1. Characterization

2. X-ray diffraction and crystal structure • X-rays have a wave length, l0.1-10Å. • This is on the size scale of the structures we wish to study X-rays interfere constructively when the interplanar spacing is related to an integer number of wavelengths in accordance with Bragg’s law:

3. Because of the numbering system, atomic planes are perpendicular to their corresponding vector, e.g., (111) is perpendicular to [111] The interplanar spacing for a cubic crystal is: Because the intensity of the diffracted beam varies depending upon the diffraction angle, knowing the angle and using Bragg’s law we can obtain the crystal structure and lattice parameter

4. Bragg’s law only describes the size and shape of the unit cell If there are parallel planes inside the unit cell, their reflections can interfere constructively and result in zero intensity of the reflected beamhence, different crystal structures will only allow reflections of particular planes according to the following rules:

5. Spectroscopy Electromagnetic energy, E = hn can excite electrons to higher molecular orbitals. The amount of energy varies with chemical structure. Wavelengths may cover the range from ultraviolet-visible (UV-VIS) to infrared (IR)

6. UV-VIS Spectrometers The source beam (at a frequency determined by the filter) is split and projected through the sample and a reference. The amount of transmitted energy is compared. This is repeated at different frequencies. If the sample absorbs energy at a particular wavelength it shows up as a difference in the amount of energy transmitted.

8. Standard curves are generated by measuring a known material in varying concentrations at a fixed wavelength (above). Concentrations of unknown samples can be determined by comparing absorbance to that of the standard curve. The amount of energy absorbed may be calculated using the Beer-Lambert law: A = elC Where A = absorbance e = molar absorption coefficient (material dependent) l = sample thickness C = molar concentration

9. Infrared (FTIR) Spectroscopy Infrared radiation excites molecules that contain a permanent dipole to vibrate strongly at resonant frequencies that are material dependent. Each material has a unique “molecular fingerprint”, allowing identification of through spectra comparison, and provides information on polymer structure and composition

10. Common types of 3-dimensional vibrations between atoms. “+” indicates movement out of the plane of the page.

11. IR spectrum of poly(styrene). Locations of high absorbance (e.g.3010-3100, 1500-1600, 690-900 above) are compared to reference data to determine structure.

12. Nuclear Magnetic Resonance (NMR) NMR excites changes in the nucleus of molecules in the radio-frequency range The nuclei behave as small magnets, whose orientation can be flipped from low to high energy states at particular field strengths by applying an external magnetic field. Biomaterials of interest are molecules containing H and C

13. NMR spectrum of poly(DL-lactic acid-b-ethylene glycol)-monomethyl ether diblock copolymer. By comparing relative shifts in resonant frequencies to a known standards (often tetramethylsilane ((CH3)4Si) the environment of the individual H atoms produces alterations in localized magnetic fields, resulting in different shifts that allow chemical structure to be distinguished.

15. Mass Spectrometry Mass spectroscopy measures the atomic or molecular masses of various species in a material. The sample is bombarded with high energy particles (typically electrons) then the irons are forced through a magnetic field, which deflects them from a linear path. Light elements are deflected more than heavy elements, allowing them to be distinguished from one another.

16. High Performance Liquid Chromatography (HPLC) and Size-Exclusion Chromatography • Provides information based on size and charge • SEC based on filtration by size • Determine molecular weight of synthetic and natural polymers System contains mobile and stationary phases Sample is dissolved into a liquid solvent (mobile phase) Porous silica or polymer beads are the stationary phase Analyte is removed from the mobile phase and retained by the porous structure Retention time is affected by the size of the analyte (i.e. smaller = longer) Residence time leads to separation of compounds by molecular weight

17. Results from SEC analysis of poly(ethylene glycol). (A) Size-exclusion chromatographs of eight PEG standards of known molecular weight, which is used to calibrate curve (B), which is used to determine the molecular weight, Mw or molecular number, Mn