The foundations of the construction of differential-prism-type automatic liquid refractometers and the factors

that lead to measurements errors, such as variations in the optical density and temperature of the liquid

being analyzed in a dynamic mode in a cell, scattering of radiation in the cell, and the wedge shape of the

glasses of the cuvette, are considered.

Key words: refractometer, index of refraction, optical density, dynamic characteristics.

The determination of the refractometric constants is a step that is widely employed in the practice of industrial con-

trol of process media. The basic goal of refractometric analyzers is to find the optical characteristics of particular media, for

example, the index of refraction and concentration of a particular substance, on the basis of a functional relationship with the

index of refraction in two- or multi-component media by means of associated media. An analysis of ternary and more com-

plex mixtures is often performed by means of a refractometric method together with determination of other physical proper-

ties and (or) chemical processing of the particular liquid.

The method of a liquid difference (or differential) prism based on a version of the Anderson prism is the most com-

mon method employed in constructing an automatic refractometer (or refractometric analyzer) for use in monitoring transpar-

ent liquids. The information parameter of a differential-prism-type refractometric analyzer is realized in the form of a variation

in the angular position of the beam as the emission interacts with the comparison liquid and liquid to be analyzed in the dif-

ferential cuvette. TIR (total internal reflection) refractometric analyzers are used to monitor nontransparent and other liquids,

including viscous suspensions, under laboratory conditions and, more rarely, when monitoring industrial flows [1].

The problems associated with the construction of differential-prism-type automatic industrial refractometric analyz-

ers are related to measurements of small variations in the index of refraction and equivalent measurements of small angular

displacements:

∆α = arcsinα – (n /n0)arcsinα,

where α is the angle between the normal to the refracting surface and the beam direction; ∆α, variation in the direction of the

beam; and n, n0, indices of refraction of the liquid being analyzed and of the comparison liquid, respectively.

For a hollow prism, the index of refraction is found from the expression [2]

where i is the angle of incidence; β, angle between output beam and normal to the exit edge of the prism; and α, refracting

angle of prism.

n ii

= −+

sin(sin cos sin )

sin,2

2

2

β α

α

Measurement Techniques, Vol. 50, No. 6, 2007

AUTOMATIC DIFFERENTIAL PRISM REFRACTOMETER

FOR MONITORING PROCESS LIQUIDS

M. A. Karabegov UDC 555.32

Research Institute for Introscopy, Spektr MNPO; e-mail: karabegov@rambler.ru. Translated from Izmeritel’naya

Tekhnika, No. 6, pp. 31–36, May, 2007. Original article submitted October 30, 2006.

0543-1972/07/5006-0619 ©2007 Springer Science+Business Media, Inc. 619

For a differential prism in which the entry and exit faces are parallel and the beams are directed along the normal to

its faces, the deviation of the beam will be given by

where α is the angle between the entering beam and the normal to the interface of the prism system; n1 and n2, indices of refrac-

tion of the first and second prism, respectively; and β, angle between the beam exiting the prism and its initial direction.

With low values of the difference N – n = ∆n, the value of ∆n is determined with respect to a shift ∆x in the image

of the slot of the illuminating collimator proportional to ∆n. Since the plane of the image of the slot is at a distance l from

the cuvette, sinα = ∆n tanα and sinβ ≈ tanβ = ∆x/l, while for a two-prism system ∆n = ∆x/l tanα and for a three-prism sys-

tem, ∆n = ∆x/2l tan(α/2).

The index of refraction of a substance depends on the concentration of a particular component, the wavelength of

the radiation, temperature, pressure, and other factors.

The dependence of the index of refraction on temperature and concentration for solutions with different temperature

coefficients is as follows:

nθ = C1[n1 + (dn1/dθ)∆θ] + C2[n2 + (dn2/dθ)∆θ],

where nθ is the index of refraction of the solution under normal conditions; C1, C2, n1, and n2, concentration and indices of

refraction of the first and second component, respectively; dn1/dθ and dn2/dθ, temperature coefficients; and ∆θ, deviation

of temperature of the solution from normal conditions.

A cuvette converter (or simply cuvette) is among the basic units of an automatic refractometric analyzer. It is usual-

ly produced in the form of a prism with plane or cylindrical faces and consisting of two tanks, a flow-through tank for the liq-

uid being analyzed and a closed tank for the comparison liquid. The closed tank is situated within the flow-through tank in

order to assure the required heat exchange between the liquids, required range of variation, and required sensitivity (Fig. 1).

A cuvette refractometer with closed tank in the form of a half-cylinder capable of rotating about an axis in order to

achieve a mounting at different angles makes it possible to regulate and establish a required range of measurements of the

device while preserving a constant value of the beam shift.

The cuvette converter is produced in the form of two coaxial cylindrical tubes (Fig. 2) in order to achieve effective

analysis of viscous, polymerizing, liquids, such as motor oils, plastics, melalite, edible substances, etc. The inner tube is

sin sin cos sin ,β α α α= − −

n n n1 22

12 2

620

1 2 3

Fig. 1. Schematic drawing of cuvette converters (closed tanks) of refractometric analyzer:

1) tank situated directly above inlet coupling to ensure good flow past of the tank (AR-1,

AR-25); 2) tank in the form of a hollow prism with two refracting faces (AR-2-V, AR-4V);

3) tank with bellows-type pressure compensator for the liquid being analyzed (RAZh-451).

designed for passage of the liquid being analyzed and the outer closed tube, which is equipped with transparent windows, for

the comparison liquid. Except for the cuvette, the optical units are situated on a bracket that moves perpendicularly to the

device’s optical axis by means of a micrometric screw, thereby creating the necessary eccentricity between the device’s opti-

cal axis A–A and the axis of symmetry B–B of the cylindrical flow-through cuvette (tube). To regulate the range of measure-

ment, the device’s optical axis is shifted relative to the axis of symmetry. The angle between the tangent to the points of entry

and exit of the beam into the flow-through tank of the cylindrical cuvette (tube) may be varied, which thus serves to simulate

a liquid differential prism with variable angle.

Depending on the index of refraction of the liquid being analyzed n and the parameters of the different units of the

devices, the information-bearing parameter, or angle of deviation β, may be calculated from the equation of the static char-

acteristic:

where N is the index of refraction of the comparison liquid and α the refracting angle.

The eccentricity H between the device’s optical axis and the axis of symmetry of the cuvette needed to obtain an

optimal value of the information parameter βopt is determined from the expression

where R is the radius of the cylindrical flow-through tank of the cuvette.

Variations in the optical density and temperature of the liquid being analyzed, scattering of radiation in the cuvette,

and wedging of the glasses forming the cuvette are among the important factors which lead to measurement errors.

The error produced as a consequence of oscillations in the optical density of the liquid being analyzed may be

described by the equation [3]

δ(∆n) = δ1(0) + δ2(∆n), (1)

where δ1(0) is a component that characterizes the null shift associated with a deviation in the optical density from a normed

value and δ2(∆n) a functional multiplicative component associated with the measured value of ∆n.

H R N N n N n= − − +sin [ ( ) /( )] sin ,β βopt opt4 2 2 2

× −

1 22 2 2( / ) sin ( / ) cos ,N n α α

β α= − − ×{arcsin [sin( ( / ) sin( / )] ( / )N N n N n1 2 2 22 2

621

1 2 3 4 5 6

7

A AB B

Fig. 2. Refractometric analyzer with cylindrical cuvette and internal channel: 1) radiator;

2) lens; 3) diaphragm; 4, 5) closed and flow-through cavity, respectively; 6) photodetector;

7) micrometric screw.

For the structure of a radiometric analyzer with serial connection of units and linear functional dependence of the

parameters on variations in the optical density ∆D of a liquid that is being analyzed, the following are valid:

δ1(0) = 0.933a2∆D / l∆nmax,

where a is the half-width of a light flux beam; l, distance from the differential cuvette to the photoelectric detector; ∆D = Dx – D0,

variation of optical density of the liquid being analyzed Dx relative to an initial value D0 and

δ2(∆n) = –1.15l tan2α(∆n)2∆D /∆nmax,

where α is the refracting angle of the curette and ∆n = n – N, difference of indices of refraction of liquid being analyzed n

and comparison liquid N.

The value of δ2(∆n) increases towards the end of the range of measurement:

δ2(∆nmax) = –1.15l tan2α∆nmax∆D.

For a refractometric analyzer with compensation structure, the error is determined by the null bias induced by a vari-

ation in the optical density of the liquid being analyzed (∆D ≠ 0), and Eq. (1) assumes the form

∆(∆n) = δ1(0),

and the relative value of the optical density

Σ(∆n) = δ2(∆n)/δ1(0) = 1.2(l tanα∆nmax/a)k2, where k = (∆n/∆nmax) ≤ 1.

With a range of measurement ∆nmax ≤ 0.001, the error of a refractometric analyzer with serial connection of units

is determined by the value of δ1(0). The error of such devices with compensatimg circuit is δ2(∆n) greater, while with

∆nmax ≥ 0.01 the devices are practically insensitive to changes in the optical density of the liquid being analyzed. The error

of a refractometric analyzer with serial connections of units where ∆D ≠ 0 grows substantially and Σ(∆n) > 10. The results

of studies made it possible to control in the standard [4] the optical density of a liquid being analyzed to a value of 0.12 per

1 cm transillumianted layer in the middle part of the spectral range, such that measurement of the index of refraction may be

performed with a specified accuracy.

Scattering of radiation in the cuvette of a refractometric analyzer [5] also leads to the occurrence of an error, since

scattering at a liquid – glass junction is less than scattering at glass – liquid or glass – air junctions. Moreover, the depen-

dence of the radiation flux Φ4 exiting the cuvette on the incoming radiation flux Φ0 is described by the relationship

Φ4(∆n) = Φ0{1 – (1/2)[sin2(γ – σ)/sin2(γ + σ)] + [tan2(γ – σ)/tan2(γ + σ)]} ×

× {1 – (1/2)[sin2(θ – β)/sin2(θ + β)] + [tan2(θ – β)/tan2(θ + β)]},

where γ = arcsin(n /Ng)sinα; σ = arcsin(N /n)sinα; θ = arcsin(n /Ng)sinε; ε = α – σ; β = arcsin(Ngsinθ); Ng, N, and n are

the indices of refraction of the glass of the cuvette and of the comparison liquid and liquid being analyzed, respectively; and

∆n = n – N, measured difference between the indices of refraction.

The nominal conversion function of a refractometric analyzer constructed from two points (initial and final) of the

range of measurementy = kΦ4(∆nmax)∆n,

where y is the output signal; k, a proportionality factor; and Φ4(∆nmax), radiation flux with ∆n = ∆nmax.

The relative error, taking into account scattering of radiation, is determined as follows:

δ(∆n) = (∆y/y)·100 = {[Φ4(∆nmax) – Φ4(∆n)]/Φ4(∆nmax)}·100.

622

Distilled water (N = 1.33) and a liquid with N = 1.4 were used as comparison liquids in order to obtain the comput-

ed values of the errors. The refracting angles of the cuvette were selected from frequently used values (α = 45, 60, and 75°).

The following types of optical glass were used to determine the dependence δ(∆n) = ƒ(Ng): crown flint glass KF 6

(Ng = 1.5), dense crown glass TK7 (Ng = 1.61), and dense flint glass TF 5 (Ng = 1.75).

For the refractometric analyzer, the error δ(∆n) (understood as a function of scattering of radiation in the cuvette)

increases with increasing α and Ng and decreases with increasing N; the greatest value of δ(∆n) is observed at the start of the

scale; δ(∆n) grows as the range of measurement is increased. With ∆nmax ≤ 0.001, the influence of scattering of radiation on

the error is negligible, though it must be taken into account when ∆nmax > 0.01.

The influence of wedging of the glasses of a differential cuvette [6] manifests itself in the form of an error in the

measurement of the index of refraction (or concentration), for example, when the comparison liquid is replaced in the closed

tank of the cuvette.

For a two-prism cuvette, the dependence of the exit angle of the beam α2 on the entrance angle α1 is described by

the equation

(sinα2 – sinα1)ψ=0 = (n – N) tanϕ, (2)

where ψ is the angle that characterizes the degree of wedging of the beam-splitter glass and ϕ the refracting angle of the cuvette.

The design of a differential cuvette assumes that the surfaces of the entrance glass A, beam-splitter glass B, and exit

glass C will all be parallel (Fig. 3). In the case of wedging, ψ3 ≠ 0, of the beam-splitter glass B, Eq. (2) may be transformed

into the form

(sinα2 – sinα1)ψ≠0 = (n – N) tanϕ + tanψ3{[Ng2 + tan2ϕ(Ng

2 – N2)]1/2 – n} ≈

≈ (n – N) tanϕ + tanψ3(Ng – n). (3)

To determine the dependence of the angle α2 on the parameters of a two-prism cuvette, taking into account the

degree of wedging of glasses A, B, and C, the device is represented in the form of a set of two cuvettes with refracting angles

ψ1 and ψ2 for glass A and ψ4 and ψ5 for glass C. The angles ψ1, ψ2 and ψ4, ψ5 characterize the deviations of the surfaces of

the entrance and exit glasses from parallelness, respectively. The angles ψ may also assume negative values.

Recalling the condition for small angles and the approximate expressions tanψi ≈ ψi and sinα ≈ α, as well as (2)

and (3), the angle of deviation of the beam

α2(N, Ng, n) = (Ng – 1)ψ1 + (N – Ng)ψ2 + (n – N) tanϕ +

+ (Ng – n)ψ3 + (Ng – n)ψ4 + (1 – Ng)ψ5, (4)

where N = N0 = 1; N0 is the index of refraction of air.

623

Fig. 3. Diagram of two-prism cuvette and path of beam.

In the zero-adjustment mode, the index of refraction of the comparison liquid and of the liquid being analyzed are

equal (N = n), moreover, (4) assumes the form

α2(N, Ng) = (Ng – 1)(ψ1 – ψ5) + (Ng – N)(ψ3 + ψ4 – ψ2).

In the general case, in the zero-adjustment mode α2(N, Ng) ≠ 0 and depends functionally on N, which makes it nec-

essary to monitor the calibration characteristic when making a transition to a different comparison liquid.

The theoretical (ideal) and actual (taking into account wedging) graduation (static) characteristics are described by

the relationships

Si = tanϕ; Sa = tanϕ – ψ3 – ψ4. (5)

In light of the wedging tolerance of optical glasses (OST 2589), the results of calculations from Eqs. (5) differ by

up to 1%.

In a device that has been calibrated for a comparison liquid with index of refraction N, a systematic error (of calibration)

∆α2 = α2(N1, Ng) – α2(N, Ng)

arises in the transition to a different comparison liquid with N1.

At the end of the range of measurement ∆nmax, this error reduces to the form

δ = ∆α2/∆nmax(tanϕ – ψ3 – ψ4) = ∆α2/∆nmaxtanϕ,

and its relative value is given as

δ = K[(ψ2 – ψ3 – ψ4) / tanϕ]·100, (6)

where K = ∆N/∆nmax is the coefficient of the ratio of indices of refraction, and ∆N = N1 – N is the difference in the indices

of refraction of the comparison liquids.

Under the condition ψ2 – ψ3 – ψ4 ≤ 3ψtol, where ψtol is the wedging tolerance angle, the error δ may be represent-

ed by the function

δ ≤ δtol = (3Kψtol / tanϕ)·100.

For a three-prism cuvette, the equation for the angle of deviation of the beam as a function of wedging assumes the

following form:

α2(N, Ng, n) = (Ng – 1)ψ1 + (N – Ng)ψ2 + 2(n – N) tanϕ +

+ (Ng – n)ψ3 + (Ng – N)ψ4 + (1 – Ng)ψ5 + (Ng – N)ψ6.

The equations characterizing the variation in the slope of the calibration characteristic are analogous to (5) and for a

three-prism curette may be written thus:

Si = 2tanϕ; Sa = 2tanϕ – ψ3.

By comparison with the slope of the theoretical calibration characteristic Si, the variation in the slope of the cali-

bration characteristic of a refractometric analyzer with three-prism cuvette with wedging within the range of tolerances does

not exceed ±1.5%.

For a three-prism cuvette, the measurement error of the index of refraction

δ = K(ψ2 – ψ4 – ψ6) /2tanϕ·100. (7)

624

The function, defined in terms of wedging tolerances of different glasses, is as follows:

δtol = (3Kψtol /2 tanϕ)·100, ψ2 – ψ4 – ψ6 ≤ 3ψtol.

If K ≤ 0.1 and the wedging ψtol > 51 or if K = 1 and the wedging ψtol = 51, recalibration will not be needed when

the comparison liquid is replaced; if K > 1, calibration of the scale is required for each comparison liquid in light of the exact

(not the limiting δtol) values of the errors δ in accordance with (6) and (7).

Automatic refractometric analyzers constitute dynamic measurement systems. These systems are used to monitor

the time-varying parameters of nonstationary industrial processes. The dynamic nature of analyzers as adjustment system sen-

sors exerts a major influence on the quality of automatic control systems, serving in many cases to determine the adjustment

error. In analyzing dynamic characteristics, an automatic refractometric analyzer may be represented in the form of a two-unit

system that incorporates a cuvette and an optico-mechanico-electronic measuring transducer. The base type of cuvette (Fig. 1)

consists of a flow-through tank 10–30 cm3 in volume and a closed tank 2–8 cm3 in volume placed within the flow-through

tank. Because of the dependence of the index of refraction of a liquid on temperature, it is necessary to investigate and opti-

mize the dynamic characteristics of the refractometric analyzer also through the temperature channel [7].

The basic dependence of the index of refraction of a liquid on temperature is described by the equation

nθ = n0 + (dn/dθ)θ + (d2n/dθ2)θ2,

where nθ and n0 are the indices of refraction of the liquid being analyzed at the temperature θ and at the initial temperature

and dn/dθ is the temperature coefficient of the liquid being analyzed.

The transfer functions of a cuvette transducer (cuvette) and of a refractometric analyzer at constant temperature of

the liquid being analyzed are described in the form

WCT(p) = y1(p)/x(p) = KCT/(TCTp + 1);

WRA(p) = y(p)/x(p) = KRAe–pτ/[(TCTp + 1)(TSSp + 1)],

where y1(p) is the output signal of the cuvette (beam deviation); x(p), input signal of cuvette and device (variation of concen-

tration of liquid being analyzed); p, Laplace operator; KCT = y1(t)/x(t)t→∞, transmission factor of cuvette; t, time; τ, time con-

stant of transport unit; TCT = V/Q, time constant of cuvette (ratio of volume of cuvette V to flow rate Q of liquid being ana-

lyzed, disregarding mixing); y(p), output signal of device; TSS, time constant of servo system (for a refractometric analyzer

with compensating structure, turnaround time of engine shaft within a complete scale at maximal speed); KSS = y(t)/y1(t)t→∞,

transmission factor of servo system; and KRA = KCTKSS = y(t)/x(t)t→∞, transmission factor of refractometric analyzer.

As the temperature of the liquid being analyzed is varied, its index of refraction and temperature also vary along with

the index of refraction of the comparison liquid in the closed tank of the curette. There thus arises a dynamic error the value

and nature of which depend on the dynamic parameters of the device. The dynamic error in the static situation is given as

εθ = b∆θ,

where b is the temperature coefficient of the index of refraction of the liquid being analyzed; ∆θ, the difference between the

temperature of the liquid being analyzed and that of the comparison liquid.

The transfer function of the closed cuvette W θCL(p) and that of the flow-through cuvette W θ

FL(p) of the tanks of the

refractometric analyzer are described with respect to the temperature channel by the relationships

W θCL(p) = θCL(p)/θin(p) = K θ

CL/(TCTp + 1)(TCLp + 1);

W θFL(p) = θout(p)/θin(p) = K θ

FL/(TCTp + 1), (8)

625

where θCL, θin, and θout is the temperature of the liquid in the closed tank and at the entry to and exit from the flow-through

tank, respectively; K θCL = θCL(t)/θin(t)t→∞ and K θ

FL = θout(t)/θin(t)t→∞, transmission factor of closed and of flow-through tank,

respectively, with respect to temperature channel; TCL = mC/αS, time constant of closed tank; m, mass of liquid; C and S,

heat capacity and area of walls of cuvette; and α, heat transmission coefficient.

The transfer function of the dynamic error of the refractometric analyzer cuvette (flow-through and closed tanks)

with respect to the temperature channel is given as

W θCT(p) = b[W θ

FL(p) – W θCL(p)].

With t → ∞, θout(t) = θCL(t) and K θCL = K θ

FL, in light of (8),

W θCT(p) = K θ

CT(p)bTCLp/(TCTp + 1)(TCLp + 1).

The transfer function of the dynamic error of the refractometric analyzer with respect to the temperature channel

W θRA(p) = W θ

CT(p) W θMT(p) or

W θRA(p) = y(p)/x(p) = K θ

RAbTCLp/[(TCTp + 1)(TSSp + 1)(TCLp + 1)], (9)

where W θMT is the transfer function of the measuring transducer and K θ

RA = y(t)/x(t)t→∞, the transmission factor of the refrac-

tometric analyzer with respect to the temperature channel.

As the temperature of the liquid being analyzed varies, the dynamic error is determined by the deviation of the out-

put signal from the steady-state value εθ(p) = y(p). In light of (9),

εθ(p) = W θRA(p)x(p).

Where the liquid being analyzed is maintained at a constant temperature and the servo system is maintained in a

tracking mode, with input action x(p) = x0/p, the dynamic error ε(t) and its integral value ε are described by the relationships

ε(t) = x0 for 0 < t < τ; ε(t) = x0exp[–(t – τ)/TCT] for t > τ; ε = x0(τ + TCT).

In discontinuous variation in the temperature of the liquid being analyzed x(p) = θin/p, the dynamic error ε(t) (Fig. 4,

curve 1) and its integral value ε assume the form

εθ(t) = bTCLθin[TCT/(TCT – TCL)exp(–t/TCT) + TCL/(TCT – TCL)exp(–t/TCL)],

εθ = bTCLθin.

A reduction in the temperature error may be achieved by means of optimization of m, C, S, and α and by decreas-

ing TCL.

Under the conditions TCL >> TCT, εθ(t) = εθmax, and t = tmax for the case where the temperature of the liquid being

analyzed varies at a constant rate (Fig. 4, curve 2)

TCL = tmax/ ln(bθin/εθmax).

The approximation error of the condition TCL >> TCT, for TCL/TCT = 2–30 does not exceed 1 sec.

626

For an input action x(p) = aθ/p2

TCL = εaθ /baθ,

where aθ is the rate of variation of the temperature of the liquid being analyzed and εaθ the steady-state value of the dynam-

ic error.

Given constant structural parameters of the cuvette, the dynamic temperature error of the refractometric analyzer

may vary in the course of operation as a function of the flow rate of the liquid being analyzed, i.e., for different values of the

time constant of the flow-through tank of the cuvette TCT.

For industrial monitoring of high-temperature viscous, polymerizing working liquids (plastic, oils, etc.), it is often

impossible to reduce the flow rate of a liquid that is being analyzed down to a level Q < Qmax. In this case, the measurement

problem is solved through use of a refractometric analyzer with cylindrical cuvette with internal duct (Fig. 2) lacking any

stagnant zones. In this case, the flow rate Q is practically unlimited.

The transfer function for a cylindrical cuvette with internal duct is described relative to the temperature channel by

the relationship

W θCT(p) = [b(TCLTjp + TCL + k2Tj]p/{(Tθp + 1)[(TCLp + 1)(Tjp + 1) – k2]},

where TCL = mCLC/(Sαj + SCLαCL); Tj = mjCj/Sαj; Tθ = mC/Qj + SCLαCL; k1 = SCLαCL/(SCLαCL + Sαj); k2 = Sαj/(SCLαCL +

+ Sαj); the subscript “j” refers to a temperature jump.

Under the conditions Qj/(Qj + SCLαCL) → 1 and SCLαCL/(Qj + SCLαCL) → 0,

W θCT(p) = [b(TCLp + 1)(Tjp + 1) – k2 – k1(Tjp + 1)] /{(Tθp + 1)[(TCLp + 1)(Tjp + 1) – k2]}.

In the case of a temperature jump, the dynamic temperature error

εθ(t) = {[b(TCLTjp1 + k2Tj + TCL)l p1t] / [(p1 – p2)(p1 – p3)]} – {[b(TCLTjp2 +

+ k2Tj + TCL)l p2t] / [(p1 – p2)(p2 – p3)]} + {[b(TCLTjp3 + k2Tj + TCL)l p3t] / [(p1 – p3)(p2 – p3)]},

where

p T p T T T T T T k T T1 2 32

11 4 2= − = − − ± + −

/ ; ( ) ( ) .,θ j CL j CL CL j CL j

627

ε, arb. units

t, sec

2 1

Fig. 4. Dynamic error of refractometric analyzer εθ as the temperature of the

liquid being analyzed varies discontinuously (1) and at a constant rate (2).

From the equations for W θCT(p) and εθ(t), it follows that the parameters of the walls of the cuvette exert a significant

influence on the heat exchange process in the cuvette. For the models that are being considered here, assuming the same con-

ditions in a refractometric analyzer with cylindrical cuvette with internal duct, the value of TCL is less than in a device with

cuvette provided with external duct and, correspondingly, lesser dynamic temperature error.

The metrological and technical parameters of automatic liquid refractometric analyzers are regulated in the stan-

dard [4].The standard has since been converted into Specification 6-83 5P1.550.009.

Metrological assurance of refractometric analyzers is based on the state accuracy chart for measuring instruments

used for the index of refraction of solid and liquid transparent substances (MI 2129-91). The chart establishes a sequence for

dissemination of the size of the unit of the index of refraction from the state primary standard of the unit of the index of refrac-

tion by means of secondary and working standards to working measuring instruments together with an indication of the errors

and the basic calibration methods [8]. Calibration of refractometers is conducted by means of standard gauges of the index

of refraction, i.e., sets of glass refractometric plates, prisms, or refractometric liquids. The plates and prisms are calibrated

with respect to the index of refraction in the range nD = 1.20–2.05 with error ±(2–2.5)⋅10–5nD. Such liquids as n-heptane,

cyclohexane, ethylene chloride, carbon tetrachloride, benzene, α-bromonaphthalene, and others that have been calibrated

with respect to index of refraction nD at the wavelength λ = 589.3 nm with temperature 20.0 ± 0.1°C in the range

1.332990–1.658443 with error ±3⋅10–5 are used as standard refractometric liquids.

REFERENCES

1. M. A. Karabegov, Izmer. Tekh., No. 11, 50 (2004); Measure. Tech., 47, No. 11, 1106 (2004).

2. B. B. Ioffe, Refractometric Methods in Chemistry [in Russian], Goskhimizdat, Leningrad (1960).

3. M. A. Karabegov, Yu. I. Komrakov, and S. A. Khurshudyan, Izmer. Tekh., No. 3, 64 (1981); Measure. Tech., 24,

No. 3, 248 (1981).

4. GOST 14941-90, Refractometric Analyzers of Liquid in the State System of Industrial Devices and Automation

Tools: General Specifications [in Russian].

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