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According to the passage, what is the relationship between the mass of drug released (M) and time (t) in the Higuchi equation?
According to the passage, what is the relationship between the mass of drug released (M) and time (t) in the Higuchi equation?
What is the first step when a tablet is introduced into water or the gastrointestinal tract?
What is the first step when a tablet is introduced into water or the gastrointestinal tract?
Which of these processes occur simultaneously with the release of a drug from an intact tablet?
Which of these processes occur simultaneously with the release of a drug from an intact tablet?
What causes the drug release to slow down over time in the described systems?
What causes the drug release to slow down over time in the described systems?
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What factors, according to the passage, does the release of a drug from a tablet depend on?
What factors, according to the passage, does the release of a drug from a tablet depend on?
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What is the primary structural characteristic of a membrane that facilitates molecular passage, according to the text?
What is the primary structural characteristic of a membrane that facilitates molecular passage, according to the text?
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How do molecules that are too large to pass through the pores of a membrane typically cross?
How do molecules that are too large to pass through the pores of a membrane typically cross?
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According to Fick's first law of diffusion, what does the negative sign in the equation $J = -D \frac{dC}{dx}$ indicate?
According to Fick's first law of diffusion, what does the negative sign in the equation $J = -D \frac{dC}{dx}$ indicate?
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In Fick's First Law of Diffusion, what does the term $\frac{dC}{dx}$ represent?
In Fick's First Law of Diffusion, what does the term $\frac{dC}{dx}$ represent?
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What condition causes diffusion to cease?
What condition causes diffusion to cease?
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In the context of the provided text, what is 'flux' (J) defined as?
In the context of the provided text, what is 'flux' (J) defined as?
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A molecule with a high diffusion coefficient (D), under a constant gradient $\frac{dC}{dx}$, would result in what type of flux (J) according to Fick’s First Law?
A molecule with a high diffusion coefficient (D), under a constant gradient $\frac{dC}{dx}$, would result in what type of flux (J) according to Fick’s First Law?
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Which factor does NOT directly influence the diffusion coefficient (D)?
Which factor does NOT directly influence the diffusion coefficient (D)?
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In Fick's second law, what is being examined in relation to time?
In Fick's second law, what is being examined in relation to time?
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What primarily causes a change in the diffusant concentration (C) within a volume element?
What primarily causes a change in the diffusant concentration (C) within a volume element?
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According to the provided text, how does the diffusivity of gas molecules compare to that in liquids or solids?
According to the provided text, how does the diffusivity of gas molecules compare to that in liquids or solids?
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What is the primary purpose of using a polymeric membrane in a diffusion cell?
What is the primary purpose of using a polymeric membrane in a diffusion cell?
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Which term describes the compartment providing the diffusant in a diffusion cell?
Which term describes the compartment providing the diffusant in a diffusion cell?
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What is the correct relationship between the change in diffusant concentration with time ($\frac{\delta C}{\delta t}$) and the change in flux with distance ($\frac{\delta J}{\delta x}$)?
What is the correct relationship between the change in diffusant concentration with time ($\frac{\delta C}{\delta t}$) and the change in flux with distance ($\frac{\delta J}{\delta x}$)?
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What is the primary distinction between Fick's first and second law?
What is the primary distinction between Fick's first and second law?
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Which of the following is true about the diffusion coefficient (D) according to the text?
Which of the following is true about the diffusion coefficient (D) according to the text?
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What does the partition coefficient (K) represent in the context of diffusion?
What does the partition coefficient (K) represent in the context of diffusion?
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When does the diffusion process follow zero-order kinetics?
When does the diffusion process follow zero-order kinetics?
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How is the permeability coefficient (P) defined?
How is the permeability coefficient (P) defined?
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What simplification occurs in the steady-state diffusion equation when we have a sink condition in the receptor compartment?
What simplification occurs in the steady-state diffusion equation when we have a sink condition in the receptor compartment?
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What units does the permeability coefficient have?
What units does the permeability coefficient have?
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In a plot of M versus t, what does the slope of the linear plot provide?
In a plot of M versus t, what does the slope of the linear plot provide?
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How can P be determined if donor concentration, Cd, changes significantly over time?
How can P be determined if donor concentration, Cd, changes significantly over time?
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What is the simplified form of the mass transfer equation (dM/dt) when sink conditions apply?
What is the simplified form of the mass transfer equation (dM/dt) when sink conditions apply?
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What does 'h' represent in the diffusion equations?
What does 'h' represent in the diffusion equations?
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What does dM/dt represent in the context of diffusion?
What does dM/dt represent in the context of diffusion?
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In steady state diffusion, what is the value of the rate of change of concentration with time ($dc/dt$)?
In steady state diffusion, what is the value of the rate of change of concentration with time ($dc/dt$)?
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What does the condition $d^2c/dx^2 = 0$ imply about the concentration gradient ($dc/dx$) during steady-state diffusion?
What does the condition $d^2c/dx^2 = 0$ imply about the concentration gradient ($dc/dx$) during steady-state diffusion?
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During steady-state diffusion, if the thickness of the barrier membrane is represented by 'h', and the concentrations on either side of the membrane are $C_1$ and $C_2$, how is the concentration gradient ($dc/dx$) calculated?
During steady-state diffusion, if the thickness of the barrier membrane is represented by 'h', and the concentrations on either side of the membrane are $C_1$ and $C_2$, how is the concentration gradient ($dc/dx$) calculated?
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Assuming diffusion coefficient is $D$, and the change of mass over time is $dM/dt$, and $S$ is the area, which equation describes Fick's first law in steady-state conditions?
Assuming diffusion coefficient is $D$, and the change of mass over time is $dM/dt$, and $S$ is the area, which equation describes Fick's first law in steady-state conditions?
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In the context of Fick's First law, if $J$ is the flux, $D$ is the diffusion coefficient, and the concentrations are $C_1$ and $C_2$ with barrier thickness $h$, which of the following equations is correct?
In the context of Fick's First law, if $J$ is the flux, $D$ is the diffusion coefficient, and the concentrations are $C_1$ and $C_2$ with barrier thickness $h$, which of the following equations is correct?
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In steady-state diffusion across a membrane, which of the following remains constant?
In steady-state diffusion across a membrane, which of the following remains constant?
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What does the relationship $dc/dx$ = a constant imply about the plot of concentration (c) against the distance across membrane (x)?
What does the relationship $dc/dx$ = a constant imply about the plot of concentration (c) against the distance across membrane (x)?
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In steady-state diffusion, which of the following is always true?
In steady-state diffusion, which of the following is always true?
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Why are the concentrations $C_1$ and $C_2$ within the membrane not easily measured?
Why are the concentrations $C_1$ and $C_2$ within the membrane not easily measured?
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In the context of steady-state diffusion, what condition must be met for Fick's first law to be applicable?
In the context of steady-state diffusion, what condition must be met for Fick's first law to be applicable?
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Study Notes
Introduction to Diffusion
- Diffusion is the process of mass transfer of individual molecules caused by random molecular motion.
- This transfer is driven by a concentration gradient.
- This process is fundamental to many pharmaceutical sciences.
Pharmaceutical Applications of Diffusion
- Drug release and dissolution from tablets, powders, and granules.
- Drug release from ointments and suppository bases.
- Permeation and distribution of drugs in living tissues.
- Passage of water vapor, gases, drugs, and additives through coatings and packaging materials.
How Diffusion Occurs
- Solutes or solvents traverse physical or biological membranes in several ways:
- Simple molecular permeation through non-porous media (depends on solubility in the membrane).
- Passage through solvent-filled pores in a membrane (influenced by pore size and shape).
Fick's Laws of Diffusion
- Fick's First Law defines flux (J) as the amount of material (M) flowing through a unit cross section (S) of a barrier in unit time (t).
- Fick's Law provides fundamental relationships for diffusion processes in pharmaceutical systems.
- Flux (J) is directly proportional to the concentration gradient (dC/dx), but in the opposite direction (-).
- The constant 'D' represents the diffusion coefficient (diffusivity) of the penetrant.
Fick's First Law
- Flux (J) is equal to - D * (dC/dx) where:
- J is the flux in grams/cm²/sec.
- D is the diffusion coefficient in cm²/sec.
- C is the concentration in g/cm³.
- x is the distance in centimeters.
- The negative sign indicates that diffusion occurs in the direction of decreasing concentration.
- Diffusion stops when the concentration gradient equals zero (dC/dx = 0).
- The diffusion coefficient depends on properties like temperature, concentration, solvent, and the chemical nature of the diffusant.
Examples of Diffusion Coefficients
- Diffusivity (diffusion coefficient) is dependent on the solute's molecular structure, temperature, and the medium through which the diffusion occurs.
- Gas molecules diffuse faster through air than liquids which diffuse faster than solids.
Fick's Second Law
- Fick's Second Law describes the rate of change of diffusant concentration (dC/dt) with time (t) at a definite location (x).
Steady State Diffusion
- In diffusion cells, two compartments separated by a membrane.
- The dispersed material is in one compartment and the solvent is in the other.
- The donor compartment is where the substance is dissolved.
- The receptor compartment is where the solvent is placed.
- A sink condition is maintained in the receptor compartment.
- Fick's First Law can be applied in a form when both concentration in donor and receptor are constant.
- dM/dt = PSCd where P is permeability coefficient
- If Cd is constant, the flux is also constant.
Drug Release and Dissolution
- Drug release is the process by which a drug leaves a drug product and is subjected to absorption, distribution, metabolism, and excretion.
- Dissolution is the process by which drug molecules are liberated from a solid phase to a solution phase.
Dissolution Testing of Drug Products
- In vitro release tests are conducted on a variety of dosage forms.
- This testing is used to determine uniformity across multiple batches.
Terminology
- Drug product: A finished dosage form that contains a drug substance.
- Drug substance: An active pharmaceutical ingredient (API) intended to exhibit a pharmacologic action.
- Immediate-release: Drug dissolves quickly for absorption.
- Modified-release: Drug is released over an extended period.
- Enteric-coated: The drug dissolves only when it reaches a more alkaline environment.
- IVIVC (in vitro-in vivo correlation): A predictive mathematical model
Drug Release Basics
- Drug release is largely based on diffusion.
- There are two categories of drug release kinetics (zero-order and first-order).
- Zero-order release: The same amount of drug is released over a given time.
- First-order release: The rate of drug release decreases over time, as the concentration of the drug decreases.
The Higuchi Model
- Higuchi developed a theoretical model that describes a linear relationship between the cumulative amount of drug released (M) and the square root of time (t1/2).
- The model assumes the drug is homogeneously dispersed throughout the matrix.
Drug Release and Dissolution Processes
- Drug release occurs through disintegration of the tablet, granules, and particles.
- Dissolution is the step where the drug dissolves into solution.
- Final drug absorption is dependent on various factors mentioned earlier in this document
The Noyes-Whitney Equation
- The Noyes-Whitney equation describes the rate of solid dissolution in a given solvent.
- The equation includes factors like diffusion coefficient, surface area of the solid, concentration difference between the solid surface and the bulk solution, and thickness of the diffusion layer.
Drug Absorption and Elimination
- There are several mechanisms for drugs to traverse biologic membranes:
- Transcellular: passing through the lipid bilayer of cells.
- Paracellular: passing through the spaces between cells.
- Membrane transporters: moving via active or facilitated diffusion.
- Cell surface receptors
Gastrointestinal Absorption of Drugs
- Passive transfer due to concentration gradients.
- Active transport using energy source.
- Factors affecting drug transport: drug type, biological components, drug state, solubility, concentration in the intestine, and membrane permeability.
pH-Partition Hypothesis
- Transport of a drug across the GI mucosa is governed by Fick's First Law.
- dM/dt is directly proportional to the concentration difference of the drug across the membrane.
Percutaneous Absorption
- Percutaneous penetration involves dissolution, diffusion through the skin, and penetration of layers.
- The stratum corneum is the most significant rate-limiting layer for drug permeation across the skin.
Colloidal Dispersions
- A dispersion is system of one or more phases dispersed in a second phase.
- Particle size categorizes dispersion as:
- Colloidal (1 nm - 1 μm): only visible with an electron microscope
- Coarse (larger than 1 μm): Visible with a light microscope
Types of Colloidal Systems
- Lyophilic (solvent-loving): A high affinity between the dispersed particles and the dispersion medium (e.g., protein in water).
- Lyophobic (solvent-hating): Little attraction between dispersed phase and dispersion medium (e.g., metal sols).
Other Colloids
- Liposomes: Lipid bilayer structures that can encapsulate drugs.
- Nanoparticles: Small particles with high surface area.
- Hydrogels
Kinetic Properties of Colloids
- Brownian motion is the random movement of colloidal particles.
- Particles larger than 0.5 µm settle via sedimentation.
Stability of Colloidal Systems
- Lyophilic sols are thermodynamically stable (stabilized by electrical charge and protective solvent sheath).
- Lyophobic sols are thermodynamically unstable and require stabilization methods such as electrostatic repulsion.
Interfacial Phenomena
- Interfaces are boundaries between immiscible phases.
- Important aspects include surface tension, interfacial tension, and adsorption.
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Description
Explore the fundamental process of diffusion and its significant applications in pharmaceutical sciences. This quiz covers key concepts including Fick's Laws, drug release mechanisms, and the behavior of solutes across membranes. Test your knowledge on how diffusion impacts drug formulation and delivery methods.
