Analytical Chemistry II

Transcription

1 Analytical Chemistry II L4: Signal processing (selected slides) Computers in analytical chemistry Data acquisition Printing final results Data processing Data storage Graphical display 1

2 Methods of using computers for analytical measurements Off-line On-line In-line Effect of noise in a current measurement In most measurements, the average noise N is constant and independent of the signal S. Signal-to-noise ratio (S/N) describes the quality of an analytical method/instrument. For a DC signal: S N = mean standard deviation = xҧ s Noisy signal Noise-free signal 2

3 Effect of signal-to-noise ratio on the clarity of spectral peaks It is impossible to detect a signal when S/N < 3. S N = 4.3 S N = 43 Sources of noise in chemical analyses Chemical analyses are affected by chemical and instrumental noise. Sources of chemical noise: o undetected variations of temperature and pressure affecting chemical equilibria o fluctuations in humidity affecting moisture content of samples o laboratory fumes that interact with samples/reagents Sources of instrumental noise: o thermal noise (thermal agitation of charge carriers) o shot noise (charge particles crossing a junction) o flicker noise (1/f, dominates at low frequencies) o environmental noise (composite of different forms of noise) 3

4 Sources of noise in a laboratory Signals can be converted to frequencies in the quiet-frequency regions to reduce noise during signal processing. Signal-to-noise enhancement Hardware-based: o grounding and shielding o analog filtering o modulation/demodulation o use of amplifiers Software-based: o ensemble averaging o digital filtering o correlation methods 4

5 Use of a low-pass filter to remove noise Low-pass filters can be used to improve S/N ratio because many instrument signals are of low frequency. The filter attenuates many of the highfrequency components, including thermal and shot noise. Similarly, band-pass filters can attenuate noise outside an expected band of signal frequencies. Ensemble averaging of a spectrum Successive sets of data stored in memory as arrays are collected and summed point by point for averaging. After the summation is complete, the data are averaged by dividing the sum for each point by the sets of data summed. 5

6 Digital filtering with the Fourier transform The original time-domain signal is converted to frequency-domain signal. The frequency-domain signal is multiplied by a signal response with upper cutoff f 0. The inverse Fourier transform recovers the filtered time-domain signal. Moving average smoothing The first few points are encompassed by bracket, averaged and plotted at the midpoint position. The bracket is moved one point to the right, and the following few points are averaged. The process is repeated until all the original data points are covered. A few (n-1)/2 points are lost due to smoothing. 6

7 Polynomial smoothing / Savitzky-Golay smoothing One performs least-squares fit of a small section of the data to a polynomial The calculated central point of the polynomial as the new smoothed data point. D 10 th degree, 77 points C 4 th degree, 13 points B 2 nd degree, 5 points A raw spectrum Analytical Chemistry II L4: Atomic absorption spectroscopy (selected slides) 7

8 Electromagnetic radiation Electric field oscillations Plane-polarized wave Two components of radiation Regions of electromagnetic spectrum Propagation of waves through a slit and diffraction of light All types of electromagnetic radiation exhibit diffraction. Diffraction is caused by interference phenomena. Wide slit Diffraction at two slits constructive interference Slit width comparable with the wavelength n = BCDE OD 8

9 electron kinetic energy Photoelectric effect When monochromatic radiation impinges on the photocathode, electrons are emitted from its surface. When the anode becomes negative, the electrons are stopped. The maximum (stopping) energy of the emitted electrons: KE m = ev 0 = h ω where h is Planck s constant, is the photon frequency, and is the work function. The photoelectric effect can only be explained by quantum model. Photocurrent is proportional to the light intensity. Stopping voltage depends on: light frequency, photocathode coating; but does not depend on: light intensity. photon frequency Energy states of chemical species quantum theory Atoms, ions, and molecules can exist only in certain discrete states, characterized by definite amounts of energy. When atoms, ions, or molecules absorb or emit radiation in making the transition from one energy state to another, the frequency or the wavelength of the radiation is related to the energy difference between the states by the equation: E 1 E 0 = h = hc where E 1 is the energy of the higher state, E 0 is the energy of the lower state, c is the speed of light, and h is the Planck constant. In atoms or ions, the energy of any state is due to the motion of electrons around the positively charged nucleus. This results in electronic states. In molecules, one can also observe vibrational states (due to interatomic vibrations) and rotational states (due to rotation of molecules around their center of mass). 9

10 Processes involved in emission spectroscopy In spectroscopy, the sample is stimulated by applying energy from heat, electricity, light, particles, or a chemical reaction. The analyte is initially in its lowest energy state (ground state). The stimulus then causes some analyte species to undergo transition to a higher energy state (excited state). We measure the electromagnetic radiation emitted as the analyte returns to the ground state or the amount of radiation absorbed or scattered during excitation. Excitation De-excitation (emission) Emission spectrum Processes involved in absorption spectroscopy When some of the incident radiation is absorbed, it promotes some of the analyte species to an excited state. In absorption spectroscopy, we only measure the amount of light absorbed as a function of wavelength. For absorption to occur, the energy of the incident photon beam must correspond to one of the energy differences. The obtained spectrum brings both qualitative and quantitative information. Lowering radiation intensity by the sample Energy levels Absorption spectrum Absorption 10

11 Transmittance and absorbance The absorption techniques require two power measurements: o before the beam has passed through the medium (P 0 ) o after the beam has passed through the medium (P) Transmittance (T) is defined as: Absorbance (A) is defined as: T = P P 0 A = log 10 T = log P 0 P Beer s Law: A = bc where b is optical pathlength, and is molar absorptivity. Single-beam photometer for absorption measurements in the visible region In photometer, the light passes through a filter to select one wavelength. The power of radiation is adjusted by a diaphragm. Two preliminary measurements are performed: o 0% T (with a mechanical shutter) to null the dark response of the system o 100% T (solvent cell in the light path) to set P 0 The solvent cell is replaced by the sample cell, and T is obtained. 11

12 Light absorption vs. emission Absorption spectrum Emission spectrum Continuous spectrum Atomic emission spectrum of sodium The two lines at nm and nm are the most intense, and responsible for the yellow color that appears when sodium salts are introduced into a flame. - Positions of bands are well-defined and characteristic of a given element - Qualitative analysis is easy in atomic spectroscopy Em Abs Na

13 Atomic emission spectrum of sodium The two lines at nm and nm are the most intense, and responsible for the yellow color that appears when sodium salts are introduced into a flame. Low resolution Medium resolution High resolution Na Atomic line widths Line broadening due to uncertainty effect o Due to the limited lifetime of excited states ( s) o Uncertainty principle: t 1 o = 1/lifetime o = ( 2 )/c o Typically: 10-5 nm (natural line widths) o See example 8-1. Doppler broadening o When an atom moves toward a photon detector and emits radiation, the detector sees wave crests more often and detects radiation of higher frequency. o When an atom moves away from a photon detector and emits radiation, the detector sees crests less frequently and detects radiation of lower frequency. o Typically: 2 orders greater than natural line widths Pressure broadening o It is caused by collisions of the emitting or absorbing species with other atoms or ions in the heated medium. o The collisions produce small changes in energy levels giving rise to a range of absorbed or emitted wavelengths. o Typically: 2-3 orders greater than natural line widths 13