EP4105585B1

EP4105585B1 - Freeze-drying method and apparatus

Info

Publication number: EP4105585B1
Application number: EP21180228.5A
Authority: EP
Inventors: Sergey Kravchenko; Nikolajs Kulesovs; Natalia Panova; Sergejs Bratarcuks; Dmitrijs Voleina
Original assignee: Cryogenic And Vacuum Systems Sia
Current assignee: Cryogenic And Vacuum Systems Sia
Priority date: 2021-06-18
Filing date: 2021-06-18
Publication date: 2023-10-11
Anticipated expiration: 2041-06-18
Also published as: EP4105585A1; WO2022263471A1

Description

Technology area

The invention relates to devices and methods for freeze-drying.

Prior art

Freeze-drying refers to the removal of moisture from frozen materials, such as food, medicine, and others, by sublimation of ice. Freeze-drying is based on the ability of ice to evaporate under certain conditions, bypassing the liquid phase. In industrial conditions, the drying process is carried out in a vacuum at a pressure of the vapor-gas medium below the pressure corresponding to the triple point of the substance phase transformation.
Freeze-drying has several advantages over traditional preservation methods: there is no need for refrigeration since dry food can be stored for a long time at positive temperatures; the sales system of such goods is simplified and the time of their sale is increased; in addition, the taste of the product remains virtually unchanged.
US 6971187 B1 and EP 2674712 A1 disclose different freeze-drying apparatuses.
A known method and device for freeze-drying ( US9459044 ). The known method includes reducing the pressure to the first vacuum pressure, as a result of which the control system automatically activates the heater. Further, the method includes increasing the pressure to the second value of a vacuum pressure exceeding the value of the first pressure, where, as a result of reaching the value of the second pressure, the control system automatically turns off the heater. The result is a decrease in pressure, reactivation of the heater, sublimation of water, and an increase in pressure, which leads to the next turn-off of the pressure-activated heater. Another freeze-drying method involves lowering the temperature in the chamber of the device to -45.5 °F or below using a refrigeration system with a one-stage vacuum pump and sublimation under reduced pressure in the chamber of the device. The freeze dryer includes a chamber, a vacuum pump, a heater, and a control system programmed with instructions in effect to cycle through the pressure-activated heater. The main disadvantage of the known solution is the occasional shutdown of the heating elements, which leads to a decrease in the supply of thermal energy to the sublimated product, that is, the intensity of sublimation decreases. This mode of operation of the device leads to an increase in the time of its operation until the desired result is achieved, thereby reducing its performance.
A known method for monitoring and controlling the process of lyophilization of a solution of a frozen product using a wireless sensor network ( US2020340743 ). The method includes arranging one or more wireless pressure sensors configured to fit into a lyophilization vial tray located in a lyophilization chamber having a plurality of product vials, wherein the wireless pressure sensors are distributed between the lyophilized product vials, thereby providing spatial pressure measurement, collection information on the spatial pressure from the specified wireless pressure sensors, calculation of the sublimation rate of the solution, and regulate the pressure and/or temperature in the lyophilization chamber so that the calculated sublimation rate remains within the specified ranges of parameters. Thus, the known process of the device operating modes control is based on the solvent evaporation rate control, and the process control is designed in such a way that the sublimation process should be the real sublimation process, and not a vacuum drying process (drying at low pressure and possibly at low temperature, but not lower than pressure and temperature of the triple point of the phase transformation of the substance). This protects the base substance from degradation, which is very important, for example, for pharmaceutical and cosmetic substances. The Navier-Stokes equation is used as a tool for determining the control actions on the sublimation process and some parameters in the sublimation chamber required to solve this equation are measured by the abovementioned sensors. The parameters required are the temperature of the gases, and precisely the gradient of the gas's temperature, which is flowing away and carry out the sublimated substance, and the pressure of the gases, in the places where the corresponding gas pressure and temperature sensors are installed. The main disadvantage of the known solution is the use of the gas temperature gradient to control the sublimation process, which only indirectly characterizes the temperature of the sublimated product, and since the solutions of substances in the sublimated products have a complex composition and the intensity of their evaporation depends not only on the temperature and pressure of the gases inside the chamber but also on the fractional the composition of the evaporated substances and their differences even for one type of sublimation products. At the same temperature and pressure of the air-vapor medium inside the chamber, the evaporation rate of the products depends on the fractional composition of the product, and over time the evaporation rate changes, since the lighter fractions volatilize easily; an example of a solution of alcohol in water - first alcohol begins to evaporate intensively, and only then, as the temperature rises, water begins to evaporate, or another example - oil rectification. Failure to take these circumstances into account leads to distortion of control actions, which reduces the quality of the sublimated product and reduces the productivity of units.

Disclosure of the invention

The invention aims to eliminate the disadvantages of prior art. This goal is achieved by the proposed method and device for freeze-drying, according to which, to control the process of sublimation of the substance, temperature T, pressure P, and the Clausius-Clapeyron equation are used as control parameters and to determine the values of control actions. Controlling influences on the sublimation process is determined by their ratio. The temperature was selected as the main parameter and the pressure was selected as the correcting control parameter. More specifically, the objective is achieved due to the technical features indicated in the independent claims.

Brief Description of Drawings

Fig. 1 is a schematic diagram of an embodiment of a freeze-drying device;
fig. 2 is a schematic diagram of one embodiment of a freeze-drying method;
fig. 3 is a schematic diagram of another embodiment of the freeze-drying method.

Detailed description of the invention

The proposed device and method for freeze-drying and the control of the sublimation process of a substance use temperature T, pressure P, and the Clausius- Clapeyron equation to determine the values of control actions as control parameters. Controlling influences on the sublimation process is determined by their ratio. As the main parameter, the temperature was selected as a more inertial process, and as the correcting control parameter, the pressure was selected as a faster process.
The proposed device (Fig. 1) contains:

a vacuum chamber-desublimator 1, in which one or more shelves 2 are located, adapted to accommodate the product to be freeze-dried; the shelf or shelves 2 are equipped with one or more heaters 3, adapted to heat the shelves 2 and maintain the predetermined temperature of the shelves 2;
a refrigeration unit 4 connected to a heat exchanger 5, which is installed in such a way as to ensure heat transfer from the desublimating surface 6 located in the vacuum chamber-desublimator 1; moreover, the desublimating surface 6 can be represented as walls of the vacuum chamber-desublimator 1, or one or more plates connected to the heat exchanger 5 with the possibility of mutual heat transfer (for taking heat from the desublimating surface 6 and cooling it);
at least one temperature sensor 7 of the desublimating surface 6, installed and configured to take temperature readings from the desublimating surface 6;
one or more temperature sensors 8 of the shelves 2, adapted to take temperature readings from the shelves 2 and, preferably, protected by housing to protect against the influence of the temperatures of other elements of the device;
at least one vacuum pump 9, installed with the possibility of pumping out gases from the vacuum chamber-desublimator 1;
at least one pressure sensor 10 was installed with the possibility of obtaining pressure readings in the vacuum chamber-desublimator 1.

Shelf temperature sensors 8, desublimating surface temperature sensor 7, pressure sensor 10 are connected to the control computer 11 with the possibility of transmitting a signal representing the data received by sensors 7, 8, 10. Vacuum pump 9, refrigeration unit 4, shelf heaters 3 are connected with a control computer 11 with the possibility of receiving and transmitting a signal to control the said elements of the device.
Moreover, the control computer 11 is connected to computer-readable hardware that storing a computer program containing machine-executable instructions (or the control computer 11 itself contains these machine-executable instructions), the execution of which causes the processor to control the freeze-drying device according to steps (iii) - (vi) of the freeze-drying method described below.
The freeze-drying process according to this invention comprises (Fig. 2 and 3):

determination of the product to be sublimated and selection of the appropriate operating mode of the device, that is, the determination of the program for the sublimation of the product filler, which contains data on the thermophysical properties of the product filler;
according to the specified mode, information about the sublimation mode is loaded into the sublimation program from the long-term memory of the control computer 11: the pressure P0 of the triple point of the product's filler substance phase transformation, the temperature of its triple point of phase transformation T0, its heat capacity ΔH, as well as the temperatures of the thermostatting levels of the shelves T_j j = 1, ..., n_T, and T_D desublimating surface 6, the temperature of the beginning T_B = T₀ , as well as the number of thermostatting levels n_T ;
the implementation of the loading of the product on one or more shelves 2 of the vacuum chamber-desublimator 1 (the product can be placed in trays, open cans, etc.);
the implementation of the sealing of the vacuum chamber-desublimator 1;
freezing the desublimating surface 6 to a temperature T_D <T0;
carrying out freezing of the shelves 2 to a temperature T_B, so that T_D <T_B =T₀ <T0;
the implementation of the evacuation of the vacuum chamber-desublimator 1 by pumping out the air-vapor medium to a pressure p₀ , so that P_D <p₀ <P0, below the pressure p₁ corresponding to the temperature T₁ of the first level of thermostatting of the substance sublimation. Moreover, the values of the pressure parameters are determined by Clausius-Clapeyron equation according to the set temperature values and the initial data of the sublimation mode

p_{2} = p_{1} \exp [- \frac{Δ H_{cy δπ, mol}}{R} \cdot (\frac{1}{T_{1}} - \frac{1}{T_{2}})]

Moreover, the sublimation process is carried out in several levels of thermostatting j from 1 to n_T, and at each of the levels of thermostatting, several cycles i from 1 to n_Tc of pressure change inside the vacuum chamber - desublimator (1) are performed. The current parameters of the sublimation process, i.e., temperature T_c and pressure p_c inside the vacuum desublimator chamber, is checked for each level and cycle of the sublimation process and compare with the parameter T_j and p_j. And further, the cycle of operation of the sublimation device vacuum pump (9) means the repeated process of pumping out the vapor-air mixture by the vacuum pump (9), from the limiting value pressure p_j, to the lower value of the pressure p_j-1, and then its subsequent growth to the value p_j due to the sublimation process. The range of cycle pressure changes is determined by control computer (11) for each thermostatting level based on the thermostatting temperature of the shelves 2 of the current T_j and the previous T_j-1 levels. For the first step, i.e., j = 1, the previous step is zero-step T_j-1 = T₀, and, accordingly, p_j-1 = p₀. Transition to another thermostatting lavel is possible both by a change in the magnitude of the pressure increase over the given time, when it does not reach the given level, i.e., p_j, or when current number n_c of sublimation cycle reaching the limiting value of the repetitive operating cycles number n_Tc of the vacuum pump, i.e., n_c ≥ n_Tc.
The pressure p₀ and the temperature T₀ of the lower-level and the temperature T₁ of the first level of sublimation j = 1, of the first cycle i = 1 coincide with the parameters of the lower level of sublimation P_B and T_B, that is, T_D < T_B = T₀ < T₁ <T0 and P_D < P_B = p₀ < p₁ < P0.
Since the initial pressure in the chamber p₀ is lower than the saturated vapor pressure at the temperature of the first thermostatting level p₁, that is, p₀ < p₁, according to the specified sublimation parameters, the filler substance begins to sublimate from the product, and since the temperature of the desublimating surface 6 T_D is below the temperature of the first level of thermostatting T₁, and at the same time the initial pressure in the chamber p₀ is higher than the saturated vapor pressure P_D corresponding to the temperature of the desublimating surface 6 T_D according to the given parameters of the sublimation mode, then the filler substance is desublimated on the desublimating surface 6 as follows as T_D < T₀ <T₁.
If the intensity of the sublimation process exceeds the intensity of the desublimation process, then the current pressure p_c in the chamber rises, and if, for a given duration t_1,1 of the sublimation process, the pressure in the vacuum chamber-desublimator 1 reaches a pressure corresponding to the temperature of thermostatting, that is, p_c = p₁, then the control computer 11 turns on the vacuum pump 9 and reduces the pressure in the vacuum chamber-desublimator 1 to the initial level p₀. The process is carried out until one of two events occurs:

either the current number of sublimation cycles n_c do not less than the specified value for this first stage, the first cycle of the sublimation process n_c ≥ n_1,1,
either for a given time t_1,1, the pressure in chamber p_c will not be able to reach the value of p₁ .

The condition is checked that the current number n_c of sublimation cycles do not exceeded the specified value for the given, first stage, the first cycle of the sublimation process n_c ≤ n₁,₁:

if the condition n_c ≤ n_1,1 is not met, then the control computer 11 transmits the sublimation device to the next level of thermostatting, which is set by the temperature T₂ of shelves 2 of the vacuum chamber-desublimator 1.
if the condition n_c < n_1,1 is satisfied, then the transition to checking the condition p_c < p₁.

The fulfillment of the condition is checked that for a given time t_1,1 the pressure p_c in the vacuum chamber-desublimator 1 did not reach the value p₁, that is, p_c < p₁:

if the condition p_c < p₁ is not met, then the control computer 11 turns on the pump 9 and lowers the pressure inside the vacuum chamber-desublimator 1 to the value p₀, and the process is repeated;
if the condition p_c < p₁ is fulfilled, then the control computer 11 transmits the device to the next level of thermostatting, which is set by the temperature T₂ of the shelves 2 of the vacuum chamber-desublimator 1.

Then, the next thermostatting level is carried out. For this, with the help of heaters 3, the shelves 2 with the product are heated, followed by their thermostatting T_j = const, and then the current pressure p_c of the sublimation process is measured by the pressure sensor 10, and the control computer 11 checks its compliance to the parameters of the i-th cycle of the j-th level of the sublimation process. That is, compliance of the current pressure value p_c to the limit value of the i-th cycle of sublimation of the j-th level of thermostatting, i.e., with p_j.
The temperature of the shelves 2 is stabilized, and, suppose, if the chamber is not equipped with some kind of vapor removal system, then the saturated vapor current pressure p_c < p_j will increase, tending to the value of p_j corresponding to the temperature T_j . $p_{2} = p_{1} \exp [- \frac{Δ H_{cy δπ, mol}}{R} \cdot (\frac{1}{T_{1}} - \frac{1}{T_{2}})]$
However, the filler substance desublimates on the desublimating surface 6, since T_D < T_c ≤ T_j for all i=1,...,n_Tc and j=1,...,n_T , decreasing the rate of current pressure p_c growth. But if the intensity of the sublimation process exceeds the intensity of the desublimation process, then the pressure in the vacuum chamber-desublimator 1 increases, and if, for a given duration t_i,j of the sublimation process, the current pressure p_c in the vacuum chamber-desublimator 1 reaches or exceeds the pressure p_j, that is, p_c ≥ p_,j, then the control computer 11 turns on the vacuum pump 9, which reduces the pressure in the vacuum desublimator 1 to the initial level p_j-1. The process is carried out until one of two events occurs:

the current number of sublimation cycles n_c has reached or exceeded the specified amount n_i,j of the cycle number of this level of the sublimation process n_c ≥ n_i,j;
for a given time t_i,j, the current pressure p_c in the chamber do not reach the specified value of pressure p_j, that is, p_c<p_j.

The condition is checked by the control computer 11, that the number of sublimation cycles n_c is more or equal to the specified value n_i,j for a given cycle of the sublimation process, that is, n_c ≥ n_i,j :

if the condition n_c ≥ n_i,j the condition is not met, then the control computer 11 of the device turns on the heaters 3 of the shelves 2 and goes to the next thermostatting level, which is set by the temperature T_j+1 of the shelves 2 of the device.
if the condition n_c ≥ n_i,j is satisfied, then the transition to checking the condition p_c < p_j is carried out.

The fulfillment of the condition is checked that for a current time t_i,j the current pressure p_c in the chamber has not reached the value p_j. i.e., p_c < p_j

if the condition p_c < p_j is not met, then the control computer 11 turns on the vacuum pump 9 and lowers the pressure inside the desublimator chamber 1 to the value p_j-1, and the process is repeated;
if the condition p_c < p_j is satisfied, then the device turns on the heaters 3 of the shelves 2 and goes to the next level of thermostatting, which is set by the temperature T_j+1 of the shelves 2 of the device.

The parameters of the upper level of the last thermostatting level, i.e., j = n_T , of the last cycle i = n_Tc coincide with the parameters of the upper level of the sublimation process, that is, T0 ≥ T_nT = const and p_c ≤ p_nT ≤ P0.
The shelves 2 with the product are heated with the heaters 3, followed by thermostatting at the temperature T_nT = const. The temperature of the shelves 2 stabilizes, the current pressure p_c begins to increase, tending to the value of p_nT corresponding to the temperature T_nT: $p_{2} = p_{1} \exp [- \frac{Δ H_{cy δπ, mol}}{R} \cdot (\frac{1}{T_{1}} - \frac{1}{T_{2}})]$
In this case, the filler substance desublimates on the desublimating surface 6, since T_D < T_nT. If the intensity of the sublimation process exceeds the intensity of the desublimation process, then the current pressure p_c in the desublimator chamber 1 increases, and if, for a given duration t_i,nT of the sublimation process, the current pressure p_c in the desublimator chamber 1 reaches pressure p_nT, then the control computer 11 of device turn on the vacuum pump 9 is turned on, which lowers the pressure in the desublimator chamber 1 to the initial level p_nT-1. The process is carried out until one of two events occurs:

the current number of sublimation cycles n_c reach or exceed the specified value of the cycle number of the thermostatting level n_c ≥ n_nT, or
for a current time t_c, the current pressure p_c in the desublimator chamber 1 does not reach its limitation value, i.e., p_c < p_nT.

The fulfillment of the condition is checked that the current number of sublimation cycles n_c lower the specified value for the given thermostatting level n_c < n_nT.

if the condition n_c < n_nT is not met, then the device switches its mode of operation to the completion of the sublimation process, that is, bringing the pressure inside the desublimator chamber 1 to the ambient pressure and the temperature of the shelves 2 to the set value, and gives a signal about the end of the sublimation cycle.
if the condition n_c < n_nT is satisfied, then the transition to the verification of the condition p_c ≤ p_nT is made.

The fulfillment of the condition is checked that for a current time t_c,nT the current pressure p_c in the chamber lower than the value p_nT , that is, p_c < p_nT.

if the condition p_c < p_nT is not met, then the control computer 11 turns on the vacuum pump 9 and lowers the pressure inside the desublimator chamber 1 to the value of p_nT-1, and the process is repeated.
if the condition p_c < p_nT is satisfied, then the control computer 11 switches the mode of its operation to complete the sublimation process, that is, to bring the pressure inside the desublimator chamber 1 to the ambient pressure and the temperature of the shelves 2 till a predetermined value and gives a signal about the end of the goods sublimation.

Next, the desublimator chamber 1 is depressurized, the desublimator chamber 1 is unloaded, and the device is turned off.

Claims

A freeze-drying device containing a vacuum chamber-desublimator (1), in which one or more shelves (2) are located, adapted to accommodate the product to be freeze-dried; wherein the shelf or shelves (2) are equipped with one or more heaters (3) adapted to heat the shelves (2) and maintain a predetermined temperature of the shelves (2); wherein the freeze-drying device further comprises a refrigeration unit (4) connected to a heat exchanger (5), which is installed in such a way as to provide heat transfer to the desublimating surface (6) located in the vacuum desublimator chamber (1); wherein the desublimating surface (6) is connected to the heat exchanger (5) with the possibility of providing mutual heat transfer for cooling the desublimating surface (6); wherein the freeze-drying device further comprises at least one temperature sensor (7) of the desublimating surface (6) is installed and configured to take temperature readings from the desublimating surface (6); wherein the freeze-drying device further comprises one or more temperature sensors (8) of the shelves (2) adapted to take temperature readings from the shelves (2) and, preferably, protected by a housing to protect against the influence of the temperature of other elements of the device; wherein the freeze-drying device further comprises at least one vacuum pump (9) installed with the possibility of pumping out gases from the vacuum desublimator chamber (1); wherein the freeze-drying device further comprises at least one pressure sensor (10) installed with the possibility of obtaining pressure readings in the vacuum desublimator chamber (1); wherein the freeze-drying device further comprises a control computer (11), connected to the sensors (7, 8 and 10) for receiving a signal from these sensors, and also connected to the vacuum pump (9), the refrigeration unit (4) and the shelf heaters (3) for receiving and transmitting a signal for providing control of the mentioned elements of the device; wherein the control computer (11) contains computer-executable instructions or the control computer (11) is connected to a computer-readable hardware storing a computer program containing computer-executable instructions, the execution of which causes the control computer (11) to perform the following steps:
(iii) freezing the desublimating surface (6) to a temperature T_D< T0;

(iv) freezing one or more shelves (2) to a temperature of the sublimation process beginning T_B, so that T_D<T_B≤T0;

characterised in that said execution further causes the control computer to perform the following steps:
(v) evacuation of the desublimator chamber (1) by evacuating the air-vapor medium with a help of vacuum pump (9) to the pressure of the onset of sublimation P_B so that P_D < P_B < P0, moreover, the pressure P0 and P_D determined for the given values of T0 and T_D according to the Clausius-Clapeyron equation $p_{2} = p_{1} \exp [- \frac{Δ H_{cy δπ, mol}}{R} \cdot (\frac{1}{T_{1}} - \frac{1}{T_{2}})]$

where:
p₂ is the saturated vapor pressure of the filler substance at temperature T₂, for the all-possible values of T₂ (for example T₂ = T_B, T₂ = T_D or others; in this case p_B = p₂, p_D = p₂ or other will be determinates in accordance of equation result);

p₁ - the pressure of saturated vapors of the filler substance at temperature T₁, for the beginning of the sublimation process p₁ = P0;

ΔH_subl,mol - molar latent heat of the phase transition taking place at temperature T, where T=(T1+ T2)/2;

T₁ - temperature of the previous thermostatting mode, for the beginning of the sublimation process T₁ = T0;

T₂ is the temperature of the subsequent thermostatting mode, for the beginning of the sublimation process T₁ = T_B ;

R = 8.314- J·K^-1 ·mol^-1 - universal gas constant;

(vi) to determine the pressure p_j according to the Clausius-Clapeyron equation, thermostatting temperature T_j of the shelves (2) is used, and then p_j is used to comparing it with the current pressure p_c in the vacuum desublimator chamber (1) that is measured by the pressure sensor (10) for the current time;
(a) if the current pressure is equal to or more than the preset pressure - the pressure is lowering by a vacuum pump (9) to a predetermined level; if less than the preset one -

(b) determining the cycle time of the pressure increase from the initial value, after pumping out the vapor-air mixture by the vacuum pump (9), to the calculated pressure value of the sublimation process, calculated based on the thermostatting temperature T_j-1 the shelves (2); if the current cycle time is less than the specified one - return to the step (vi), if equal to or greater than the specified one -

(c) determining the number of cycles; if the number of cycles is less than the specified one - go to step (e), if equal or more -

(d) determining the current pressure; if the current pressure is not less than the preset one - return to step (v), if less than the preset one -

(e) determining the number of thermostatting levels; if the number of thermostatting levels is less than the specified one, heating the shelves (2) by heaters (3) to the next thermostatting level, determining the upper-pressure limit of the next thermostatting level according to the Clausius-Clapeyron equation; if the number of thermostatting levels is greater than or equal to the specified one, the device is shut down.
The device according to claim 1, characterized in that steps (c) and (d) of said computer-executable instructions are combined into one step, which forces the processor to determine the number of cycles and the current pressure in the vacuum desublimator chamber (1); if the number of cycles not less than the specified one or the current pressure is lower than specified one - go to step (e); if the number of cycles is less than the specified one or the current pressure is not less than the specified one - transmit to the mentioned step (a) determining the current pressure; pumping down the pressure to the previous level; if the current pressure is lower than the preset one, transmit the sublimation process to perform next thermostating level: heating of the device shelves (2) to the next level of temperature, determination of the upper-pressure limit corresponding to this temperature using Clausius-Clapeyron equation, and transmit the sublimation process to the step (vi), if it is not less than the preset one, the pressure is lowered by the vacuum pump (9) to the preset level and returns to step (vi) if it is lower than the preset one, go to step (e).
The device according to any one of claims 1-2, characterized in that the desublimating surface (6) is made in the form of the walls of the vacuum desublimator chamber (1) or in the form of one or more plates connected to the heat exchanger (5) with the possibility of providing mutual heat transfer.
A freeze-drying method comprising the following steps:
(i) loading the product onto one or more shelves (2) of the vacuum desublimator (1);

(ii) sealing the vacuum desublimator chamber (1);

(iii) freezing the desublimating surface (6) to a temperature T_D< T0;

(iv) freezing one or more shelves (2) to a temperature of the sublimation process beginning T_B , so that T_D<T_B≤T0;
characterised in that the method further comprises the following steps:
(v) evacuation of the desublimator chamber (1) by pumping out the air-vapor medium with a vacuum pump (9) to the pressure of the onset of sublimation P_B so that P_D < P_B < P0, moreover, the pressure P_B and P_D is determined for the given values of T_B and T_D according to the Clausius-Clapeyron equation $p_{2} = p_{1} \exp [- \frac{Δ H_{cy δπ, mol}}{R} \cdot (\frac{1}{T_{1}} - \frac{1}{T_{2}})]$

where:
p₂ is the saturated vapor pressure of the filler substance at temperature T₂, for the all-possible values of T₂ (for example T₂ = T_B, T₂ = T_D or others; in this case p_B = p₂, P_D = p₂ or other will be determinates in accordance of equation result);

p₁ - the pressure of saturated vapors of the filler substance at temperature T₁, for the beginning of the sublimation process p₁ = P0;

ΔH_subl,mol - molar latent heat of the phase transition taking place at temperature T, where T=(T1+ T2)/2;

T₁ - temperature of the previous thermostatting mode, for the beginning of the sublimation process T₁ = T0;

T₂ is the temperature of the subsequent thermostatting mode, for the beginning of the sublimation process T₁ = T_B ;

R = 8.314- J·K^-1 ·mol ^-1 - universal gas constant;

(vi) thermostatting temperature T_j of the shelves (2) is used to determine the pressure p_j according to the Clausius-Clapeyron equation; p_j is used to compare it with the current pressure p_c in the vacuum desublimator chamber (1) that is measured by the pressure sensor (10) for the current time;
(a) if the current pressure is greater than or equal to the preset pressure - pumping down the pressure to the previous level, if less than the preset one -

(b) determining the cycle time of the pressure increase from the initial value, after pumping out the vapor-air mixture by a vacuum pump (9), to the calculated pressure value of the sublimation process, calculated based on the thermostatting temperature of the shelves (2); if the current cycle time is less than the specified one - return to the step (vi), if equal to or greater than the specified one -

(c) determining the number of cycles; if the number of cycles not less than the specified one - go to step (e), if equal or more -

(d) determining the current pressure; if the current pressure not less than the preset one - the pressure is lowered by a vacuum pump (9) to a predetermined level and return to step (vi), if less than the preset one -

(e) determination of the number of thermostatting levels; if the number of thermostatting levels is less than the specified one, heating the shelves (2) by heaters (3) to the next thermostatting level, determining the upper-pressure limit of the next thermostatting level according to the Clausius-Clapeyron equation; if the number of thermostatting levels is greater than or equal to the specified one, the device is shut down.
The method according to claim 4, characterized in that steps (c) and (d), i.e., determination of the number of cycles and determining the current pressure are combined into one step, which determines the number of cycles and the current pressure in the vacuum desublimator chamber (1); if the number of cycles not less than the specified number or the current pressure lower than the specified one - go to step (e), if the number of cycles less than specified one or the current pressure not less than the specified one - lowering the pressure in the vacuum chamber-decublimator (1) to the lower preset level and return to step (vi); (j) determining the current pressure; if the current pressure is equal to or more than a given one - the pressure the pressure is lowered by a vacuum pump (9) to a predetermined level and return to step (vi), if less than a given one - go to step (e).