Influence of thermal noise on the accuracy of mass determination according to the straubel method

33

Thetmochimica Acta, 103 (1986) 33-38 Ekevier Science Pubfiehers B.V., Amsterdam - Printed in The Netherlands

INFLUENCE

OF

THERMAL

ACCORDING

TO

THE

C. l-i.

A

NOISE

STRAUREL

MASSEN , J.A.

ACCURACY

OF

MASS

DETERMINATION

METHOD

POUtIS’

Department,

Physics

ON THE

,

E. RODENS'

Eindhoven

and H. STRAUDEL?

University

of

Technology

(The

Netherlands) 'Institut fiir Anorganische und Analytische Chemie der JohannesGutenberg-Universitat, Mainz (Federal Republic of Germany) %et-gweg

7, D-8973

Vorderhindelang

(Federal

Republic

of Germany)

ABSTRACT According to Straubel *s method, a small, charged particle is suspended in a three-plate condenser, connected with d.c. and a.c. voltages. Using this arrangement, mass variations can be measured because the particle retains its charge for hours even when reactions with the surrouding gas take place. It was pussible to measure mass changes of particles 3 /urn in diameter as a result af adsorption or desorption down to 0.1 pg. This paper deals with the influence of Brownian motion on the particle. The acting force,and hence, the weighing accuracy is calculated to be of the same order of magnitude and this seems to be the limit of resolution. INTRODUCTION

Straobel

(ref. suspended

particles and

2,3) changes

Lyon

of

sented.

1) described


small

Using

particles

this method

due to sorption,

- in

combination

The device

and droplets,

at

Stokes

mm

e.g. 40

and arranged

in a transparent

to observe

experiment

the particle

11 consists

lar plates,

drop

plastic

mass

was premass varia-

procescses or

optically

and -

mass,

of a capacitor

in diameter,

(ref.

to measure

evaporation

OF

charged

Uxbridge

respectively,

it was possible

simultaneously

00406031/86/$03.60

localizing

conferences

condensation

with the

(Fig.

the

of

4) the use of that method

tions

to determine

At

in air.

a method

spaced tube.

with

three

at intervals Each

Q 1936EbevierScienceFubkaheru B.V.

plate

circu-

of 12 mm

has a cen-

34

Fig.

1. Arrangement observation

tral bore hole, ther version voltage plate high

is equipped 2 kV,

exactly

field such

across a

middle

50 Hz is applied small

particles

will be trapped in its center

below the plate.

plate

12

mm

between

carrying

but, accarding

plater

- so called

way

that the particle

plate.

The particles

lamp and observed

through

as shown

in Fig. 2,

recorded

on a film.

hole. the

a

in the inhomogeneous

is centered

or droplets

a lateral

intermediate sufficiently

field

of

a d.c.

plates

in the level

of

can be illuminated

stereomicroscope

the

somewhat

applying

Millikan

Ano-

If an c1.c.

to its mass,

The mass can be counterbalanced

the outer

in diameter.

bore

with a slit-shaped

the ground,

charge

hole,

in the intermediate

of about and

of a three-plate-capacitar, particle mean% of a lateral stereomicroscope.

by

- in the by a

(Fig. 11 or,

by a laser beam and the diffraction

patterns

35

2.

Fig.

Schematic

drawing of a three-plate-capacitor. Illumination of a suspended droplet by a laser rhoordad phatosraphically

The trapped

particle

by the surrounding above Far

a certain further

that

changes

Because

the particle

suitable

the charge of

variation

- Also field

is raised

to oscillate.

is increased

just

its charge

below

for

the determination

many

of mass

P

/m

the particle

Mass

of

is the

Milfikan

mass mC by a d-c. field We obtain

observations

P'

variations

the

particle:

G! of the particle.

Am

measure

this arrangement

for

subsequent

to

may be used

methods

counterbalancing

mined

voltage

starts

retains

including

and - damped

are possible.

mass of the the suspended

case

suddenly

the voltage

variolrs measurements

position

If the a-c.

the particle

determinations

Different

- nest

in a stable

air - unmoving.

value,

voltage.

hours,

remains

beam,

a value

at constant

variations

method: acting

on

for CJ/mror - in

G! directly

up to 1/20OC~:,may

the mass

be

deter-

(ref. 1). the

onset

depends

the mass particle repeated

of

oscillation

on the ratio

variation

in some

are obtained determination

from

in function

Q/mP

cases.

and

may

be

Relative

the relation

of the voltage

of the applied used

mass

Amp/me

U, at which

to

a-c.

determine

changes

=Au,

of

/U,

the

by

oscillation

36

starts.

coefficient change5 mass

of

Because

only relative

of particle

variations

magnesium

perchlorate

of water particles

constant

the particle

mass according is

shaped

boring.

the

according

we measured and

3 /urn in diameter

cor-

down

ta 0.1 pg

to

particle

to Stokes

using

tilts

and to calculate

the candenser

and the fall

inclination

The method

the

measure

law.

measurement

the

to

veloci‘ty,

measured

is

with

without

is Limited

ta particles

spherical

particles

bigger

100 /urn in diameter.

Optically,

the

diameter

determined

by

rings.

some cases

In

measuring

suspended

particle,

particle

mass

measured

observation

For diameters

/urn may

pattern. be hardly Particles

t,7>,

suspended discharges.

because As

particle,

below

Furthermore, stimulated

a

io limited

result

and

Using

is

the

shwwn

and only

1st us say,

to

stabilize

can no Longer

voftages

investigations

to same respect.

be

from sire

below,

of high mass particles

consequence,

can

from the optical

particle

particles

high

the

in the condenser.

to oscillate

the corresponding

the

is known

density

that means

2 /urn the

be

by melting

The unknown

methods

can

diffraction

of the material

air pressures

of these

between

can be generated

can be calculated.

of the suspended

as diffraction

h-efs.

spheres

distances

Ef the density

limitations

reflexivity.

of the

at trro different

Practical

material

little

chloride

it is possible

The condenser

k?sil?g the particle.

3

of about

the condemsar

convenient

raduced

this method

on cafcium

rate of fall of a spherical

HWe

Thus,only

(ref. 2).

switching-off

than

density,

Using

vapour

friction

can be made neglecting

to a. mass of 40 pg. Mass variations

were observed

slit

and mean

can be measured.

isotherms

responding

on the squat-e of

determinations

diameter

sorption

- BY

dependence

the

generate

of high

be gas

density

condenrsar

with

37 slit-shaped particle

the measuring

more

than

100

the

of

est i mat i on

calculate

the stochastic

motion

particle.

increased

can be

to

/urn.

the

e+fect

forces and

of the particle The assessment

of

influencing compare

is valid

noise

we

can

the localization

or

thermal

it

with

for both,

the

weight

of the

the Millikan

method

the a.c.-experiment. Let

air.

consider

us

one spherical

This particle

and from

below.

will be hit by air molecules of each

to statistical

fluctuations

which

average

number

N of

OI-

below

from

N = 7t'r*F

where

vth

P n -- kT

Boltzmann

cause

molecules,

. is the number

in above

from

is submitted

the Brownian m,

suspended

both

collisions

mass

motion.

colliding

from

The above

by:

the

of molecules

p the pressure

per m3

velocity force

of the gas molecules

acting

on

the

,

T

the

absolute

(F'a), k = 1.4 :< 10-=

k-i- % and vt,,= WI is the mean i 1

constant

of

these

t-j

tm

the thermal

tainity

gas

can be estimated

CK),

temperature

(radius

particle

The number

of

range

NOISE

Far

and

of

diameters

THERMAL

the

hole

bare

particle

vertical in m/s.

is

J/K

$L

the

component The

uncer-

1 #q ¶J, trill

The resulting

force dF

on the particle

becomes:

(2)

Replacing

N and vth results

where

stands

M

of

the

molar

in:

mass

6 .0 x 10z6 kmol-' . The disturbing particle

radius.

For the numerical

and

force

N,

for

AF

Avogadro's is proporional

assessment

of the

number to the

resolution

38 limit

of the method

we insert

can be used for practical We take

the

.TO(:B K,

M

ambient (air) =

4 F w

29 kg/m


pg

motion

yields

and

this

above:

radius

which

3 n 10e6 m.

Fa, and the temperature

. We chose

a reasonable

or oscillating

and we obtain:

of the disturbing

to the

in the value

T =

time t, = 10 s

p.article,

for the uncertainty is clase

particle

as discussed

p = 10

2 :< tn-45 N. This estimation

Prownian wO.2

reasons

pressure,

for observing the falling

the smallest

force

due to

mass changes

mentioned

of

before

Zf.

REFERENCES 1

a

9 4

Straubel, Technisches Messen 48 (1981) 6, 199-210. Ii. G. Hiihme, E. Robens, H. Straubel, G. Walter, in S.C. Revan, S.J. Gregg, N.D. ParE:yns (Eds.f: Progress in Vacuum Micrdbalance Techniques, Vol. 2; Heyden, London i973, pp. 169-174. and Thermal Analysis. K.Sh. Mikhail, E. Robens: Microstructure of Solid Surfaces; Wiley, Chichester 1983, pp" 319~321,337-338. H. Straubel, in C. Eyraud, M. Escoubes: Frogress in Vacuum Microbalance Techniques, V.3; Heyden, London 1975, pp. 319-529,

5 b

H. H.

Straubel, Straubel,

7

E. Straubel,

Environmental

J.

Electrostatics

Atmospheric

10

(1981)

223-228.

Pollution 1978, Studies in Amsterdam 1979. Science Vol. 1, Elsevier, H. Straubel, J. Aerosol Sci. 15 (19841 6, 301-305 in: