (rc), and one concsponding to the distance between unbondcd atoms, the van der Waals radius (Tv).

:.\IODELLIXG OF CHE:.\UCAL STRUC'rU.RES 9

F or space-filling models, choose a sphere of suitable diameter to represent the van der \Vaals radius, 1·v, and cut off a portion corresponding to the approximate covalent radius, 1·0 . In this way states of aggregation may be represented by packing molecules in close contact in accordance with known crystallographic da t~.

Tables of approximate van der ·waals and covalent radii are given below for those units most :frequently needed in schools. The covalent radii are t aken for single bonds, but slight shortening occurs for multiple bonds. It is debatable if this shortening can be illustrated accurately with these models. If in any one model t his feature requires emphasis it is suggested that the ·hortening be exaggerated.

TABLE II

Appr·ox. Appt·ox. Diameter van der covalen t of nearest

Atom ""aals radius (A) suitable radi w~ (A) sphere (in.)

c 1·7 0·77 I t N 1·5 0·7 I t 0 hl 0·6 H s I · .3 I ·O I i p 1·9 l·I 2 Si 2·0 I ·2 2 Cl I ·S 1·0 I } Br I ·9 1·1 2 I 2· 1 ]·3 2 H 1·0 0·3 I

i\'fany molecular crystals are organic in natm·e, and in choosing a suitable and economic scale the price of carbon atoms becomes a governing factor. The above \alues fit well the previously used scale of t in. = l A.

Model 2. P rotein o:-Holix (after P auling) Colours: Black , Whito, Gt·oy, Blue, R ed

If close representation to actual size is required spheres can be reduced in size by some 10- 20 per cent, depending upon their density, by rolling under pressure, e.g. under a sheet of t hick glass. H owever, this process is tedious and need only be used if it becomes essential for one or two simple molecules to be modelled extremely accurately.

To fabricate organic structures it is essential to be a ble to cut tetrahedral carbon atoms from 1!-in. spheres in quantity . For this purpose some form of mechanical aid is essential, and working drawings are sho·wn (Fig. 3) for a j ig which has proved very successful.

JIG lW R CUTTISG 'l'E'fRAHEDRA

The jig, made in hardwood by a member of our sta ff, is designed to present spheres at the correct angle for cutting off the faces of a regular tetrahedron with an adjustable depth of cut . The depth of cut is controlled by the thickness of packing (P) - thin plywood or cardboard is suitable. The depth of cut should normally represent about 0·8 A (average value of 1"v""'~"c, Table II) for a single bond. On the present scale this is about ~- in. and for this reason the cutting guide of the jig is about ~- in. from the inner face of the end of the jig. With smaller spheres a ~-in. cut, if the central atom is multi-bonded , removes so much of the sphere t hat its 't eaching value' is destroyed by being virtually hidden. It is t herefore preferable to sacrifice accuracy, making a somewhat shallower cut (after adjusting the packing) so that the centra l atom .is still just visible. In such a case it is advisable to make and present both models with appropriate comment.

To use the jig a sphere is passed down the sloping guide and pressed against t he packing, and the fil'St face is cut with a tenon saw. I t is t hen turned so t hat the cut face is flat against one side of the V groove of t he sloping guide, passed down the guide to the packing and the second face cut. The third and fourth faces are cut with t he two previously cut faces in contact with the sides of the V groove.

Simpler mechanical aids can be devised for

10 EDUCATION IN CHEMISTRY

A

-=;-1

f--L---.----'----1- r r A,

END ELEVATION

Scale: ot....... ......... '-------12 _ __..~_--"-4 _ _.~..s _ _.~..6 _ _J7

cutting planar atoms, of bond-angle 120°, but satisfactory results are obtained by cutting by eye over an equilateral triangle drawn on paper. This method is recommended for uncommon bond-angles.

It has been found possible to use this 109!0 (tetrahedral angle) jig for structures in which the angle is not quite 109}0

, because spheres soften somewhat under the influence of glue and on pressing into shape tend to adjust to the more correct bond angle. Any angle of 109± 5° can be so accommo­dated.

PUNCHING SPHERES FOR

BALL-A~D-STICK :HODELS

If it is desired to construct 'ball-and-stick' models, mechanical assistance is needed to

Fig. 3

--

f l

-1--

t -

SECTION THROUGH A- A,

/ ~

- -

PLAN

Model 3. NaCl (Sodium Chloride)

Colours; Red (Small Spheres), Green (Large Spheres)

p

' '

MODELLIXG OF CHEi\'liCAL STRUCTURES 11

punch or drill spheres for 4-1, 6- 1 and 8- 1 structures. A t emplate described by ~Ir H. Basso~rl of F ieldston School, New York, has proved invaluable for this purpose and can be used as an aid if needed in modelling CsCl and NaCl.

To make t he template two pieces of packing-case cardboard (corrugated sand­wich type) are marked out as shown in Fig. 4. The rad ial lines are very heavily

A~------------~Gr-------------~8

c H D

Scale: 0 2 3 4

Fig. 4

grooved, and the central circle, corresponding to a t ight fit of the sphere to be punched, is cut out. Separate templates are needed for each size of sphere. The two pieces are glued together, so that the grooved radial lines (and central cut-outs) correspond a.nu form guide lines for punches. The punches are best made by pointing suitable lengths of fs--in. welding rod on a grindstonf'.

Model 4. P 40 6 and P.010

Colours: Light Yellow (L arge Spheres), Blue (Small Spheres)

For tetrahedral holes a sphere is located centrally in the template, punched along AX and BX, rotated through 00° about GH and punched along CX and DX.

For 8- 1 structmes the sphere is placed cen trally and punched along AX, BX, CX and DX ; it is then rotated through 90° about GH and the procedure repeated.

For 6-l structures the sphere is punched along EX, FX, GX and HX, rotated about GH t hrough 90°, and repunched along EX and FX.

Cocktail sticks inser ted into the punch holes can be used successfully for these ball-and-stick models.

Model 5. Ice I Colou1·s: Blue (Large Spheres), ·white

)lACROMOLECULAR STRUCTURES

It has not been found possible to get a good model by assembling by eye. For diamond (i.VIodel 6) it is necessary for the spheres to be punched or cut tetrahedrally to obtain an accurate start. To model ice I , spheres representing oxygen atoms are punched tetra­hedrally (:Y[odel 5) ; two of the punched posit ions arc then cut and glued to hydrogen to ma.ke water molecules ; and the other two punch-marks are linked by cocktail sticks to hydrogen of neighbouring water molecules to simulate hydrogen bonds. About t in. of t he cocktail st ick is visible, the rest is embedded with glue in the spheres. This is the method adopted by the author to represent hydrogen bonds in general.

12 EDUCATION IN CHEIIIISTRY

Model 6. Diamond Colou1·: Black

CLOSE PACKING OF SPIIERES

Cubic and hexagonal close packing can be demonstrated by glueing layers of spheres together as shown in Fig. 5. It is found that

Scale: 0 2 4

Fig. 5

two alternative positions are possible for a third layer placed above the two below­either

(a) directly over first-layer spheres (hexa­gonal close packing)

or (b ) over spaces between first-layer spheres (cubic close packing).

LAYER STRUCTURES

A graphite model is made from 1!-in. spheres cut for 120° bond-angles. It should be noted that two alternative ways of placing a third layer over two lower layers are possible,

demonstrating the existence of et.- and ,8-graphite. It is necessary to use at least 24 carbon atoms per layer to obtain a model of sufficient size to make this clear.

Molybdenum disulphide, the automobile lubricant additive, has a layer structure, which can be modelled from data provided by Wells.5

GEO>\IETRICAL ISOJ-lERS

Spheres, instead of being glued, can be bored with a hot metal rod. Holes are made centrally and perpendicularly through bond­ing faces towards the centre, and the spheres are then threaded on elastic under slight tension. (Dow polystyrene spheres will not -stand up to this treatment.) If cyclohexane is modelled by this method the 'boat' and 'chair' forms are easily interconverted to supplement the permanent models of each form.

COi'ofPLEX S1.'RUCTURES

By assembling spheres on elastic after cut­ting to the correct bond angles, the suggested ex-helix of proteins (Model 2) can be success­fully modelled. About 36 skeletal carbon and nitrogen atoms are assembled in correct order on elastic. On tightening the elastic, and with slight shaking, t he skeletal atoms tend to coil in a hel:i.x. Slight adjustment is required so that the hydrogen-bonded groups move into the correct relative positions. After adding carbonyl oxygen, H 's and red spheres to represent amino acid residues the structure is finally hydrogen­bonded with cocktail sticks and glued up.

Nylon 66 (Model 1) can be modelled without elastic as it is more regular and comparatively 'straight. '

GLUEING OF SPHERES

A cheap and satisfactory adhesive is made by dissolving scrap polystyrene in benzene to form a saturated solution. Evostik is satisfactory but tends to soften the spheres; Bostik has less softening effect but dries more slowly.

COLOURING THE SPHERES

Water-based paints (emulsion paints) have been found to be highly satisfactory for

MODELLING O:F CHEMICAL STRUCTURES 13

colouring spheres, and a complete range of colours is available commercially. In the interests of economy attempts have been made to colour spheres by dyeing, following instructions and using materials kindly provided by the Dyestuffs Division of I.O.I. Ltd, but with disappointing results from a range of dyes in aqueous suspension.

olvent penetration of t he spheres appears negligible and the dyes were not retained on the smooth surface. Better results were obtained with American Dow polystyrene spheres, the rough surface of these permitting penetration of the dyestuff.

The scheme of coloms recommended by the author has been adopted in order that t he student can readily identify the various atoms in a structure. It is, of course, made clear that we cannot say that atoms themselves are coloured but the colour used is t he familiar colour or property of that element in some familiar or known state of aggregation.

Various colour schemes are listed below for guidance.

TABLE III

COLOU R SCHEMES FOR MOLECULAR MODELS

Atom Author Courtaulds CHEM Study

H white cremn white c black black black 0 blue red red X grey blue blue Cl green green green )leta! reel or orange silver-grey aluminium

paint .F light green light green light green Br red -brown blue-green brown I violet dark green violet p yellow-white purple maroon s yellow-green yellow yellow

SUGGESTED STRUCTURES FOR MODELLING

l. Ionic: N aOI and OsOl. 2. Layer: lVIoS2 (see Wells5) , graphite,

Odi2•

3. Macmmolecular: ZnS ; diamond; ice I ; linked Si04 t etrahedra (silicates).

4. Fibrous: nylon 66; protein chain and (Z-hel:Lx; atactic and isotactic poly­isopropylene.

5. Molec~tlarstructures:cyclohexane (boat­chair) ; maleic-fumaric acid; hexa­methylene tetramine; azobenzene (cis­tmns); o-nitrophenol. Simpler organic molecules to demons­trate isomerism, asymmetry etc. (here the field is wide).

6. Simple inorgcmic st1·uct~tres: PC15 ; phos­phorus oxyacids; P4 , P40 6 and P40 10

(Model 4); S8, and zig-zag S puckered chains; simple anions (003

2-, N03-,

8032-, 8042-, P04

3- etc.); and hydrated cations, e.g. Al(K20)G3+ ; H20 2 and 0 3 ;

halogen molecules to illustrate relative sizes ; chlorine oxyacids; chlorides of second-period elements andj or third­period elements.

REFERENCES

l. Sanderson, R. T., Teaching Chemist1·y with Models. P rinceton and London: D. Van Nostrand, 1962.

2. Elford Plastics, Wood Street, Eiland, Yorkshire. 3. Star B and Co., Broad and Commerce Streets,

Portsmouth , Virginia, U .S.A. 4. Private communication. 5. Wells, A . F., Structural I norganic Chemistry.

Third Edition. Clarendon Press : Oxford Uni ­vers ity Press, 1962.

In addition, cla.ta for modelling purposes can l::e obtained by reference to: Pauling, L., 'l'he Natw·e of the Chemical Bond and

the Stntetttre of ll!folecules and Crystals. An introduction to modem structural Chemistry. Third Edition. I thaca, New York: Cornell U niversity Pross ; London: Oxford University Pross, 1960.

·wyckoff, R. W'., C1-ystal Structu1·es. New York and London: Interscience Publishers I nc., 1960.

'J.'ables of interatomic distances and configumtion in M~olecules and Ions. Chern. Soc., Spec. Pub!. 11, 1958.