The Structure of Materials
1.5 STRUCTURE OF BIOLOGICS
1.5.3 Soft Biologics
STRUCTURE OF BIOLOGICS 125
Cooperative Learning Exercise 1.8
The crystal structure of hydroxyapatite, shown in Figure 1.90, is a hexagonal unit cell with a=9.42 ˚A and c=6.88 ˚A. The relationship between interplanar diffraction spacing,d, and the lattice parameter for the HCP structure, analogous to Eqs. (1.33) and (1.34), is
d= 1
4 3
h2+hk+k2 a2 +l2
c2
The diffraction pattern for various forms of hydroxyapatite is shown in the Historical Highlight on page 122. Use this information to calculate the following.
Person 1: Use Bragg’s Law [Equation (1.35)] to calculate thed-spacing (in nm) for the first diffraction peak in hydroxyapatite. Assume a first-order diffraction and an X-ray source ofλ=0.1537 nm.
Person 2: Derive a relationship in simplest terms for thed-spacing of hydroxyapatite in terms of the Miller indices only (h, k, andl). Use the cell parameters in nm.
Combine your information to determine the Miller indices of the first diffraction peak for hydroxyapatite.
Answer :
= d 0.355nm;
1
2 d
= 1.51(h + 2
+ hk
2 k + ) 2.82l
; 2
(hkl)
= (111) for2
= θ
◦ 25 .
Osteoblast Osteoclast Collagen fibers Blood vessel
Figure 1.92 The structure of human bone. Reprinted with permission from S. K. Ritter,Chemi- cal & Engineering News, p. 27, August 25, 1997. Copyright1997 American Chemical Society.
numerous others, have all been used to repair or replace bone in humans. A review of the structure and effectiveness of these different materials is beyond the scope of this text, but the reader should be aware that this is one of the developing areas of materials engineering. Refer to some of the more recent review articles available on this topic [10–14], and keep an eye out for new developments as they come along.
soft biological materials are highly diversified, performing a myriad of highly spe- cialized and/or combinatorial functions. Earlier, we classified tissue into four general categories (muscle, nervous, epithelial, and connective). Although connective tissue is primarily a hard material, there are a number of connective tissues that are more like the other soft tissues, inasmuch as they do not have a significant fraction of the cal- cium phosphate-based inorganic phase. Instead of taking the traditional biology-based approach to classifying and characterizing soft materials, let us instead concentrate on four important proteins found in the extracellular matrix that allow these tissue types to execute their intended functions, as well as control our ability to introduce foreign objects—biomaterials—into the human body. These proteins are collagen, elastin, fibronectin, andlaminin.
Collagen is one of the most important and abundant substances in the human body.
It is not a single protein, but rather a group of at least five different proteins that have a similar structure. Collagen contains 30% glycine, 20% proline and hydroxyproline, and a modified version of hydroxylysine. The secondary structure of collagen is a triple helix (see Figure 1.93), but not an α-helix, because the high proline content prevents the formation of theα-helix. The three chains in the helix may be identical or different. There are at least 10 different types of collagen found in connective tissue (see Table 1.36), with types I–III having the ability to form fibers calledfibrils. Type I collagen is the principal structural component of most tissue. Type II and III collagens
Figure 1.93 Electron photomicrograph of collagen. Reprinted, by permission, fromChemistry of Advanced Materials, L. V. Interrante and M. J. Hampden-Smith, editors, p. 507. Copyright
1998 by Wiley-VCH, New York.
STRUCTURE OF BIOLOGICS 127
Table 1.36 Types of Collagen Found in Tissuea Collagen
Type Tissue or Organ Location
I Tendon, skin, bone and fascia Thick extracellular fibrils and fibers
II Cartilage Thin fibrils around cartilage cells
III Cardiovascular tissue Intermediate-size extracellular fibrils
IV Basement membranes Network-forming component
V Tendon, skin and cardiovascular tissue Pericellular matrix around cells VI Cardiovascular tissue, placenta, uterus,
liver, kidney, skin, ligament and cornea
Extracellular matrix
VII Skin Anchoring fibrils
VIII Cardiovascular tissue Around endothelial cells
IX Cartilage Extracellular matrix
X Cartilage Extracellular matrix
1α,2α,3α Cartilage Extracellular matrix
aSee G. R. Martin, R. Timpl, R. K. Muller, and K. Kuhn,Trends Biochem. Sci.,9, 285 (1985).
cytoplasm
protein
plasma membrane actin cytoskeleton
fibronectin (an adhesive glycoprotein)
extracellular matrix (collagens, proteoglycans)
fibronectin receptor (an integrin)
R G D
Figure 1.94 The function of integrin. From H. R. Matthews, R. Freedland, and R. L. Miesfeld, Biochemistry: A Short Course. Copyright1997 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
are found in cartilage (II) and cardiovascular tissue (III), among other places. Type IV collagen is found in basement membranes, which are sheet-like structures found beneath epithelial cells or blood vessel linings (endothelial cells).
Elastin is a protein also found in connective tissue that imparts an ability for these tissues to undergo large shape and size changes without permanent damage to the
tissue. Elastin is the amorphous component (up to 90%) of elastic fibers that are found in the extracellular matrix of most tissue. For example, the aorta has an elastin content as high as 30–60% of the dry weight—higher than that of any other tissue. Skin, in contrast, contains less than 5% elastin by weight. Elastin is similar to collagen in that it is composed of about 33% glycine and 13% proline, but it contains no hydroxyproline, and contains 10–14% valine and 21–24% alanine. The later two amino acids are nonpolar and do not form hydrogen bonds with water molecules. There are a number of crosslinks between the elastin chains, as one would expect for an elastic substance.
Fibronectin and laminin are adhesion proteins responsible for linking the outer surface of cells to collagens and other components in the extracellular matrix.
Both fibronectin and laminin areglycoproteins—proteins that contain polysaccharide residues. Fibronectin binds to cells through a tripeptide sequence (–Arg–Gly–Glu–) called RGD, which binds to the fibronectin receptor, one of a family of cellular transmembrane proteins called integrins (see Figure 1.94). Integrins link the extracellular matrix to the cytoskeleton. We will discuss integrins in more detail in Chapter 3.
REFERENCES Cited References
1. Index of Polymer Trade Names, Fachinformationszentrum Chemie GmbH, Berlin, 1987.
2. www.matweb.com/search/SearchTradeName.asp
3. Sung, Y. M., K.-Y. Yon, S. A. Dunn, and J. A. Koutsky, Wetting behavior and mullite for- mation at the interface of inviscid melt-spun CaO–Al2O3 fibre-reinforced Al–Si (4032) composite,J. Mater. Sci., 29, 5583 – 5588 (1994).
4. Suchanek, W., and M. Yoshimura, Processing and properties of hydroxyapatite-based bio- materials for use as hard tissue replacement implants.J. Mater. Res.,13(1), 94 (1998).
5. de Jong, W. F.,Rec. Trav. Chem. Pays-Bas,45, 445 (1926).
6. Mehmen, M.,Z. Kristallogr.,75, 323 (1930).
7. St. Naray-Szabo,Z. Kristallogr.,75, 387 (1930).
8. Posner, A., A. Perloff, and A. F. Diorio,Acta Crystallogr.,11, 308 (1958).
9. Narasaraju, T. S., and D. E. Phebe, Some physico-chemical aspects of hydroxyapatite,J.
Mater. Sci.,31, 1 (1996).
10. Ritter, S. K., Boning up,Chem. Eng. News, August 25, 1997, p. 27.
11. Lavernia, C., and J. M. Schoenung, Calcium phosphate ceramics as bone substitutes,Ceram.
Bull.,70(1), 95 (1991).
12. Kelsey, D. J., G. S. Springer, and S. B. Goodman, Composite implant for bone replacement, J. Compos. Mater.,31(16), 1593 (1997).
13. Dee, K. C., and R. Bizios, Proactive biomaterials and bone tissue engineering, Biotech.
Bioeng.,50, 438 (1996).
14. Mansur, C., M. Pope, M. R. Pascucci, and S. Shivkumar, Zirconia-calcium phosphate com- posite for bone replacement,Ceram. Int.,24, 77 (1998).
General
Wyckoff, R. W. G.,Crystal Structures, 2nd ed., Interscience, New York, 1963.
Ralls, Kenneth M., T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engi- neering, John Wiley & Sons, New York, 1976.
REFERENCES 129
Jastrzebski, Z., The Nature and Properties of Engineering Materials, 2nd ed., John Wiley &
Sons, New York, 1976.
Barrett, Craig R., W. D. Nix, and A. S. Tetelman, The Principles of Engineering Materials, Prentice-Hall, New York, 1973.
Callister, William D.,Materials Science and Engineering, An Introduction, 5th ed., John Wiley
& Sons, New York, 2000.
Handbook of Industrial Materials, 2nd ed., Elsevier, Oxford, 1992.
Encyclopedia of Chemical Technology, H. Mark et al., eds., John Wiley & Sons, New York, 1972.
Treatise on Materials Science and Technology, Vols, 1 – 19, Academic Press, New York.
Taylor, G. D.,Construction Materials, Longman Scientific, Essex, 1991.
Materials Chemistry, L. V. Interrante, L. A. Casper, and A. B. Ellis, eds., ACS Advances in Chemistry Series, Volume 245, American Chemical Society, Washington, D.C., 1995.
Materials Handbook, G. S. Brady and H. R. Clauser, eds., 13th ed., McGraw-Hill, New York, 1991.
Amato, I.,Stuff—The Materials The World Is Made Of, Basic Books, New York, 1997.
Metals
Darkin, L. S. and R. W. Gurry,Physical Chemistry of Metals, McGraw-Hill, New York, 1953.
Metals Handbook, 9th ed., ASM Handbook Committee, W. H. Cubberly, director, American Society for Metals, Metals Park, OH, 1978.
Ceramics
Kingery, W. D., H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 3rd ed., John Wiley & Sons, New York, 1993.
Somiya, S.Advanced Technical Ceramics, Academic Press, New York, 1989.
Yanagida, H, K. Koumoto, and M. Miyayama,The Chemistry of Ceramics, John Wiley & Sons, New York, 1996.
Glass
Doremus, R. H.,Glass Science, John Wiley & Sons, New York, 1973.
Scholze, H.,Glass—Nature, Structure and Properties, Springer-Verlag, New York, 1991.
Morey, G. W.,The Properties of Glass, 2nd ed., Reinhold, New York, 1954.
Bansal, N. P., and R. H. Doremus, Handbook of Glass Properties, Academic Press, Orlando, FL, 1986.
Experimental Techniques of Glass Science, C. J. Simmons and O. H. El-Bayoumi, eds., Ameri- can Ceramic Society, Westerville, OH, 1993.
Polymers
Billmeyer, F. W.,Textbook of Polymer Science, 3rd ed., John Wiley & Sons, New York, 1984.
Encyclopedia of Polymer Science and Engineering, Herman F. Mark, et al., eds., John Wiley &
Sons, New York, 1985.
Hiemenz, P.,Polymer Chemistry, Marcel Dekker, New York, 1984.
Rodriguez, F.,Principles of Polymer Systems, 2nd ed., McGraw-Hill, New York, 1982.
Tadokoro, H.,Structure of Crystalline Polymers, Krieger, Malabar, FL, 1990.
Liquid Crystalline Polymers
Cser, F., Relationship between chemistry and properties of liquid crystalline polymers,Mater.
Forum,14, 81 – 91 (1990).
Chung, T.-S, The recent developments of Thermotropic Liquid Crystalline Polymers, Polym.
Eng. Sci.,26(13), 901 – 919 (1986).
Goodby, J. W., Melting phenomena and liquid-crystalline behavior, Chemlog Highlights, 11, 3 – 7 (1987).
Fergason, J. L., Liquid Crystals,Sci. Am.,211(2), 76 (1964).
Composites
Composite Materials Handbook, M. Schwartz, ed., 2nd ed., McGraw-Hill, New York, 1984.
Concise Encyclopedia of Composite Materials, A. Kelly, ed., Pergamon, Elmsford, New York, 1994.
Suresh, S., and A. Mortensen,Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behavior of Graded Metals and Metal–Ceramic Composites, Ashgate Publishing Co., Brookfield, VT (1999).
Biologics
Matthews, H. R., R. Freedland, and R. L. Miesfeld,Biochemistry: A Short Course, John Wiley
& Sons, New York, 1997.
Schumm, D. E.,Essentials of Biochemistry, 2nd ed., Little, Brown & Co., Boston, 1995.
Houston, M. E., Biochemistry Primer for Exercise Science, Human Kinetics, Champaign, IL, 1995.
Silver, F. H.,Biological Materials: Structure, Mechanical Properties, and Modeling of Soft Tis- sues, New York University Press, New York, 1987.
DeCoursey, R. M., and J. L. Renfro,The Human Body, 5th ed., McGraw-Hill, New York, 1980.
PROBLEMS Level I
1.I.1 Calculate the force of attraction between a K+ and O2− ion whose centers are separated by a distance of 2.0 nm.
1.I.2 Estimate the % ionic character of the interatomic bonds in the following com- pounds: TiO2, ZnTe, CsCl, InSb, and MgCl2.
1.I.3 An amino acid has three ionizable groups, theα-amino andα-carbonyl groups and a side chain that can be positively charged. The pK values are 7, 3, and 11, respectively. Which of the following pH values is nearest to the isoelectric point (the point at which the overall net charge is zero) for this amino acid:
1.1, 5.3, 12.2? Explain your answer.
1.I.4 Calculate the radius of a palladium atom, given that Pd has an FCC crystal structure, a density of 12.0 g/cm3, and an atomic weight of 106.4 g/mol.
1.I.5 Cite the indices of the direction that results from the intersection of each of the following pair of planes within a cubic crystal: (a) (110) and (111) planes;
(b) (110) and (110) planes; (c) (101) and (001) planes.
PROBLEMS 131
1.I.6 (a) Can fully cured Bakelite be ground up and reused? Explain. (b) Can poly- ethylene be ground up and reused? Explain.
1.I.7 (a) Calculate the molecular weight of polystyrene having x=100,000. (b) Calculate the approximate extended chain length of one of the molecules.
1.I.8 In the formaldehyde molecule, H2CO, a double bond exists between the car- bon and oxygen atoms. (a) What type of hybridization is involved? (b) The molecule is found to be planar; one bond between the C and O atoms is a σ bond, and the other is aπ bond. With a simple sketch, show the atomic orbital overlap that is responsible for theπ bond.
1.I.9 Calculate the energy of vacancy formation in aluminum, given that the equi- librium number of vacancies at 500◦C is 7.57×1023 m−3. State your assump- tions.
1.I.10 Draw an orthorhombic cell, and within that cell draw a [211] direction and a (021) plane.
1.I.11 Which of the following molecules is (are) paramagnetic: O22+; Be22+; F22+? 1.I.12 Estimate the coordination number for the cation in each of these ceramic
oxides: Al2O3, B2O3, CaO, MgO, SiO2, and TiO2.
1.I.13 Which ions or atoms of the following pairs have the greatest radius: K/K+; O/O2−; H/He; Co/Ni; Li/Cl; Li+/Cl−; Co2+/Ni2+?
1.I.14 Draw structural formulas comparing starch with cellulose.
1.I.15 Show the centers of positive and negative charge in (i) CCl4, (ii) C2H2Cl2, and (iii) CH3Cl. Which of these molecules can have two forms?
1.I.16 Which of the following substitutions in anα-helical part of a protein is most likely to affect the function of the protein: Glu→Asp; Lys→Arg; Val→Phe;
Ser→Cys; or Gln→Pro?
Level II
1.II.1 A somewhat inaccurate, but geometrically convenient way of visualizing car- bon bonding is to consider the carbon nucleus at the center of a tetrahedron with four valence electron clouds extending to corners of the tetrahedron. In this scheme, a carbon–carbon single bond represents tetrahedra joined tip- to-tip, a double bond represents tetrahedra joined edge-to-edge, and a triple bond represents tetrahedra joined face-to-face. Calculate the expected ratio of single, double, and triple bond lengths according to this geometrical interpre- tation and compare with the measured bond lengths shown below. Comment on your results.
Bond Type Bond Length (nm) C–C single bond 0.154 C–C double bond 0.134 C–C triple bond 0.120
1.II.2 A recent article [James, K. and J. Kohn, New biomaterials for tissue engineer- ing, MRS Bull., 21(11), 22–26 (1996)] describes the use of tyrosine-derived
polycarbonates for tissue engineering, specifically as a resorbable substrate for small bone fixation. Three similar polycarbonates (DTE, DTH, and DTO) were considered, all having the general structure shown below where the size of the
“pendant” chain (side chain in the circle) can be varied during synthesis. If x=2, the pendant chain contains an ethyl group, and the polymer is called DTE (“E” for ethyl). Similarly,x=6 for DTH (“hexyl”) andx=8 for DTO (“octyl”). If the weight average molecular weight for DTH is 350,000, what is its number average degree of polymerization, assuming that it is monodis- persed?
O CH2 CH2 C O
NH CH CH2 O C
O
C O
O
(CH2)x−1 CH3
diphenol component
n
1.II.3 For both FCC and BCC crystal structures, the Burger’s vector b may be expressed as
b= 12a[hkl]
whereais the unit cell length and [hkl] is the crystallographic direction having the greatest linear atomic density. (a) What are the Burger’s vector representa- tions for FCC, BCC, and SC structures? (b) If the magnitude of the Burger’s vector |b|is
|b| = 12a(h2+k2+l2)
1 2
determine the values of|b| for aluminum and tungsten.
1.II.4 Bragg’s Law [Eq. (1.35)] is a necessary but not sufficient condition for diffrac- tion by real crystals. It specifies when diffraction will occur for unit cells having atoms positioned only at cell corners. However, atoms situated at other sites (e.g., face and interior positions in FCC or BCC) act as extra scattering cen- ters, which can produce out-of-phase scattering at certain Bragg angles. The net result is the absence of some diffracted beams that, according to Eq. (1.35), should be present. For example, for the BCC crystal structure,h+k+l must be even if diffraction is to occur, whereas for FCC, h, k, and l must all be either odd or even. Use this information to determine the Miller indices for the first five reflections that are present for a single atom BCC and FCC unit cell.
The first reflection is defined to be the one closest to 2θ =0. (Contributed by Brian Grady)
1.II.5 Indicate which of the following pairs of metals would not be likely to form a continuous series of solid solutions: Ta–W; Pt–Pb, Co–Ni, Co–Zn, and Ti–Ta.
Check your predictions in the Metals Handbook.
PROBLEMS 133
1.II.6 An article related to acrylic bone cements [Abboud, M. et al., PMMA-based composite materials with reactive ceramic fillers: IV. Radiopacifying particles embedded in PMMA beads for acrylic bone cements, J. Biomed. Mater. Res., 53(6), 728 (2000)] provides the following information on the PMMA matrix used in these cements:Mw=295,000;Mw/Mn=2.2. Calculate the number average degree of polymerization for the PMMA used in this study.
Level III
1.III.1 Al2O3 will form a limited solid solution in MgO. At a specific temperature called the “eutectic temperature” (1995◦C), approximately 18 wt% of Al2O3
is soluble in MgO. Predict the change in density on the basis of (a) interstitial Al3+ ions and (b) substitutional Al3+ ions.
1.III.2 The three materials listed in the table below are available in either fiber or sheet form. Each material may also be used as a matrix. The individ- ual physical and chemical characteristics listed in the table are independent of geometry.
Strength (kpsi) Density (g/cm3) Oxidation Resistance
Polymer 1 1 Poor
Metal 97 7 Poor
Ceramic 21 3 Excellent
Design a composite that has good oxidation resistance, a density of less than 3.0 g/cm3 and anisotropicstrength of at least 30 kpsi. You need not use all three materials in your design.
Assume:
ž Density is a summation effect; the total density is a weight average of the components.
ž Oxidation resistance is a complementary effect.
ž Strength is either an interactive or a summation effect, depending on the form of the material. The total strength of the composite is three times the strength of the matrix for one-dimensional fiber orientation in a fiber- matrix composite (FMC). The total strength is two times the strength of the matrix for two-dimensional fiber orientation in an FMC. Three- dimensional (random) fiber orientation, or a nonfibrous composite causes the total strength to be a weight average of all the components.
Describe the form (e.g., fiber, matrix, layer, etc.) of each material in your composite and the weight fraction of each component. Also indicate the com- posite density and strength. Make a diagram of your composite, indicating the different components and any important features.
1.III.3* As an oxide modifier (such as Na2O) is added to silica glass, the oxygen- to-silicon ratio increases, and it is empirically observed that the limit of glass formation is reached when O/Si is about 2.5 to 3. Explain, in terms of structure, why a soda–silica mixture such that 2<O/Si<2.5 will form a glass, whereas a soda–silica mixture such that O/Si = 3 will crystallize rather than forming a glass.
1.III.4 In an article [M. S. Dresselhaus et al., Hydrogen adsorption in carbon mate- rials, MRS Bull.,24(11), 45 (1999)] on the storage of molecular hydrogen, the use of carbon as an economical, safe, hydrogen storage medium for a hydrogen-fueled transportation system is discussed. Use the following excerpts from this article to provide answers to the following questions.
“To gain insight into the hydrogen adsorption problem, it is first necessary to review a few basic facts about hydrogen molecules and the surfaces to which they might bind. In the ground state, the hydrogen molecule is nearly spherical . . . and the intermolecular interaction between H2 molecules is weak. Experimentally, solid hydrogen at 4.2 K forms a hexagonal close- packed structure, with lattice parametersa=3.76 ˚A andc=6.14 ˚A.”
(a) What is the axial ratio for the hexagonal cell of solid hydrogen molecules?
(b) What is the theoretical axial ratio for a hexagonal cell? (c) Compare your answers to parts (a) and (b). What does the difference between them, if any, mean physically?
The article continues:
“Using purely geometric arguments, we can thus gain a simple geomet- ric estimate for the close-packing capacity of hydrogen molecules above a plane of graphite. Graphite has a honeycomb structure, with an in-plane lat- tice parameter,ag=2.46 ˚A and an interplanar separation of 3.35 ˚A. Since the value of the. . .diameter for the hydrogen molecule is greater than ag, the closest packing of hydrogen molecules would have to be incommen- surate with the (graphite surface). Commensurate H2 adsorption on a two- dimensional. . . superlattice would yield a lattice constant ofa=4.26 ˚A.”
(See figure below.)
Relative density of a√ 3×√
3 commensurate (top) and an incommensurate (bottom) monolayer of H2on a graphite surface. Reprinted, by permission, from M. S. Dresselhaus, K. A. Williams, and P. C. Eklund,MRS Bulletin,24(11), p. 47. Copyright1999 by Materials Research Society.