Podcast
Questions and Answers
What are the two primary steps involved in the process of crystallization?
What are the two primary steps involved in the process of crystallization?
- Nucleation and growth (correct)
- Cooling and heating
- Melting and solidifying
- Nucleation and formation
What type of nucleation occurs on foreign bodies like dust particles?
What type of nucleation occurs on foreign bodies like dust particles?
- Random nucleation
- Sporadic nucleation
- Homogeneous nucleation
- Heterogeneous nucleation (correct)
What happens to the number of nuclei formed as the temperature of crystallization decreases?
What happens to the number of nuclei formed as the temperature of crystallization decreases?
- It increases due to enhanced undercooling (correct)
- It decreases due to diminished energy levels
- It remains constant regardless of the temperature
- It increases due to higher thermal motion
What is the mathematical relationship between spherulite radius and time during growth?
What is the mathematical relationship between spherulite radius and time during growth?
What occurs to the growth rate v as supercooling is increased initially?
What occurs to the growth rate v as supercooling is increased initially?
What ultimately happens to the growth rate v if the crystallization temperature is lowered excessively?
What ultimately happens to the growth rate v if the crystallization temperature is lowered excessively?
What factor significantly influences the number of large spherulites formed during crystallization?
What factor significantly influences the number of large spherulites formed during crystallization?
Which statement best describes the effect of crystallization temperature on thermodynamic driving force?
Which statement best describes the effect of crystallization temperature on thermodynamic driving force?
What is the general form of the Avrami equation that includes types of nucleation and growth?
What is the general form of the Avrami equation that includes types of nucleation and growth?
What is typically easier to measure during the crystallization process?
What is typically easier to measure during the crystallization process?
In the equation for Vt, how is the final volume V∞ defined?
In the equation for Vt, how is the final volume V∞ defined?
How can the Avrami exponent n be determined experimentally?
How can the Avrami exponent n be determined experimentally?
What does the term 'dilatometry' refer to in the context of monitoring crystallization?
What does the term 'dilatometry' refer to in the context of monitoring crystallization?
Which equation directly correlates the volume changes during crystallization?
Which equation directly correlates the volume changes during crystallization?
Why can the value of the Avrami exponent n vary with time?
Why can the value of the Avrami exponent n vary with time?
What is a potential issue when estimating the Avrami exponent n from experimental data?
What is a potential issue when estimating the Avrami exponent n from experimental data?
What happens to viscosity as the temperature is reduced?
What happens to viscosity as the temperature is reduced?
In the equation for mass of spherulitic material, what does ρL represent?
In the equation for mass of spherulitic material, what does ρL represent?
What is the primary factor that determines the number of nucleated spherulites formed over time?
What is the primary factor that determines the number of nucleated spherulites formed over time?
What is the relationship between the time interval dt and the mass of spherulitic material, dWs?
What is the relationship between the time interval dt and the mass of spherulitic material, dWs?
What does the variable W0 represent in the context of crystallization?
What does the variable W0 represent in the context of crystallization?
What does the equation $W_s = \frac{\pi N v^3 \rho_s t^4}{3 \rho_L} + W_0$ represent?
What does the equation $W_s = \frac{\pi N v^3 \rho_s t^4}{3 \rho_L} + W_0$ represent?
What effect does the reduction in overall volume of the system have during crystallization?
What effect does the reduction in overall volume of the system have during crystallization?
Which of the following signifies that the equations discussed are applicable only at early stages of crystallization?
Which of the following signifies that the equations discussed are applicable only at early stages of crystallization?
Flashcards
Nucleation
Nucleation
The formation of a new, stable, ordered structure (crystal) within a liquid or solution.
Crystal Growth
Crystal Growth
The process where existing nuclei grow in size by adding more molecules to the crystal lattice.
Homogeneous Nucleation
Homogeneous Nucleation
Nucleation that occurs spontaneously within the liquid or melt without the presence of foreign particles.
Heterogeneous Nucleation
Heterogeneous Nucleation
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Undercooling
Undercooling
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Spherulite
Spherulite
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Growth Rate
Growth Rate
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Peak Growth Rate
Peak Growth Rate
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Viscosity in crystallization
Viscosity in crystallization
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Nucleation Rate (N)
Nucleation Rate (N)
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Spherulitic Mass (Ws)
Spherulitic Mass (Ws)
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Initial Mass (Wo)
Initial Mass (Wo)
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Spherulite Volume
Spherulite Volume
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Crystallization Kinetics Equation
Crystallization Kinetics Equation
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Spherulite Growth
Spherulite Growth
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Avrami equation
Avrami equation
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Avrami exponent (n)
Avrami exponent (n)
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Dilatometry
Dilatometry
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Initial volume (V0)
Initial volume (V0)
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Final volume (V∞)
Final volume (V∞)
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Volume at time t (Vt)
Volume at time t (Vt)
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Volume fraction of crystalline material (WL/W0)
Volume fraction of crystalline material (WL/W0)
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Change in specimen volume
Change in specimen volume
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Study Notes
Crystallization Kinetics
- Crystallization involves two steps: nucleation and growth
- Nuclei are ordered regions, stable below the melting temperature
- Nucleation can be homogeneous (random in the melt) or heterogeneous (on foreign particles)
- Growth occurs by the addition of chains
- Nucleation rate depends on temperature; low undercooling yields fewer, large spherulites; high undercooling yields many, small spherulites
- Radius of growing spherulites (r) is linearly related to time (t) by r = vt (v is the growth rate)
- Growth rate (v) is strongly dependent on crystallization temperature; increased supercooling leads to a rapid increase then peaks and decreases with further lowering of temperature. This peak is due to competing thermodynamic driving force and viscosity
Overall Crystallization Kinetics
- Cooled polymer melt forms spherulites over time
- Assuming homogeneous nucleation and constant nucleation rate (N), the total number of nuclei formed in time interval dt is NW₀dt/PL (where PL is liquid polymer density)
- Nuclei grow into spherulites, and the mass of a spherulite is 4πr³ρs/3 (r is radius, ρs is spherulite density)
- Total mass of spherulitic material (dWs) formed over a time interval dt = (4πr³ρsNW₀t³)/(3PL)
- Analysis of specimen volume change (rather than mass) simplifies crystallization analysis
- Specimen volume (Vt) is related to time by the Avrami equation.
- The Avrami exponent (n) is determined from a plot of log{ln[(Vt-V∞)/(Vo-V∞)]} against log t
- The slope of the plot gives n, describing nucleation, and growth mechanisms
- Plotting these graphs helps understand nucleation and growth mechanics of crystallization in the polymer.
- Dilatometry is a practical method used to monitor changes in specimen volume during analysis.
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