Young D.C. - Computational chemistry (2001)(en)
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40.3 PROPERTIES 313
Commercially produced elastic materials have a number of additives. Fillers, such as carbon black, increase tensile strength and elasticity by forming weak cross links between chains. This also makes a material sti¨er and increases toughness. Plasticizers may be added to soften the material. Determining the e¨ect of additives is generally done experimentally, although mesoscale methods have the potential to simulate this.
40.3.4Glass-transition Temperature
It is generally recognized that polymers with ¯exible chains tend to have low glass-transition temperatures. However, there is not yet any completely reliable way of making quantitative predictions. Group additivity methods have been proposed, but are only reliable for limited classes of compounds. The best method available is a structure±property relationship, which predicts Tg based on cohesive energy, the solubility parameter, and structural parameters that quantify chain rigidity. Methods combining group additivity with results from molecular mechanics simulations have also yielded encouraging results.
40.3.5Volumetric Properties
The van der Waals volume of a molecule is the volume actually occupied by the atoms. It is reliably computed with a group additivity technique. Connectivity indices can also be used.
The molar volume is usually larger than the van der Waals volume because two additional in¯uences must be added. The ®rst is the amount of empty space in the bulk material due to constraints on how tightly together the chains can pack. The second is the additional space needed to accommodate the vibrational motion of the atoms at a given temperature.
Many polymers expand with increasing temperature. This can be predicted with simple analytic equations relating the volume at a given temperature V…T† to the van der Waals volume Vw and the glass transition temperature, such as
V…T† ˆ Vw 1:42 ‡ 0:15 |
T |
…40:1† |
Tg |
However, this approach is of limited predictive usefulness due to the di½culty in predicting Tg accurately. Methods have been proposed for computing the molar volume at 298 K and thus extrapolation to other temperatures, which results in some improvement. These use connectivity indices. Note that it is necessary to employ di¨erent thermal expansion equations above and below Tg.
40.3.6Thermodynamic Properties
Thermodynamic properties, such as enthalpy, energy, entropy, and the like, are related to one another. Thus, some information must be obtained from the
314 40 POLYMERS
polymer structure, whereas other data are obtained through thermodynamic relationships. Most often, it is heat capacity as a function of temperature Cp…T† that is computed from the molecular structure.
The heat capacity can be computed by examining the vibrational motion of the atoms and rotational degrees of freedom. There is a discontinuous change in heat capacity upon melting. Thus, di¨erent algorithms are used for solidand liquid-phase heat capacities. These algorithms assume di¨erent amounts of freedom of motion.
40.3.7Solubility Parameters
The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers.
40.3.8Optical Properties
Computed optical properties tend not to be extremely accurate for polymers. The optical absorption spectra (UV/VIS) must be computed from semiempirical or ab initio calculations. Vibrational spectra (IR) can be computed with some molecular mechanics or orbital-based methods. The refractive index is most often calculated from a group additivity technique, with a correction for density.
40.3.9Mechanical Properties
For engineering applications, mechanical properties are extremely important. They are expressed as stress±strain relationships that quantify the amount of energy (stress) required to give a certain amount of deformation of the material (strain). These properties are dependent on crystallinity, orientation, and cross linking. They are also dependent on the material processing, thus making them di½cult to predict with molecular modeling techniques. Mesocscale techniques are probably the best a priori prediction method for these. However, structure± property relationships are often used instead for practical reasons (simplicity and minimal computer time). This section will focus on the simpler cases of completely crystalline and completely amorphous phases.
Several techniques are applicable to amorphous phases. QSPR techniques give mechanical properties as a function of glass transition temperature and the repeat unit size. These techniques are not reliable near the glass transition temperature. Molecular mechanics can also be used if the structure was obtained with a molecular-mechanics-based simulation. This consists of ®nding an energy for a section of the bulk material (often within a periodic boundary) and then shifting the size of the box and reoptimizing to obtain a second energy. Molecular dynamics and Monte Carlo simulations can be used to predict behavior near the glass-transition temperature.
BIBLIOGRAPHY 315
The molar sound velocity can be predicted with group additivity techniques. It, in turn, may be used to predict the mechanical properties due to highfrequency deformations.
Rubbery materials are usually lightly cross-linked. Their properties depend on the mean distance between cross links and chain rigidity. Cross linking can be quanti®ed by the use of functions derived from graph theory, such as the Rao or molar Hartmann functions. These can be incorporated into both group additivity and QSPR equations.
For crystalline polymers, the bulk modulus can be obtained from bandstructure calculations. Molecular mechanics calculations can also be used, provided that the crystal structure was optimized with the same method.
40.3.10Thermal Stability
It is important to know whether a polymer will be stable, that is, whether it will not decompose at a given temperature. There are several measures of thermal stability, the most important of which (from an economic standpoint) is the Underwriters Laboratories (UL) temperature index.
Unfortunately, there is not at a present a computational method for predicting the UL temperature index. There is a QSPR method for predicting Td; 1=2, the temperature of half-decomposition, meaning the temperature at which a material loses half of its mass due to pyrolysis. The QSPR method uses a connectivity index and weights for the number of various functional groups.
40.4RECOMMENDATIONS
Polymer modeling is a fast-growing ®eld. It remains primarily the realm of experts because the preferred methods and limitations of existing methods are still changing, thus requiring the researcher to constantly stay abreast of new developments. Group additivity and QSPR methods have been the mainstay of the ®eld due to the di½culty of alternative methods. However, mesoscale and other bulk simulations are becoming more commonplace. Researchers are advised to ®rst consider what properties need to be computed and to then explore the methods and software packages available for those speci®c properties.
BIBLIOGRAPHY
Books discussing polymer modeling are
A.K. RappeÂ, C. J. Casewit, Molecular Mechanics Across Chemistry University Science Books, Sausalito (1997).
J. Bicerano, Prediction of Polymer Properties Marcel Dekker, New York (1996).
Polymeric Systems, Adv. Chem. Phys. vol 94 (1996).
316 40 POLYMERS
A.Ya. Gol'dman, Prediction of the Deformation Properties of Polymeric and Composit Materials American Chemical Society, Washington (1994).
Computational Modeling of Polymers J. Bicerano, Ed., Dekker, new York (1992). Computer Simulation of Polymers E. A. Coulbourne, Ed., Longman-Harlow, London
(1992).
Computer Simulation of Polymers R. J. Roe, Ed., Prentice Hall, New York (1991).
H. R. Allcock, F. W. Lampe, Contemporary Polymer Chemistry Prentice-Hall, Englewood Cli¨s (1990).
D. W. van Krevelen, Propertis of Polymers Elsevier, Amsterdam (1990).
P.J. Flory, Statistical Mechanics of Chain Molecules Hanser, New York (1989).
Review articles covering polymer modeling in general are
J.J. Ladik, Encycl. Comput. Chem. 1, 591 (1998).
I.Szleifer, Encycl. Comput. Chem. 3, 2114 (1998).
V.Galiatsatos, Rev. Comput. Chem. 6, 149 (1995).
A.Baumgaertner, Top. Appl. Phys. 71, 285 (1992).
K.A. Dill, J. Naghizadeh, J. A. Marqusee, Ann. Rev. Phys. Chem. 39, 425 (1988).
Reviews of polymer dynamics are
J. Skolnick, A. Kolinski, Adv. Chem. Phys. 78, 223 (1990).
T. P. Lodge, N. A. Rotstein, S. Prager, Adv. Chem. Phys. 79, 1 (1990).
A review of graph theory techniques for describing polymers is
S. I. Kuchanov, S. V. Korolev, S. V. Panykov, Adv. Chem. Phys. 72, 115 (1988).
A review of liquid crystal modeling is
G. Marrucci, F. Greco, Adv. Chem. Phys. 86, 331 (1993).
A review of Monte Carlo simulations is
J. J. de Pablo, F. A. Escobedo, Encycl. Comput. Chem. 3, 1763 (1998).
Reviews of optical property simulation are
G. Orlandi, F. Zerbetto, M. Z. Zgierski, Chem. Rev. 91, 867 (1991). J.-M. AndreÂ, J. Delhalle, Chem. Rev. 91, 843 (1991).
Phase behavior modeling is reviewed in
K. S. Schweizer, J. G. Curro, Adv. Chem. Phys. 98, 1 (1997).
A.Yethiraj, Encycl. Comput. Chem. 3, 2119 (1998).
Quantum mechanical modeling of polymer systems is reviewed in
M. KerteÂsz, Adv. Quantum Chem. 15, 161 (1982). J.-M. AndreÂ, Adv. Quantum Chem. 12, 65 (1980).
BIBLIOGRAPHY 317
A review of semiempirical calculation applied to polymers is
J. J. P. Stewart, Encycl. Comput. Chem. 3, 2130 (1998).
Reviews of the statistical mechanical aspects of the problem are
K. W. Foreman, K. F. Freed, Adv. Chem. Phys. 103, 335 (1998).
S. G. Whittington, Adv. Chem. Phys. 51, 1 (1982).
H. Yamakawa, Ann. Rev. Phys. Chem. 25, 179 (1974).
K. F. Freed, Adv. Chem. Phys. 22, 1 (1972).
Computational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems. David C. Young Copyright ( 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-33368-9 (Hardback); 0-471-22065-5 (Electronic)
41 Solids and Surfaces
Solids can be crystalline, molecular crystals, or amorphous. Molecular crystals are ordered solids with individual molecules still identi®able in the crystal. There is some disparity in chemical research. This is because experimental molecular geometries most often come from the X-ray di¨raction of crystalline compounds, whereas the most well-developed computational techniques are for modeling gas-phase compounds. Meanwhile, the information many chemists are most worried about is the solution-phase behavior of a compound.
41.1CONTINUUM MODELS
The modeling of solids as a continuum with a given shear strength, and the like is often used for predicting mechanical properties. These are modeled using ®nite element or ®nite di¨erence techniques. This type of modeling is usually employed by engineers for structural analysis. It will not be discussed further here.
41.2CLUSTERS
One way to model a solid is to use software designed for gas-phase molecular computations. A large enough piece of the solid can be modeled so that the region in the center for practical purposes describes the region at the center of an in®nite crystal. This is called a cluster calculation.
When this calculation is done, the structure must be truncated in some fashion. If no particular truncation is used, the atoms at the outer edge of the cluster will have dangling bonds. This changes the behavior of those atoms, which in turn will a¨ect adjacent atoms that, in turn, requires more atoms in the simulation. For covalent bonded organic compounds, truncating the structure with hydrogen atoms is very reasonable since the electronegativity of a hydrogen atom is similar to that of a carbon atom and H atoms take the least amount of computational resources. For very ionic compounds, a set of point charges, called a Madelung potential, is reasonable. For compounds in between these two extremes, the choices are not so clear and must be made on a case-by- case basis. It is often necessary to perform a small study to determine which is the best choice.
318
41.7 RECOMMENDATIONS 319
41.3BAND STRUCTURES
As described in the chapter on band structures, these calculations reproduce the electronic structure of in®nite solids. This is important for a number of types of studies, such as modeling compounds for use in solar cells, in which it is important to know whether the band gap is a direct or indirect gap. Band structure calculations are ideal for modeling an in®nite regular crystal, but not for modeling surface chemistry or defect sites.
41.4DEFECT CALCULATIONS
The chemistry of interest is often not merely the in®nite crystal, but rather how some other species will interact with that crystal. As such, it is necessary to model a system that is an in®nite crystal except for a particular site where something is di¨erent. The same techniques for doing this can be used, regardless of whether it refers to a defect within the crystal or something binding to the surface. The most common technique is a Mott±Littleton defect calculation. This technique embeds a defect in an in®nite crystal, which can be considered a local perturbation to the band structure.
41.5MOLECULAR DYNAMICS AND MONTE CARLO METHODS
Molecular mechanics methods have been used particularly for simulating surface±liquid interactions. Molecular mechanics calculations are called e¨ective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force ®eld is parameterized correctly.
41.6AMORPHOUS MATERIALS
The modeling of amorphous solids is a more di½cult problem. This is because there is no rigorous way to determine the structure of an amorphous compound or even de®ne when it has been found. There are algorithms for building up a structure that has various hybridizations and size rings according to some statistical distribution. Such calculations cannot be made more e½cient by the use of symmetry.
41.7RECOMMENDATIONS
Overall, solid-state modeling requires more time on the part of the researcher and often more CPU-intensive calculations. Researchers are advised to plan on
320 41 SOLIDS AND SURFACES
investing a signi®cant amount of time learning and using solid-state modeling techniques.
BIBLIOGRAPHY
Some books on modeling these systems are
Theoretical Aspects and Computer Modelling of the Molecular Solid State A. Gavezotti, Ed., John Wiley & Sons, New York (1997).
C.Pisani, Quantum-Mechanical Ab Initio Calculation of the Properties of Crystalline Materials Springer-Verlag, New York (1996).
R.Ho¨mann, Solids and Surfaces; A Chemist's View of bonding in Extended Structures
VCH, New York (1988).
Structure and Bonding in Noncrystalline Solids G. E. Walrafen, A. G. Revesz, Eds., Plenum, New York (1986).
D. L. Goodstein, States of Matter Dover, New York (1985).
W. A. Harrison, Solid State Theory Dover, New York (1979).
B. Donovan, Elementary Theory of Metals Pergamon, Oxford (1967).
Reviews of solid state modeling in general are
A. Gavezzotti, S. L. Price, Encycl. Comput. Chem. 1, 641 (1998).
The application of ab initio methods is reviewed in
J. Sauer, Chem. Rev. 89, 199 (1989).
F.E. Harris, Theoretical Chemistry Advances and Perspectives D. Henderson (Ed.) 1, 147, Academic Press, New York (1975).
J. KouteckyÂ, Adv. Chem. Phys. 9, 85 (1965).
Surface adsorption is reviewed in
W. Stelle, Chem. Rev. 93, 2355 (1993).
E.Shustorovich, Modelling of Molecular Structures and Properties J.-L. Rivail, Ed., 119, Elsevier, Amsterdam (1990).
M. Simonetta, A. Gavezzotti, Adv. Quantum Chem. 12, 103 (1990). P. J. Feibelman, Ann. Rev. Phys. Chem. 40, 261 (1989).
M. M. Dubinin, Chem. Rev. 60, 235 (1960).
Amorphous solid simulation is reviewed in
C.A. Angell, J. H. R. Clarke, L. W. Woodcock, Adv. Chem. Phys. 48, 397 (1981).
Binding at surface sites is reviewed in
P. S. Bagus, F. Illas, Encycl. Comput. Chem. 4, 2870 (1998).
J. Sauer, P. Ugliengo, E. Garrone, V. R. Saunders, Chem. Rev. 94, 2095 (1994). E. I. Solomon, P. M. Jones, J. A. May, Chem. Rev. 93, 2623 (1993).
BIBLIOGRAPHY |
321 |
Cluster calculations are reviewed in
D. Michael, P. Mingos, Chem. Soc. Rev. 15, 31 (1986).
Electric double layer modeling is reviewed in
R. Parsons, Chem. Rev. 90, 813 (1990).
The application of molecular mechanics methods is reviewed in
A. M. Stoneham, J. H. Harding, Ann. Rev. Phys. Chem. 37, 53 (1986).
A review of methods for predicting properties of solids and surfaces is
E. Wimmer, Encycl. Comput. Chem. 3, 1559 (1998).
Reactions and dynamics at surfaces are reviewed in
D. G. Musaev, K. Morokuma, Adv. Chem. Phys. 95, 61 (1996). W. Schmickler, Chem. Rev. 96, 3177 (1996).
B. J. Garrison, P. B. Skodali, D. Srivastava, Chem. Rev. 96, 1327 (1996). B. J. Garrison, D. Srivastava, Ann. Rev. Phys. Chem. 46, 373 (1995).
B. J. Garrison, Chem. Soc. Rev. 21, 155 (1992).
J. W. Gadzuk, Ann. Rev. Phys. Chem. 39, 395 (1988). R. B. Gerber, Chem. Rev. 87, 29 (1987).
T. F. George, K.-T. Lee, W. C. Murphy, M. Hutchinson, H.-W. Lee, Theory of Chemical Reaction Dynamics Volume IV M. Baer, Ed., 139, CRC, Boca Ratan (1985).
Semiempirical modeling is reviewed in
F.Ruette, A. J. HernaÂndez, Computational Chemistry: Structure, Interactions, Reactivity Part B S. Fraga, Ed., 637, Elsevier, Amsterdam (1992).
Predicting the structure of crystalline solids is reviewed in
P. Verwer, Rev. Comput. Chem. 12, 327 (1998).
B. P. van Eijck, Encycl. Comput. Chem. 1, 636 (1998).
J. K. Burdett, Adv. Chem. Phys. 49, 47 (1982).
T. Kihara, A. Koide, Adv. Chem. Phys. 33, 51 (1975).
Solid vibrations and dynamics are reviewed in
M. J. Klein, L. J. Lewis, Chem. Rev. 90, 459 (1990).
W. J. Briels, A. P. J. Janson, A. van Der Avoird, Adv. Quantum Chem. 18, 131 (1986). O. Schnepp, N. Jacobi, Adv. Chem. Phys. 22, 205 (1972).
Computational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems. David C. Young Copyright ( 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-33368-9 (Hardback); 0-471-22065-5 (Electronic)
APPENDIX A
Software Packages
Most of the computational techniques discussed in this text have been included in a number of software packages. The general techniques are uniquely de®ned, meaning that a HF calculation with a given basis set on a particular molecule will give the exact same results regardless of which program is used. However, the choice of software is still important. Software packages di¨er in cost, functionality, e½ciency, ease of use, automation, and robustness. These concerns make an enormous di¨erence in determining what computational projects can be completed successfully and how much work will be involved.
This appendix is not intended to provide a comprehensive listing of computational chemistry software packages. Some of the software packages listed here are included because they are very widely used. Others are included because they pertained to topics discussed in this book. A few relevant pieces of software were omitted because we were not able to obtain an evaluation copy prior to publication.
Program functionality and prices change rapidly. Because of this, we have not made an attempt to list all the functions of each program. Many of the software packages can be purchased at various prices, depending on the options purchased and the existence of discounts, such as for academic use. Individual companies should be contacted for current price information. The pricing information given in this appendix is in the form of general price ranges. These are listed in Table A.1.
We have arranged this chapter by classes of software. The choice of which section each software package is listed in is based on the most common use of the package, rather than every detail of functionality. We have attempted to give an indication of what types of problems the software packages generally are or are not useful for. There are expected to be exceptions to all of these generalities. The reader of this book is urged to consider each package's speci®c application and discuss it with experienced computational chemists and the representatives of the software companies involved.
A.1 INTEGRATED PACKAGES
These are software packages that have the ability to perform computations using several computational techniques. Most also have an integrated graphic user interface.
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