1. 서 론 모든 조건을 만족시키는 분석법?

분석: 조성(화학) 과 함량

정성분석(qualitative), 정량분석(quantitative)

분석방법 분류

고전분석법 (화학분석법): 용액내 (화학)반응 등에 기초

기기분석법 (정성, 정량분석): 물리화학적 특성 정밀기기

일반적 감도(sensitivity)가 고전보다 좋다.

그러나 일괄적으로 말하기는 어렵다.

기기분석에는 어떠한 신호 이용???

고전 —separation by extraction, precipitation, distillation etc.; identification by color, mp, bp, solubility, odor, refractive index etc.; quantification by gravimetry or titrimetry

기기—requires electrically powered instrument to measure chemical, physical properties; sometimes used to assist classical methods 분광화학적 분석법

분리/분석법 전기분석법

기기 구 성: 신호발생장치 검출기 신호처리장치 및 출력변환기 판독장치

분석용 기기 : 사람이 직접 검출 혹은 이해할 수 없는 분석신호를 검출, 이해할 수 있는 신호의 형태로 변환

일반적 분석 과정

1. 분석 목적 결정

2. 시료 채취 및 보관(sampling and storage)

3. 시료 준비 (pretreatment or sample preparation)

4. 분석방법 결정

(choice of analytical method)

5. 분석 및 결과 평가 Complex 소프라도, 앨토, 테너, 베이스 등

1. 목적 결정

정성, 정량 ?

무엇(금속/비금속, 액체/기체..)분석

어떤 농도 수준 요구 ppm, ppb level ?

어떤 정도의 정확성/정밀성?

요구되는 시간, 시료수, 비용 등

2. 시료 채취 및 보관 (Sampling and Sample Storage)

Representative sample collection

Constituent concentration remains stable

Contamination problems 방지

Type of storage container (material, freezing

needed?)

• Inorganic constituents – plastics and Teflon

• Organic constituents – glass, metal, Teflon

시료채취: 대표성, 채취시료 stable, 오염방지, 채취 용기

(1) 기본 시료 채취 접근법

접근법 시료# 치우침 채취원리

판단 judgmental

smallest largest history or visual assessment of technical judgment

체계적 systematic

larger smaller consistent grid or pattern

무계획 random

largest smallest simple random selection

(2) 시료 형태: gas, liquid and solid….

Laboratory equipment

beaker

graduated cylinder

volumetric flask

volumetric pipet

Mohr pipet

serological pipet

micropipettors & syringes

beaker Notoriously inaccurate Precision ±10% at best

graduated cylinder • For non-critical work

• Precision typically ±1%

• Calibrated to deliver (TD) or to contain (TC) the indicated volume

volumetric flask • For exacting work in

preparing analytes, standards

• Precision typically ±0.01%

• Calibrated to contain (TC) the indicated volume

volumetric pipet • For exacting work

• Precision typically 0.01%

• Calibrated to deliver (TD) the indicated volume

mohr pipet

• A graduated pipet, much less precise than volumetric pipets

• Precision typically ±1%

• Calibrated to deliver (TD) the indicated volume

serological pipet

• Similar to Mohr pipet, with provision for sterile filter

• May be calibrated to deliver (TD) or to contain (TC); the latter requires blow-out to deliver indicated volume

micropipettors & syringes

• Ideal for small volumes, from less than 1 L to 5000 L

• Precision typically ±1% or less depending on volume

• Versatile but relatively expensive

기구 (채취, 보존) 선정

용기세정 ppm 용: 경질유리용기, 플라스틱용기

ppb - ppt 용기 세정 방법 :

시료보관(organics) 주의 사항 VOCs

microbial degradation

photolytic decomposition

저장용기로부터 오염

loss of analyte on the container walls 암소보관, 질산첨가, 황산 첨가등

중금속 저장 polyethylene 저장용기 > 유리저장 용기

acidified

scrupulous(꼼꼼한) cleaning of bottles

mass measurements

• analytical balance, top-loading balance, triple-beam balance

• For exacting work

• Modern instruments use electromagnetic strain gauge

• Precision typically ±0.1 mg

• Capacity often limited to 100-200 g total

Analytical balance

• Top loading balance – For routine work

– Modern instruments use electromagnetic strain gauge

– Precision typically ±0.01 g

– High capacity, typically 1 kg

• Triple-beam balance – For routine work

– Uses simple balance beam mechanism

– Precision typically ±0.1 g

– Very high capacity

3. 시료 (전)처리(준비) #separation and/or concentration of analyte from a complex matrix (분리/농축) # dissolution of solids

분석방법에 맞도록 시료처리

chemical extraction, distillation, separation, precipitation

물리적 전처리: 분쇄 등

화학적 전처리 (시료용해, 재만들기)

시료용해 : 성분과 조성 변화에 주의 물, acids

재만들기 ashing (건식재/고온, 습식재/농황산)

성분분리 - 방해물질 제거 목적/침전, 용매추출

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정수수 (pure water):

입자, 전기전도도, TOC, 미생물 등

증류수(distilled water) 여과 (filterated water)

이온(교환) (deionized water)

역삼투압 (RO)

유기물 흡착(활성탄 등)

살균 (자외선)

실험실용 물 분류(ASTM 4등급) laboratory grade (type Ⅲ, IV)/일반적 정성분석

analytical grade (type Ⅱ)/정량분석

reagent grade (type Ⅰ)/생명공학

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Ion-exchange

초순수제조에 가장 많이 사용 공급수에 존재하는 이온은 이온교환수지에 의해 제거 이온수지의 -H 와 -OH에 의하여 치환되는 방식이다. H 이온과 OH 이온은 결합되어 물 분자를 형성한다.

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Reverse osmosis 역삼투(Reverse osmosis, RO)는 증류와 이온교환정제법

의 부족한 점을 많이 극복한 정제법 삼투 현상은 자연적인 과정. 물 고농도 용액 쪽으로 반

투막을 통과

물의 흐름은 고농도의 용액이 저농도의 농도와 같아질 때까지 계속 (삼투 평형, osmotic equilibrium).

반투막에 걸려 있는 삼투압보다 더 큰 압력이 고농도 용액 쪽의 반투막에 걸릴 경우, 정상적인 삼투 현상이 역으로 됨.

순수한 물은 고농도의 용액으로부터 저농도 용액 쪽으로 반투막을 통과 고농도에 포함된 이온등의 불순물로부터 순수한 물이 반투막을 빠져나가 분리 역삼투 기초이론

Reverse osmosis

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Microporous filtration (미세입자 여과) : 미세입자 여과막 (microporous filtration membranes)은 0.1 m 이상의 모든 입자 및 미생물을 걸러내는데 사용. 많은 시스템에서는 0.05 m 까지 완벽하게 걸러내는 "ultra- micro filters" 를 사용.

UF(ultra-filtration, 한외여과 ) : 여과구멍 크기가 약간 큰 것(보통 0.001~0.02 m)을 제외하고는 역삼투 막과 디자인에서는 거의 같다. ultrafilters는 입자, 박테리아, 파이로젠 등이 제거되는 초순수를 만드는데 뛰어난 기술이다.

• 시약 등급 (reagent grade)

– 공업용(technical pure; T.P.) 시약

– 화학용 (C.P.) 시약

– 1급(extrapure reagent; E.P.)시약

– 특급시약 (guaranted reagent; G.R.)

• 순도 (purity) ?

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Data reduction and experimental error (자료 환원/변형 및 실험적 오차) • Data Reduction means to mathematically

process raw signal information into a form that can be easily understood and communicated

• All measurements have experimental error

• Two types of error

– Systematic (also called determinate errors)

– Random (also called indeterminate errors)

불확정

Systematic Errors

• arise from flaws in equipment or experimental design

• predictable (예측가능) • have a definite value and a known cause • reproducible with precision • can usually be corrected fairly easily • examples

– Analyte of interest in reagents (blank) – Error in making standards – Instrument not calibrated properly

Detection of systematic errors

• Analyze samples of known composition

– Standard Reference material

– Develop a calibration curve

• Analyze “blank” samples

– Verify that the instrument will give a zero result

• Obtain results for a sample using multiple instruments

– Verifies the accuracy of the instrument

Random errors • unpredictable and non-correctable changes in

signal for replicate measurements.

• arises from an unknown source that cannot be controlled

• caused by unknown and unpredictable changes in the experiment (measuring instruments or environmental conditions).

• examples – Variations in how an individual or individuals read the

measurements

– Instrumentation noise (기기잡음/Ch 1.4)

• always present and cannot always be corrected for

• correction for “noise” requires an understanding of random distributions

Random Error: results in a scatter of results centered on the true value

for repeated measurements on a single sample.

Systematic Error: results in all measurements exhibiting a definite

difference from the true value

Random Error Systematic Error

plot of the number of occurrences or population of each measurement (Gaussian curve)

comparison of random and systematic errors (random error affects precision, systematic

error affects accuracy)

Characterization of random distributions

• If a continuous random variable is

normally distributed or has a normal

probability distribution(정규확률분포), then a

relative frequency histogram of the random

variable has the shape of a normal or

Gaussian curve (bell-shaped and

symmetric).

Characterization of random distributions – The normal distribution

• A normal distribution is bell-shaped and symmetric.

• The distribution is characterized by the mean, (x or m, mu) and the standard deviation (s or s, sigma).

• The mean defines the center value and standard deviation defines the spread.

-

Characterization of random distributions – The Standard Deviation

• The standard deviation is the distance from the mean to the inflection point(변곡점) of the normal curve; the place where the curve changes from concave(오목) down to concave up.

• A smaller standard deviation means that your results are more reproducible (they don’t vary as much from measurement to measurement).

Standard Deviations and Areas Under the Normal Curve

• For any normal curve with mean mu (m) and standard deviation sigma (s): – 68 percent of the observations

fall within ±1 standard deviation of the mean.

– 95 percent of observation fall within ± 2 standard deviations.

– 99.7 percent of observations fall within ± 3 standard deviations of the mean.

Standard Deviation

• Standard Deviation – measures how closely the data are clustered about the mean. – The smaller the deviation, the more precise

the measurements

• We distinguish two types of standard deviations based on the number of samples involved – Population Standard Deviation (σ) – (N > 20)

– Sample Standard Deviation (s) - (N < 20)

Calculating a Standard Deviation

• Based on the difference between each value (xi) and the mean ( x or µ).

• Also based on the degrees of freedom

– For a sample std. dev. the degrees of freedom = N – 1

– For a population std. dev. The degrees of freedom = N

_

N

xN

i i

0

2)(

1

)(0

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N

xxs

N

i i

Curve Symmetry and Number of Observations :

• Symmetry increases as the number of observations increases

Distribution of distance measurements for projectile

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Distribution of distance measurements for projectile

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Distribution of distance measurements for projectile

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Distribution of distance measurements for projectile

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Distribution of distance measurements for projectile

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Distribution of distance measurements for projectile

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N = 100

N = 40 N = 200

N = 500

N = 1000

N = 5000

분석방법 결정/결과평가 공인된 방법 사용

신속성, 용이성/편리성, 조작자 숙련도, 이용가능성, 비용

정(밀)도 precision

정확도 accuracy

감도 sensitivity

검출한계 detection limit

정량한계 limit of determination

선택성(selectivity) ability to discriminate analyte of interest from complex background.

반복정도(repeatability)

재현정도(reproducibility)

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Difference between accuracy and precision

Low accuracy, low precision

Precision(정밀도) – reproducibility of replicate measurements on a single sample

Accuracy(정확도) – agreement between measured conc.

and true conc.

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정밀도 (precision) 표현법

절대편차 (absolute deviation) di=Ixi – xI

평균편차 (mean deviation) di = ∑ 절대편차/N

범위(range) R = xmax – xmin

s (표준편차) = √ ∑ (di2)/N-1

변동계수(coefficient of variation)(s/평균)*100%

상대표준편차의 백분율, 흐트러짐 정도

분산, 가변도(variance) s2 = ∑(di2)/N-1

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정확도(accuracy)표현법

절대(평균)오차 = (Xi – Xt) 참값과 실험값의 차

이

상대오차(relative error): 오차를 참값에 대한

백분율 (절대오차/ Xt * 100)%

상대정확도: 측정값(평균값)을 참값에 대한 백분율

로 표시 (측정값/ Xt * 100)%

예제) 2.5 g의 시료가 2.52g으로 측정되었다. 절대오차, 상대오차 및 상대정확도를 구하시오.

Sensitivity(민)감도

• The sensitivity of an instrument or method describes the ability to discriminate between small differences in analyte concentration

• 분석 물질사이의 작은 농도 차이를 식별할 수 있는 능력

• Calibration Sensitivity = the slope of a calibration curve at the concentration of interest

Analyte Concentration [A]

Sig

nal (S

)

Slope = S/[A] =

sensitivity

검정감도(calibration sen.) = 기울기 S(측정신호)=mC + Sb(바탕신호)

분석감도(analytical sen.)

(재현성을 고려한 감도)

A= m/sb

(sb=신호의 표준편차)

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검출한계 (detection limit) 주어진 신뢰도 수준에서 검출 가능한 분석물질의 최소농도 또는 무게

잡음(N)의 k배의 신호(S)를 나타내는 농도

Signal must be bigger than random noise of blank

Minimum signal: Smin = 평균Sblank + ksblank (1)

(평균바탕신호 + k*바탕신호 표준편차)

From statistics k=3 or more (at 95% confidence level) 바탕신호 표준편차 (sblank)

Sm = mCm + Sblank(바탕신호) Cm=(Sm- Sb)/m (2)

The LOD (limit of detection; DL) is the conc. at which one is 95% confidence the analyte is present in the sample. LOD = 3sb/m

The LOQ (- quantitation) is the smallest conc. at which a reasonable precision can be obtained. LOQ = 10sb/m

Detection Limit(DL, LOD) • Detection Limit is defined as the minimum

concentration (or weight) of analyte that can be confidently detected above the background or noise signal.

Two types: 1. Blank Limited (e.g. analyte in reagents)

2. Instrument Limited (e.g. electrical “noise” in the instrument signal)

Detection Limit (based on a blank signal) is defined as: 3x the standard deviation of a blank signal; reported as concentration units. D.L. = 3sblank

Determination of Detection Limit from Instrumental Noise

• A detection limit signal is estimated from a signal to noise ratio (S/N) of 2-3

• This is interpreted to mean a peak that is 2-3 times the average height of instrumental noise

Dynamic range

검출한계 분석물질이 확실하게 존재 여부 확실. 그러나

정량치의 신뢰여부 불확실.

LOQ(정량농도 한계): k=10

LOL(limit of linearity 선형농도 한계): 신호가 더 이상 농도에 비례하지 않는 지점

측정 가능한 농도 범위?

Working Range (Calibration Range)

• Reported as the range in concentration from the lowest to the highest analyte concentration that can reliably be quantified – Low end – detection

limit

– High end – end of linear region or the highest standard used

Sig

nal (S

)

Limit of Linearity

Analyte Concentration [A]

Detection Limit

Working

Range

Working Range vs. Dynamic Range in Quantitative Assays For any quantitative assay, the distinction between the dynamic range of an assay versus working range of an assay is an important consideration. Many believe the working range of an assay and the dynamic range of an assay are one and the same. However, this is not the case. Here we discuss the distinction between these two terms. For quantitative assays the dynamic range of an assay is described as the lowest to the highest concentration of an analyte that can be reliably detected by the assay. This is sometimes referred to as the lower and upper limits of detection (LLOD and ULOD, respectively). Although signal is detected, the accuracy and precision of this number may vary beyond what is acceptable to report as an accurate measure of the concentration of the target. Although still a useful measure, dynamic range is not as rigorous a measure of the true range of the assay. For most labs, the working assay range is a more meaningful measure of the upper and lower limits of quantitation (ULOQ/LLOQ) of an assay. The working range of an assay is commonly defined as the range over which analyte concentrations can be quantitated with acceptable precision and reliability. Because this is a stricter measure and requires both sensitivity and accuracy, the working range is typically narrower than the dynamic range. However, it is a more reliable measure of the true range of concentrations that can be accurately quantitated. As compared to the dynamic range, the values associated with working range of an assay are both precise (defined as how reproducible multiple measurements or calculations are) and accurate (defined as how close a measured or calculated quantity is to its true value).

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시료기질속에 포함되어 있는 다른 화학종으로부터 방해를 얼마나 받지 않느냐 하는 정도

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결과 분석 signal: 시료에 대한 기기분석의 결과

blank signal: analyte를 함유하고 있지 않은 시료에 대한 signal

대부분의 경우 신호는 analyte 농도에 비례

S = mC + Sb m= sensitivity; Sb=blank signal

standard curve (검량선)

How reproducible? – precision

How close to true value? – accuracy/bias

How small a difference can be measured? – sensitivity

What range of amounts? – dynamic range

How much interference? - selectivity

Illustration of the distribution of noise - replicate absorbance measurements

Trial Absorbance Trial Absorbance

1 0.488 26 0.483

2 0.480 27 0.482

3 0.486 28 0.491

4 0.473 29 0.481

5 0.475 30 0.469

6 0.482 31 0.485

7 0.486 32 0.477

8 0.482 33 0.476

9 0.481 34 0.483

10 0.490 35 0.476

11 0.480 36 0.490

12 0.489 37 0.488

13 0.478 38 0.471

14 0.471 39 0.48615 0.482 40 0.478

16 0.483 41 0.486

17 0.488 42 0.482

18 0.475 43 0.477

19 0.480 44 0.477

20 0.494 45 0.486

21 0.492 46 0.478

22 0.484 47 0.483

23 0.481 48 0.480

24 0.487 49 0.48325 0.478 50 0.479

Absorbance Number in

Range Range Frequency

0.469 1 2.0%

0.472 2 4.0%

0.475 3 6.0%

0.478 9 18.0%

0.481 8 16.0%

0.484 11 22.0%

0.487 7 14.0%

0.490 6 12.0%

0.493 2 4.0%

0.496 1 2.0%

Total 50 100.0%

MEAN = 0.482

STD = 0.0056